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<li class="minerva__tab selected"> <a class="minerva__tab-text" href="/wiki/Music_theory" rel="" data-event-name="tabs.subject">Article</a> </li> <li class="minerva__tab "> <a class="minerva__tab-text" href="/wiki/Talk:Music_theory" rel="discussion" data-event-name="tabs.talk">Talk</a> </li> </ul> <nav class="page-actions-menu"> <ul id="p-views" class="page-actions-menu__list"> <li id="language-selector" class="page-actions-menu__list-item"> <a role="button" href="#p-lang" data-mw="interface" data-event-name="menu.languages" title="Language" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet language-selector"> Language </a> </li> <li id="page-actions-watch" class="page-actions-menu__list-item"> <a role="button" id="ca-watch" href="/w/index.php?title=Special:UserLogin&returnto=Music+theory" data-event-name="menu.watch" class="cdx-button cdx-button--size-large cdx-button--fake-button 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theoretical frameworks for understanding the practices and possibilities of <a href="/wiki/Music" title="Music">music</a>. <a href="/wiki/The_Oxford_Companion_to_Music" title="The Oxford Companion to Music">The Oxford Companion to Music</a> describes three interrelated uses of the term "music theory": The first is the "<a href="/wiki/Elements_of_music" title="Elements of music">rudiments</a>", that are needed to understand <a href="/wiki/Musical_notation" title="Musical notation">music notation</a> (<a href="/wiki/Key_signature" title="Key signature">key signatures</a>, <a href="/wiki/Time_signature" title="Time signature">time signatures</a>, and <a href="/wiki/Chord_chart" title="Chord chart">rhythmic notation</a>); the second is learning scholars' views on music from <a href="/wiki/Ancient_history" title="Ancient history">antiquity</a> to the present; the third is a sub-topic of <a href="/wiki/Musicology" title="Musicology">musicology</a> that "seeks to define processes and general principles in music". The musicological approach to theory differs from music analysis "in that it takes as its starting-point not the individual work or performance but the fundamental materials from which it is built."<a href="#cite_note-1">[1]</a> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Gaffurio_Pythagoras.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Gaffurio_Pythagoras.png/280px-Gaffurio_Pythagoras.png" decoding="async" width="280" height="364" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Gaffurio_Pythagoras.png/420px-Gaffurio_Pythagoras.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Gaffurio_Pythagoras.png/560px-Gaffurio_Pythagoras.png 2x" data-file-width="2000" data-file-height="2600"></a><figcaption><a href="/wiki/Jubal_(Bible)" title="Jubal (Bible)">Jubal</a>, <a href="/wiki/Pythagoras" title="Pythagoras">Pythagoras</a> and <a href="/wiki/Philolaus" title="Philolaus">Philolaus</a> engaged in theoretical investigations, in a woodcut from <a href="/wiki/Franchinus_Gaffurius" title="Franchinus Gaffurius">Franchinus Gaffurius</a>, Theorica musicæ (1492)</figcaption></figure> Music theory is frequently concerned with describing how musicians and composers make music, including <a href="/wiki/Musical_tuning" title="Musical tuning">tuning systems</a> and composition methods among other topics. Because of the ever-expanding conception of <a href="/wiki/Definition_of_music" title="Definition of music">what constitutes music</a>, a more inclusive definition could be the consideration of any sonic phenomena, including silence. This is not an absolute guideline, however; for example, the study of "music" in the <a href="/wiki/Quadrivium" title="Quadrivium">Quadrivium</a> <a href="/wiki/Liberal_arts_education" title="Liberal arts education">liberal arts university</a> curriculum, that was common in <a href="/wiki/Middle_Ages" title="Middle Ages">medieval Europe</a>, was an abstract system of proportions that was carefully studied at a distance from actual musical practice.<a href="#cite_note-3">[n 1]</a> But this medieval discipline became the basis for tuning systems in later centuries and is generally included in modern scholarship on the history of music theory.<a href="#cite_note-4">[n 2]</a> Music theory as a practical discipline encompasses the methods and concepts that composers and other musicians use in creating and performing music. The development, preservation, and transmission of music theory in this sense may be found in oral and written music-making traditions, <a href="/wiki/Musical_instrument" title="Musical instrument">musical instruments</a>, and other <a href="/wiki/Artifact_(archaeology)" title="Artifact (archaeology)">artifacts</a>. For example, ancient instruments from <a href="/wiki/Prehistoric_music" title="Prehistoric music">prehistoric</a> sites around the world reveal details about the music they produced and potentially something of the musical theory that might have been used by their makers. In ancient and living cultures around the world, the deep and long roots of music theory are visible in instruments, oral traditions, and current music-making. Many cultures have also considered music theory in more formal ways such as written <a href="/wiki/Treatise" title="Treatise">treatises</a> and <a href="/wiki/Musical_notation" title="Musical notation">music notation</a>. Practical and scholarly traditions overlap, as many practical treatises about music place themselves within a tradition of other treatises, which are cited regularly just as <a href="/wiki/Scholarly_writing" class="mw-redirect" title="Scholarly writing">scholarly writing</a> cites earlier research. In modern academia, music theory is a subfield of <a href="/wiki/Musicology" title="Musicology">musicology</a>, the wider study of musical cultures and history. <a href="/wiki/Guido_Adler" title="Guido Adler">Guido Adler</a>, however, in one of the texts that founded musicology in the late 19th century, wrote that "the science of music originated at the same time as the art of sounds".<a href="#cite_note-5">[3]</a>, where "the science of music" (Musikwissenschaft) obviously meant "music theory". Adler added that music only could exist when one began measuring pitches and comparing them to each other. He concluded that "all people for which one can speak of an art of sounds also have a science of sounds".<a href="#cite_note-6">[4]</a> One must deduce that music theory exists in all musical cultures of the world. Music theory is often concerned with abstract musical aspects such as <a href="/wiki/Musical_tuning" title="Musical tuning">tuning</a> and tonal systems, <a href="/wiki/Scale_(music)" title="Scale (music)">scales</a>, <a href="/wiki/Consonance_and_dissonance" title="Consonance and dissonance">consonance and dissonance</a>, and rhythmic relationships. There is also a body of theory concerning practical aspects, such as the creation or the performance of music, <a href="/wiki/Orchestration" title="Orchestration">orchestration</a>, <a href="/wiki/Ornament_(music)" title="Ornament (music)">ornamentation</a>, improvisation, and <a href="/wiki/Electronic_music" title="Electronic music">electronic sound</a> production.<a href="#cite_note-FOOTNOTEPalisca_and_Bentn.d.Theory,_theorists._1._Definitions-7">[5]</a> A person who researches or teaches music theory is a music theorist. University study, typically to the <a href="/wiki/Master_of_Arts" title="Master of Arts">MA</a> or <a href="/wiki/Doctor_of_Philosophy" title="Doctor of Philosophy">PhD</a> level, is required to teach as a tenure-track music theorist in a US or Canadian university. Methods of analysis include mathematics, graphic analysis, and especially analysis enabled by western music notation. Comparative, descriptive, statistical, and other methods are also used. Music theory <a href="/wiki/Textbook" title="Textbook">textbooks</a>, especially in the United States of America, often include elements of <a href="/wiki/Musical_acoustics" title="Musical acoustics">musical acoustics</a>, considerations of <a href="/wiki/Musical_notation" title="Musical notation">musical notation</a>, and techniques of tonal <a href="/wiki/Musical_composition" title="Musical composition">composition</a> (<a href="/wiki/Harmony" title="Harmony">harmony</a> and <a href="/wiki/Counterpoint" title="Counterpoint">counterpoint</a>), among other topics. <div id="toc" class="toc" role="navigation" aria-labelledby="mw-toc-heading"><input type="checkbox" role="button" id="toctogglecheckbox" class="toctogglecheckbox" style="display:none"><div class="toctitle" lang="en" dir="ltr"><h2 id="mw-toc-heading">Contents</h2><label class="toctogglelabel" for="toctogglecheckbox"></label></div> <ul> <li class="toclevel-1 tocsection-1"><a href="#History">1 History</a> <ul> <li class="toclevel-2 tocsection-2"><a href="#Antiquity">1.1 Antiquity</a> <ul> <li class="toclevel-3 tocsection-3"><a href="#Mesopotamia">1.1.1 Mesopotamia</a></li> <li class="toclevel-3 tocsection-4"><a href="#China">1.1.2 China</a></li> <li class="toclevel-3 tocsection-5"><a href="#India">1.1.3 India</a></li> <li class="toclevel-3 tocsection-6"><a href="#Greece">1.1.4 Greece</a></li> </ul> </li> <li class="toclevel-2 tocsection-7"><a href="#Post-classical">1.2 Post-classical</a> <ul> <li class="toclevel-3 tocsection-8"><a href="#China_2">1.2.1 China</a></li> <li class="toclevel-3 tocsection-9"><a href="#Arabic_countries_/_Persian_countries">1.2.2 Arabic countries / Persian countries</a></li> <li class="toclevel-3 tocsection-10"><a href="#Europe">1.2.3 Europe</a></li> </ul> </li> <li class="toclevel-2 tocsection-11"><a href="#Modern">1.3 Modern</a> <ul> <li class="toclevel-3 tocsection-12"><a href="#Middle_Eastern_and_Central_Asian_countries">1.3.1 Middle Eastern and Central Asian countries</a></li> <li class="toclevel-3 tocsection-13"><a href="#Europe_2">1.3.2 Europe</a></li> </ul> </li> <li class="toclevel-2 tocsection-14"><a href="#Contemporary">1.4 Contemporary</a></li> </ul> </li> <li class="toclevel-1 tocsection-15"><a href="#Fundamentals_of_music">2 Fundamentals of music</a> <ul> <li class="toclevel-2 tocsection-16"><a href="#Pitch">2.1 Pitch</a></li> <li class="toclevel-2 tocsection-17"><a href="#Scales_and_modes">2.2 Scales and modes</a></li> <li class="toclevel-2 tocsection-18"><a href="#Consonance_and_dissonance">2.3 Consonance and dissonance</a></li> <li class="toclevel-2 tocsection-19"><a href="#Rhythm">2.4 Rhythm</a></li> <li class="toclevel-2 tocsection-20"><a href="#Melody">2.5 Melody</a></li> <li class="toclevel-2 tocsection-21"><a href="#Chord">2.6 Chord</a></li> <li class="toclevel-2 tocsection-22"><a href="#Harmony">2.7 Harmony</a></li> <li class="toclevel-2 tocsection-23"><a href="#Timbre">2.8 Timbre</a> <ul> <li class="toclevel-3 tocsection-24"><a href="#Dynamics">2.8.1 Dynamics</a></li> <li class="toclevel-3 tocsection-25"><a href="#Articulation">2.8.2 Articulation</a></li> </ul> </li> <li class="toclevel-2 tocsection-26"><a href="#Texture">2.9 Texture</a></li> <li class="toclevel-2 tocsection-27"><a href="#Form_or_structure">2.10 Form or structure</a></li> <li class="toclevel-2 tocsection-28"><a href="#Expression">2.11 Expression</a></li> <li class="toclevel-2 tocsection-29"><a href="#Notation">2.12 Notation</a></li> </ul> </li> <li class="toclevel-1 tocsection-30"><a href="#As_academic_discipline">3 As academic discipline</a> <ul> <li class="toclevel-2 tocsection-31"><a href="#Analysis">3.1 Analysis</a></li> <li class="toclevel-2 tocsection-32"><a href="#Music_perception_and_cognition">3.2 Music perception and cognition</a></li> <li class="toclevel-2 tocsection-33"><a href="#Genre_and_technique">3.3 Genre and technique</a></li> <li class="toclevel-2 tocsection-34"><a href="#Mathematics">3.4 Mathematics</a></li> <li class="toclevel-2 tocsection-35"><a href="#Serial_composition_and_set_theory">3.5 Serial composition and set theory</a></li> <li class="toclevel-2 tocsection-36"><a href="#Musical_semiotics">3.6 Musical semiotics</a></li> <li class="toclevel-2 tocsection-37"><a href="#Education_and_careers">3.7 Education and careers</a></li> </ul> </li> <li class="toclevel-1 tocsection-38"><a href="#See_also">4 See also</a></li> <li class="toclevel-1 tocsection-39"><a href="#Notes">5 Notes</a></li> <li class="toclevel-1 tocsection-40"><a href="#References">6 References</a> <ul> <li class="toclevel-2 tocsection-41"><a href="#Sources">6.1 Sources</a></li> </ul> </li> <li class="toclevel-1 tocsection-42"><a href="#Further_reading">7 Further reading</a></li> <li class="toclevel-1 tocsection-43"><a href="#External_links">8 External links</a></li> </ul> </div> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(1)"><h2 id="History">History</h2> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=1" title="Edit section: History" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-1 collapsible-block" id="mf-section-1"> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/History_of_music" title="History of music">History of music</a></div> <div class="mw-heading mw-heading3"><h3 id="Antiquity">Antiquity</h3> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=2" title="Edit section: Antiquity" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Ancient_music" title="Ancient music">Ancient music</a></div> <div class="mw-heading mw-heading4"><h4 id="Mesopotamia">Mesopotamia</h4> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=3" title="Edit section: Mesopotamia" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Music_of_Mesopotamia" title="Music of Mesopotamia">Music of Mesopotamia</a></div> Several surviving <a href="/wiki/Sumerian_language" title="Sumerian language">Sumerian</a> and <a href="/wiki/Akkadian_language" title="Akkadian language">Akkadian</a> <a href="/wiki/Clay_tablet" title="Clay tablet">clay tablets</a> include musical information of a theoretical nature, mainly lists of <a href="/wiki/Interval_(music)" title="Interval (music)">intervals</a> and <a href="/wiki/Musical_tuning" title="Musical tuning">tunings</a>.<a href="#cite_note-8">[6]</a> The scholar Sam Mirelman reports that the earliest of these texts dates from before 1500 BCE, a millennium earlier than surviving evidence from any other culture of comparable musical thought. Further, "All the Mesopotamian texts [about music] are united by the use of a terminology for music that, according to the approximate dating of the texts, was in use for over 1,000 years."<a href="#cite_note-FOOTNOTEMirelman201343%E2%80%9344-9">[7]</a> <div class="mw-heading mw-heading4"><h4 id="China">China</h4> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=4" title="Edit section: China" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Music_of_China" title="Music of China">Music of China</a> and <a href="/wiki/Chinese_musicology" title="Chinese musicology">Chinese musicology</a></div> Much of Chinese music history and theory remains unclear.<a href="#cite_note-Lam-10">[8]</a> Chinese theory starts from numbers, the main musical numbers being twelve, five and eight. Twelve refers to the number of pitches on which the scales can be constructed. The <a href="/wiki/L%C3%BCshi_chunqiu" class="mw-redirect" title="Lüshi chunqiu">Lüshi chunqiu</a> from about 238 BCE recalls the legend of <a href="/wiki/Ling_Lun" title="Ling Lun">Ling Lun</a>. On order of the <a href="/wiki/Yellow_Emperor" title="Yellow Emperor">Yellow Emperor</a>, Ling Lun collected twelve <a href="/wiki/Bamboo" title="Bamboo">bamboo</a> lengths with thick and even nodes. Blowing on one of these like a pipe, he found its sound agreeable and named it huangzhong, the "Yellow Bell." He then heard <a href="/wiki/Fenghuang" title="Fenghuang">phoenixes</a> singing. The male and female phoenix each sang six tones. Ling Lun cut his bamboo pipes to match the pitches of the phoenixes, producing twelve pitch pipes in two sets: six from the male phoenix and six from the female: these were called the lülü or later the shierlü.<a href="#cite_note-FOOTNOTEService2013-11">[9]</a> <blockquote>Apart from technical and structural aspects, ancient Chinese music theory also discusses topics such as the nature and functions of music. The <a href="/wiki/Record_of_Music" title="Record of Music">Yueji</a> ("Record of music", c1st and 2nd centuries BCE), for example, manifests <a href="/wiki/Confucianism" title="Confucianism">Confucian</a> moral theories of understanding music in its social context. Studied and implemented by Confucian scholar-officials [...], these theories helped form a musical Confucianism that overshadowed but did not erase rival approaches. These include the assertion of <a href="/wiki/Mozi" title="Mozi">Mozi</a> (c. 468 – c. 376 BCE) that music wasted human and material resources, and <a href="/wiki/Laozi" title="Laozi">Laozi</a>'s claim that the greatest music had no sounds. [...] Even the music of the <a href="/wiki/Guqin" title="Guqin">qin zither</a>, a genre closely affiliated with Confucian scholar-officials, includes many works with <a href="/wiki/Taoism" title="Taoism">Daoist</a> references, such as Tianfeng huanpei ("Heavenly Breeze and Sounds of Jade Pendants").<a href="#cite_note-Lam-10">[8]</a></blockquote> <div class="mw-heading mw-heading4"><h4 id="India">India</h4> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=5" title="Edit section: India" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Music_of_India" title="Music of India">Music of India</a></div> The <a href="/wiki/Samaveda" title="Samaveda">Samaveda</a> and <a href="/wiki/Yajurveda" title="Yajurveda">Yajurveda</a> (c. 1200 – 1000 BCE) are among the earliest testimonies of Indian music, but properly speaking, they contain no theory. The <a href="/wiki/Natya_Shastra" title="Natya Shastra">Natya Shastra</a>, written between 200 BCE to 200 CE, discusses intervals (<a href="/wiki/Shruti_(music)" title="Shruti (music)">Śrutis</a>), scales (Grāmas), consonances and dissonances, classes of melodic structure (Mūrchanās, modes?), melodic types (Jātis), instruments, etc.<a href="#cite_note-12">[10]</a> <div class="mw-heading mw-heading4"><h4 id="Greece">Greece</h4> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=6" title="Edit section: Greece" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Musical_system_of_ancient_Greece" title="Musical system of ancient Greece">Musical system of ancient Greece</a> and <a href="/wiki/List_of_music_theorists#Antiquity" title="List of music theorists">List of music theorists § Antiquity</a></div> Early preserved Greek writings on music theory include two types of works:<a href="#cite_note-13">[11]</a> <ul><li>technical manuals describing the Greek musical system including notation, scales, consonance and dissonance, rhythm, and types of musical compositions;</li> <li>treatises on the way in which music reveals universal patterns of order leading to the highest levels of knowledge and understanding.</li></ul> Several names of theorists are known before these works, including <a href="/wiki/Pythagoras" title="Pythagoras">Pythagoras</a> (<abbr title="circa">c.</abbr> 570 ~ <abbr title="circa">c.</abbr> 495 BCE), <a href="/wiki/Philolaus" title="Philolaus">Philolaus</a> (<abbr title="circa">c.</abbr> 470 ~ (<abbr title="circa">c.</abbr> 385 BCE), <a href="/wiki/Archytas" title="Archytas">Archytas</a> (428–347 BCE), and others. Works of the first type (technical manuals) include <ul><li><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFAnonymous_(erroneously_attributed_to_Euclid)1989" class="citation book cs1 cs1-prop-long-vol">Anonymous (erroneously attributed to <a href="/wiki/Euclid" title="Euclid">Euclid</a>) (1989) [4th–3rd century BCE]. Barker, Andrew (ed.). Κατατομή κανόνος [Division of the Canon]. Greek Musical Writings. Vol. 2: Harmonic and Acoustic Theory. Cambridge, UK: Cambridge University Press. pp. 191–208. English trans.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%3Cspan+class%3D%22texhtml+%22+%3E%CE%9A%CE%B1%CF%84%CE%B1%CF%84%CE%BF%CE%BC%CE%AE+%CE%BA%CE%B1%CE%BD%CF%8C%CE%BD%CE%BF%CF%82%3C%2Fspan%3E&rft.place=Cambridge%2C+UK&rft.series=Greek+Musical+Writings&rft.pages=191-208&rft.pub=Cambridge+University+Press&rft.date=1989&rft.au=Anonymous+%28erroneously+attributed+to+Euclid%29&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusic+theory" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTheon_of_Smyrna" class="citation book cs1 cs1-prop-foreign-lang-source"><a href="/wiki/Theon_of_Smyrna" title="Theon of Smyrna">Theon of Smyrna</a>. Τωv κατά τό μαθηματικόν χρησίμων είς τήν Πλάτωνος άνάγνωσις [On the Mathematics Useful for Understanding Plato] (in Greek). 115–140 CE.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%3Cspan+class%3D%22texhtml+%22+%3E%CE%A4%CF%89v+%CE%BA%CE%B1%CF%84%CE%AC+%CF%84%CF%8C+%CE%BC%CE%B1%CE%B8%CE%B7%CE%BC%CE%B1%CF%84%CE%B9%CE%BA%CF%8C%CE%BD+%CF%87%CF%81%CE%B7%CF%83%CE%AF%CE%BC%CF%89%CE%BD+%CE%B5%CE%AF%CF%82+%CF%84%CE%AE%CE%BD+%CE%A0%CE%BB%CE%AC%CF%84%CF%89%CE%BD%CE%BF%CF%82+%CE%AC%CE%BD%CE%AC%CE%B3%CE%BD%CF%89%CF%83%CE%B9%CF%82%3C%2Fspan%3E&rft.au=Theon+of+Smyrna&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusic+theory" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNicomachus_of_Gerasa" class="citation book cs1"><a href="/wiki/Nicomachus#Manual_of_Harmonics" title="Nicomachus">Nicomachus of Gerasa</a>. Άρμονικόν έγχειρίδιον [Manual of Harmonics]. 100–150 CE.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%3Cspan+class%3D%22texhtml+%22+%3E%CE%86%CF%81%CE%BC%CE%BF%CE%BD%CE%B9%CE%BA%CF%8C%CE%BD+%CE%AD%CE%B3%CF%87%CE%B5%CE%B9%CF%81%CE%AF%CE%B4%CE%B9%CE%BF%CE%BD%3C%2Fspan%3E&rft.au=Nicomachus+of+Gerasa&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusic+theory" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCleonides" class="citation book cs1 cs1-prop-foreign-lang-source"><a href="/wiki/Cleonides" title="Cleonides">Cleonides</a>. Είσαγωγή άρμονική [Introduction to Harmonics] (in Greek). 2nd century CE.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%CE%95%CE%AF%CF%83%CE%B1%CE%B3%CF%89%CE%B3%CE%AE+%CE%AC%CF%81%CE%BC%CE%BF%CE%BD%CE%B9%CE%BA%CE%AE&rft.au=Cleonides&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusic+theory" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGaudentius" class="citation book cs1 cs1-prop-foreign-lang-source"><a href="/wiki/Gaudentius_(music_theorist)" title="Gaudentius (music theorist)">Gaudentius</a>. Άρμονική είσαγωγή [Harmonic Introduction] (in Greek). 3rd or 4th century CE.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%3Cspan+class%3D%22texhtml+%22+%3E%CE%86%CF%81%CE%BC%CE%BF%CE%BD%CE%B9%CE%BA%CE%AE+%CE%B5%CE%AF%CF%83%CE%B1%CE%B3%CF%89%CE%B3%CE%AE%3C%2Fspan%3E&rft.au=Gaudentius&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusic+theory" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBacchius_Geron" class="citation book cs1">Bacchius Geron. Είσαγωγή τέχνης μουσικής [Introduction to the Art of Music]. 4th century CE or later.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%3Cspan+class%3D%22texhtml+%22+%3E%CE%95%CE%AF%CF%83%CE%B1%CE%B3%CF%89%CE%B3%CE%AE+%CF%84%CE%AD%CF%87%CE%BD%CE%B7%CF%82+%CE%BC%CE%BF%CF%85%CF%83%CE%B9%CE%BA%CE%AE%CF%82%3C%2Fspan%3E&rft.au=Bacchius+Geron&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusic+theory" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAlypius_of_Alexandria" class="citation book cs1 cs1-prop-foreign-lang-source"><a href="/wiki/Alypius_of_Alexandria" title="Alypius of Alexandria">Alypius of Alexandria</a>. Είσαγωγή μουσική [Introduction to Music] (in Greek). 4th–5th century CE.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%3Cspan+class%3D%22texhtml+%22+%3E%CE%95%CE%AF%CF%83%CE%B1%CE%B3%CF%89%CE%B3%CE%AE+%CE%BC%CE%BF%CF%85%CF%83%CE%B9%CE%BA%CE%AE%3C%2Fspan%3E&rft.au=Alypius+of+Alexandria&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusic+theory" class="Z3988"></li></ul> More philosophical treatises of the second type include <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAristoxenus" class="citation book cs1 cs1-prop-foreign-lang-source"><a href="/wiki/Aristoxenus" title="Aristoxenus">Aristoxenus</a>. Άρμονικά στοιχεία [Harmonic Elements] (in Greek). 375~360 BCE, before 320 BCE.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%3Cspan+class%3D%22texhtml+%22+%3E%CE%86%CF%81%CE%BC%CE%BF%CE%BD%CE%B9%CE%BA%CE%AC+%CF%83%CF%84%CE%BF%CE%B9%CF%87%CE%B5%CE%AF%CE%B1%3C%2Fspan%3E&rft.au=Aristoxenus&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusic+theory" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAristoxenus" class="citation book cs1 cs1-prop-foreign-lang-source"><a href="/wiki/Aristoxenus" title="Aristoxenus">Aristoxenus</a>. Ρυθμικά στοιχεία [Rhythmic Elements] (in Greek).</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%3Cspan+class%3D%22texhtml+%22+%3E%CE%A1%CF%85%CE%B8%CE%BC%CE%B9%CE%BA%CE%AC+%CF%83%CF%84%CE%BF%CE%B9%CF%87%CE%B5%CE%AF%CE%B1%3C%2Fspan%3E&rft.au=Aristoxenus&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusic+theory" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPtolemaios_(Πτολεμαίος)" class="citation book cs1 cs1-prop-foreign-lang-source"><a href="/wiki/Ptolemy" title="Ptolemy">Ptolemaios (Πτολεμαίος), Claudius</a>. Άρμονικά [Harmonics] (in Greek). 127–148 CE.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%3Cspan+class%3D%22texhtml+%22+%3E%CE%86%CF%81%CE%BC%CE%BF%CE%BD%CE%B9%CE%BA%CE%AC%3C%2Fspan%3E&rft.aulast=Ptolemaios+%28%3Cspan+class%3D%22texhtml+%22+%3E%CE%A0%CF%84%CE%BF%CE%BB%CE%B5%CE%BC%CE%B1%CE%AF%CE%BF%CF%82%3C%2Fspan%3E%29&rft.aufirst=Claudius&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusic+theory" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPorphyrius" class="citation book cs1 cs1-prop-foreign-lang-source"><a href="/wiki/Porphyry_(philosopher)" title="Porphyry (philosopher)">Porphyrius</a>. Είς τά άρμονικά Πτολεμαίον ύπόμνημα [On Ptolemy's Harmonics] (in Greek). <abbr title="circa">c.</abbr> 232~233 – <abbr title="circa">c.</abbr> 305 CE.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%3Cspan+class%3D%22texhtml+%22+%3E%CE%95%CE%AF%CF%82+%CF%84%CE%AC+%CE%AC%CF%81%CE%BC%CE%BF%CE%BD%CE%B9%CE%BA%CE%AC+%CE%A0%CF%84%CE%BF%CE%BB%CE%B5%CE%BC%CE%B1%CE%AF%CE%BF%CE%BD+%CF%8D%CF%80%CF%8C%CE%BC%CE%BD%CE%B7%CE%BC%CE%B1%3C%2Fspan%3E&rft.au=Porphyrius&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusic+theory" class="Z3988"></li></ul> <div class="mw-heading mw-heading3"><h3 id="Post-classical">Post-classical</h3> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=7" title="Edit section: Post-classical" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/List_of_music_theorists#Post-classical" title="List of music theorists">List of music theorists § Post-classical</a>, and <a href="/wiki/List_of_medieval_music_theorists" title="List of medieval music theorists">List of medieval music theorists</a></div> <div class="mw-heading mw-heading4"><h4 id="China_2">China</h4> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=8" title="Edit section: China" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> The <a href="/wiki/Pipa" title="Pipa">pipa</a> instrument carried with it a theory of musical modes that subsequently led to the Sui and Tang theory of 84 musical modes.<a href="#cite_note-Lam-10">[8]</a> <div class="mw-heading mw-heading4"><h4 id="Arabic_countries_/_Persian_countries">Arabic countries / Persian countries</h4> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=9" title="Edit section: Arabic countries / Persian countries" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Medieval Arabic music theorists include:<a href="#cite_note-14">[n 3]</a> <ul><li>Abū Yūsuf Ya'qūb <a href="/wiki/Al-Kindi#Music_theory" title="Al-Kindi">al-Kindi</a> (Bagdad, 873 CE), who uses the first twelve letters of the alphabet to describe the twelve frets on five strings of the <a href="/wiki/Oud" title="Oud">oud</a>, producing a chromatic scale of 25 degrees.<a href="#cite_note-FOOTNOTEManik196924%E2%80%9333-15">[12]</a></li> <li>[Yaḥyā ibn] al-<a href="/wiki/Banu_Munajjim" class="mw-redirect" title="Banu Munajjim">Munajjim</a> (Baghdad, 856–912), author of Risāla fī al-mūsīqī ("Treatise on music", MS GB-Lbl Oriental 2361) which describes a <a href="/wiki/Pythagorean_tuning" title="Pythagorean tuning">Pythagorean tuning</a> of the <a href="/wiki/Oud" title="Oud">oud</a> and a system of eight modes perhaps inspired by <a href="/wiki/Ishaq_al-Mawsili" title="Ishaq al-Mawsili">Ishaq al-Mawsili</a> (767–850).<a href="#cite_note-16">[13]</a></li> <li>Abū n-Nașr Muḥammad <a href="/wiki/Al-Farabi#Music" title="Al-Farabi">al-Fārābi</a> (Persia, 872? – Damas, 950 or 951 CE), author of <a href="/wiki/Kitab_al-Musiqa_al-Kabir" title="Kitab al-Musiqa al-Kabir">Kitab al-Musiqa al-Kabir</a> ("The Great Book of Music").<a href="#cite_note-17">[14]</a></li> <li>'Ali ibn al-Husayn ul-Isfahānī (897–967), known as <a href="/wiki/Abu_al-Faraj_al-Isfahani" title="Abu al-Faraj al-Isfahani">Abu al-Faraj al-Isfahani</a>, author of Kitāb al-Aghānī ("The Book of Songs").</li> <li>Abū 'Alī al-Ḥusayn ibn ʿAbd-Allāh ibn Sīnā, known as <a href="/wiki/Avicenna" title="Avicenna">Avicenna</a> (c. 980 – 1037), whose contribution to music theory consists mainly in Chapter 12 of the section on mathematics of his Kitab Al-Shifa ("<a href="/wiki/The_Book_of_Healing" title="The Book of Healing">The Book of Healing</a>").<a href="#cite_note-FOOTNOTEd'Erlanger1930%E2%80%93562:103%E2%80%93245-18">[15]</a></li> <li>al-Ḥasan ibn Aḥmad ibn 'Ali al-Kātib, author of Kamāl adab al Ghinā' ("The Perfection of Musical Knowledge"), copied in 1225 (Istanbul, Topkapi Museum, Ms 1727).<a href="#cite_note-FOOTNOTEShiloah1964-19">[16]</a></li> <li><a href="/wiki/Safi_al-Din_al-Urmawi" title="Safi al-Din al-Urmawi">Safi al-Din al-Urmawi</a> (1216–1294 CE), author of the Kitabu al-Adwār ("Treatise of musical cycles") and ar-Risālah aš-Šarafiyyah ("Epistle to Šaraf").<a href="#cite_note-FOOTNOTEd'Erlanger1930%E2%80%93563:1%E2%80%93182-20">[17]</a></li> <li>Mubārak Šāh, commentator of Safi al-Din's Kitāb al-Adwār (<a href="/wiki/British_Museum" title="British Museum">British Museum</a>, Ms 823).<a href="#cite_note-21">[18]</a></li> <li>Anon. LXI, Anonymous commentary on Safi al-Din's Kitāb al-Adwār.<a href="#cite_note-FOOTNOTEGhrab2009-22">[19]</a></li> <li>Shams al-dῑn al-Saydᾱwῑ Al-Dhahabῑ (14th century CE (?)), music theorist. Author of Urjῡza fi'l-mῡsῑqᾱ ("A Didactic Poem on Music").<a href="#cite_note-Shiloah-2003-23">[20]</a></li></ul> <div class="mw-heading mw-heading4"><h4 id="Europe">Europe</h4> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=10" title="Edit section: Europe" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> The Latin treatise De institutione musica by the Roman philosopher <a href="/wiki/Boethius" title="Boethius">Boethius</a> (written c. 500, translated as Fundamentals of Music<a href="#cite_note-FOOTNOTEBoethius1989-2">[2]</a>) was a touchstone for other writings on music in medieval Europe. Boethius represented Classical authority on music during the Middle Ages, as the Greek writings on which he based his work were not read or translated by later Europeans until the 15th century.<a href="#cite_note-FOOTNOTEPalisca_and_Bentn.d.%C2%A75_Early_Middle_Ages-24">[21]</a> This treatise carefully maintains distance from the actual practice of music, focusing mostly on the mathematical proportions involved in tuning systems and on the moral character of particular modes. Several centuries later, treatises began to appear which dealt with the actual composition of pieces of music in the <a href="/wiki/Plainchant" class="mw-redirect" title="Plainchant">plainchant</a> tradition.<a href="#cite_note-25">[22]</a> At the end of the ninth century, <a href="/wiki/Hucbald" title="Hucbald">Hucbald</a> worked towards more precise pitch notation for the <a href="/wiki/Neume" title="Neume">neumes</a> used to record plainchant. <a href="/wiki/Guido_d%27Arezzo" class="mw-redirect" title="Guido d'Arezzo">Guido d'Arezzo</a> wrote a letter to Michael of Pomposa in 1028, entitled Epistola de ignoto cantu,<a href="#cite_note-26">[23]</a> in which he introduced the practice of using syllables to describe notes and intervals. This was the source of the hexachordal <a href="/wiki/Solmization" title="Solmization">solmization</a> that was to be used until the end of the Middle Ages. Guido also wrote about emotional qualities of the modes, the phrase structure of plainchant, the temporal meaning of the neumes, etc.; his chapters on polyphony "come closer to describing and illustrating real music than any previous account" in the Western tradition.<a href="#cite_note-FOOTNOTEPalisca_and_Bentn.d.%C2%A75_Early_Middle_Ages-24">[21]</a> During the thirteenth century, a new rhythm system called <a href="/wiki/Mensural_notation" title="Mensural notation">mensural notation</a> grew out of an earlier, more limited method of notating rhythms in terms of fixed repetitive patterns, the so-called rhythmic modes, which were developed in France around 1200. An early form of mensural notation was first described and codified in the treatise Ars cantus mensurabilis ("The art of measured chant") by <a href="/wiki/Franco_of_Cologne" title="Franco of Cologne">Franco of Cologne</a> (c. 1280). Mensural notation used different note shapes to specify different durations, allowing scribes to capture rhythms which varied instead of repeating the same fixed pattern; it is a proportional notation, in the sense that each note value is equal to two or three times the shorter value, or half or a third of the longer value. This same notation, transformed through various extensions and improvements during the Renaissance, forms the basis for rhythmic notation in <a href="/wiki/European_classical_music" class="mw-redirect" title="European classical music">European classical music</a> today. <div class="mw-heading mw-heading3"><h3 id="Modern">Modern</h3> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=11" title="Edit section: Modern" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <div class="mw-heading mw-heading4"><h4 id="Middle_Eastern_and_Central_Asian_countries">Middle Eastern and Central Asian countries</h4> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=12" title="Edit section: Middle Eastern and Central Asian countries" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <ul><li>Bāqiyā Nāyinῑ (Uzbekistan, 17th century CE), Uzbek author and music theorist. Author of Zamzama e wahdat-i-mῡsῑqῑ ["The Chanting of Unity in Music"].<a href="#cite_note-Shiloah-2003-23">[20]</a></li> <li>Baron Francois Rodolphe d'Erlanger (Tunis, Tunisia, 1910–1932 CE), French musicologist. Author of La musique arabe and Ta'rῑkh al-mῡsῑqᾱ al-arabiyya wa-usῡluha wa-tatawwurᾱtuha ["A History of Arabian Music, its principles and its Development"]</li></ul> D'Erlanger divulges that the Arabic music scale is derived from the Greek music scale, and that Arabic music is connected to certain features of Arabic culture, such as astrology.<a href="#cite_note-Shiloah-2003-23">[20]</a> <div class="mw-heading mw-heading4"><h4 id="Europe_2">Europe</h4> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=13" title="Edit section: Europe" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <ul><li>Renaissance</li></ul> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/List_of_music_theorists#15th_and_16th_centuries" title="List of music theorists">List of music theorists § 15th and 16th centuries</a></div> <ul><li>Baroque</li></ul> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/List_of_music_theorists#17th_century" title="List of music theorists">List of music theorists § 17th century</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/List_of_music_theorists#18th_century" title="List of music theorists">List of music theorists § 18th century</a></div> <ul><li>1750–1900 <ul><li>As Western musical influence spread throughout the world in the 1800s, musicians adopted Western theory as an international standard—but other theoretical traditions in both textual and oral traditions remain in use. For example, the long and rich musical traditions unique to ancient and current cultures of Africa are primarily oral, but describe specific forms, genres, performance practices, tunings, and other aspects of music theory.<a href="#cite_note-FOOTNOTEKubik2010passim-27">[24]</a><a href="#cite_note-FOOTNOTEEkwueme1974passim-28">[25]</a></li> <li><a href="/wiki/Sacred_harp" class="mw-redirect" title="Sacred harp">Sacred harp</a> music uses a different kind of scale and theory in practice. The music focuses on the solfege "fa, sol, la" on the music scale. Sacred Harp also employs a different notation involving "shape notes", or notes that are shaped to correspond to a certain solfege syllable on the music scale. Sacred Harp music and its music theory originated with Reverend Thomas Symmes in 1720, where he developed a system for "singing by note" to help his church members with note accuracy.<a href="#cite_note-29">[26]</a></li></ul></li></ul> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/List_of_music_theorists#19th_century" title="List of music theorists">List of music theorists § 19th century</a></div> <div class="mw-heading mw-heading3"><h3 id="Contemporary">Contemporary</h3> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=14" title="Edit section: Contemporary" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/List_of_music_theorists#20th_century" title="List of music theorists">List of music theorists § 20th century</a>, and <a href="/wiki/List_of_music_theorists#21st_century" title="List of music theorists">List of music theorists § 21st century</a></div> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(2)"><h2 id="Fundamentals_of_music">Fundamentals of music</h2> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=15" title="Edit section: Fundamentals of music" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-2 collapsible-block" id="mf-section-2"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Aspect_of_music" class="mw-redirect" title="Aspect of music">Aspect of music</a></div> Music is composed of <a href="/wiki/Aural" class="mw-redirect" title="Aural">aural</a> phenomena; "music theory" considers how those phenomena apply in music. Music theory considers melody, rhythm, counterpoint, harmony, form, tonal systems, scales, tuning, intervals, consonance, dissonance, durational proportions, the acoustics of pitch systems, composition, performance, orchestration, ornamentation, improvisation, electronic sound production, etc.<a href="#cite_note-FOOTNOTEPalisca_and_Bentn.d.-30">[27]</a> <div class="mw-heading mw-heading3"><h3 id="Pitch">Pitch</h3> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=16" title="Edit section: Pitch" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Pitch_(music)" title="Pitch (music)">Pitch (music)</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Middle_C.png" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Middle_C.png/220px-Middle_C.png" decoding="async" width="220" height="103" class="mw-file-element" data-file-width="539" data-file-height="252"></noscript><span class="lazy-image-placeholder" style="width: 220px;height: 103px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Middle_C.png/220px-Middle_C.png" data-width="220" data-height="103" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Middle_C.png/330px-Middle_C.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/03/Middle_C.png/440px-Middle_C.png 2x" data-class="mw-file-element"> </a><figcaption>Middle C (261.626 Hz)<audio id="mwe_player_0" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-mwtitle="Middle_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/e/e2/Middle_C.mid" type="audio/midi" data-width="0" data-height="0"></source><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e2/Middle_C.mid/Middle_C.mid.ogg" type='audio/ogg; codecs="vorbis"' data-transcodekey="ogg" data-width="0" data-height="0"></source><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e2/Middle_C.mid/Middle_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0"></source></audio></figcaption></figure> Pitch is the lowness or highness of a <a href="/wiki/Musical_tone" title="Musical tone">tone</a>, for example the difference between <a href="/wiki/Middle_C" class="mw-redirect" title="Middle C">middle C</a> and a higher C. The frequency of the sound waves producing a pitch can be measured precisely, but the perception of pitch is more complex because single notes from natural sources are usually a complex mix of many frequencies. Accordingly, theorists often describe pitch as a subjective sensation rather than an objective measurement of sound.&#91;[[Wikipedia:Citing_sources|<span_title="This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(August_2014)">page&nbsp;needed]]&#93;_31-0' class="reference"><a href="#cite_note-FOOTNOTEHartmann2005%5B%5BCategory:Wikipedia_articles_needing_page_number_citations_from_August_2014%5D%5D<sup_class=%22noprint_Inline-Template_%22_style=%22white-space:nowrap;%22>&#91;%5B%5BWikipedia:Citing_sources%7C<span_title=%22This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(August_2014)%22>page&nbsp;needed%5D%5D&#93;-31">[28]</a> Specific frequencies are often assigned letter names. Today most orchestras assign <a href="/wiki/Concert_A" class="mw-redirect" title="Concert A">concert A</a> (the A above <a href="/wiki/Middle_C" class="mw-redirect" title="Middle C">middle C</a> on the piano) to the frequency of 440 Hz. This assignment is somewhat arbitrary; for example, in 1859 France, the same A was tuned to 435 Hz. Such differences can have a noticeable effect on the timbre of instruments and other phenomena. Thus, in <a href="/wiki/Historically_informed_performance" title="Historically informed performance">historically informed performance</a> of older music, tuning is often set to match the tuning used in the period when it was written. Additionally, many cultures do not attempt to standardize pitch, often considering that it should be allowed to vary depending on genre, style, mood, etc. The difference in pitch between two notes is called an <a href="/wiki/Interval_(music)" title="Interval (music)">interval</a>. The most basic interval is the <a href="/wiki/Unison" title="Unison">unison</a>, which is simply two notes of the same pitch. The <a href="/wiki/Octave" title="Octave">octave</a> interval is two pitches that are either double or half the frequency of one another. The unique characteristics of octaves gave rise to the concept of <a href="/wiki/Pitch_class" title="Pitch class">pitch class</a>: pitches of the same letter name that occur in different octaves may be grouped into a single "class" by ignoring the difference in octave. For example, a high C and a low C are members of the same pitch class—the class that contains all C's. &#91;[[Wikipedia:Citing_sources|<span_title="This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(October_2014)">page&nbsp;needed]]&#93;_32-0' class="reference"><a href="#cite_note-FOOTNOTEBartlette_and_Laitz2010%5B%5BCategory:Wikipedia_articles_needing_page_number_citations_from_October_2014%5D%5D<sup_class=%22noprint_Inline-Template_%22_style=%22white-space:nowrap;%22>&#91;%5B%5BWikipedia:Citing_sources%7C<span_title=%22This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(October_2014)%22>page&nbsp;needed%5D%5D&#93;-32">[29]</a> <a href="/wiki/Musical_tuning" title="Musical tuning">Musical tuning</a> systems, or temperaments, determine the precise size of intervals. Tuning systems vary widely within and between world cultures. In <a href="/wiki/Western_culture" title="Western culture">Western culture</a>, there have long been several competing tuning systems, all with different qualities. Internationally, the system known as <a href="/wiki/Equal_temperament" title="Equal temperament">equal temperament</a> is most commonly used today because it is considered the most satisfactory compromise that allows instruments of fixed tuning (e.g. the piano) to sound acceptably in tune in all keys. <div class="mw-heading mw-heading3"><h3 id="Scales_and_modes">Scales and modes</h3> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=17" title="Edit section: Scales and modes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Musical_scale" class="mw-redirect" title="Musical scale">Musical scale</a> and <a href="/wiki/Musical_mode" class="mw-redirect" title="Musical mode">Musical mode</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:C_major_scale.png" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/c/ce/C_major_scale.png" decoding="async" width="276" height="53" class="mw-file-element" data-file-width="276" data-file-height="53"></noscript><span class="lazy-image-placeholder" style="width: 276px;height: 53px;" data-src="//upload.wikimedia.org/wikipedia/commons/c/ce/C_major_scale.png" data-width="276" data-height="53" data-class="mw-file-element"> </a><figcaption>A pattern of whole and half steps in the Ionian mode or major scale on C<audio id="mwe_player_1" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-mwtitle="Ionian_mode_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/9/99/Ionian_mode_C.mid" type="audio/midi" data-width="0" data-height="0"></source><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/99/Ionian_mode_C.mid/Ionian_mode_C.mid.ogg" type='audio/ogg; codecs="vorbis"' data-transcodekey="ogg" data-width="0" data-height="0"></source><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/99/Ionian_mode_C.mid/Ionian_mode_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0"></source></audio></figcaption></figure> Notes can be arranged in a variety of <a href="/wiki/Scale_(music)" title="Scale (music)">scales</a> and <a href="/wiki/Musical_mode" class="mw-redirect" title="Musical mode">modes</a>. Western music theory generally divides the octave into a series of twelve pitches, called a <a href="/wiki/Chromatic_scale" title="Chromatic scale">chromatic scale</a>, within which the interval between adjacent tones is called a <a href="/wiki/Semitone" title="Semitone">semitone</a>, or half step. Selecting tones from this set of 12 and arranging them in patterns of semitones and whole tones creates other scales.&#91;[[Wikipedia:Citing_sources|<span_title="This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(August_2014)">page&nbsp;needed]]&#93;_33-0' class="reference"><a href="#cite_note-FOOTNOTETouma1996%5B%5BCategory:Wikipedia_articles_needing_page_number_citations_from_August_2014%5D%5D<sup_class=%22noprint_Inline-Template_%22_style=%22white-space:nowrap;%22>&#91;%5B%5BWikipedia:Citing_sources%7C<span_title=%22This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(August_2014)%22>page&nbsp;needed%5D%5D&#93;-33">[30]</a> The most commonly encountered scales are the seven-toned <a href="/wiki/Major_scale" title="Major scale">major</a>, the <a href="/wiki/Harmonic_minor" class="mw-redirect" title="Harmonic minor">harmonic minor</a>, the <a href="/wiki/Melodic_minor" class="mw-redirect" title="Melodic minor">melodic minor</a>, and the <a href="/wiki/Natural_minor" class="mw-redirect" title="Natural minor">natural minor</a>. Other examples of scales are the <a href="/wiki/Octatonic_scale" title="Octatonic scale">octatonic scale</a> and the <a href="/wiki/Pentatonic" class="mw-redirect" title="Pentatonic">pentatonic</a> or five-tone scale, which is common in <a href="/wiki/Folk_music" title="Folk music">folk music</a> and <a href="/wiki/Blues" title="Blues">blues</a>. Non-Western cultures often use scales that do not correspond with an equally divided twelve-tone division of the octave. For example, classical <a href="/wiki/Ottoman_classical_music" class="mw-redirect" title="Ottoman classical music">Ottoman</a>, <a href="/wiki/Persian_classical_music" class="mw-redirect" title="Persian classical music">Persian</a>, <a href="/wiki/Indian_classical_music" title="Indian classical music">Indian</a> and <a href="/wiki/Arabic_music" title="Arabic music">Arabic</a> musical systems often make use of multiples of quarter tones (half the size of a semitone, as the name indicates), for instance in 'neutral' seconds (three quarter tones) or 'neutral' thirds (seven quarter tones)—they do not normally use the quarter tone itself as a direct interval.&#91;[[Wikipedia:Citing_sources|<span_title="This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(August_2014)">page&nbsp;needed]]&#93;_33-1' class="reference"><a href="#cite_note-FOOTNOTETouma1996%5B%5BCategory:Wikipedia_articles_needing_page_number_citations_from_August_2014%5D%5D<sup_class=%22noprint_Inline-Template_%22_style=%22white-space:nowrap;%22>&#91;%5B%5BWikipedia:Citing_sources%7C<span_title=%22This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(August_2014)%22>page&nbsp;needed%5D%5D&#93;-33">[30]</a> In traditional Western notation, the scale used for a composition is usually indicated by a <a href="/wiki/Key_signature" title="Key signature">key signature</a> at the beginning to designate the pitches that make up that scale. As the music progresses, the pitches used may change and introduce a different scale. Music can be <a href="/wiki/Transposition_(music)" title="Transposition (music)">transposed</a> from one scale to another for various purposes, often to accommodate the range of a vocalist. Such transposition raises or lowers the overall pitch range, but preserves the intervallic relationships of the original scale. For example, transposition from the key of C major to D major raises all pitches of the scale of C major equally by a <a href="/wiki/Whole_tone" class="mw-redirect" title="Whole tone">whole tone</a>. Since the interval relationships remain unchanged, transposition may be unnoticed by a listener, however other qualities may change noticeably because transposition changes the relationship of the overall pitch <a href="/wiki/Range_(music)" title="Range (music)">range</a> compared to the range of the instruments or voices that perform the music. This often affects the music's overall sound, as well as having technical implications for the performers.<a href="#cite_note-FOOTNOTEForsyth193573%E2%80%9374-34">[31]</a> The interrelationship of the keys most commonly used in Western tonal music is conveniently shown by the <a href="/wiki/Circle_of_fifths" title="Circle of fifths">circle of fifths</a>. Unique key signatures are also sometimes devised for a particular composition. During the Baroque period, emotional associations with specific keys, known as the <a href="/wiki/Doctrine_of_the_affections" title="Doctrine of the affections">doctrine of the affections</a>, were an important topic in music theory, but the unique tonal colorings of keys that gave rise to that doctrine were largely erased with the adoption of equal temperament. However, many musicians continue to feel that certain keys are more appropriate to certain emotions than others. <a href="/wiki/Indian_classical_music" title="Indian classical music">Indian classical music</a> theory continues to strongly associate keys with emotional states, times of day, and other extra-musical concepts and notably, does not employ equal temperament. <div class="mw-heading mw-heading3"><h3 id="Consonance_and_dissonance">Consonance and dissonance</h3> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=18" title="Edit section: Consonance and dissonance" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Consonance_and_dissonance" title="Consonance and dissonance">Consonance and dissonance</a></div> <style data-mw-deduplicate="TemplateStyles:r1237032888/mw-parser-output/.tmulti">.mw-parser-output .tmulti .multiimageinner{display:flex;flex-direction:column}.mw-parser-output .tmulti .trow{display:flex;flex-direction:row;clear:left;flex-wrap:wrap;width:100%;box-sizing:border-box}.mw-parser-output .tmulti .tsingle{margin:1px;float:left}.mw-parser-output .tmulti .theader{clear:both;font-weight:bold;text-align:center;align-self:center;background-color:transparent;width:100%}.mw-parser-output .tmulti .thumbcaption{background-color:transparent}.mw-parser-output .tmulti .text-align-left{text-align:left}.mw-parser-output .tmulti .text-align-right{text-align:right}.mw-parser-output .tmulti .text-align-center{text-align:center}@media all and (max-width:720px){.mw-parser-output .tmulti .thumbinner{width:100%!important;box-sizing:border-box;max-width:none!important;align-items:center}.mw-parser-output .tmulti .trow{justify-content:center}.mw-parser-output .tmulti .tsingle{float:none!important;max-width:100%!important;box-sizing:border-box;text-align:center}.mw-parser-output .tmulti .tsingle .thumbcaption{text-align:left}.mw-parser-output .tmulti .trow>.thumbcaption{text-align:center}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .tmulti .multiimageinner img{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmulti .multiimageinner img{background-color:white}}</style><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:358px;max-width:358px"><div class="trow"><div class="tsingle" style="width:177px;max-width:177px"><div class="thumbimage"><a href="/wiki/File:Perfect_octave_on_C.png" class="mw-file-description"><noscript><img alt="A consonance" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Perfect_octave_on_C.png/175px-Perfect_octave_on_C.png" decoding="async" width="175" height="82" class="mw-file-element" data-file-width="539" data-file-height="252"></noscript><span class="lazy-image-placeholder" style="width: 175px;height: 82px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Perfect_octave_on_C.png/175px-Perfect_octave_on_C.png" data-alt="A consonance" data-width="175" data-height="82" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Perfect_octave_on_C.png/263px-Perfect_octave_on_C.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Perfect_octave_on_C.png/350px-Perfect_octave_on_C.png 2x" data-class="mw-file-element"> </a></div><div class="thumbcaption"><a href="/wiki/Perfect_octave" class="mw-redirect" title="Perfect octave">Perfect octave</a>, a consonant interval<audio id="mwe_player_2" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-durationhint="7" data-mwtitle="Perfect_octave_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/f/f0/Perfect_octave_on_C.mid" type="audio/midi" data-width="0" data-height="0"></source><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/f/f0/Perfect_octave_on_C.mid/Perfect_octave_on_C.mid.ogg" type='audio/ogg; codecs="vorbis"' data-transcodekey="ogg" data-width="0" data-height="0"></source><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/f/f0/Perfect_octave_on_C.mid/Perfect_octave_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0"></source></audio></div></div><div class="tsingle" style="width:177px;max-width:177px"><div class="thumbimage"><a href="/wiki/File:Minor_second_on_C.png" class="mw-file-description"><noscript><img alt="A dissonance" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Minor_second_on_C.png/175px-Minor_second_on_C.png" decoding="async" width="175" height="81" class="mw-file-element" data-file-width="542" data-file-height="252"></noscript><span class="lazy-image-placeholder" style="width: 175px;height: 81px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Minor_second_on_C.png/175px-Minor_second_on_C.png" data-alt="A dissonance" data-width="175" data-height="81" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Minor_second_on_C.png/263px-Minor_second_on_C.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Minor_second_on_C.png/350px-Minor_second_on_C.png 2x" data-class="mw-file-element"> </a></div><div class="thumbcaption"><a href="/wiki/Minor_second" class="mw-redirect" title="Minor second">Minor second</a>, a dissonant interval<audio id="mwe_player_3" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-mwtitle="Minor_second_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/8/8a/Minor_second_on_C.mid" type="audio/midi" data-width="0" data-height="0"></source><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/8a/Minor_second_on_C.mid/Minor_second_on_C.mid.ogg" type='audio/ogg; codecs="vorbis"' data-transcodekey="ogg" data-width="0" data-height="0"></source><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/8a/Minor_second_on_C.mid/Minor_second_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0"></source></audio></div></div></div></div></div> <a href="/wiki/Consonance_and_dissonance" title="Consonance and dissonance">Consonance and dissonance</a> are subjective qualities of the sonority of intervals that vary widely in different cultures and over the ages. Consonance (or concord) is the quality of an interval or chord that seems stable and complete in itself. Dissonance (or discord) is the opposite in that it feels incomplete and "wants to" resolve to a consonant interval. Dissonant intervals seem to clash. Consonant intervals seem to sound comfortable together. Commonly, perfect fourths, fifths, and octaves and all major and minor thirds and sixths are considered consonant. All others are dissonant to a greater or lesser degree.&#91;[[Wikipedia:Citing_sources|<span_title="This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(August_2014)">page&nbsp;needed]]&#93;_35-0' class="reference"><a href="#cite_note-FOOTNOTELatham2002%5B%5BCategory:Wikipedia_articles_needing_page_number_citations_from_August_2014%5D%5D<sup_class=%22noprint_Inline-Template_%22_style=%22white-space:nowrap;%22>&#91;%5B%5BWikipedia:Citing_sources%7C<span_title=%22This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(August_2014)%22>page&nbsp;needed%5D%5D&#93;-35">[32]</a> Context and many other aspects can affect apparent dissonance and consonance. For example, in a Debussy prelude, a major second may sound stable and consonant, while the same interval may sound dissonant in a Bach fugue. In the <a href="/wiki/Common_practice_period" title="Common practice period">Common practice era</a>, the perfect fourth is considered dissonant when not supported by a lower third or fifth. Since the early 20th century, <a href="/wiki/Arnold_Schoenberg" title="Arnold Schoenberg">Arnold Schoenberg</a>'s concept of "emancipated" dissonance, in which traditionally dissonant intervals can be treated as "higher," more remote consonances, has become more widely accepted.&#91;[[Wikipedia:Citing_sources|<span_title="This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(August_2014)">page&nbsp;needed]]&#93;_35-1' class="reference"><a href="#cite_note-FOOTNOTELatham2002%5B%5BCategory:Wikipedia_articles_needing_page_number_citations_from_August_2014%5D%5D<sup_class=%22noprint_Inline-Template_%22_style=%22white-space:nowrap;%22>&#91;%5B%5BWikipedia:Citing_sources%7C<span_title=%22This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(August_2014)%22>page&nbsp;needed%5D%5D&#93;-35">[32]</a> <div class="mw-heading mw-heading3"><h3 id="Rhythm">Rhythm</h3> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=19" title="Edit section: Rhythm" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Rhythm" title="Rhythm">Rhythm</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Metric_levels.svg" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/82/Metric_levels.svg/290px-Metric_levels.svg.png" decoding="async" width="290" height="135" class="mw-file-element" data-file-width="1460" data-file-height="680"></noscript><span class="lazy-image-placeholder" style="width: 290px;height: 135px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/8/82/Metric_levels.svg/290px-Metric_levels.svg.png" data-width="290" data-height="135" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/82/Metric_levels.svg/435px-Metric_levels.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/82/Metric_levels.svg/580px-Metric_levels.svg.png 2x" data-class="mw-file-element"> </a><figcaption><a href="/wiki/Metric_level" class="mw-redirect" title="Metric level">Metric levels</a>: beat level shown in middle with division levels above and multiple levels below</figcaption></figure> Rhythm is produced by the sequential arrangement of sounds and silences in time. <a href="/wiki/Metre_(music)" title="Metre (music)">Meter</a> measures music in regular pulse groupings, called <a href="/wiki/Bar_(music)" title="Bar (music)">measures or bars</a>. The <a href="/wiki/Time_signature" title="Time signature">time signature</a> or meter signature specifies how many beats are in a measure, and which value of written note is counted or felt as a single beat. Through increased stress, or variations in duration or articulation, particular tones may be accented. There are conventions in most musical traditions for regular and hierarchical accentuation of beats to reinforce a given meter. <a href="/wiki/Syncopation" title="Syncopation">Syncopated</a> rhythms contradict those conventions by accenting unexpected parts of the beat.<a href="#cite_note-36">[33]</a> Playing simultaneous rhythms in more than one time signature is called <a href="/wiki/Polyrhythm" title="Polyrhythm">polyrhythm</a>.<a href="#cite_note-37">[34]</a> In recent years, rhythm and meter have become an important area of research among music scholars. The most highly cited of these recent scholars are <a href="/wiki/Maury_Yeston" title="Maury Yeston">Maury Yeston</a>,<a href="#cite_note-FOOTNOTEYeston1976-38">[35]</a> <a href="/wiki/Fred_Lerdahl" title="Fred Lerdahl">Fred Lerdahl</a> and <a href="/wiki/Ray_Jackendoff" title="Ray Jackendoff">Ray Jackendoff</a>,<a href="#cite_note-FOOTNOTELerdahl_and_Jackendoff1985-39">[36]</a> <a href="/wiki/Jonathan_Kramer" title="Jonathan Kramer">Jonathan Kramer</a>,<a href="#cite_note-FOOTNOTEKramer1988-40">[37]</a> and Justin London.<a href="#cite_note-FOOTNOTELondon2004-41">[38]</a> <div class="mw-heading mw-heading3"><h3 id="Melody">Melody</h3> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=20" title="Edit section: Melody" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Melody" title="Melody">Melody</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Pop_Goes_the_Weasel_melody.PNG" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Pop_Goes_the_Weasel_melody.PNG/290px-Pop_Goes_the_Weasel_melody.PNG" decoding="async" width="290" height="96" class="mw-file-element" data-file-width="1444" data-file-height="478"></noscript><span class="lazy-image-placeholder" style="width: 290px;height: 96px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Pop_Goes_the_Weasel_melody.PNG/290px-Pop_Goes_the_Weasel_melody.PNG" data-width="290" data-height="96" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Pop_Goes_the_Weasel_melody.PNG/435px-Pop_Goes_the_Weasel_melody.PNG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Pop_Goes_the_Weasel_melody.PNG/580px-Pop_Goes_the_Weasel_melody.PNG 2x" data-class="mw-file-element"> </a><figcaption>"<a href="/wiki/Pop_Goes_the_Weasel" title="Pop Goes the Weasel">Pop Goes the Weasel</a>" melody&#91;[[Wikipedia:Citing_sources|<span_title="This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(September_2012)">page&nbsp;needed]]&#93;_42-0' class="reference"><a href="#cite_note-FOOTNOTEKliewer1975%5B%5BCategory:Wikipedia_articles_needing_page_number_citations_from_September_2012%5D%5D<sup_class=%22noprint_Inline-Template_%22_style=%22white-space:nowrap;%22>&#91;%5B%5BWikipedia:Citing_sources%7C<span_title=%22This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(September_2012)%22>page&nbsp;needed%5D%5D&#93;-42">[39]</a><audio id="mwe_player_4" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-durationhint="12" data-mwtitle="Pop_Goes_the_Weasel.ogg" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/d/d5/Pop_Goes_the_Weasel.ogg" type='audio/ogg; codecs="vorbis"' data-width="0" data-height="0"></source><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/d/d5/Pop_Goes_the_Weasel.ogg/Pop_Goes_the_Weasel.ogg.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0"></source><track src="https://commons.wikimedia.org/w/api.php?action=timedtext&title=File%3APop_Goes_the_Weasel.ogg&lang=en&trackformat=vtt&origin=%2A" kind="subtitles" type="text/vtt" srclang="en" label="English ‪(en)‬" data-dir="ltr"></track></audio></figcaption></figure> A <a href="/wiki/Melody" title="Melody">melody</a> is a group of musical sounds in agreeable succession or arrangement.<a href="#cite_note-43">[40]</a> Because melody is such a prominent aspect in so much music, its construction and other qualities are a primary interest of music theory. The basic elements of melody are pitch, duration, rhythm, and tempo. The tones of a melody are usually drawn from pitch systems such as <a href="/wiki/Musical_scale" class="mw-redirect" title="Musical scale">scales</a> or <a href="/wiki/Musical_mode" class="mw-redirect" title="Musical mode">modes</a>. Melody may consist, to increasing degree, of the figure, motive, semi-phrase, antecedent and consequent phrase, and period or sentence. The period may be considered the complete melody, however some examples combine two periods, or use other combinations of constituents to create larger form melodies.<a href="#cite_note-FOOTNOTEStein19793%E2%80%9347-44">[41]</a> <div style="clear:both;" class=""></div> <div class="mw-heading mw-heading3"><h3 id="Chord">Chord</h3> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=21" title="Edit section: Chord" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Chord_(music)" title="Chord (music)">Chord (music)</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:C_triad.svg" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c1/C_triad.svg/150px-C_triad.svg.png" decoding="async" width="150" height="125" class="mw-file-element" data-file-width="90" data-file-height="75"></noscript><span class="lazy-image-placeholder" style="width: 150px;height: 125px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c1/C_triad.svg/150px-C_triad.svg.png" data-width="150" data-height="125" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c1/C_triad.svg/225px-C_triad.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c1/C_triad.svg/300px-C_triad.svg.png 2x" data-class="mw-file-element"> </a><figcaption>C major triad represented in <a href="/wiki/Staff_notation" class="mw-redirect" title="Staff notation">staff notation</a>. <span data-nosnippet="" id="ooui-php-1" class="ext-phonos-PhonosButton noexcerpt oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-ooui='{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/5\/51\/Just_major_triad_on_C.mid\/Just_major_triad_on_C.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"Play"},"data":{"ipa":"","text":"","lang":"en","wikibase":"","file":"Just major triad on C.mid"},"classes":["ext-phonos-PhonosButton","noexcerpt"]}'><a role="button" tabindex="0" href="//upload.wikimedia.org/wikipedia/commons/transcoded/5/51/Just_major_triad_on_C.mid/Just_major_triad_on_C.mid.mp3" rel="nofollow" aria-label="Play audio" title="Play audio" class="oo-ui-buttonElement-button">Play</a><a href="/wiki/File:Just_major_triad_on_C.mid" title="File:Just major triad on C.mid">ⓘ</a> in <a href="/wiki/Just_intonation" title="Just intonation">just intonation</a> <span data-nosnippet="" id="ooui-php-2" class="ext-phonos-PhonosButton noexcerpt oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-ooui='{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/6\/60\/Major_triad_on_C.mid\/Major_triad_on_C.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"Play"},"data":{"ipa":"","text":"","lang":"en","wikibase":"","file":"Major triad on C.mid"},"classes":["ext-phonos-PhonosButton","noexcerpt"]}'><a role="button" tabindex="0" href="//upload.wikimedia.org/wikipedia/commons/transcoded/6/60/Major_triad_on_C.mid/Major_triad_on_C.mid.mp3" rel="nofollow" aria-label="Play audio" title="Play audio" class="oo-ui-buttonElement-button">Play</a><a href="/wiki/File:Major_triad_on_C.mid" title="File:Major triad on C.mid">ⓘ</a> in <a href="/wiki/Equal_temperament" title="Equal temperament">Equal temperament</a> <span data-nosnippet="" id="ooui-php-3" class="ext-phonos-PhonosButton noexcerpt oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-ooui='{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/4\/47\/Quarter-comma_meantone_major_chord_on_C.mid\/Quarter-comma_meantone_major_chord_on_C.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"Play"},"data":{"ipa":"","text":"","lang":"en","wikibase":"","file":"Quarter-comma meantone major chord on C.mid"},"classes":["ext-phonos-PhonosButton","noexcerpt"]}'><a role="button" tabindex="0" href="//upload.wikimedia.org/wikipedia/commons/transcoded/4/47/Quarter-comma_meantone_major_chord_on_C.mid/Quarter-comma_meantone_major_chord_on_C.mid.mp3" rel="nofollow" aria-label="Play audio" title="Play audio" class="oo-ui-buttonElement-button">Play</a><a href="/wiki/File:Quarter-comma_meantone_major_chord_on_C.mid" title="File:Quarter-comma meantone major chord on C.mid">ⓘ</a> in <a href="/wiki/Meantone_temperament" title="Meantone temperament">1/4-comma meantone</a> <span data-nosnippet="" id="ooui-php-4" class="ext-phonos-PhonosButton noexcerpt oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-ooui='{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/d\/df\/Young_temperament_major_chord_on_C.mid\/Young_temperament_major_chord_on_C.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"Play"},"data":{"ipa":"","text":"","lang":"en","wikibase":"","file":"Young temperament major chord on C.mid"},"classes":["ext-phonos-PhonosButton","noexcerpt"]}'><a role="button" tabindex="0" href="//upload.wikimedia.org/wikipedia/commons/transcoded/d/df/Young_temperament_major_chord_on_C.mid/Young_temperament_major_chord_on_C.mid.mp3" rel="nofollow" aria-label="Play audio" title="Play audio" class="oo-ui-buttonElement-button">Play</a><a href="/wiki/File:Young_temperament_major_chord_on_C.mid" title="File:Young temperament major chord on C.mid">ⓘ</a> in <a href="/wiki/Young_temperament" title="Young temperament">Young temperament</a> <span data-nosnippet="" id="ooui-php-5" class="ext-phonos-PhonosButton noexcerpt oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-ooui='{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/6\/63\/Pythagorean_major_chord_on_C.mid\/Pythagorean_major_chord_on_C.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"Play"},"data":{"ipa":"","text":"","lang":"en","wikibase":"","file":"Pythagorean major chord on C.mid"},"classes":["ext-phonos-PhonosButton","noexcerpt"]}'><a role="button" tabindex="0" href="//upload.wikimedia.org/wikipedia/commons/transcoded/6/63/Pythagorean_major_chord_on_C.mid/Pythagorean_major_chord_on_C.mid.mp3" rel="nofollow" aria-label="Play audio" title="Play audio" class="oo-ui-buttonElement-button">Play</a><a href="/wiki/File:Pythagorean_major_chord_on_C.mid" title="File:Pythagorean major chord on C.mid">ⓘ</a> in <a href="/wiki/Pythagorean_tuning" title="Pythagorean tuning">Pythagorean tuning</a> </figcaption></figure> A chord, in music, is any <a href="/wiki/Harmony" title="Harmony">harmonic</a> set of three or more <a href="/wiki/Musical_note" title="Musical note">notes</a> that is heard as if sounding <a href="/wiki/Simultaneity_(music)" title="Simultaneity (music)">simultaneously</a>.<a href="#cite_note-FOOTNOTEBenward_and_Saker2003-45">[42]</a>: <span title='Page / location: pp. 67, 359 Quotation: "A chord is a harmonic unit with at least three different tones sounding simultaneously." "A combination of three or more pitches sounding at the same time."' class="tooltip tooltip-dashed" style="border-bottom: 1px dashed;">pp. 67, 359 <a href="#cite_note-FOOTNOTEK%C3%A1rolyi1965-46">[43]</a>: p. 63 These need not actually be played together: <a href="/wiki/Arpeggio" title="Arpeggio">arpeggios</a> and broken chords may, for many practical and theoretical purposes, constitute chords. Chords and <a href="/wiki/Chord_progression" title="Chord progression">sequences of chords</a> are frequently used in modern Western, West African,<a href="#cite_note-FOOTNOTEMitchell2008-47">[44]</a> and Oceanian&#91;[[Wikipedia:Citing_sources|<span_title="This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(July_2015)">page&nbsp;needed]]&#93;_48-0' class="reference"><a href="#cite_note-FOOTNOTELinkelsn.d.%5B%5BCategory:Wikipedia_articles_needing_page_number_citations_from_July_2015%5D%5D<sup_class=%22noprint_Inline-Template_%22_style=%22white-space:nowrap;%22>&#91;%5B%5BWikipedia:Citing_sources%7C<span_title=%22This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(July_2015)%22>page&nbsp;needed%5D%5D&#93;-48">[45]</a> music, whereas they are absent from the music of many other parts of the world.<a href="#cite_note-FOOTNOTEMalm1996-49">[46]</a>: <span title='Page / location: p. 15 Quotation: "Indeed this harmonic orientation is one of the major differences between Western and much non-Western music."' class="tooltip tooltip-dashed" style="border-bottom: 1px dashed;">p. 15 The most frequently encountered chords are <a href="/wiki/Triad_(music)" title="Triad (music)">triads</a>, so called because they consist of three distinct notes: further notes may be added to give <a href="/wiki/Seventh_chord" title="Seventh chord">seventh chords</a>, <a href="/wiki/Extended_chord" title="Extended chord">extended chords</a>, or <a href="/wiki/Added_tone_chord" title="Added tone chord">added tone chords</a>. The most <a href="/wiki/Common_chord_(music)" title="Common chord (music)">common chords</a> are the <a href="/wiki/Major_chord" title="Major chord">major</a> and <a href="/wiki/Minor_chord" title="Minor chord">minor</a> <a href="/wiki/Triad_(music)" title="Triad (music)">triads</a> and then the <a href="/wiki/Augmented_triad" title="Augmented triad">augmented</a> and <a href="/wiki/Diminished_triad" title="Diminished triad">diminished</a> <a href="/wiki/Triad_(music)" title="Triad (music)">triads</a>. The descriptions major, minor, augmented, and diminished are sometimes referred to collectively as chordal quality. Chords are also commonly classed by their <a href="/wiki/Root_(chord)" title="Root (chord)">root</a> note—so, for instance, the chord C major may be described as a triad of major quality built on the note C. Chords may also be classified by <a href="/wiki/Inverted_chord" class="mw-redirect" title="Inverted chord">inversion</a>, the order in which the notes are stacked. A series of chords is called a <a href="/wiki/Chord_progression" title="Chord progression">chord progression</a>. Although any chord may in principle be followed by any other chord, certain patterns of chords have been accepted as establishing <a href="/wiki/Key_(music)" title="Key (music)">key</a> in <a href="/wiki/Common_practice_harmony" class="mw-redirect" title="Common practice harmony">common-practice harmony</a>. To describe this, chords are numbered, using <a href="/wiki/Roman_numerals" title="Roman numerals">Roman numerals</a> (upward from the key-note),<a href="#cite_note-FOOTNOTESchoenberg19831%E2%80%932-50">[47]</a> per their <a href="/wiki/Diatonic_function" class="mw-redirect" title="Diatonic function">diatonic function</a>. Common ways of <a href="#Notation">notating or representing chords</a><a href="#cite_note-FOOTNOTEBenward_and_Saker200377-51">[48]</a> in western music other than conventional <a href="/wiki/Staff_notation" class="mw-redirect" title="Staff notation">staff notation</a> include <a href="/wiki/Roman_numerals#Music_theory" title="Roman numerals">Roman numerals</a>, <a href="/wiki/Figured_bass" title="Figured bass">figured bass</a> (much used in the <a href="/wiki/Baroque_music" title="Baroque music">Baroque era</a>), <a href="/wiki/Chord_letter" class="mw-redirect" title="Chord letter">chord letters</a> (sometimes used in modern <a href="/wiki/Musicology" title="Musicology">musicology</a>), and various systems of <a href="/wiki/Chord_chart" title="Chord chart">chord charts</a> typically found in the <a href="/wiki/Lead_sheet" title="Lead sheet">lead sheets</a> used in <a href="/wiki/Chord_names_and_symbols_(popular_music)" class="mw-redirect" title="Chord names and symbols (popular music)">popular music</a> to lay out the sequence of chords so that the musician may play accompaniment chords or improvise a solo. <div class="mw-heading mw-heading3"><h3 id="Harmony">Harmony</h3> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=22" title="Edit section: Harmony" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Harmony" title="Harmony">Harmony</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:US_Navy_080615-N-7656R-003_Navy_Band_Northwest%27s_Barbershop_Quartet_win_the_hearts_of_the_audience_with_a_John_Philip_Sousa_rendition_of.jpg" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f1/US_Navy_080615-N-7656R-003_Navy_Band_Northwest%27s_Barbershop_Quartet_win_the_hearts_of_the_audience_with_a_John_Philip_Sousa_rendition_of.jpg/220px-US_Navy_080615-N-7656R-003_Navy_Band_Northwest%27s_Barbershop_Quartet_win_the_hearts_of_the_audience_with_a_John_Philip_Sousa_rendition_of.jpg" decoding="async" width="220" height="157" class="mw-file-element" data-file-width="2658" data-file-height="1899"></noscript><span class="lazy-image-placeholder" style="width: 220px;height: 157px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f1/US_Navy_080615-N-7656R-003_Navy_Band_Northwest%27s_Barbershop_Quartet_win_the_hearts_of_the_audience_with_a_John_Philip_Sousa_rendition_of.jpg/220px-US_Navy_080615-N-7656R-003_Navy_Band_Northwest%27s_Barbershop_Quartet_win_the_hearts_of_the_audience_with_a_John_Philip_Sousa_rendition_of.jpg" data-width="220" data-height="157" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f1/US_Navy_080615-N-7656R-003_Navy_Band_Northwest%27s_Barbershop_Quartet_win_the_hearts_of_the_audience_with_a_John_Philip_Sousa_rendition_of.jpg/330px-US_Navy_080615-N-7656R-003_Navy_Band_Northwest%27s_Barbershop_Quartet_win_the_hearts_of_the_audience_with_a_John_Philip_Sousa_rendition_of.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f1/US_Navy_080615-N-7656R-003_Navy_Band_Northwest%27s_Barbershop_Quartet_win_the_hearts_of_the_audience_with_a_John_Philip_Sousa_rendition_of.jpg/440px-US_Navy_080615-N-7656R-003_Navy_Band_Northwest%27s_Barbershop_Quartet_win_the_hearts_of_the_audience_with_a_John_Philip_Sousa_rendition_of.jpg 2x" data-class="mw-file-element"> </a><figcaption><a href="/wiki/Barbershop_quartet" title="Barbershop quartet">Barbershop quartets</a>, such as this US Navy group, sing 4-part pieces, made up of a melody line (normally the second-highest voice, called the "lead") and 3 harmony parts.</figcaption></figure> In music, harmony is the use of simultaneous <a href="/wiki/Pitch_(music)" title="Pitch (music)">pitches</a> (<a href="/wiki/Timbre" title="Timbre">tones</a>, <a href="/wiki/Note_(music)" class="mw-redirect" title="Note (music)">notes</a>), or <a href="/wiki/Chord_(music)" title="Chord (music)">chords</a>.<a href="#cite_note-FOOTNOTEMalm1996-49">[46]</a>: <span title='Page / location: p. 15 Quotation: "Homophonic texture... is more common in Western music, where tunes are often built on chords (harmonies) that move in progressions. Indeed this harmonic orientation is one of the major differences between Western and much non-Western music."' class="tooltip tooltip-dashed" style="border-bottom: 1px dashed;">p. 15 The study of harmony involves chords and their construction and <a href="/wiki/Chord_progression" title="Chord progression">chord progressions</a> and the principles of connection that govern them.<a href="#cite_note-FOOTNOTEDahlhaus2009-52">[49]</a> Harmony is often said to refer to the "vertical" aspect of music, as distinguished from <a href="/wiki/Melody" title="Melody">melodic line</a>, or the "horizontal" aspect.<a href="#cite_note-FOOTNOTEJamini2005147-53">[50]</a> <a href="/wiki/Counterpoint" title="Counterpoint">Counterpoint</a>, which refers to the interweaving of melodic lines, and <a href="/wiki/Polyphony" title="Polyphony">polyphony</a>, which refers to the relationship of separate independent voices, is thus sometimes distinguished from harmony.<a href="#cite_note-54">[51]</a> In <a href="/wiki/Popular_harmony" class="mw-redirect" title="Popular harmony">popular</a> and <a href="/wiki/Jazz_harmony" title="Jazz harmony">jazz harmony</a>, chords are named by their <a href="/wiki/Root_(chord)" title="Root (chord)">root</a> plus various terms and characters indicating their qualities. For example, a <a href="/wiki/Lead_sheet" title="Lead sheet">lead sheet</a> may indicate chords such as C major, D minor, and G dominant seventh. In many types of music, notably Baroque, Romantic, modern, and jazz, chords are often augmented with "tensions". A tension is an additional chord member that creates a relatively <a href="/wiki/Consonance_and_dissonance" title="Consonance and dissonance">dissonant interval</a> in relation to the bass. It is part of a chord, but is not one of the chord tones (1 3 5 7). Typically, in the classical <a href="/wiki/Common_practice_period" title="Common practice period">common practice period</a> a dissonant chord (chord with tension) "resolves" to a consonant chord. <a href="/wiki/Harmonization" title="Harmonization">Harmonization</a> usually sounds pleasant to the ear when there is a balance between the consonant and dissonant sounds. In simple words, that occurs when there is a balance between "tense" and "relaxed" moments.<a href="#cite_note-55">[52]</a>[<a href="/wiki/Wikipedia:Reliable_sources" title="Wikipedia:Reliable sources">unreliable source?</a>] <div class="mw-heading mw-heading3"><h3 id="Timbre">Timbre</h3> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=23" title="Edit section: Timbre" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Timbre" title="Timbre">Timbre</a></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:9577_Guitarz1970_Clean_E9_Guitar_Chord_(Mike_Tribulas).jpg" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/9577_Guitarz1970_Clean_E9_Guitar_Chord_%28Mike_Tribulas%29.jpg/220px-9577_Guitarz1970_Clean_E9_Guitar_Chord_%28Mike_Tribulas%29.jpg" decoding="async" width="220" height="146" class="mw-file-element" data-file-width="587" data-file-height="389"></noscript><span class="lazy-image-placeholder" style="width: 220px;height: 146px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/9577_Guitarz1970_Clean_E9_Guitar_Chord_%28Mike_Tribulas%29.jpg/220px-9577_Guitarz1970_Clean_E9_Guitar_Chord_%28Mike_Tribulas%29.jpg" data-width="220" data-height="146" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/9577_Guitarz1970_Clean_E9_Guitar_Chord_%28Mike_Tribulas%29.jpg/330px-9577_Guitarz1970_Clean_E9_Guitar_Chord_%28Mike_Tribulas%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/60/9577_Guitarz1970_Clean_E9_Guitar_Chord_%28Mike_Tribulas%29.jpg/440px-9577_Guitarz1970_Clean_E9_Guitar_Chord_%28Mike_Tribulas%29.jpg 2x" data-class="mw-file-element"> </a><figcaption><a href="/wiki/Spectrogram" title="Spectrogram">Spectrogram</a> of the first second of an E9 chord played on a Fender Stratocaster guitar with noiseless pickups. Below is the E9 chord audio: <audio id="mwe_player_5" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-durationhint="13" data-mwtitle="9577_Guitarz1970_Clean_E9_Guitar_Chord_(Mike_Tribulas).ogg" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/c/cc/9577_Guitarz1970_Clean_E9_Guitar_Chord_%28Mike_Tribulas%29.ogg" type='audio/ogg; codecs="vorbis"' data-width="0" data-height="0"></source><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/c/cc/9577_Guitarz1970_Clean_E9_Guitar_Chord_%28Mike_Tribulas%29.ogg/9577_Guitarz1970_Clean_E9_Guitar_Chord_%28Mike_Tribulas%29.ogg.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0"></source></audio> </figcaption></figure>Timbre, sometimes called "color", or "tone color," is the principal phenomenon that allows us to distinguish one instrument from another when both play at the same pitch and volume, a quality of a voice or instrument often described in terms like bright, dull, shrill, etc. It is of considerable interest in music theory, especially because it is one component of music that has as yet, no standardized nomenclature. It has been called "... the psychoacoustician's multidimensional waste-basket category for everything that cannot be labeled pitch or loudness,"<a href="#cite_note-FOOTNOTEMcAdams_and_Bregman197934-56">[53]</a> but can be accurately described and analyzed by <a href="/wiki/Fourier_analysis" title="Fourier analysis">Fourier analysis</a> and other methods<a href="#cite_note-FOOTNOTEMannelln.d.-57">[54]</a> because it results from the combination of all sound <a href="/wiki/Audio_frequency" title="Audio frequency">frequencies</a>, attack and release envelopes, and other qualities that a tone comprises. <a href="/wiki/Timbre" title="Timbre">Timbre</a> is principally determined by two things: (1) the relative balance of <a href="/wiki/Overtones" class="mw-redirect" title="Overtones">overtones</a> produced by a given instrument due its construction (e.g. shape, material), and (2) the <a href="/wiki/Envelope_(waves)" title="Envelope (waves)">envelope</a> of the sound (including changes in the overtone structure over time). Timbre varies widely between different instruments, voices, and to lesser degree, between instruments of the same type due to variations in their construction, and significantly, the performer's technique. The timbre of most instruments can be changed by employing different techniques while playing. For example, the timbre of a trumpet changes when a mute is inserted into the bell, the player changes their embouchure, or volume.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] A voice can change its timbre by the way the performer manipulates their vocal apparatus, (e.g. the shape of the vocal cavity or mouth). Musical notation frequently specifies alteration in timbre by changes in sounding technique, volume, accent, and other means. These are indicated variously by symbolic and verbal instruction. For example, the word dolce (sweetly) indicates a non-specific, but commonly understood soft and "sweet" timbre. Sul tasto instructs a string player to bow near or over the fingerboard to produce a less brilliant sound. Cuivre instructs a brass player to produce a forced and stridently brassy sound. Accent symbols like marcato (^) and dynamic indications (pp) can also indicate changes in timbre.<a href="#cite_note-58">[55]</a> <div class="mw-heading mw-heading4"><h4 id="Dynamics">Dynamics</h4> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=24" title="Edit section: Dynamics" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Unreferenced_section plainlinks metadata ambox ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-text"><div class="mbox-text-span">This section does not <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">cite</a> any <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">sources</a>. Please help <a href="/wiki/Special:EditPage/Music_theory" title="Special:EditPage/Music theory">improve this section</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and <a href="/wiki/Wikipedia:Verifiability#Burden_of_evidence" title="Wikipedia:Verifiability">removed</a>. (July 2015) (<a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a>)</div></td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Dynamics_(music)" title="Dynamics (music)">Dynamics (music)</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Music_hairpins.svg" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/43/Music_hairpins.svg/290px-Music_hairpins.svg.png" decoding="async" width="290" height="74" class="mw-file-element" data-file-width="512" data-file-height="131"></noscript><span class="lazy-image-placeholder" style="width: 290px;height: 74px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/4/43/Music_hairpins.svg/290px-Music_hairpins.svg.png" data-width="290" data-height="74" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/43/Music_hairpins.svg/435px-Music_hairpins.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/43/Music_hairpins.svg/580px-Music_hairpins.svg.png 2x" data-class="mw-file-element"> </a><figcaption>Illustration of hairpins in musical notation</figcaption></figure> In music, "<a href="/wiki/Dynamics_(music)" title="Dynamics (music)">dynamics</a>" normally refers to variations of intensity or volume, as may be measured by physicists and audio engineers in <a href="/wiki/Decibels" class="mw-redirect" title="Decibels">decibels</a> or <a href="/wiki/Phon" title="Phon">phons</a>. In music notation, however, dynamics are not treated as absolute values, but as relative ones. Because they are usually measured subjectively, there are factors besides amplitude that affect the performance or perception of intensity, such as timbre, vibrato, and articulation. The conventional indications of dynamics are abbreviations for Italian words like forte (f) for loud and piano (p) for soft. These two basic notations are modified by indications including mezzo piano (mp) for moderately soft (literally "half soft") and mezzo forte (mf) for moderately loud, sforzando or sforzato (sfz) for a surging or "pushed" attack, or fortepiano (fp) for a loud attack with a sudden decrease to a soft level. The full span of these markings usually range from a nearly inaudible pianissississimo (pppp) to a loud-as-possible fortissississimo (ffff). Greater extremes of pppppp and fffff and nuances such as p+ or più piano are sometimes found. Other systems of indicating volume are also used in both notation and analysis: dB (decibels), numerical scales, colored or different sized notes, words in languages other than Italian, and symbols such as those for progressively increasing volume (crescendo) or decreasing volume (diminuendo or decrescendo), often called "<a href="/wiki/Dynamics_(music)" title="Dynamics (music)">hairpins</a>" when indicated with diverging or converging lines as shown in the graphic above. <div class="mw-heading mw-heading4"><h4 id="Articulation">Articulation</h4> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=25" title="Edit section: Articulation" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Unreferenced_section plainlinks metadata ambox ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-text"><div class="mbox-text-span">This section does not <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">cite</a> any <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">sources</a>. Please help <a href="/wiki/Special:EditPage/Music_theory" title="Special:EditPage/Music theory">improve this section</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and <a href="/wiki/Wikipedia:Verifiability#Burden_of_evidence" title="Wikipedia:Verifiability">removed</a>. (July 2015) (<a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a>)</div></td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Articulation_(music)" title="Articulation (music)">Articulation (music)</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Notation_accents1.png" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Notation_accents1.png/310px-Notation_accents1.png" decoding="async" width="310" height="68" class="mw-file-element" data-file-width="500" data-file-height="110"></noscript><span class="lazy-image-placeholder" style="width: 310px;height: 68px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Notation_accents1.png/310px-Notation_accents1.png" data-width="310" data-height="68" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Notation_accents1.png/465px-Notation_accents1.png 1.5x, //upload.wikimedia.org/wikipedia/commons/0/0e/Notation_accents1.png 2x" data-class="mw-file-element"> </a><figcaption>Examples of articulation marks. From left to right: <a href="/wiki/Staccato" title="Staccato">staccato</a>, <a href="/wiki/Staccatissimo" class="mw-redirect" title="Staccatissimo">staccatissimo</a>, <a href="/wiki/Martellato" class="mw-redirect" title="Martellato">martellato</a>, <a href="/wiki/Accent_(music)" title="Accent (music)">accent</a>, <a href="/wiki/Tenuto" title="Tenuto">tenuto</a>.</figcaption></figure> Articulation is the way the performer sounds notes. For example, <a href="/wiki/Staccato" title="Staccato">staccato</a> is the shortening of duration compared to the written note value, <a href="/wiki/Legato" title="Legato">legato</a> performs the notes in a smoothly joined sequence with no separation. Articulation is often described rather than quantified, therefore there is room to interpret how to execute precisely each articulation. For example, staccato is often referred to as "separated" or "detached" rather than having a defined or numbered amount by which to reduce the notated duration. Violin players use a variety of techniques to perform different qualities of staccato. The manner in which a performer decides to execute a given articulation is usually based on the context of the piece or phrase, but many articulation symbols and verbal instructions depend on the instrument and musical period (e.g. viol, wind; classical, baroque; etc.). There is a set of articulations that most instruments and voices perform in common. They are—from long to short: legato (smooth, connected); <a href="/wiki/Tenuto" title="Tenuto">tenuto</a> (pressed or played to full notated duration); <a href="/wiki/Marcato" title="Marcato">marcato</a> (accented and detached); staccato ("separated", "detached"); <a href="/wiki/Martel%C3%A9_(bowstroke)" title="Martelé (bowstroke)">martelé</a> (heavily accented or "hammered").[<a href="/wiki/Category:All_self-contradictory_articles" title="Category:All self-contradictory articles"><span title='The accompanying illustration names "staccato", "tenuto", and three other articulations not listed here. Are these synonyms and, if so, which are synonyms of which? Neither list is cited to a reliable source. (March 2020)'>contradictory</a>] Many of these can be combined to create certain "in-between" articulations. For example, <a href="/wiki/Portato" title="Portato">portato</a> is the combination of tenuto and staccato. Some instruments have unique methods by which to produce sounds, such as <a href="/wiki/Spiccato" title="Spiccato">spiccato</a> for bowed strings, where the bow bounces off the string. <div class="mw-heading mw-heading3"><h3 id="Texture">Texture</h3> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=26" title="Edit section: Texture" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Musical_texture" class="mw-redirect" title="Musical texture">Musical texture</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Sousa_-_%22Washington_Post_March,%22_m._1-7.png" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Sousa_-_%22Washington_Post_March%2C%22_m._1-7.png/260px-Sousa_-_%22Washington_Post_March%2C%22_m._1-7.png" decoding="async" width="260" height="53" class="mw-file-element" data-file-width="2238" data-file-height="452"></noscript><span class="lazy-image-placeholder" style="width: 260px;height: 53px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Sousa_-_%22Washington_Post_March%2C%22_m._1-7.png/260px-Sousa_-_%22Washington_Post_March%2C%22_m._1-7.png" data-width="260" data-height="53" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Sousa_-_%22Washington_Post_March%2C%22_m._1-7.png/390px-Sousa_-_%22Washington_Post_March%2C%22_m._1-7.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Sousa_-_%22Washington_Post_March%2C%22_m._1-7.png/520px-Sousa_-_%22Washington_Post_March%2C%22_m._1-7.png 2x" data-class="mw-file-element"> </a><figcaption>Introduction to <a href="/wiki/John_Philip_Sousa" title="John Philip Sousa">Sousa</a>'s "<a href="/wiki/The_Washington_Post_(march)" title="The Washington Post (march)">Washington Post March</a>," mm. 1–7 features <a href="/wiki/Octave_doubling" class="mw-redirect" title="Octave doubling">octave doubling</a> <a href="#cite_note-FOOTNOTEBenward_and_Saker2003133-59">[56]</a> and a homorhythmic texture<audio id="mwe_player_6" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-mwtitle='Sousa_-_"Washington_Post_March,"_m._1-7.mid' data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/c/c7/Sousa_-_%22Washington_Post_March%2C%22_m._1-7.mid" type="audio/midi" data-width="0" data-height="0"></source><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/c/c7/Sousa_-_%22Washington_Post_March%2C%22_m._1-7.mid/Sousa_-_%22Washington_Post_March%2C%22_m._1-7.mid.ogg" type='audio/ogg; codecs="vorbis"' data-transcodekey="ogg" data-width="0" data-height="0"></source><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/c/c7/Sousa_-_%22Washington_Post_March%2C%22_m._1-7.mid/Sousa_-_%22Washington_Post_March%2C%22_m._1-7.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0"></source><track src="https://commons.wikimedia.org/w/api.php?action=timedtext&title=File%3ASousa_-_%22Washington_Post_March%2C%22_m._1-7.mid&lang=en&trackformat=vtt&origin=%2A" kind="subtitles" type="text/vtt" srclang="en" label="English ‪(en)‬" data-dir="ltr"></track></audio></figcaption></figure> In music, texture is how the <a href="/wiki/Melody" title="Melody">melodic</a>, <a href="/wiki/Rhythm" title="Rhythm">rhythmic</a>, and <a href="/wiki/Harmony" title="Harmony">harmonic</a> materials are combined in a <a href="/wiki/Musical_composition" title="Musical composition">composition</a>, thus determining the overall quality of the sound in a piece. Texture is often described in regard to the density, or thickness, and <a href="/wiki/Range_(music)" title="Range (music)">range</a>, or width, between lowest and highest pitches, in relative terms as well as more specifically distinguished according to the number of voices, or parts, and the relationship between these voices. For example, a thick texture contains many "layers" of instruments. One of these layers could be a string section, or another brass. The thickness also is affected by the number and the richness of the instruments playing the piece. The thickness varies from light to thick. A lightly textured piece will have light, sparse scoring. A thickly or heavily textured piece will be scored for many instruments. A piece's texture may be affected by the number and character of parts playing at once, the <a href="/wiki/Timbre" title="Timbre">timbre</a> of the instruments or voices playing these parts and the harmony, <a href="/wiki/Tempo" title="Tempo">tempo</a>, and rhythms used.&#91;[[Wikipedia:Citing_sources|<span_title="This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(July_2015)">page&nbsp;needed]]&#93;_60-0' class="reference"><a href="#cite_note-FOOTNOTEBenward_and_Saker2003%5B%5BCategory:Wikipedia_articles_needing_page_number_citations_from_July_2015%5D%5D<sup_class=%22noprint_Inline-Template_%22_style=%22white-space:nowrap;%22>&#91;%5B%5BWikipedia:Citing_sources%7C<span_title=%22This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(July_2015)%22>page&nbsp;needed%5D%5D&#93;-60">[57]</a> The types categorized by number and relationship of parts are analyzed and determined through the labeling of primary textural elements: primary melody, secondary melody, parallel supporting melody, static support, harmonic support, rhythmic support, and harmonic and rhythmic support.<a href="#cite_note-FOOTNOTEIsaac_and_Russell2003136-61">[58]</a>[<a href="/wiki/Wikipedia:CITESHORT" class="mw-redirect" title="Wikipedia:CITESHORT">incomplete short citation</a>] Common types included <a href="/wiki/Monophony" title="Monophony">monophonic</a> texture (a single melodic voice, such as a piece for solo soprano or solo flute), biphonic texture (two melodic voices, such as a duo for bassoon and flute in which the bassoon plays a drone note and the flute plays the melody), <a href="/wiki/Polyphonic" class="mw-redirect" title="Polyphonic">polyphonic</a> texture and <a href="/wiki/Homophony" title="Homophony">homophonic</a> texture (chords accompanying a melody).[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] <div class="mw-heading mw-heading3"><h3 id="Form_or_structure">Form or structure</h3> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=27" title="Edit section: Form or structure" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Canon_example.png" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Canon_example.png/220px-Canon_example.png" decoding="async" width="220" height="122" class="mw-file-element" data-file-width="965" data-file-height="533"></noscript><span class="lazy-image-placeholder" style="width: 220px;height: 122px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Canon_example.png/220px-Canon_example.png" data-width="220" data-height="122" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Canon_example.png/330px-Canon_example.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Canon_example.png/440px-Canon_example.png 2x" data-class="mw-file-element"> </a><figcaption>A musical <a href="/wiki/Canon_(music)" title="Canon (music)">canon</a>. Encyclopaedia Britannica calls a "canon" both a compositional technique and a musical form.<a href="#cite_note-62">[59]</a></figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Musical_form" title="Musical form">Musical form</a></div> The term musical form (or musical architecture) refers to the overall structure or plan of a piece of music, and it describes the layout of a composition as divided into sections.<a href="#cite_note-FOOTNOTEBrandt2007-63">[60]</a> In the tenth edition of <a href="/wiki/The_Oxford_Companion_to_Music" title="The Oxford Companion to Music">The Oxford Companion to Music</a>, <a href="/wiki/Percy_Scholes" title="Percy Scholes">Percy Scholes</a> defines musical form as "a series of strategies designed to find a successful mean between the opposite extremes of unrelieved repetition and unrelieved alteration."<a href="#cite_note-FOOTNOTEScholes1977-64">[61]</a> According to <a href="/wiki/Richard_Middleton_(musicologist)" title="Richard Middleton (musicologist)">Richard Middleton</a>, musical form is "the shape or structure of the work." He describes it through difference: the distance moved from a <a href="/wiki/Repetition_(music)" title="Repetition (music)">repeat</a>; the latter being the smallest difference. Difference is quantitative and qualitative: how far, and of what type, different. In many cases, form depends on statement and <a href="/wiki/Restatement_(music)" class="mw-redirect" title="Restatement (music)">restatement</a>, unity and variety, and <a href="/wiki/Contrast_(music)" title="Contrast (music)">contrast</a> and connection.&#91;[[Wikipedia:Citing_sources|<span_title="This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(July_2015)">page&nbsp;needed]]&#93;_65-0' class="reference"><a href="#cite_note-FOOTNOTEMiddleton1999%5B%5BCategory:Wikipedia_articles_needing_page_number_citations_from_July_2015%5D%5D<sup_class=%22noprint_Inline-Template_%22_style=%22white-space:nowrap;%22>&#91;%5B%5BWikipedia:Citing_sources%7C<span_title=%22This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(July_2015)%22>page&nbsp;needed%5D%5D&#93;-65">[62]</a> <div class="mw-heading mw-heading3"><h3 id="Expression">Expression</h3> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=28" title="Edit section: Expression" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Musical_expression" title="Musical expression">Musical expression</a></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:1Francisco20violinista.jpg" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/1Francisco20violinista.jpg/220px-1Francisco20violinista.jpg" decoding="async" width="220" height="165" class="mw-file-element" data-file-width="2592" data-file-height="1944"></noscript><span class="lazy-image-placeholder" style="width: 220px;height: 165px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/1Francisco20violinista.jpg/220px-1Francisco20violinista.jpg" data-width="220" data-height="165" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/1Francisco20violinista.jpg/330px-1Francisco20violinista.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/91/1Francisco20violinista.jpg/440px-1Francisco20violinista.jpg 2x" data-class="mw-file-element"> </a><figcaption>A violinist performing</figcaption></figure> Musical expression is the art of playing or singing music with emotional communication. The elements of music that comprise expression include dynamic indications, such as forte or piano, <a href="/wiki/Musical_phrasing" title="Musical phrasing">phrasing</a>, differing qualities of timbre and articulation, color, intensity, energy and excitement. All of these devices can be incorporated by the performer. A performer aims to elicit responses of sympathetic feeling in the audience, and to excite, calm or otherwise sway the audience's physical and emotional responses. Musical expression is sometimes thought to be produced by a combination of other parameters, and sometimes described as a transcendent quality that is more than the sum of measurable quantities such as pitch or duration. Expression on instruments can be closely related to the role of the breath in singing, and the voice's natural ability to express feelings, sentiment and deep emotions.[<a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify">clarification needed</a>] Whether these can somehow be categorized is perhaps the realm of academics, who view expression as an element of musical performance that embodies a consistently recognizable <a href="/wiki/Emotion" title="Emotion">emotion</a>, ideally causing a <a href="/wiki/Emotional_contagion" title="Emotional contagion">sympathetic emotional response</a> in its listeners.<a href="#cite_note-FOOTNOTELondonn.d.-66">[63]</a> The emotional content of musical expression is distinct from the emotional content of specific sounds (e.g., a startlingly-loud 'bang') and of learned associations (e.g., a <a href="/wiki/National_anthem" title="National anthem">national anthem</a>), but can rarely be completely separated from its context.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] The components of musical expression continue to be the subject of extensive and unresolved dispute.&#91;[[Wikipedia:Citing_sources|<span_title="This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(July_2015)">page&nbsp;needed]]&#93;_67-0' class="reference"><a href="#cite_note-FOOTNOTEAvison1752%5B%5BCategory:Wikipedia_articles_needing_page_number_citations_from_July_2015%5D%5D<sup_class=%22noprint_Inline-Template_%22_style=%22white-space:nowrap;%22>&#91;%5B%5BWikipedia:Citing_sources%7C<span_title=%22This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(July_2015)%22>page&nbsp;needed%5D%5D&#93;-67">[64]</a>&#91;[[Wikipedia:Citing_sources|<span_title="This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(July_2015)">page&nbsp;needed]]&#93;_68-0' class="reference"><a href="#cite_note-FOOTNOTEChristiani1885%5B%5BCategory:Wikipedia_articles_needing_page_number_citations_from_July_2015%5D%5D<sup_class=%22noprint_Inline-Template_%22_style=%22white-space:nowrap;%22>&#91;%5B%5BWikipedia:Citing_sources%7C<span_title=%22This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(July_2015)%22>page&nbsp;needed%5D%5D&#93;-68">[65]</a>&#91;[[Wikipedia:Citing_sources|<span_title="This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(July_2015)">page&nbsp;needed]]&#93;_69-0' class="reference"><a href="#cite_note-FOOTNOTELussy1892%5B%5BCategory:Wikipedia_articles_needing_page_number_citations_from_July_2015%5D%5D<sup_class=%22noprint_Inline-Template_%22_style=%22white-space:nowrap;%22>&#91;%5B%5BWikipedia:Citing_sources%7C<span_title=%22This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(July_2015)%22>page&nbsp;needed%5D%5D&#93;-69">[66]</a>&#91;[[Wikipedia:Citing_sources|<span_title="This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(July_2015)">page&nbsp;needed]]&#93;_70-0' class="reference"><a href="#cite_note-FOOTNOTEDarwin1913%5B%5BCategory:Wikipedia_articles_needing_page_number_citations_from_July_2015%5D%5D<sup_class=%22noprint_Inline-Template_%22_style=%22white-space:nowrap;%22>&#91;%5B%5BWikipedia:Citing_sources%7C<span_title=%22This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(July_2015)%22>page&nbsp;needed%5D%5D&#93;-70">[67]</a>&#91;[[Wikipedia:Citing_sources|<span_title="This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(July_2015)">page&nbsp;needed]]&#93;_71-0' class="reference"><a href="#cite_note-FOOTNOTESorantin1932%5B%5BCategory:Wikipedia_articles_needing_page_number_citations_from_July_2015%5D%5D<sup_class=%22noprint_Inline-Template_%22_style=%22white-space:nowrap;%22>&#91;%5B%5BWikipedia:Citing_sources%7C<span_title=%22This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(July_2015)%22>page&nbsp;needed%5D%5D&#93;-71">[68]</a>&#91;[[Wikipedia:Citing_sources|<span_title="This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(July_2015)">page&nbsp;needed]]&#93;_72-0' class="reference"><a href="#cite_note-FOOTNOTEDavies1994%5B%5BCategory:Wikipedia_articles_needing_page_number_citations_from_July_2015%5D%5D<sup_class=%22noprint_Inline-Template_%22_style=%22white-space:nowrap;%22>&#91;%5B%5BWikipedia:Citing_sources%7C<span_title=%22This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(July_2015)%22>page&nbsp;needed%5D%5D&#93;-72">[69]</a> <div class="mw-heading mw-heading3"><h3 id="Notation">Notation</h3> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=29" title="Edit section: Notation" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Musical_notation" title="Musical notation">Musical notation</a> and <a href="/wiki/Sheet_music" title="Sheet music">Sheet music</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Tibetanmusicalscore.jpg" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/74/Tibetanmusicalscore.jpg/220px-Tibetanmusicalscore.jpg" decoding="async" width="220" height="44" class="mw-file-element" data-file-width="640" data-file-height="129"></noscript><span class="lazy-image-placeholder" style="width: 220px;height: 44px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/7/74/Tibetanmusicalscore.jpg/220px-Tibetanmusicalscore.jpg" data-width="220" data-height="44" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/74/Tibetanmusicalscore.jpg/330px-Tibetanmusicalscore.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/74/Tibetanmusicalscore.jpg/440px-Tibetanmusicalscore.jpg 2x" data-class="mw-file-element"> </a><figcaption><a href="/wiki/Tibet" title="Tibet">Tibetan</a> musical score from the 19th century</figcaption></figure> Musical notation is the written or symbolized representation of music. This is most often achieved by the use of commonly understood graphic symbols and written verbal instructions and their abbreviations. There are many systems of music notation from different cultures and different ages. Traditional Western notation evolved during the Middle Ages and remains an area of experimentation and innovation.&#91;[[Wikipedia:Citing_sources|<span_title="This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(August_2014)">page&nbsp;needed]]&#93;Stone1980[[Category:Wikipedia_articles_needing_page_number_citations_from_August_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;[[Wikipedia:Citing_sources|<span_title="This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(August_2014)">page&nbsp;needed]]&#93;_73-0' class="reference"><a href="#cite_note-FOOTNOTERead1969%5B%5BCategory:Wikipedia_articles_needing_page_number_citations_from_August_2014%5D%5D<sup_class=%22noprint_Inline-Template_%22_style=%22white-space:nowrap;%22>&#91;%5B%5BWikipedia:Citing_sources%7C<span_title=%22This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(August_2014)%22>page&nbsp;needed%5D%5D&#93;Stone1980%5B%5BCategory:Wikipedia_articles_needing_page_number_citations_from_August_2014%5D%5D<sup_class=%22noprint_Inline-Template_%22_style=%22white-space:nowrap;%22>&#91;%5B%5BWikipedia:Citing_sources%7C<span_title=%22This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(August_2014)%22>page&nbsp;needed%5D%5D&#93;-73">[70]</a> In the 2000s, computer <a href="/wiki/File_formats" class="mw-redirect" title="File formats">file formats</a> have become important as well.<a href="#cite_note-FOOTNOTECastan2009-74">[71]</a> Spoken language and <a href="/wiki/Kod%C3%A1ly_Method#Hand_signs" class="mw-redirect" title="Kodály Method">hand signs</a> are also used to symbolically represent music, primarily in teaching. In standard Western music notation, tones are represented graphically by symbols (notes) placed on a <a href="/wiki/Staff_(music)" title="Staff (music)">staff</a> or staves, the vertical axis corresponding to pitch and the horizontal axis corresponding to time. Note head shapes, stems, flags, ties and dots are used to indicate duration. Additional symbols indicate keys, dynamics, accents, rests, etc. Verbal instructions from the conductor are often used to indicate tempo, technique, and other aspects. In Western music, a range of different music notation systems are used. In Western Classical music, conductors use printed scores that show all of the instruments' parts and orchestra members read parts with their musical lines written out. In popular styles of music, much less of the music may be notated. A rock band may go into a recording session with just a handwritten <a href="/wiki/Chord_chart" title="Chord chart">chord chart</a> indicating the song's <a href="/wiki/Chord_progression" title="Chord progression">chord progression</a> using chord names (e.g., C major, D minor, G7, etc.). All of the chord voicings, rhythms and accompaniment figures are improvised by the band members. </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(3)"><h2 id="As_academic_discipline">As academic discipline</h2> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=30" title="Edit section: As academic discipline" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-3 collapsible-block" id="mf-section-3"> The scholarly study of music theory in the twentieth century has a number of different subfields, each of which takes a different perspective on what are the primary phenomenon of interest and the most useful methods for investigation. <div class="mw-heading mw-heading3"><h3 id="Analysis">Analysis</h3> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=31" title="Edit section: Analysis" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Musical_analysis" title="Musical analysis">Musical analysis</a>, <a href="/wiki/Schenkerian_analysis" title="Schenkerian analysis">Schenkerian analysis</a>, and <a href="/wiki/Transformational_theory" title="Transformational theory">Transformational theory</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Debussy_Pelleas_et_Melisande_prelude_opening.PNG" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/59/Debussy_Pelleas_et_Melisande_prelude_opening.PNG/290px-Debussy_Pelleas_et_Melisande_prelude_opening.PNG" decoding="async" width="290" height="154" class="mw-file-element" data-file-width="437" data-file-height="232"></noscript><span class="lazy-image-placeholder" style="width: 290px;height: 154px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/5/59/Debussy_Pelleas_et_Melisande_prelude_opening.PNG/290px-Debussy_Pelleas_et_Melisande_prelude_opening.PNG" data-width="290" data-height="154" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/59/Debussy_Pelleas_et_Melisande_prelude_opening.PNG/435px-Debussy_Pelleas_et_Melisande_prelude_opening.PNG 1.5x, //upload.wikimedia.org/wikipedia/commons/5/59/Debussy_Pelleas_et_Melisande_prelude_opening.PNG 2x" data-class="mw-file-element"> </a><figcaption>Typically a given work is analyzed by more than one person and different or divergent analyses are created. For instance, the first two bars of the prelude to <a href="/wiki/Claude_Debussy" title="Claude Debussy">Claude Debussy</a>'s <a href="/wiki/Pell%C3%A9as_et_M%C3%A9lisande_(opera)" title="Pelléas et Mélisande (opera)">Pelléas et Melisande</a> are analyzed differently by Leibowitz, Laloy, van Appledorn, and Christ. Leibowitz analyses this succession harmonically as D minor:I–VII–V, ignoring melodic motion, Laloy analyses the succession as D:I–V, seeing the G in the second measure as an <a href="/wiki/Musical_ornamentation" class="mw-redirect" title="Musical ornamentation">ornament</a>, and both van Appledorn and Christ analyse the succession as D:I–VII. <span data-nosnippet="" id="ooui-php-6" class="ext-phonos-PhonosButton noexcerpt oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-ooui='{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/2\/2a\/Debussy_Pelleas_et_Melisande-prelude_opening.mid\/Debussy_Pelleas_et_Melisande-prelude_opening.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"Play"},"data":{"ipa":"","text":"","lang":"en","wikibase":"","file":"Debussy Pelleas et Melisande-prelude opening.mid"},"classes":["ext-phonos-PhonosButton","noexcerpt"]}'><a role="button" tabindex="0" href="//upload.wikimedia.org/wikipedia/commons/transcoded/2/2a/Debussy_Pelleas_et_Melisande-prelude_opening.mid/Debussy_Pelleas_et_Melisande-prelude_opening.mid.mp3" rel="nofollow" aria-label="Play audio" title="Play audio" class="oo-ui-buttonElement-button">Play</a><a href="/wiki/File:Debussy_Pelleas_et_Melisande-prelude_opening.mid" title="File:Debussy Pelleas et Melisande-prelude opening.mid">ⓘ</a></figcaption></figure> Musical analysis is the attempt to answer the question how does this music work? The method employed to answer this question, and indeed exactly what is meant by the question, differs from analyst to analyst, and according to the purpose of the analysis. According to <a href="/wiki/Ian_Bent" title="Ian Bent">Ian Bent</a>, "analysis, as a pursuit in its own right, came to be established only in the late 19th century; its emergence as an approach and method can be traced back to the 1750s. However, it existed as a scholarly tool, albeit an auxiliary one, from the <a href="/wiki/Middle_Ages" title="Middle Ages">Middle Ages</a> onwards."<a href="#cite_note-FOOTNOTEBent19876-75">[72]</a>[<a href="/wiki/Wikipedia:CITESHORT" class="mw-redirect" title="Wikipedia:CITESHORT">incomplete short citation</a>] <a href="/wiki/Adolf_Bernhard_Marx" title="Adolf Bernhard Marx">Adolf Bernhard Marx</a> was influential in formalising concepts about composition and music understanding towards the second half of the 19th century. The principle of analysis has been variously criticized, especially by composers, such as <a href="/wiki/Edgard_Var%C3%A8se" title="Edgard Varèse">Edgard Varèse</a>'s claim that, "to explain by means of [analysis] is to decompose, to mutilate the spirit of a work".<a href="#cite_note-76">[73]</a> <a href="/wiki/Schenkerian_analysis" title="Schenkerian analysis">Schenkerian analysis</a> is a method of musical analysis of tonal music based on the theories of <a href="/wiki/Heinrich_Schenker" title="Heinrich Schenker">Heinrich Schenker</a> (1868–1935). The goal of a Schenkerian analysis is to interpret the underlying structure of a tonal work and to help reading the score according to that structure. The theory's basic tenets can be viewed as a way of defining <a href="/wiki/Tonality" title="Tonality">tonality</a> in music. A Schenkerian analysis of a passage of music shows hierarchical relationships among its pitches, and draws conclusions about the structure of the passage from this hierarchy. The analysis makes use of a specialized symbolic form of musical notation that Schenker devised to demonstrate various <a href="/wiki/Schenkerian_analysis#Techniques_of_prolongation" title="Schenkerian analysis">techniques of elaboration</a>. The most fundamental concept of Schenker's theory of tonality may be that of tonal space.<a href="#cite_note-77">[74]</a> The intervals between the notes of the tonic triad form a tonal space that is filled with passing and neighbour notes, producing new triads and new tonal spaces, open for further elaborations until the surface of the work (the score) is reached. Although Schenker himself usually presents his analyses in the generative direction, starting from the <a href="/wiki/Fundamental_structure" title="Fundamental structure">fundamental structure</a> (Ursatz) to reach the score, the practice of Schenkerian analysis more often is reductive, starting from the score and showing how it can be reduced to its fundamental structure. The graph of the Ursatz is arrhythmic, as is a strict-counterpoint cantus firmus exercise.<a href="#cite_note-FOOTNOTESchenker1979p._15,_%C2%A7_21-78">[75]</a> Even at intermediate levels of the reduction, rhythmic notation (open and closed noteheads, beams and flags) shows not rhythm but the hierarchical relationships between the pitch-events. Schenkerian analysis is subjective. There is no mechanical procedure involved and the analysis reflects the musical intuitions of the analyst.&#91;[[Wikipedia:Citing_sources|<span_title="This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(July_2015)">page&nbsp;needed]]&#93;_79-0' class="reference"><a href="#cite_note-FOOTNOTESnarrenberg1997%5B%5BCategory:Wikipedia_articles_needing_page_number_citations_from_July_2015%5D%5D<sup_class=%22noprint_Inline-Template_%22_style=%22white-space:nowrap;%22>&#91;%5B%5BWikipedia:Citing_sources%7C<span_title=%22This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(July_2015)%22>page&nbsp;needed%5D%5D&#93;-79">[76]</a> The analysis represents a way of hearing (and reading) a piece of music. Transformational theory is a branch of music theory developed by <a href="/wiki/David_Lewin" title="David Lewin">David Lewin</a> in the 1980s, and formally introduced in his 1987 work, Generalized Musical Intervals and Transformations. The theory, which models <a href="/wiki/Transformation_(music)" title="Transformation (music)">musical transformations</a> as elements of a <a href="/wiki/Group_theory" title="Group theory">mathematical group</a>, can be used to analyze both <a href="/wiki/Tonality" title="Tonality">tonal</a> and <a href="/wiki/Atonal_music" class="mw-redirect" title="Atonal music">atonal music</a>. The goal of transformational theory is to change the focus from musical objects—such as the "C <a href="/wiki/Major_chord" title="Major chord">major chord</a>" or "G major chord"—to relations between objects. Thus, instead of saying that a C major chord is followed by G major, a transformational theorist might say that the first chord has been "transformed" into the second by the "<a href="/wiki/Dominant_(music)" title="Dominant (music)">Dominant</a> operation." (Symbolically, one might write "Dominant(C major) = G major.") While traditional <a href="/wiki/Set_theory_(music)" title="Set theory (music)">musical set theory</a> focuses on the makeup of musical objects, transformational theory focuses on the <a href="/wiki/Interval_(music)" title="Interval (music)">intervals</a> or types of musical motion that can occur. According to Lewin's description of this change in emphasis, "[The transformational] attitude does not ask for some observed measure of extension between reified 'points'; rather it asks: 'If I am at s and wish to get to t, what characteristic gesture should I perform in order to arrive there?'"<a href="#cite_note-FOOTNOTELewin1987159-80">[77]</a> <div class="mw-heading mw-heading3"><h3 id="Music_perception_and_cognition">Music perception and cognition</h3> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=32" title="Edit section: Music perception and cognition" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Music_psychology" title="Music psychology">Music psychology</a>, <a href="/wiki/Fred_Lerdahl" title="Fred Lerdahl">Fred Lerdahl</a>, and <a href="/wiki/Ray_Jackendoff" title="Ray Jackendoff">Ray Jackendoff</a></div> Music psychology or the psychology of music may be regarded as a branch of both <a href="/wiki/Psychology" title="Psychology">psychology</a> and <a href="/wiki/Musicology" title="Musicology">musicology</a>. It aims to explain and understand musical <a href="/wiki/Behavior" title="Behavior">behavior</a> and <a href="/wiki/Experience" title="Experience">experience</a>, including the processes through which music is perceived, created, responded to, and incorporated into everyday life.<a href="#cite_note-FOOTNOTETan,_Peter,_and_Rom20102-81">[78]</a><a href="#cite_note-FOOTNOTEThompsonn.d.320-82">[79]</a> Modern music psychology is primarily <a href="/wiki/Empirical_research" title="Empirical research">empirical</a>; its knowledge tends to advance on the basis of interpretations of data collected by systematic <a href="/wiki/Observation" title="Observation">observation</a> of and interaction with <a href="/wiki/Human_subject_research" title="Human subject research">human participants</a>. Music psychology is a field of research with practical relevance for many areas, including music <a href="/wiki/Musical_technique" title="Musical technique">performance</a>, <a href="/wiki/Music_composition" class="mw-redirect" title="Music composition">composition</a>, <a href="/wiki/Music_education" title="Music education">education</a>, <a href="/wiki/Music_criticism" title="Music criticism">criticism</a>, and <a href="/wiki/Music_therapy" title="Music therapy">therapy</a>, as well as investigations of human <a href="/wiki/Aptitude" title="Aptitude">aptitude</a>, skill, <a href="/wiki/Intelligence" title="Intelligence">intelligence</a>, creativity, and <a href="/wiki/Social_behavior" title="Social behavior">social behavior</a>. Music psychology can shed light on non-psychological aspects of <a href="/wiki/Musicology" title="Musicology">musicology</a> and musical practice. For example, it contributes to music theory through investigations of the <a href="/wiki/Perception" title="Perception">perception</a> and <a href="/wiki/Cognitive_musicology" title="Cognitive musicology">computational modelling</a> of musical structures such as <a href="/wiki/Melody" title="Melody">melody</a>, <a href="/wiki/Harmony" title="Harmony">harmony</a>, <a href="/wiki/Tonality" title="Tonality">tonality</a>, <a href="/wiki/Rhythm" title="Rhythm">rhythm</a>, <a href="/wiki/Meter_(music)" class="mw-redirect" title="Meter (music)">meter</a>, and <a href="/wiki/Musical_form" title="Musical form">form</a>. Research in <a href="/wiki/Music_history" title="Music history">music history</a> can benefit from systematic study of the history of <a href="/wiki/Musical_syntax" title="Musical syntax">musical syntax</a>, or from psychological analyses of composers and compositions in relation to perceptual, affective, and social responses to their music. <div class="mw-heading mw-heading3"><h3 id="Genre_and_technique">Genre and technique</h3> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=33" title="Edit section: Genre and technique" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Music_genre" title="Music genre">Music genre</a> and <a href="/wiki/Musical_technique" title="Musical technique">Musical technique</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Bundesarchiv_B_145_Bild-F008930-0019,_Beethovenhalle_Bonn,_Kammerkonzert_K%C3%B6lner_Trio.jpg" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Bundesarchiv_B_145_Bild-F008930-0019%2C_Beethovenhalle_Bonn%2C_Kammerkonzert_K%C3%B6lner_Trio.jpg/220px-Bundesarchiv_B_145_Bild-F008930-0019%2C_Beethovenhalle_Bonn%2C_Kammerkonzert_K%C3%B6lner_Trio.jpg" decoding="async" width="220" height="138" class="mw-file-element" data-file-width="789" data-file-height="495"></noscript><span class="lazy-image-placeholder" style="width: 220px;height: 138px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Bundesarchiv_B_145_Bild-F008930-0019%2C_Beethovenhalle_Bonn%2C_Kammerkonzert_K%C3%B6lner_Trio.jpg/220px-Bundesarchiv_B_145_Bild-F008930-0019%2C_Beethovenhalle_Bonn%2C_Kammerkonzert_K%C3%B6lner_Trio.jpg" data-width="220" data-height="138" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Bundesarchiv_B_145_Bild-F008930-0019%2C_Beethovenhalle_Bonn%2C_Kammerkonzert_K%C3%B6lner_Trio.jpg/330px-Bundesarchiv_B_145_Bild-F008930-0019%2C_Beethovenhalle_Bonn%2C_Kammerkonzert_K%C3%B6lner_Trio.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Bundesarchiv_B_145_Bild-F008930-0019%2C_Beethovenhalle_Bonn%2C_Kammerkonzert_K%C3%B6lner_Trio.jpg/440px-Bundesarchiv_B_145_Bild-F008930-0019%2C_Beethovenhalle_Bonn%2C_Kammerkonzert_K%C3%B6lner_Trio.jpg 2x" data-class="mw-file-element"> </a><figcaption>A Classical <a href="/wiki/Piano_trio" title="Piano trio">piano trio</a> is a group that plays <a href="/wiki/Chamber_music" title="Chamber music">chamber music</a>, including <a href="/wiki/Sonata" title="Sonata">sonatas</a>. The term "piano trio" also refers to works composed for such a group.</figcaption></figure> A music genre is a conventional category that identifies some pieces of music as belonging to a shared tradition or set of conventions.<a href="#cite_note-FOOTNOTESamsonn.d.-83">[80]</a> It is to be distinguished from <a href="/wiki/Musical_form" title="Musical form">musical form</a> and musical style, although in practice these terms are sometimes used interchangeably.<a href="#cite_note-FOOTNOTEWong2011-84">[81]</a>[<a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">failed verification</a>] Music can be divided into different <a href="/wiki/Genres" class="mw-redirect" title="Genres">genres</a> in many different ways. The artistic nature of music means that these classifications are often subjective and controversial, and some genres may overlap. There are even varying academic definitions of the term genre itself. In his book Form in Tonal Music, Douglass M. Green distinguishes between genre and <a href="/wiki/Musical_form" title="Musical form">form</a>. He lists <a href="/wiki/Madrigal_(music)" class="mw-redirect" title="Madrigal (music)">madrigal</a>, <a href="/wiki/Motet" title="Motet">motet</a>, <a href="/wiki/Canzona" title="Canzona">canzona</a>, <a href="/wiki/Ricercar" title="Ricercar">ricercar</a>, and dance as examples of genres from the <a href="/wiki/Renaissance_music" title="Renaissance music">Renaissance</a> period. To further clarify the meaning of genre, Green writes, "Beethoven's Op. 61 and Mendelssohn's Op. 64 are identical in genre—both are violin concertos—but different in form. However, Mozart's Rondo for Piano, K. 511, and the Agnus Dei from his Mass, K. 317 are quite different in genre but happen to be similar in form."<a href="#cite_note-FOOTNOTEGreen19791-85">[82]</a> Some, like <a href="/wiki/Peter_van_der_Merwe_(musicologist)" title="Peter van der Merwe (musicologist)">Peter van der Merwe</a>, treat the terms genre and style as the same, saying that genre should be defined as pieces of music that came from the same style or "basic musical language."<a href="#cite_note-FOOTNOTEvan_der_Merwe19893-86">[83]</a> Others, such as Allan F. Moore, state that genre and style are two separate terms, and that secondary characteristics such as subject matter can also differentiate between genres.<a href="#cite_note-FOOTNOTEMoore2001432%E2%80%9333-87">[84]</a> A music genre or subgenre may also be defined by the <a href="/wiki/Musical_technique" title="Musical technique">musical techniques</a>, the style, the cultural context, and the content and spirit of the themes. Geographical origin is sometimes used to identify a music genre, though a single geographical category will often include a wide variety of subgenres. Timothy Laurie argues that "since the early 1980s, genre has graduated from being a subset of popular music studies to being an almost ubiquitous framework for constituting and evaluating musical research objects".<a href="#cite_note-FOOTNOTELaurie2014284-88">[85]</a> Musical technique is the ability of <a href="/wiki/Musical_instrument" title="Musical instrument">instrumental</a> and vocal musicians to exert optimal control of their instruments or <a href="/wiki/Vocal_cords" title="Vocal cords">vocal cords</a> to produce precise musical effects. Improving technique generally entails practicing exercises that improve muscular sensitivity and agility. To improve technique, musicians often practice fundamental patterns of notes such as the <a href="/wiki/Natural_minor" class="mw-redirect" title="Natural minor">natural</a>, <a href="/wiki/Minor_scale" title="Minor scale">minor</a>, <a href="/wiki/Major_scale" title="Major scale">major</a>, and <a href="/wiki/Chromatic_scale" title="Chromatic scale">chromatic scales</a>, <a href="/wiki/Minor_triad" class="mw-redirect" title="Minor triad">minor</a> and <a href="/wiki/Major_triad" class="mw-redirect" title="Major triad">major triads</a>, <a href="/wiki/Dominant_seventh_chord" title="Dominant seventh chord">dominant</a> and <a href="/wiki/Diminished_seventh" title="Diminished seventh">diminished sevenths</a>, formula patterns and <a href="/wiki/Arpeggio" title="Arpeggio">arpeggios</a>. For example, <a href="/wiki/Triad_(music)" title="Triad (music)">triads</a> and <a href="/wiki/Seventh_chord" title="Seventh chord">sevenths</a> teach how to play chords with accuracy and speed. <a href="/wiki/Scale_(music)" title="Scale (music)">Scales</a> teach how to move quickly and gracefully from one note to another (usually by step). Arpeggios teach how to play <a href="/wiki/Broken_chord" class="mw-redirect" title="Broken chord">broken chords</a> over larger intervals. Many of these components of music are found in compositions, for example, a scale is a very common element of classical and romantic era compositions.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] <a href="/wiki/Heinrich_Schenker" title="Heinrich Schenker">Heinrich Schenker</a> argued that musical technique's "most striking and distinctive characteristic" is <a href="/wiki/Repetition_(music)" title="Repetition (music)">repetition</a>.<a href="#cite_note-FOOTNOTEKivy1993327-89">[86]</a> Works known as <a href="/wiki/%C3%89tude" title="Étude">études</a> (meaning "study") are also frequently used for the improvement of technique. <div class="mw-heading mw-heading3"><h3 id="Mathematics">Mathematics</h3> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=34" title="Edit section: Mathematics" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Music_and_mathematics" title="Music and mathematics">Music and mathematics</a></div> Music theorists sometimes use mathematics to understand music, and although music has no <a href="/wiki/Axiomatic" class="mw-redirect" title="Axiomatic">axiomatic</a> foundation in modern mathematics, mathematics is "the basis of sound" and sound itself "in its musical aspects... exhibits a remarkable array of number properties", simply because nature itself "is amazingly mathematical".<a href="#cite_note-FOOTNOTESmith_Brindle198742%E2%80%9343-90">[87]</a> The attempt to structure and communicate new ways of composing and hearing music has led to musical applications of <a href="/wiki/Set_theory" title="Set theory">set theory</a>, <a href="/wiki/Abstract_algebra" title="Abstract algebra">abstract algebra</a> and <a href="/wiki/Number_theory" title="Number theory">number theory</a>. Some composers have incorporated the <a href="/wiki/Golden_ratio" title="Golden ratio">golden ratio</a> and <a href="/wiki/Fibonacci_numbers" class="mw-redirect" title="Fibonacci numbers">Fibonacci numbers</a> into their work.<a href="#cite_note-FOOTNOTESmith_Brindle1987chapter_6,_''passim''-91">[88]</a>&#91;[[Wikipedia:Citing_sources|<span_title="This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(July_2015)">page&nbsp;needed]]&#93;_92-0' class="reference"><a href="#cite_note-FOOTNOTEGarland_and_Kahn1995%5B%5BCategory:Wikipedia_articles_needing_page_number_citations_from_July_2015%5D%5D<sup_class=%22noprint_Inline-Template_%22_style=%22white-space:nowrap;%22>&#91;%5B%5BWikipedia:Citing_sources%7C<span_title=%22This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(July_2015)%22>page&nbsp;needed%5D%5D&#93;-92">[89]</a> There is a long history of examining the relationships between music and mathematics. Though ancient Chinese, Egyptians and Mesopotamians are known to have studied the mathematical principles of sound,<a href="#cite_note-FOOTNOTESmith_Brindle198742-93">[90]</a> the <a href="/wiki/Pythagoreanism" title="Pythagoreanism">Pythagoreans</a> (in particular <a href="/wiki/Philolaus" title="Philolaus">Philolaus</a> and <a href="/wiki/Archytas" title="Archytas">Archytas</a>)<a href="#cite_note-FOOTNOTEPurwins200522%E2%80%9324-94">[91]</a> of ancient Greece were the first researchers known to have investigated the expression of <a href="/wiki/Musical_scale" class="mw-redirect" title="Musical scale">musical scales</a> in terms of numerical <a href="/wiki/Ratio" title="Ratio">ratios</a>. <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:HarmonicIdentities.Names.Frequencies.svg" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/27/HarmonicIdentities.Names.Frequencies.svg/400px-HarmonicIdentities.Names.Frequencies.svg.png" decoding="async" width="400" height="73" class="mw-file-element" data-file-width="717" data-file-height="130"></noscript><span class="lazy-image-placeholder" style="width: 400px;height: 73px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/2/27/HarmonicIdentities.Names.Frequencies.svg/400px-HarmonicIdentities.Names.Frequencies.svg.png" data-width="400" data-height="73" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/27/HarmonicIdentities.Names.Frequencies.svg/600px-HarmonicIdentities.Names.Frequencies.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/27/HarmonicIdentities.Names.Frequencies.svg/800px-HarmonicIdentities.Names.Frequencies.svg.png 2x" data-class="mw-file-element"> </a><figcaption>The first 16 harmonics, their names and frequencies, showing the exponential nature of the octave and the simple fractional nature of non-octave harmonics</figcaption></figure> In the modern era, musical <a href="/wiki/Set_theory" title="Set theory">set theory</a> uses the language of mathematical set theory in an elementary way to organize musical objects and describe their relationships. To analyze the structure of a piece of (typically atonal) music using musical set theory, one usually starts with a set of tones, which could form motives or chords. By applying simple operations such as <a href="/wiki/Transposition_(music)" title="Transposition (music)">transposition</a> and <a href="/wiki/Melodic_inversion" class="mw-redirect" title="Melodic inversion">inversion</a>, one can discover deep structures in the music. Operations such as transposition and inversion are called <a href="/wiki/Isometries" class="mw-redirect" title="Isometries">isometries</a> because they preserve the intervals between tones in a set. Expanding on the methods of musical set theory, some theorists have used abstract algebra to analyze music. For example, the pitch classes in an equally tempered octave form an <a href="/wiki/Abelian_group" title="Abelian group">abelian group</a> with 12 elements. It is possible to describe <a href="/wiki/Just_intonation" title="Just intonation">just intonation</a> in terms of a <a href="/wiki/Free_abelian_group" title="Free abelian group">free abelian group</a>.<a href="#cite_note-FOOTNOTEWohl2005-95">[92]</a> <div class="mw-heading mw-heading3"><h3 id="Serial_composition_and_set_theory">Serial composition and set theory</h3> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=35" title="Edit section: Serial composition and set theory" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Berg%27s_Lyric_Suite_Mov._I_tone_row_B-P.PNG" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Berg%27s_Lyric_Suite_Mov._I_tone_row_B-P.PNG/220px-Berg%27s_Lyric_Suite_Mov._I_tone_row_B-P.PNG" decoding="async" width="220" height="73" class="mw-file-element" data-file-width="1058" data-file-height="352"></noscript><span class="lazy-image-placeholder" style="width: 220px;height: 73px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Berg%27s_Lyric_Suite_Mov._I_tone_row_B-P.PNG/220px-Berg%27s_Lyric_Suite_Mov._I_tone_row_B-P.PNG" data-width="220" data-height="73" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Berg%27s_Lyric_Suite_Mov._I_tone_row_B-P.PNG/330px-Berg%27s_Lyric_Suite_Mov._I_tone_row_B-P.PNG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Berg%27s_Lyric_Suite_Mov._I_tone_row_B-P.PNG/440px-Berg%27s_Lyric_Suite_Mov._I_tone_row_B-P.PNG 2x" data-class="mw-file-element"> </a><figcaption>Tone row from <a href="/wiki/Alban_Berg" title="Alban Berg">Alban Berg</a>'s <a href="/wiki/Lyric_Suite_(Berg)" title="Lyric Suite (Berg)">Lyric Suite</a>, movement I<audio id="mwe_player_7" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-mwtitle="Berg's_Lyric_Suite_Mov._I_tone_row_B-P.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/f/fb/Berg%27s_Lyric_Suite_Mov._I_tone_row_B-P.mid" type="audio/midi" data-width="0" data-height="0"></source><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/f/fb/Berg%27s_Lyric_Suite_Mov._I_tone_row_B-P.mid/Berg%27s_Lyric_Suite_Mov._I_tone_row_B-P.mid.ogg" type='audio/ogg; codecs="vorbis"' data-transcodekey="ogg" data-width="0" data-height="0"></source><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/f/fb/Berg%27s_Lyric_Suite_Mov._I_tone_row_B-P.mid/Berg%27s_Lyric_Suite_Mov._I_tone_row_B-P.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0"></source></audio></figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Serialism" title="Serialism">Serialism</a>, <a href="/wiki/Set_theory_(music)" title="Set theory (music)">Set theory (music)</a>, <a href="/wiki/Arnold_Schoenberg" title="Arnold Schoenberg">Arnold Schoenberg</a>, <a href="/wiki/Milton_Babbitt" title="Milton Babbitt">Milton Babbitt</a>, <a href="/wiki/David_Lewin" title="David Lewin">David Lewin</a>, and <a href="/wiki/Allen_Forte" title="Allen Forte">Allen Forte</a></div> In music theory, serialism is a method or technique of <a href="/wiki/Musical_composition" title="Musical composition">composition</a> that uses a series of values to manipulate different <a href="/wiki/Aspect_of_music" class="mw-redirect" title="Aspect of music">musical elements</a>. Serialism began primarily with <a href="/wiki/Arnold_Schoenberg" title="Arnold Schoenberg">Arnold Schoenberg</a>'s <a href="/wiki/Twelve-tone_technique" title="Twelve-tone technique">twelve-tone technique</a>, though his contemporaries were also working to establish serialism as one example of <a href="/wiki/Atonality" title="Atonality">post-tonal</a> thinking. Twelve-tone technique orders the twelve notes of the <a href="/wiki/Chromatic_scale" title="Chromatic scale">chromatic scale</a>, forming a <a href="/wiki/Tone_row" title="Tone row">row</a> or series and providing a unifying basis for a composition's <a href="/wiki/Melody" title="Melody">melody</a>, <a href="/wiki/Harmony" title="Harmony">harmony</a>, structural progressions, and <a href="/wiki/Variation_(music)" title="Variation (music)">variations</a>. Other types of serialism also work with <a href="/wiki/Set_(music)" title="Set (music)">sets</a>, collections of objects, but not necessarily with fixed-order series, and extend the technique to other musical dimensions (often called "<a href="/wiki/Parameter_(music)" class="mw-redirect" title="Parameter (music)">parameters</a>"), such as <a href="/wiki/Duration_(music)" title="Duration (music)">duration</a>, <a href="/wiki/Dynamics_(music)" title="Dynamics (music)">dynamics</a>, and <a href="/wiki/Timbre" title="Timbre">timbre</a>. The idea of serialism is also applied in various ways in the visual arts, design, and architecture<a href="#cite_note-96">[93]</a> "Integral serialism" or "total serialism" is the use of series for aspects such as duration, dynamics, and register as well as pitch. <a href="#cite_note-FOOTNOTEWhittall2008273-97">[94]</a> Other terms, used especially in Europe to distinguish post-World War II serial music from twelve-tone music and its American extensions, are "general serialism" and "multiple serialism".<a href="#cite_note-FOOTNOTEGrant20015%E2%80%936-98">[95]</a> Musical set theory provides concepts for categorizing musical objects and describing their relationships. Many of the notions were first elaborated by <a href="/wiki/Howard_Hanson" title="Howard Hanson">Howard Hanson</a> (1960) in connection with tonal music, and then mostly developed in connection with atonal music by theorists such as <a href="/wiki/Allen_Forte" title="Allen Forte">Allen Forte</a> (1973), drawing on the work in twelve-tone theory of Milton Babbitt. The concepts of set theory are very general and can be applied to tonal and atonal styles in any equally tempered tuning system, and to some extent more generally than that.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] One branch of musical set theory deals with collections (sets and permutations) of pitches and pitch classes (pitch-class set theory), which may be ordered or unordered, and can be related by musical operations such as <a href="/wiki/Transposition_(music)" title="Transposition (music)">transposition</a>, <a href="/wiki/Melodic_inversion" class="mw-redirect" title="Melodic inversion">inversion</a>, and <a href="/wiki/Complement_(music)" title="Complement (music)">complementation</a>. The methods of musical set theory are sometimes applied to the analysis of rhythm as well.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] <div class="mw-heading mw-heading3"><h3 id="Musical_semiotics">Musical semiotics</h3> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=36" title="Edit section: Musical semiotics" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Music_semiology" title="Music semiology">Music semiology</a> and <a href="/wiki/Jean-Jacques_Nattiez" title="Jean-Jacques Nattiez">Jean-Jacques Nattiez</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Roman_Jakobson.jpg" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Roman_Jakobson.jpg/170px-Roman_Jakobson.jpg" decoding="async" width="170" height="215" class="mw-file-element" data-file-width="317" data-file-height="400"></noscript><span class="lazy-image-placeholder" style="width: 170px;height: 215px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Roman_Jakobson.jpg/170px-Roman_Jakobson.jpg" data-width="170" data-height="215" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Roman_Jakobson.jpg/255px-Roman_Jakobson.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/f/fc/Roman_Jakobson.jpg 2x" data-class="mw-file-element"> </a><figcaption>Semiotician <a href="/wiki/Roman_Jakobson" title="Roman Jakobson">Roman Jakobson</a></figcaption></figure> Music semiology (<a href="/wiki/Semiotics" title="Semiotics">semiotics</a>) is the study of signs as they pertain to music on a variety of levels. Following <a href="/wiki/Roman_Jakobson" title="Roman Jakobson">Roman Jakobson</a>, <a href="/wiki/Kofi_Agawu" class="mw-redirect" title="Kofi Agawu">Kofi Agawu</a> adopts the idea of musical semiosis being introversive or extroversive—that is, musical signs within a text and without.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] "Topics", or various musical conventions (such as horn calls, dance forms, and styles), have been treated suggestively by Agawu, among others.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] The notion of <a href="/wiki/Musical_Gestures" class="mw-redirect" title="Musical Gestures">gesture</a> is beginning to play a large role in musico-semiotic enquiry.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] <dl><dd>"There are strong arguments that music inhabits a semiological realm which, on both <a href="/wiki/Ontogenetic" class="mw-redirect" title="Ontogenetic">ontogenetic</a> and <a href="/wiki/Phylogenetic" class="mw-redirect" title="Phylogenetic">phylogenetic</a> levels, has developmental priority over verbal language."<a href="#cite_note-FOOTNOTEMiddleton1990172-99">[96]</a><a href="#cite_note-FOOTNOTENattiez1976-100">[97]</a><a href="#cite_note-FOOTNOTENattiez1990-101">[98]</a><a href="#cite_note-FOOTNOTENattiez1989-102">[99]</a><a href="#cite_note-FOOTNOTEStefani1973-103">[100]</a><a href="#cite_note-FOOTNOTEStefani1976-104">[101]</a><a href="#cite_note-FOOTNOTEBaroni1983-105">[102]</a><a href="#cite_note-FOOTNOTE''Semiotica''198766:1%E2%80%933-106">[103]</a>[<a href="/wiki/Wikipedia:CITESHORT" class="mw-redirect" title="Wikipedia:CITESHORT">incomplete short citation</a>][<a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify">clarification needed</a>]</dd></dl> Writers on music semiology include Kofi Agawu (on topical theory,[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] <a href="/wiki/Heinrich_Schenker" title="Heinrich Schenker">Heinrich Schenker</a>,<a href="#cite_note-FOOTNOTEDunsbyStopford198149%E2%80%9353-107">[104]</a><a href="#cite_note-FOOTNOTEMee%C3%B9s201781%E2%80%9396-108">[105]</a> Robert Hatten (on topic, gesture)[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>], <a href="/wiki/Raymond_Monelle" title="Raymond Monelle">Raymond Monelle</a> (on topic, musical meaning)[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>], <a href="/wiki/Jean-Jacques_Nattiez" title="Jean-Jacques Nattiez">Jean-Jacques Nattiez</a> (on introversive taxonomic analysis and ethnomusicological applications)[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>], <a href="/wiki/Anthony_Newcomb" title="Anthony Newcomb">Anthony Newcomb</a> (on narrativity)[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>], and <a href="/wiki/Eero_Tarasti" title="Eero Tarasti">Eero Tarasti</a>[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>]. <a href="/wiki/Roland_Barthes" title="Roland Barthes">Roland Barthes</a>, himself a semiotician and skilled amateur pianist, wrote about music in Image-Music-Text,[<a href="/wiki/Wikipedia:Citing_sources#What_information_to_include" title="Wikipedia:Citing sources">full citation needed</a>] The Responsibilities of Form,[<a href="/wiki/Wikipedia:Citing_sources#What_information_to_include" title="Wikipedia:Citing sources">full citation needed</a>] and Eiffel Tower,[<a href="/wiki/Wikipedia:Citing_sources#What_information_to_include" title="Wikipedia:Citing sources">full citation needed</a>] though he did not consider music to be a semiotic system[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>]. Signs, meanings in music, happen essentially through the connotations of sounds, and through the social construction, appropriation and amplification of certain meanings associated with these connotations. The work of <a href="/wiki/Philip_Tagg" title="Philip Tagg">Philip Tagg</a> (Ten Little Tunes,[<a href="/wiki/Wikipedia:Citing_sources#What_information_to_include" title="Wikipedia:Citing sources">full citation needed</a>] Fernando the Flute,[<a href="/wiki/Wikipedia:Citing_sources#What_information_to_include" title="Wikipedia:Citing sources">full citation needed</a>] Music's Meanings[<a href="/wiki/Wikipedia:Citing_sources#What_information_to_include" title="Wikipedia:Citing sources">full citation needed</a>]) provides one of the most complete and systematic analysis of the relation between musical structures and connotations in western and especially popular, television and film music. The work of <a href="/wiki/Leonard_B._Meyer" title="Leonard B. Meyer">Leonard B. Meyer</a> in Style and Music[<a href="/wiki/Wikipedia:Citing_sources#What_information_to_include" title="Wikipedia:Citing sources">full citation needed</a>] theorizes the relationship between ideologies and musical structures and the phenomena of style change, and focuses on romanticism as a case study. <div class="mw-heading mw-heading3"><h3 id="Education_and_careers">Education and careers</h3> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=37" title="Edit section: Education and careers" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Pat_Carpenter_picture.JPG" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Pat_Carpenter_picture.JPG/220px-Pat_Carpenter_picture.JPG" decoding="async" width="220" height="214" class="mw-file-element" data-file-width="726" data-file-height="705"></noscript><span class="lazy-image-placeholder" style="width: 220px;height: 214px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Pat_Carpenter_picture.JPG/220px-Pat_Carpenter_picture.JPG" data-width="220" data-height="214" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Pat_Carpenter_picture.JPG/330px-Pat_Carpenter_picture.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Pat_Carpenter_picture.JPG/440px-Pat_Carpenter_picture.JPG 2x" data-class="mw-file-element"> </a><figcaption><a href="/wiki/Columbia_University" title="Columbia University">Columbia University</a> music theorist <a href="/wiki/Patricia_Carpenter_(music_theorist)" title="Patricia Carpenter (music theorist)">Pat Carpenter</a> in an undated photo</figcaption></figure> Music theory in the practical sense has been a part of education at conservatories and music schools for centuries, but the status music theory currently has within academic institutions is relatively recent. In the 1970s, few universities had dedicated music theory programs, many music theorists had been trained as composers or historians, and there was a belief among theorists that the teaching of music theory was inadequate and that the subject was not properly recognised as a scholarly discipline in its own right.<a href="#cite_note-FOOTNOTEMcCrelessn.d.-109">[106]</a> A growing number of scholars began promoting the idea that music theory should be taught by theorists, rather than composers, performers or music historians.<a href="#cite_note-FOOTNOTEMcCrelessn.d.-109">[106]</a> This led to the founding of the <a href="/wiki/Society_for_Music_Theory" title="Society for Music Theory">Society for Music Theory</a> in the United States in 1977. In Europe, the French Société d'Analyse musicale was founded in 1985. It called the First European Conference of Music Analysis for 1989, which resulted in the foundation of the Société belge d'Analyse musicale in Belgium and the Gruppo analisi e teoria musicale in Italy the same year, the Society for Music Analysis in the UK in 1991, the Vereniging voor Muziektheorie in the Netherlands in 1999 and the Gesellschaft für Musiktheorie in Germany in 2000.<a href="#cite_note-FOOTNOTEMee%C3%B9s2015111-110">[107]</a> They were later followed by the Russian Society for Music Theory in 2013, the Polish Society for Music Analysis in 2015 and the Sociedad de Análisis y Teoría Musical in Spain in 2020, and others are in construction. These societies coordinate the publication of music theory scholarship and support the professional development of music theory researchers. They formed in 2018 a network of European societies for Theory and/or Analysis of Music, the <a rel="nofollow" class="external text" href="https://europeanmusictheory.eu/">EuroT&AM</a> As part of their initial training, music theorists will typically complete a <a href="/wiki/B.Mus" class="mw-redirect" title="B.Mus">B.Mus</a> or a <a href="/wiki/Bachelor_of_Arts" title="Bachelor of Arts">B.A.</a> in music (or a related field) and in many cases an M.A. in music theory. Some individuals apply directly from a bachelor's degree to a PhD, and in these cases, they may not receive an M.A. In the 2010s, given the increasingly interdisciplinary nature of university graduate programs, some applicants for music theory PhD programs may have academic training both in music and outside of music (e.g., a student may apply with a B.Mus. and a Masters in Music Composition or Philosophy of Music). Most music theorists work as instructors, lecturers or professors in colleges, universities or <a href="/wiki/Music_school" title="Music school">conservatories</a>. The job market for tenure-track professor positions is very competitive: with an average of around 25 tenure-track positions advertised per year in the past decade, 80–100 PhD graduates are produced each year (according to the Survey of Earned Doctorates) who compete not only with each other for those positions but with job seekers that received PhD's in previous years who are still searching for a tenure-track job. Applicants must hold a completed PhD or the equivalent degree (or expect to receive one within a year of being hired—called an "ABD", for "<a href="/wiki/All_But_Dissertation" class="mw-redirect" title="All But Dissertation">All But Dissertation</a>" stage) and (for more senior positions) have a strong record of publishing in peer-reviewed journals. Some PhD-holding music theorists are only able to find insecure positions as <a href="/wiki/Sessional_lecturer" title="Sessional lecturer">sessional lecturers</a>. The job tasks of a music theorist are the same as those of a professor in any other humanities discipline: teaching undergraduate and/or graduate classes in this area of specialization and, in many cases some general courses (such as <a href="/wiki/Music_appreciation" title="Music appreciation">Music appreciation</a> or Introduction to Music Theory), conducting research in this area of expertise, publishing research articles in peer-reviewed journals, authoring book chapters, books or textbooks, traveling to conferences to present papers and learn about research in the field, and, if the program includes a graduate school, supervising M.A. and PhD students and giving them guidance on the preparation of their theses and dissertations. Some music theory professors may take on senior administrative positions in their institution, such as <a href="/wiki/Dean_(education)" title="Dean (education)">Dean</a> or Chair of the School of Music. </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(4)"><h2 id="See_also">See also</h2> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=38" title="Edit section: See also" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-4 collapsible-block" id="mf-section-4"> <ul><li><a href="/wiki/List_of_music_theorists" title="List of music theorists">List of music theorists</a></li> <li><a href="/wiki/Music_psychology" title="Music psychology">Music psychology</a></li> <li><a href="/wiki/Musicology" title="Musicology">Musicology</a></li> <li><a href="/wiki/Theory_of_painting" title="Theory of painting">Theory of painting</a></li></ul> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(5)"><h2 id="Notes">Notes</h2> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=39" title="Edit section: Notes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-5 collapsible-block" id="mf-section-5"> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 45em;"> <ol class="references"> <li id="cite_note-3"><a href="#cite_ref-3">^</a> See Boethius's De institutione musica,<a href="#cite_note-FOOTNOTEBoethius1989-2">[2]</a> in which he disdains "musica instrumentalis" as beneath the "true" musician who studies music in the abstract: Multo enim est maius atque auctius scire, quod quisque faciat, quam ipsum illud efficere, quod sciat ("It is much better to know what one does than to do what one knows"). </li> <li id="cite_note-4"><a href="#cite_ref-4">^</a> See, for example, chapters 4–7 of Christensen, Thomas (2002). The Cambridge History of Western Music Theory. Cambridge, UK: Cambridge University Press. </li> <li id="cite_note-14"><a href="#cite_ref-14">^</a> See the <a href="/wiki/List_of_music_theorists#7th%E2%80%9314th_centuries" title="List of music theorists">List of music theorists#7th–14th centuries</a>, which includes several Arabic theorists; see also <a href="#CITEREFd'Erlanger1930%E2%80%9356">d'Erlanger 1930–56</a>, 1:xv-xxiv. </li> </ol></div> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(6)"><h2 id="References">References</h2> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=40" title="Edit section: References" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-6 collapsible-block" id="mf-section-6"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><a href="#cite_ref-1">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFallows2011" class="citation book cs1">Fallows, David (2011). "Theory". <a rel="nofollow" class="external text" href="http://www.oxfordmusiconline.com/subscriber/article/opr/t114/e6759.">The Oxford Companion to Music</a>. Oxford Music Online. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0199579037" title="Special:BookSources/978-0199579037"><bdi>978-0199579037</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Theory&rft.btitle=The+Oxford+Companion+to+Music&rft.pub=Oxford+Music+Online&rft.date=2011&rft.isbn=978-0199579037&rft.aulast=Fallows&rft.aufirst=David&rft_id=http%3A%2F%2Fwww.oxfordmusiconline.com%2Fsubscriber%2Farticle%2Fopr%2Ft114%2Fe6759.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusic+theory" class="Z3988"> </li> <li id="cite_note-FOOTNOTEBoethius1989-2">^ <a href="#cite_ref-FOOTNOTEBoethius1989_2-0">a</a> <a href="#cite_ref-FOOTNOTEBoethius1989_2-1">b</a> <a href="#CITEREFBoethius1989">Boethius 1989</a>. </li> <li id="cite_note-5"><a href="#cite_ref-5">^</a> Guido Adler, "Umfang, Methode und Ziel der Musikwissenschaft", Vierteljahrsschrift für Musikwissenschaft 1 (1885), p. 5: Die Musikwissenschaft entstand gleichzeitig mit der Tonkunst. </li> <li id="cite_note-6"><a href="#cite_ref-6">^</a> Ibid. </li> <li id="cite_note-FOOTNOTEPalisca_and_Bentn.d.Theory,_theorists._1._Definitions-7"><a href="#cite_ref-FOOTNOTEPalisca_and_Bentn.d.Theory,_theorists._1._Definitions_7-0">^</a> <a href="#CITEREFPalisca_and_Bentn.d.">Palisca and Bent n.d.</a>, Theory, theorists. 1. Definitions. </li> <li id="cite_note-8"><a href="#cite_ref-8">^</a> <a href="#CITEREFMirelman2010">Mirelman 2010</a>; <a href="#CITEREFMirelman2013">Mirelman 2013</a>; <a href="#CITEREFWulstan1968">Wulstan 1968</a>; <a href="#CITEREFK%C3%BCmmel1970">Kümmel 1970</a>; <a href="#CITEREFKilmer1971">Kilmer 1971</a>; <a href="#CITEREFKilmer_and_Mirelmann.d.">Kilmer and Mirelman n.d.</a> </li> <li id="cite_note-FOOTNOTEMirelman201343–44-9"><a href="#cite_ref-FOOTNOTEMirelman201343%E2%80%9344_9-0">^</a> <a href="#CITEREFMirelman2013">Mirelman 2013</a>, 43–44. </li> <li id="cite_note-Lam-10">^ <a href="#cite_ref-Lam_10-0">a</a> <a href="#cite_ref-Lam_10-1">b</a> <a href="#cite_ref-Lam_10-2">c</a> <a href="#CITEREFLam">Lam</a> </li> <li id="cite_note-FOOTNOTEService2013-11"><a href="#cite_ref-FOOTNOTEService2013_11-0">^</a> <a href="#CITEREFService2013">Service 2013</a>. </li> <li id="cite_note-12"><a href="#cite_ref-12">^</a> The Nāțyaśāstra, A Treatise on Hindu Dramaturgy and Histrionics, attributed to Bharata Muni, translated from the Sanskrit with introduction and notes by Manomohan Ghosh, vol. II, Calcutta, The Asiatic Society, 1961. See particularly pp. 5–19 of the Introduction, The Ancient Indian Theory and Practice of Music. </li> <li id="cite_note-13"><a href="#cite_ref-13">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMathiesen2002" class="citation book cs1"><a href="/wiki/Thomas_J._Mathiesen" title="Thomas J. Mathiesen">Mathiesen, T.J.</a> (2002). "Greek music theory". In Christensen, T. (ed.). The Cambridge History of Western Music Theory. Cambridge, UK: Cambridge University Press. pp. 112–113.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Greek+music+theory&rft.btitle=The+Cambridge+History+of+Western+Music+Theory&rft.place=Cambridge%2C+UK&rft.pages=112-113&rft.pub=Cambridge+University+Press&rft.date=2002&rft.aulast=Mathiesen&rft.aufirst=T.J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusic+theory" class="Z3988"> </li> <li id="cite_note-FOOTNOTEManik196924–33-15"><a href="#cite_ref-FOOTNOTEManik196924%E2%80%9333_15-0">^</a> <a href="#CITEREFManik1969">Manik 1969</a>, 24–33. </li> <li id="cite_note-16"><a href="#cite_ref-16">^</a> <a href="#CITEREFWright2001a">Wright 2001a</a>; <a href="#CITEREFWright2001b">Wright 2001b</a>; <a href="#CITEREFManik1969">Manik 1969</a>, 22–24. </li> <li id="cite_note-17"><a href="#cite_ref-17">^</a> Rodolphe d'Erlanger, La Musique arabe, vol. I, pp. 1–306; vol. II, pp. 1–101. </li> <li id="cite_note-FOOTNOTEd'Erlanger1930–562:103–245-18"><a href="#cite_ref-FOOTNOTEd'Erlanger1930%E2%80%93562:103%E2%80%93245_18-0">^</a> <a href="#CITEREFd'Erlanger1930%E2%80%9356">d'Erlanger 1930–56</a>, 2:103–245. </li> <li id="cite_note-FOOTNOTEShiloah1964-19"><a href="#cite_ref-FOOTNOTEShiloah1964_19-0">^</a> <a href="#CITEREFShiloah1964">Shiloah 1964</a>. </li> <li id="cite_note-FOOTNOTEd'Erlanger1930–563:1–182-20"><a href="#cite_ref-FOOTNOTEd'Erlanger1930%E2%80%93563:1%E2%80%93182_20-0">^</a> <a href="#CITEREFd'Erlanger1930%E2%80%9356">d'Erlanger 1930–56</a>, 3:1–182. </li> <li id="cite_note-21"><a href="#cite_ref-21">^</a> Anon. LXII in Amnon Shiloah, The Theory of Music in Arabic Writings (c. 900–1900): Descriptive Catalogue of Manuscripts in Libraries of Europe and the U.S.A., RISM, München, G. Henle Verlag, 1979. See <a href="#CITEREFd'Erlanger1930%E2%80%9356">d'Erlanger 1930–56</a>, 3:183–566 </li> <li id="cite_note-FOOTNOTEGhrab2009-22"><a href="#cite_ref-FOOTNOTEGhrab2009_22-0">^</a> <a href="#CITEREFGhrab2009">Ghrab 2009</a>. </li> <li id="cite_note-Shiloah-2003-23">^ <a href="#cite_ref-Shiloah-2003_23-0">a</a> <a href="#cite_ref-Shiloah-2003_23-1">b</a> <a href="#cite_ref-Shiloah-2003_23-2">c</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShiloah2003" class="citation book cs1">Shiloah, Amnon (2003). <a rel="nofollow" class="external text" href="https://archive.org/details/sacredharp00buel/page/48">The Theory of Music in Arabic Writings (c. 900–1900)</a>. Germany: G. Henle Verlag Munchen. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/sacredharp00buel/page/48">48, 58, 60–61</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8203-0426-7" title="Special:BookSources/978-0-8203-0426-7"><bdi>978-0-8203-0426-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Theory+of+Music+in+Arabic+Writings+%28c.+900%E2%80%931900%29&rft.place=Germany&rft.pages=48%2C+58%2C+60-61&rft.pub=G.+Henle+Verlag+Munchen&rft.date=2003&rft.isbn=978-0-8203-0426-7&rft.aulast=Shiloah&rft.aufirst=Amnon&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fsacredharp00buel%2Fpage%2F48&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusic+theory" class="Z3988"> </li> <li id="cite_note-FOOTNOTEPalisca_and_Bentn.d.§5_Early_Middle_Ages-24">^ <a href="#cite_ref-FOOTNOTEPalisca_and_Bentn.d.%C2%A75_Early_Middle_Ages_24-0">a</a> <a href="#cite_ref-FOOTNOTEPalisca_and_Bentn.d.%C2%A75_Early_Middle_Ages_24-1">b</a> <a href="#CITEREFPalisca_and_Bentn.d.">Palisca and Bent n.d.</a>, §5 Early Middle Ages. </li> <li id="cite_note-25"><a href="#cite_ref-25">^</a> <a href="#CITEREFPalisca_and_Bentn.d.">Palisca and Bent n.d.</a>, Theory, theorists §5 Early Middle Ages: "Boethius could provide a model only for that part of theory which underlies but does not give rules for composition or performance. The first surviving strictly musical treatise of Carolingian times is directed towards musical practice, the Musica disciplina of Aurelian of Réôme (9th century)." </li> <li id="cite_note-26"><a href="#cite_ref-26">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.hs-augsburg.de/~harsch/gui_epi.html">"Guy Aretini's letter to the unknown : modern translation of the letter"</a>. Hs-augsburg.de. Retrieved 3 March 2022.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Hs-augsburg.de&rft.atitle=Guy+Aretini%27s+letter+to+the+unknown+%3A+modern+translation+of+the+letter&rft_id=http%3A%2F%2Fwww.hs-augsburg.de%2F~harsch%2Fgui_epi.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusic+theory" class="Z3988"> </li> <li id="cite_note-FOOTNOTEKubik2010passim-27"><a href="#cite_ref-FOOTNOTEKubik2010passim_27-0">^</a> <a href="#CITEREFKubik2010">Kubik 2010</a>, passim. </li> <li id="cite_note-FOOTNOTEEkwueme1974passim-28"><a href="#cite_ref-FOOTNOTEEkwueme1974passim_28-0">^</a> <a href="#CITEREFEkwueme1974">Ekwueme 1974</a>, passim. </li> <li id="cite_note-29"><a href="#cite_ref-29">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCobb1978" class="citation book cs1">Cobb, Buell E. Jr. (1978). <a rel="nofollow" class="external text" href="https://archive.org/details/sacredharp00buel/page/4">The Sacred Harp: A Tradition and Its Music</a>. United States of America: The University of Georgia Press Athens. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/sacredharp00buel/page/4">4–5, 60–61</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8203-0426-7" title="Special:BookSources/978-0-8203-0426-7"><bdi>978-0-8203-0426-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Sacred+Harp%3A+A+Tradition+and+Its+Music&rft.place=United+States+of+America&rft.pages=4-5%2C+60-61&rft.pub=The+University+of+Georgia+Press+Athens&rft.date=1978&rft.isbn=978-0-8203-0426-7&rft.aulast=Cobb&rft.aufirst=Buell+E.+Jr.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fsacredharp00buel%2Fpage%2F4&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusic+theory" class="Z3988"> </li> <li id="cite_note-FOOTNOTEPalisca_and_Bentn.d.-30"><a href="#cite_ref-FOOTNOTEPalisca_and_Bentn.d._30-0">^</a> <a href="#CITEREFPalisca_and_Bentn.d.">Palisca and Bent n.d</a>. </li> <li id='cite_note-FOOTNOTEHartmann2005[[Category:Wikipedia_articles_needing_page_number_citations_from_August_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;[[Wikipedia:Citing_sources|<span_title="This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(August_2014)">page&nbsp;needed]]&#93;-31'><a href="#cite_ref-FOOTNOTEHartmann2005%5B%5BCategory:Wikipedia_articles_needing_page_number_citations_from_August_2014%5D%5D<sup_class=%22noprint_Inline-Template_%22_style=%22white-space:nowrap;%22>&#91;%5B%5BWikipedia:Citing_sources%7C<span_title=%22This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(August_2014)%22>page&nbsp;needed%5D%5D&#93;_31-0">^</a> <a href="#CITEREFHartmann2005">Hartmann 2005</a>, [<a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">page needed</a>]. </li> <li id='cite_note-FOOTNOTEBartlette_and_Laitz2010[[Category:Wikipedia_articles_needing_page_number_citations_from_October_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;[[Wikipedia:Citing_sources|<span_title="This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(October_2014)">page&nbsp;needed]]&#93;-32'><a href="#cite_ref-FOOTNOTEBartlette_and_Laitz2010%5B%5BCategory:Wikipedia_articles_needing_page_number_citations_from_October_2014%5D%5D<sup_class=%22noprint_Inline-Template_%22_style=%22white-space:nowrap;%22>&#91;%5B%5BWikipedia:Citing_sources%7C<span_title=%22This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(October_2014)%22>page&nbsp;needed%5D%5D&#93;_32-0">^</a> <a href="#CITEREFBartlette_and_Laitz2010">Bartlette and Laitz 2010</a>, [<a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">page needed</a>]. </li> <li id='cite_note-FOOTNOTETouma1996[[Category:Wikipedia_articles_needing_page_number_citations_from_August_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;[[Wikipedia:Citing_sources|<span_title="This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(August_2014)">page&nbsp;needed]]&#93;-33'>^ <a href="#cite_ref-FOOTNOTETouma1996%5B%5BCategory:Wikipedia_articles_needing_page_number_citations_from_August_2014%5D%5D<sup_class=%22noprint_Inline-Template_%22_style=%22white-space:nowrap;%22>&#91;%5B%5BWikipedia:Citing_sources%7C<span_title=%22This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(August_2014)%22>page&nbsp;needed%5D%5D&#93;_33-0">a</a> <a href="#cite_ref-FOOTNOTETouma1996%5B%5BCategory:Wikipedia_articles_needing_page_number_citations_from_August_2014%5D%5D<sup_class=%22noprint_Inline-Template_%22_style=%22white-space:nowrap;%22>&#91;%5B%5BWikipedia:Citing_sources%7C<span_title=%22This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(August_2014)%22>page&nbsp;needed%5D%5D&#93;_33-1">b</a> <a href="#CITEREFTouma1996">Touma 1996</a>, [<a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">page needed</a>]. </li> <li id="cite_note-FOOTNOTEForsyth193573–74-34"><a href="#cite_ref-FOOTNOTEForsyth193573%E2%80%9374_34-0">^</a> <a href="#CITEREFForsyth1935">Forsyth 1935</a>, 73–74. </li> <li id='cite_note-FOOTNOTELatham2002[[Category:Wikipedia_articles_needing_page_number_citations_from_August_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;[[Wikipedia:Citing_sources|<span_title="This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(August_2014)">page&nbsp;needed]]&#93;-35'>^ <a href="#cite_ref-FOOTNOTELatham2002%5B%5BCategory:Wikipedia_articles_needing_page_number_citations_from_August_2014%5D%5D<sup_class=%22noprint_Inline-Template_%22_style=%22white-space:nowrap;%22>&#91;%5B%5BWikipedia:Citing_sources%7C<span_title=%22This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(August_2014)%22>page&nbsp;needed%5D%5D&#93;_35-0">a</a> <a href="#cite_ref-FOOTNOTELatham2002%5B%5BCategory:Wikipedia_articles_needing_page_number_citations_from_August_2014%5D%5D<sup_class=%22noprint_Inline-Template_%22_style=%22white-space:nowrap;%22>&#91;%5B%5BWikipedia:Citing_sources%7C<span_title=%22This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(August_2014)%22>page&nbsp;needed%5D%5D&#93;_35-1">b</a> <a href="#CITEREFLatham2002">Latham 2002</a>, [<a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">page needed</a>]. </li> <li id="cite_note-36"><a href="#cite_ref-36">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1">"Syncopation". <a rel="nofollow" class="external text" href="https://www.oxfordreference.com/display/10.1093/acref/9780199579037.001.0001/acref-9780199579037-e-6605?rskey=S0uJUr&result=1">The Oxford Dictionary of Music</a>. Oxford University Press. 2013. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0199578108" title="Special:BookSources/978-0199578108"><bdi>978-0199578108</bdi></a>. <q>Syncopation is achieved by accenting a weak instead of a strong beat, by putting rests on strong beats, by holding on over strong beats, and by introducing a sudden change of time‐signature.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Syncopation&rft.btitle=The+Oxford+Dictionary+of+Music&rft.pub=Oxford+University+Press&rft.date=2013&rft.isbn=978-0199578108&rft_id=https%3A%2F%2Fwww.oxfordreference.com%2Fdisplay%2F10.1093%2Facref%2F9780199579037.001.0001%2Facref-9780199579037-e-6605%3Frskey%3DS0uJUr%26result%3D1&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusic+theory" class="Z3988"> </li> <li id="cite_note-37"><a href="#cite_ref-37">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.oxfordmusiconline.com/subscriber/article/grove/music/22059">"Polyrhythm"</a>. 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href="#cite_ref-FOOTNOTEBenward_and_Saker2003%5B%5BCategory:Wikipedia_articles_needing_page_number_citations_from_July_2015%5D%5D<sup_class=%22noprint_Inline-Template_%22_style=%22white-space:nowrap;%22>&#91;%5B%5BWikipedia:Citing_sources%7C<span_title=%22This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(July_2015)%22>page&nbsp;needed%5D%5D&#93;_60-0">^</a> <a href="#CITEREFBenward_and_Saker2003">Benward and Saker 2003</a>, [<a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">page needed</a>]. </li> <li id="cite_note-FOOTNOTEIsaac_and_Russell2003136-61"><a href="#cite_ref-FOOTNOTEIsaac_and_Russell2003136_61-0">^</a> <a href="#CITEREFIsaac_and_Russell2003">Isaac and Russell 2003</a>, 136. sfn error: no target: CITEREFIsaac_and_Russell2003 (<a href="/wiki/Category:Harv_and_Sfn_template_errors" title="Category:Harv and Sfn template errors">help</a>) </li> <li id="cite_note-62"><a href="#cite_ref-62">^</a> <a rel="nofollow" class="external text" href="https://www.britannica.com/art/canon-music">Canon: music</a> at the <a href="/wiki/Encyclop%C3%A6dia_Britannica" title="Encyclopædia Britannica">Encyclopædia Britannica</a> </li> <li id="cite_note-FOOTNOTEBrandt2007-63"><a href="#cite_ref-FOOTNOTEBrandt2007_63-0">^</a> <a href="#CITEREFBrandt2007">Brandt 2007</a>. </li> <li id="cite_note-FOOTNOTEScholes1977-64"><a href="#cite_ref-FOOTNOTEScholes1977_64-0">^</a> <a href="#CITEREFScholes1977">Scholes 1977</a>. </li> <li id='cite_note-FOOTNOTEMiddleton1999[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2015]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;[[Wikipedia:Citing_sources|<span_title="This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(July_2015)">page&nbsp;needed]]&#93;-65'><a 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id='cite_note-FOOTNOTEDavies1994[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2015]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;[[Wikipedia:Citing_sources|<span_title="This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(July_2015)">page&nbsp;needed]]&#93;-72'><a href="#cite_ref-FOOTNOTEDavies1994%5B%5BCategory:Wikipedia_articles_needing_page_number_citations_from_July_2015%5D%5D<sup_class=%22noprint_Inline-Template_%22_style=%22white-space:nowrap;%22>&#91;%5B%5BWikipedia:Citing_sources%7C<span_title=%22This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(July_2015)%22>page&nbsp;needed%5D%5D&#93;_72-0">^</a> <a href="#CITEREFDavies1994">Davies 1994</a>, [<a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">page needed</a>]. </li> <li id='cite_note-FOOTNOTERead1969[[Category:Wikipedia_articles_needing_page_number_citations_from_August_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;[[Wikipedia:Citing_sources|<span_title="This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(August_2014)">page&nbsp;needed]]&#93;Stone1980[[Category:Wikipedia_articles_needing_page_number_citations_from_August_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;[[Wikipedia:Citing_sources|<span_title="This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(August_2014)">page&nbsp;needed]]&#93;-73'><a href="#cite_ref-FOOTNOTERead1969%5B%5BCategory:Wikipedia_articles_needing_page_number_citations_from_August_2014%5D%5D<sup_class=%22noprint_Inline-Template_%22_style=%22white-space:nowrap;%22>&#91;%5B%5BWikipedia:Citing_sources%7C<span_title=%22This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(August_2014)%22>page&nbsp;needed%5D%5D&#93;Stone1980%5B%5BCategory:Wikipedia_articles_needing_page_number_citations_from_August_2014%5D%5D<sup_class=%22noprint_Inline-Template_%22_style=%22white-space:nowrap;%22>&#91;%5B%5BWikipedia:Citing_sources%7C<span_title=%22This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(August_2014)%22>page&nbsp;needed%5D%5D&#93;_73-0">^</a> <a href="#CITEREFRead1969">Read 1969</a>, [<a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">page needed</a>]; <a href="#CITEREFStone1980">Stone 1980</a>, [<a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">page needed</a>]. </li> <li id="cite_note-FOOTNOTECastan2009-74"><a href="#cite_ref-FOOTNOTECastan2009_74-0">^</a> <a href="#CITEREFCastan2009">Castan 2009</a>. </li> <li id="cite_note-FOOTNOTEBent19876-75"><a href="#cite_ref-FOOTNOTEBent19876_75-0">^</a> <a href="#CITEREFBent1987">Bent 1987</a>, 6. </li> <li id="cite_note-76"><a href="#cite_ref-76">^</a> Quoted in <a href="#CITEREFBernard1981">Bernard 1981</a>, 1 </li> <li id="cite_note-77"><a href="#cite_ref-77">^</a> Schenker described the concept in a paper titled Erläuterungen ("Elucidations"), which he published four times between 1924 and 1926: Der Tonwille (Vienna, Tonwille Verlag, 1924) vol. 8–9, pp. 49–51, vol. 10, pp. 40–42; Das Meisterwerk in der Musik (München, Drei Masken Verlag), vol. 1 (1925), pp. 201–05; 2 (1926), pp. 193–97. English translation, Der Tonwille, Oxford University Press, vol. 2, pp. 117–18 (the translation, although made from vols. 8–9 of the German original, gives as original pagination that of Das Meisterwerk 1; the text is the same). The concept of tonal space is still present in <a href="#CITEREFSchenker1979">Schenker (1979</a>, especially p. 14, § 13), but less clearly than in the earlier presentation. </li> <li id="cite_note-FOOTNOTESchenker1979p._15,_§_21-78"><a href="#cite_ref-FOOTNOTESchenker1979p._15,_%C2%A7_21_78-0">^</a> <a href="#CITEREFSchenker1979">Schenker 1979</a>, p. 15, § 21. </li> <li id='cite_note-FOOTNOTESnarrenberg1997[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2015]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;[[Wikipedia:Citing_sources|<span_title="This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(July_2015)">page&nbsp;needed]]&#93;-79'><a href="#cite_ref-FOOTNOTESnarrenberg1997%5B%5BCategory:Wikipedia_articles_needing_page_number_citations_from_July_2015%5D%5D<sup_class=%22noprint_Inline-Template_%22_style=%22white-space:nowrap;%22>&#91;%5B%5BWikipedia:Citing_sources%7C<span_title=%22This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(July_2015)%22>page&nbsp;needed%5D%5D&#93;_79-0">^</a> <a href="#CITEREFSnarrenberg1997">Snarrenberg 1997</a>, [<a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">page needed</a>]. </li> <li id="cite_note-FOOTNOTELewin1987159-80"><a href="#cite_ref-FOOTNOTELewin1987159_80-0">^</a> <a href="#CITEREFLewin1987">Lewin 1987</a>, 159. </li> <li id="cite_note-FOOTNOTETan,_Peter,_and_Rom20102-81"><a href="#cite_ref-FOOTNOTETan,_Peter,_and_Rom20102_81-0">^</a> <a href="#CITEREFTan,_Peter,_and_Rom2010">Tan, Peter, and Rom 2010</a>, 2. </li> <li id="cite_note-FOOTNOTEThompsonn.d.320-82"><a href="#cite_ref-FOOTNOTEThompsonn.d.320_82-0">^</a> <a href="#CITEREFThompsonn.d.">Thompson n.d.</a>, 320. </li> <li id="cite_note-FOOTNOTESamsonn.d.-83"><a href="#cite_ref-FOOTNOTESamsonn.d._83-0">^</a> <a href="#CITEREFSamsonn.d.">Samson n.d</a>. </li> <li id="cite_note-FOOTNOTEWong2011-84"><a href="#cite_ref-FOOTNOTEWong2011_84-0">^</a> <a href="#CITEREFWong2011">Wong 2011</a>. </li> <li id="cite_note-FOOTNOTEGreen19791-85"><a href="#cite_ref-FOOTNOTEGreen19791_85-0">^</a> <a href="#CITEREFGreen1979">Green 1979</a>, 1. </li> <li id="cite_note-FOOTNOTEvan_der_Merwe19893-86"><a href="#cite_ref-FOOTNOTEvan_der_Merwe19893_86-0">^</a> <a href="#CITEREFvan_der_Merwe1989">van der Merwe 1989</a>, 3. </li> <li id="cite_note-FOOTNOTEMoore2001432–33-87"><a href="#cite_ref-FOOTNOTEMoore2001432%E2%80%9333_87-0">^</a> <a href="#CITEREFMoore2001">Moore 2001</a>, 432–33. </li> <li id="cite_note-FOOTNOTELaurie2014284-88"><a href="#cite_ref-FOOTNOTELaurie2014284_88-0">^</a> <a href="#CITEREFLaurie2014">Laurie 2014</a>, 284. </li> <li id="cite_note-FOOTNOTEKivy1993327-89"><a href="#cite_ref-FOOTNOTEKivy1993327_89-0">^</a> <a href="#CITEREFKivy1993">Kivy 1993</a>, 327. </li> <li id="cite_note-FOOTNOTESmith_Brindle198742–43-90"><a href="#cite_ref-FOOTNOTESmith_Brindle198742%E2%80%9343_90-0">^</a> <a href="#CITEREFSmith_Brindle1987">Smith Brindle 1987</a>, 42–43. </li> <li id="cite_note-FOOTNOTESmith_Brindle1987chapter_6,_''passim''-91"><a href="#cite_ref-FOOTNOTESmith_Brindle1987chapter_6,_''passim''_91-0">^</a> <a href="#CITEREFSmith_Brindle1987">Smith Brindle 1987</a>, chapter 6, passim. </li> <li id='cite_note-FOOTNOTEGarland_and_Kahn1995[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2015]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;[[Wikipedia:Citing_sources|<span_title="This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(July_2015)">page&nbsp;needed]]&#93;-92'><a href="#cite_ref-FOOTNOTEGarland_and_Kahn1995%5B%5BCategory:Wikipedia_articles_needing_page_number_citations_from_July_2015%5D%5D<sup_class=%22noprint_Inline-Template_%22_style=%22white-space:nowrap;%22>&#91;%5B%5BWikipedia:Citing_sources%7C<span_title=%22This_citation_requires_a_reference_to_the_specific_page_or_range_of_pages_in_which_the_material_appears.&#32;(July_2015)%22>page&nbsp;needed%5D%5D&#93;_92-0">^</a> <a href="#CITEREFGarland_and_Kahn1995">Garland and Kahn 1995</a>, [<a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">page needed</a>]. </li> <li id="cite_note-FOOTNOTESmith_Brindle198742-93"><a href="#cite_ref-FOOTNOTESmith_Brindle198742_93-0">^</a> <a href="#CITEREFSmith_Brindle1987">Smith Brindle 1987</a>, 42. </li> <li id="cite_note-FOOTNOTEPurwins200522–24-94"><a href="#cite_ref-FOOTNOTEPurwins200522%E2%80%9324_94-0">^</a> <a href="#CITEREFPurwins2005">Purwins 2005</a>, 22–24. </li> <li id="cite_note-FOOTNOTEWohl2005-95"><a href="#cite_ref-FOOTNOTEWohl2005_95-0">^</a> <a href="#CITEREFWohl2005">Wohl 2005</a>. </li> <li id="cite_note-96"><a href="#cite_ref-96">^</a> <a href="#CITEREFBandur2001">Bandur 2001</a>, 5, 12, 74; <a href="#CITEREFGerstner1964">Gerstner 1964</a>, passim </li> <li id="cite_note-FOOTNOTEWhittall2008273-97"><a href="#cite_ref-FOOTNOTEWhittall2008273_97-0">^</a> <a href="#CITEREFWhittall2008">Whittall 2008</a>, 273. </li> <li id="cite_note-FOOTNOTEGrant20015–6-98"><a href="#cite_ref-FOOTNOTEGrant20015%E2%80%936_98-0">^</a> <a href="#CITEREFGrant2001">Grant 2001</a>, 5–6. </li> <li id="cite_note-FOOTNOTEMiddleton1990172-99"><a href="#cite_ref-FOOTNOTEMiddleton1990172_99-0">^</a> <a href="#CITEREFMiddleton1990">Middleton 1990</a>, 172. </li> <li id="cite_note-FOOTNOTENattiez1976-100"><a href="#cite_ref-FOOTNOTENattiez1976_100-0">^</a> <a href="#CITEREFNattiez1976">Nattiez 1976</a>. </li> <li id="cite_note-FOOTNOTENattiez1990-101"><a href="#cite_ref-FOOTNOTENattiez1990_101-0">^</a> <a href="#CITEREFNattiez1990">Nattiez 1990</a>. </li> <li id="cite_note-FOOTNOTENattiez1989-102"><a href="#cite_ref-FOOTNOTENattiez1989_102-0">^</a> <a href="#CITEREFNattiez1989">Nattiez1989</a>. </li> <li id="cite_note-FOOTNOTEStefani1973-103"><a href="#cite_ref-FOOTNOTEStefani1973_103-0">^</a> <a href="#CITEREFStefani1973">Stefani 1973</a>. </li> <li id="cite_note-FOOTNOTEStefani1976-104"><a href="#cite_ref-FOOTNOTEStefani1976_104-0">^</a> <a href="#CITEREFStefani1976">Stefani 1976</a>. </li> <li id="cite_note-FOOTNOTEBaroni1983-105"><a href="#cite_ref-FOOTNOTEBaroni1983_105-0">^</a> <a href="#CITEREFBaroni1983">Baroni 1983</a>. </li> <li id="cite_note-FOOTNOTE''Semiotica''198766:1–3-106"><a href="#cite_ref-FOOTNOTE''Semiotica''198766:1%E2%80%933_106-0">^</a> <a href="#CITEREFSemiotica1987">Semiotica 1987</a>, 66:1–3. sfn error: no target: CITEREFSemiotica1987 (<a href="/wiki/Category:Harv_and_Sfn_template_errors" title="Category:Harv and Sfn template errors">help</a>) </li> <li id="cite_note-FOOTNOTEDunsbyStopford198149–53-107"><a href="#cite_ref-FOOTNOTEDunsbyStopford198149%E2%80%9353_107-0">^</a> <a href="#CITEREFDunsbyStopford1981">Dunsby & Stopford 1981</a>, 49–53. </li> <li id="cite_note-FOOTNOTEMeeùs201781–96-108"><a href="#cite_ref-FOOTNOTEMee%C3%B9s201781%E2%80%9396_108-0">^</a> <a href="#CITEREFMee%C3%B9s2017">Meeùs 2017</a>, 81–96. </li> <li id="cite_note-FOOTNOTEMcCrelessn.d.-109">^ <a href="#cite_ref-FOOTNOTEMcCrelessn.d._109-0">a</a> <a href="#cite_ref-FOOTNOTEMcCrelessn.d._109-1">b</a> <a href="#CITEREFMcCrelessn.d.">McCreless n.d</a>. </li> <li id="cite_note-FOOTNOTEMeeùs2015111-110"><a href="#cite_ref-FOOTNOTEMee%C3%B9s2015111_110-0">^</a> <a href="#CITEREFMee%C3%B9s2015">Meeùs 2015</a>, 111. </li> </ol></div></div> <div class="mw-heading mw-heading3"><h3 id="Sources">Sources</h3> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=41" title="Edit section: Sources" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 45em;"> <ul><li><style data-mw-deduplicate="TemplateStyles:r1041539562">.mw-parser-output .citation{word-wrap:break-word}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}</style><cite class="citation wikicite" id="CITEREFAvison1752"><a href="/wiki/Charles_Avison" title="Charles Avison">Avison, Charles</a> (1752). An Essay on Musical Expression. London: C. Davis.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFBandur2001">Bandur, Markus. 2001. Aesthetics of Total Serialism: Contemporary Research from Music to Architecture. Basel, Boston and Berlin: Birkhäuser.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFBaroni1983">Baroni, Mario (1983). "The Concept of Musical Grammar", translated by Simon Maguire and William Drabkin. <a href="/wiki/Music_Analysis_(journal)" title="Music Analysis (journal)">Music Analysis</a> 2, no. 2:175–208.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFBartlette_and_Laitz2010">Bartlette, Christopher, and Steven G. Laitz (2010). Graduate Review of Tonal Theory. New York: Oxford University Press. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-537698-2" title="Special:BookSources/978-0-19-537698-2">978-0-19-537698-2</a>.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFBent1987">Bent, Ian (1987). Analysis, The New Grove Handbooks in Music <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-333-41732-1" title="Special:BookSources/0-333-41732-1">0-333-41732-1</a>.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFBenward_and_Saker2003">Benward, Bruce, and Marilyn Nadine Saker (2003). Music: In Theory and Practice, seventh edition, 2 volumes. Boston: McGraw-Hill <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-294262-0" title="Special:BookSources/978-0-07-294262-0">978-0-07-294262-0</a>.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFBernard1981">Bernard, Jonathan (1981). "Pitch/Register in the Music of Edgar Varèse." <a href="/wiki/Music_Theory_Spectrum" title="Music Theory Spectrum">Music Theory Spectrum</a> 3: 1–25.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBoethius1989" class="citation book cs1"><a href="/wiki/Boethius" title="Boethius">Boethius, Anicius Manlius Severinus</a> (1989). <a href="/wiki/Claude_V._Palisca" title="Claude V. Palisca">Claude V. Palisca</a> (ed.). <a rel="nofollow" class="external text" href="https://classicalliberalarts.com/wp-content/uploads/BOETHIUS-Bower-1989-Fundamentals_of_Music.pdf">Fundamentals of Music</a> (PDF) (Translation of De institutione musica). Translated by Calvin M. Bower. New Haven and London: Yale University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-300-03943-6" title="Special:BookSources/978-0-300-03943-6"><bdi>978-0-300-03943-6</bdi></a> – via classicalliberalarts.com.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fundamentals+of+Music&rft.place=New+Haven+and+London&rft.pub=Yale+University+Press&rft.date=1989&rft.isbn=978-0-300-03943-6&rft.aulast=Boethius&rft.aufirst=Anicius+Manlius+Severinus&rft_id=https%3A%2F%2Fclassicalliberalarts.com%2Fwp-content%2Fuploads%2FBOETHIUS-Bower-1989-Fundamentals_of_Music.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusic+theory" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFBrandt2007">Brandt, Anthony (2007). "<a rel="nofollow" class="external text" href="http://cnx.org/content/m11629/1.13/">Musical Form</a>". Connexions (11 January; accessed 11 September 2011).</cite>[<a href="/wiki/Wikipedia:Reliable_sources" title="Wikipedia:Reliable sources">unreliable source?</a>]</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFCastan2009">Castan, Gerd (2009). "<a rel="nofollow" class="external text" href="http://www.music-notation.info/en/compmus/notationformats.html">Musical Notation Codes</a>". Music-Notation.info (Accessed 1 May 2010).</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFChristiani1885">Christiani, Adolph Friedrich (1885). The Principles of Expression in Pianoforte Playing. New York: Harper & Brothers.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFDahlhaus2009"><a href="/wiki/Carl_Dahlhaus" title="Carl Dahlhaus">Dahlhaus, Carl</a> (2009). "Harmony". Grove Music Online, edited by Deane Root (reviewed 11 December; accessed 30 July 2015).</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFDarwin1913"><a href="/wiki/Charles_Darwin" title="Charles Darwin">Darwin, Charles</a> (1913). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=KRULAAAAIAAJ">The Expression of the Emotions in Man and Animals</a>. New York: D. Appleton and Company.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFDavies1994">Davies, Stephen (1994). Musical Meaning and Expression. 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"The Case for a Schenkerian Semiotic". <a href="/wiki/Music_Theory_Spectrum" title="Music Theory Spectrum">Music Theory Spectrum</a>. 3: 49–53. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F746133">10.2307/746133</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/746133">746133</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Music+Theory+Spectrum&rft.atitle=The+Case+for+a+Schenkerian+Semiotic&rft.volume=3&rft.pages=49-53&rft.date=1981&rft_id=info%3Adoi%2F10.2307%2F746133&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F746133%23id-name%3DJSTOR&rft.aulast=Dunsby&rft.aufirst=Jonathan&rft.au=Stopford%2C+John&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusic+theory" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFEkwueme1974"><a href="/wiki/Lazarus_Ekwueme" title="Lazarus Ekwueme">Ekwueme, Laz E. 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[<a href="/wiki/Wikipedia:Citing_sources#What_information_to_include" title="Wikipedia:Citing sources">full citation needed</a>]: Penguin Books.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFKilmer1971">Kilmer, Anne D. (1971). "The Discovery of an Ancient Mesopotamian Theory of Music". <a href="/wiki/Proceedings_of_the_American_Philosophical_Society" title="Proceedings of the American Philosophical Society">Proceedings of the American Philosophical Society</a> 115, no. 2:131–149.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFKilmer_and_Mirelmann.d.">Kilmer, Anne, and Sam Mirelman. n.d. "<a rel="nofollow" class="external text" href="http://www.oxfordmusiconline.com/subscriber/article/grove/music/18485">Mesopotamia. 8. 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"<a rel="nofollow" class="external text" href="http://theoryofmusic.wordpress.com/2008/01/16/an-explanation-for-the-emergence-of-jazz-1956/">An Explanation for the Emergence of Jazz (1956)</a>", Theory of Music (16 January):[<a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">page needed</a>].</cite>[<a href="/wiki/Wikipedia:Reliable_sources" title="Wikipedia:Reliable sources">unreliable source?</a>]</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFMoore2001">Moore, Allan F. (2001). "<a rel="nofollow" class="external text" href="https://www.jstor.org/stable/3526163">Categorical Conventions in Music Discourse: Style and Genre</a>". <a href="/wiki/Music_%26_Letters" title="Music & Letters">Music & Letters</a> 82, no. 3 (August): 432–442.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFNattiez1976"><a href="/wiki/Jean-Jacques_Nattiez" title="Jean-Jacques Nattiez">Nattiez, Jean-Jacques</a> (1976). Fondements d'une sémiologie de la musique. Collection Esthétique. Paris: Union générale d'éditions. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-2264000033" title="Special:BookSources/978-2264000033">978-2264000033</a>.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFNattiez1989">Nattiez, Jean-Jacques(1989). Proust as Musician, translated by Derrick Puffett. Cambridge and New York: Cambridge University Press. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-36349-5" title="Special:BookSources/978-0-521-36349-5">978-0-521-36349-5</a>, <a href="/wiki/Special:BookSources/978-0-521-02802-8" title="Special:BookSources/978-0-521-02802-8">978-0-521-02802-8</a>.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFNattiez1990">Nattiez, Jean-Jacques (1990). Music and Discourse: Toward a Semiology of Music, translated by <a href="/wiki/Carolyn_Abbate" title="Carolyn Abbate">Carolyn Abbate</a> of Musicologie generale et semiologie. Princeton: Princeton University Press. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-691-09136-5" title="Special:BookSources/978-0-691-09136-5">978-0-691-09136-5</a> (cloth); <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-691-02714-2" title="Special:BookSources/978-0-691-02714-2">978-0-691-02714-2</a> (pbk).</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFOED" class="citation encyclopaedia cs1"><a rel="nofollow" class="external text" href="https://www.oed.com/search/dictionary/?q=theory%2C+%27%27n%27%27.%3Csup%3E1%3C%2Fsup%3E">"theory, n.1"</a>. <a href="/wiki/Oxford_English_Dictionary" title="Oxford English Dictionary">Oxford English Dictionary</a> (Online ed.). <a href="/wiki/Oxford_University_Press" title="Oxford University Press">Oxford University Press</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=theory%2C+n.%3Csup%3E1%3C%2Fsup%3E&rft.btitle=Oxford+English+Dictionary&rft.edition=Online&rft.pub=Oxford+University+Press&rft_id=https%3A%2F%2Fwww.oed.com%2Fsearch%2Fdictionary%2F%3Fq%3Dtheory%252C%2B%2527%2527n%2527%2527.%253Csup%253E1%253C%252Fsup%253E&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusic+theory" class="Z3988"> (Subscription or <a rel="nofollow" class="external text" href="https://www.oed.com/public/login/loggingin#withyourlibrary">participating institution membership</a> required.)</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFPalisca_and_Bentn.d."><a href="/wiki/Claude_V._Palisca" title="Claude V. Palisca">Palisca, Claude V.</a>, and <a href="/wiki/Ian_Bent" title="Ian Bent">Ian D. Bent</a>. n.d. "Theory, Theorists". <a href="/wiki/Grove_Music_Online" class="mw-redirect" title="Grove Music Online">Grove Music Online</a>, edited by Deane Root. Oxford University Press (accessed 17 December 2014).</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFPurwins2005">Purwins, Hendrik (2005). "<a rel="nofollow" class="external text" href="https://ccrma.stanford.edu/~purwins/purwinsPhD.pdf">Profiles of Pitch Classes Circularity of Relative Pitch and Key: Experiments, Models, Computational Music Analysis, and Perspectives</a>". Doktor der Naturwissenschaften diss. Berlin: Technischen Universität Berlin.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFRead1969"><a href="/wiki/Gardner_Read" title="Gardner Read">Read, Gardner</a> (1969). Music Notation: A Manual of Modern Practice, second edition. Boston, Allyn and Bacon. Reprinted, London: Gollancz, 1974. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780575017580" title="Special:BookSources/9780575017580">9780575017580</a>. Reprinted, London: Gollancz, 1978. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0575025547" title="Special:BookSources/978-0575025547">978-0575025547</a>. Reprinted, New York: Taplinger Publishing, 1979. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0800854591" title="Special:BookSources/978-0800854591">978-0800854591</a>, <a href="/wiki/Special:BookSources/978-0800854539" title="Special:BookSources/978-0800854539">978-0800854539</a>.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFSamsonn.d."><a href="/wiki/Jim_Samson" title="Jim Samson">Samson, Jim</a>. "<a rel="nofollow" class="external text" href="http://www.oxfordmusiconline.com/subscriber/article/grove/music/40599">Genre</a>". In <a href="/wiki/Grove_Music_Online" class="mw-redirect" title="Grove Music Online">Grove Music Online</a>, edited by Deane Root. Oxford Music Online. Accessed 4 March 2012</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFSchenker1979"><a href="/wiki/Heinrich_Schenker" title="Heinrich Schenker">Schenker, Heinrich</a> (1979). Free Composition. Translated and edited by <a href="/wiki/Ernst_Oster" title="Ernst Oster">Ernst Oster</a>. New York and London, Longman.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFSchoenberg1983"><a href="/wiki/Arnold_Schoenberg" title="Arnold Schoenberg">Schoenberg, Arnold</a> (1983). Structural Functions of Harmony, revised edition with corrections, edited by <a href="/wiki/Leonard_Stein" title="Leonard Stein">Leonard Stein</a>. London and Boston: Faber and Faber. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-571-13000-9" title="Special:BookSources/978-0-571-13000-9">978-0-571-13000-9</a>.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFScholes1977"><a href="/wiki/Percy_Scholes" title="Percy Scholes">Scholes, Percy A.</a> (1977). "Form". The Oxford Companion to Music, tenth edition. Oxford and New York: Oxford University Press.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFService2013">Service, Jonathan (2013). "<a rel="nofollow" class="external text" href="http://www.hcs.harvard.edu/soundingchina/Service.html">Chinese Music Theory</a>". Transmission/Transformation: Sounding China in Enlightenment Europe. Cambridge: Harvard University Department of Music (web, accessed 17 December 2015).</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFShiloah1964">Shiloah, Amnon (1964). <a rel="nofollow" class="external text" href="http://www.persee.fr/doc/ephe_0000-0001_1964_num_1_1_4883">La perfection des connaissances musicales: Traduction annotée du traité de musique arabe d'al-Ḥasan ibn Aḥmad ibn 'Ali al-Kātib</a> École pratique des hautes études. 4e section, Sciences historiques et philologiques, Annuaire 1964–1965 97, no. 1: 451–456.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFSmith_Brindle1987"><a href="/wiki/Reginald_Smith_Brindle" title="Reginald Smith Brindle">Smith Brindle, Reginald</a> (1987). The New Music: The Avant-Garde Since 1945, second edition. Oxford and New York: Oxford University Press. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-315471-1" title="Special:BookSources/978-0-19-315471-1">978-0-19-315471-1</a>, <a href="/wiki/Special:BookSources/978-0-19-315468-1" title="Special:BookSources/978-0-19-315468-1">978-0-19-315468-1</a> (cloth & pbk).</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFSnarrenberg1997">Snarrenberg, Robert (1997). Schenker's Interpretive Practice. Cambridge Studies in Music Theory and Analysis 11. Cambridge University Press. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0521497264" title="Special:BookSources/0521497264">0521497264</a>.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFSorantin1932">Sorantin, Erich (1932). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=B7dFAAAAMAAJ">The Problem of Musical Expression: A Philosophical and Psychological Study</a>. Nashville: Marshall and Bruce</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFStefani1973">Stefani, Gino (1973). "Sémiotique en musicologie". Versus 5:20–42.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFStefani1976">Stefani, Gino (1976). Introduzione alla semiotica della musica. Palermo: Sellerio editore.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStein1979" class="citation book cs1"><a href="/wiki/Leon_Stein" title="Leon Stein">Stein, Leon</a> (1979). Structure and Style: The Study and Analysis of Musical Forms. Princeton, New Jersey: Summy-Birchard Music. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-87487-164-7" title="Special:BookSources/978-0-87487-164-7"><bdi>978-0-87487-164-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Structure+and+Style%3A+The+Study+and+Analysis+of+Musical+Forms&rft.place=Princeton%2C+New+Jersey&rft.pub=Summy-Birchard+Music&rft.date=1979&rft.isbn=978-0-87487-164-7&rft.aulast=Stein&rft.aufirst=Leon&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusic+theory" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStone1980" class="citation book cs1">Stone, Kurt (1980). Music Notation in the Twentieth Century. New York: W. W. Norton. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-393-95053-3" title="Special:BookSources/978-0-393-95053-3"><bdi>978-0-393-95053-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Music+Notation+in+the+Twentieth+Century&rft.place=New+York&rft.pub=W.+W.+Norton&rft.date=1980&rft.isbn=978-0-393-95053-3&rft.aulast=Stone&rft.aufirst=Kurt&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusic+theory" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFTan,_Peter,_and_Rom2010">Tan, Siu-Lan, Pfordresher Peter, and Harré Rom (2010). Psychology of Music: From Sound to Significance. New York: Psychology Press. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-84169-868-7" title="Special:BookSources/978-1-84169-868-7">978-1-84169-868-7</a>.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFThompsonn.d."><a href="/wiki/William_Forde_Thompson" title="William Forde Thompson">Thompson, William Forde</a> (n.d.). Music, Thought, and Feeling: Understanding the Psychology of Music, second edition. New York: Oxford University Press. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-19-537707-9" title="Special:BookSources/0-19-537707-9">0-19-537707-9</a>.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFTouma1996"><a href="/wiki/Habib_Hassan_Touma" title="Habib Hassan Touma">Touma, Habib Hassan</a> (1996). The Music of the Arabs, new expanded edition, translated by Laurie Schwartz. Portland, Oregon: Amadeus Press. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-931340-88-8" title="Special:BookSources/0-931340-88-8">0-931340-88-8</a>.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFvan_der_Merwe1989" class="citation book cs1"><a href="/wiki/Peter_van_der_Merwe_(musicologist)" title="Peter van der Merwe (musicologist)">van der Merwe, Peter</a> (1989). <a rel="nofollow" class="external text" href="https://archive.org/details/originsofpopular0000vand">Origins of the Popular Style: The Antecedents of Twentieth-Century Popular Music</a>. Oxford: Clarendon Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-316121-4" title="Special:BookSources/978-0-19-316121-4"><bdi>978-0-19-316121-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Origins+of+the+Popular+Style%3A+The+Antecedents+of+Twentieth-Century+Popular+Music&rft.place=Oxford&rft.pub=Clarendon+Press&rft.date=1989&rft.isbn=978-0-19-316121-4&rft.aulast=van+der+Merwe&rft.aufirst=Peter&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Foriginsofpopular0000vand&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusic+theory" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFWhittall2008"><a href="/wiki/Arnold_Whittall" title="Arnold Whittall">Whittall, Arnold</a> (2008). The Cambridge Introduction to Serialism. Cambridge Introductions to Music. New York: Cambridge University Press. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-86341-4" title="Special:BookSources/978-0-521-86341-4">978-0-521-86341-4</a>, <a href="/wiki/Special:BookSources/978-0-521-68200-8" title="Special:BookSources/978-0-521-68200-8">978-0-521-68200-8</a> (cloth & pbk).</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFWohl2005">Wohl, Gennady. (2005). "<a rel="nofollow" class="external text" href="http://sonantometry.blogspot.com/2007_05_01_archive.html">Algebra of Tonal Functions</a>", translated by Mykhaylo Khramov. Sonantometry Blogspot (16 June; accessed 31 July 2015).</cite>[<a href="/wiki/Wikipedia:Reliable_sources" title="Wikipedia:Reliable sources">unreliable source?</a>]</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFWong2011">Wong, Janice (2011). "<a rel="nofollow" class="external text" href="http://mastersofmedia.hum.uva.nl/2011/04/26/visualising-music-the-problems-with-genre-classification/">Visualising Music: The Problems with Genre Classification</a>". Masters of Media blog site (accessed 11 August 2015).</cite>[<a href="/wiki/Wikipedia:Reliable_sources" title="Wikipedia:Reliable sources">unreliable source?</a>]</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFWright2001a">Wright, Owen (2001a). "Munajjim, al- [Yaḥyā ibn]". <a href="/wiki/The_New_Grove_Dictionary_of_Music_and_Musicians" title="The New Grove Dictionary of Music and Musicians">The New Grove Dictionary of Music and Musicians</a>, second edition, edited by <a href="/wiki/Stanley_Sadie" title="Stanley Sadie">Stanley Sadie</a> and <a href="/wiki/John_Tyrrell_(musicologist)" title="John Tyrrell (musicologist)">John Tyrrell</a>. London: Macmillan. Reprinted in <a href="/wiki/Grove_Music_Online" class="mw-redirect" title="Grove Music Online">Grove Music Online</a>, Oxford Music Online. (subscription required).</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFWright2001b">Wright, Owen (2001b). "<a rel="nofollow" class="external text" href="http://www.oxfordmusiconline.com/subscriber/article/grove/music/01139pg1">Arab Music, §1: Art Music, 2. The Early Period (to 900 CE), (iv) Early Theory</a>". The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan. Reprinted in Grove Music Online, Oxford Music Online. (subscription required).</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFWulstan1968">Wulstan, David (1968). "The Tuning of the Babylonian Harp". Iraq 30: 215–28.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFYeston1976" class="citation book cs1"><a href="/wiki/Maury_Yeston" title="Maury Yeston">Yeston, Maury</a> (1976). The Stratification of Musical Rhythm. New Haven: Yale University Press.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Stratification+of+Musical+Rhythm&rft.place=New+Haven&rft.pub=Yale+University+Press&rft.date=1976&rft.aulast=Yeston&rft.aufirst=Maury&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusic+theory" class="Z3988"></li></ul> </div> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(7)"><h2 id="Further_reading">Further reading</h2> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=42" title="Edit section: Further reading" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-7 collapsible-block" id="mf-section-7"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1184024115"><div class="div-col" style="column-width: 45em;"> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFApelDaniel1960" class="citation book cs1"><a href="/wiki/Willi_Apel" title="Willi Apel">Apel, Willi</a>; Daniel, Ralph T. (1960). The Harvard Brief Dictionary of Music. New York: Simon & Schuster Inc. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-671-73747-3" title="Special:BookSources/0-671-73747-3"><bdi>0-671-73747-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Harvard+Brief+Dictionary+of+Music&rft.place=New+York&rft.pub=Simon+%26+Schuster+Inc.&rft.date=1960&rft.isbn=0-671-73747-3&rft.aulast=Apel&rft.aufirst=Willi&rft.au=Daniel%2C+Ralph+T.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusic+theory" class="Z3988"></li> <li><a href="/wiki/Aristoxenus" title="Aristoxenus">Aristoxenus</a> (1902). Aristoxenou Harmonika stoicheia: The Harmonics of Aristoxenus, Greek text edited with an English translation and notes by Henry Marcam. Oxford: The Clarendon Press.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBakkegardMorris1961" class="citation journal cs1">Bakkegard, B. M.; Morris, E. A. (1961). "Seventh Century Flutes from Arizona". Ethnomusicology. 5 (3): 184. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F924518">10.2307/924518</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/924518">924518</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Ethnomusicology&rft.atitle=Seventh+Century+Flutes+from+Arizona&rft.volume=5&rft.issue=3&rft.pages=184&rft.date=1961&rft_id=info%3Adoi%2F10.2307%2F924518&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F924518%23id-name%3DJSTOR&rft.aulast=Bakkegard&rft.aufirst=B.+M.&rft.au=Morris%2C+E.+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusic+theory" class="Z3988"></li> <li>Bakshi, Haresh (2005). 101 Raga-s for the 21st Century and Beyond: A Music Lover's Guide to Hindustani Music. 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London: Macmillan.</li> <li>Benward, Bruce, Barbara Garvey Jackson, and Bruce R. Jackson. (2000). Practical Beginning Theory: A Fundamentals Worktext, 8th edition, Boston: McGraw-Hill. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-697-34397-9" title="Special:BookSources/0-697-34397-9">0-697-34397-9</a>. [First edition 1963]</li> <li>Benward, Bruce, and Marilyn Nadine Saker (2009). Music in Theory and Practice, eighth edition, vol. 2. Boston: McGraw-Hill. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-310188-0" title="Special:BookSources/978-0-07-310188-0">978-0-07-310188-0</a>.</li> <li>Billmeier, Uschi (1999). Mamady Keïta: A Life for the Djembé – Traditional Rhythms of the Malinké, fourth edition. Kirchhasel-Uhlstädt: Arun-Verlag. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-935581-52-3" title="Special:BookSources/978-3-935581-52-3">978-3-935581-52-3</a>.</li> <li><a href="/wiki/Benjamin_Boretz" title="Benjamin Boretz">Boretz, Benjamin</a> (1995). Meta-Variations: Studies in the Foundations of Musical Thought. Red Hook, New York: Open Space.</li> <li>Both, Arnd Adje (2009). "Music Archaeology: Some Methodological and Theoretical Considerations". <a href="/wiki/Yearbook_for_Traditional_Music" title="Yearbook for Traditional Music">Yearbook for Traditional Music</a> 41:1–11. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/25735475">25735475</a></li> <li><a href="/wiki/Albert_Bregman" title="Albert Bregman">Bregman, Albert</a> (1994). Auditory Scene Analysis: The Perceptual Organization of Sound. Cambridge: MIT Press. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-262-52195-4" title="Special:BookSources/0-262-52195-4">0-262-52195-4</a>.</li> <li><a href="/wiki/Mark_Brill" title="Mark Brill">Brill, Mark</a> (2012). "Music of the Ancient Maya: New Venues of Research". Paper presented at AMS-SW Conference Fall 2012. Texas State University[<a href="/wiki/Wikipedia:Citing_sources#What_information_to_include" title="Wikipedia:Citing sources">full citation needed</a>]</li> <li>Brown, James Murray (1967). A Handbook of Musical Knowledge, 2 vols. London: Trinity College of Music.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1">Cavanagh, Lynn (1999). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090325223741/http://www.wam.hr/Arhiva/US/Cavanagh_440Hz.pdf">"A Brief History of the Establishment of International Standard Pitch A=440 Hertz"</a> (PDF). Archived from <a rel="nofollow" class="external text" href="http://www.wam.hr/Arhiva/US/Cavanagh_440Hz.pdf">the original</a> (PDF) on 25 March 2009.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=A+Brief+History+of+the+Establishment+of+International+Standard+Pitch+A%3D440+Hertz&rft.date=1999&rft.aulast=Cavanagh&rft.aufirst=Lynn&rft_id=http%3A%2F%2Fwww.wam.hr%2FArhiva%2FUS%2FCavanagh_440Hz.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusic+theory" class="Z3988"> (Accessed 1 May 2010)</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1">Charry, Eric (2000). Mande Music: Traditional and Modern Music of the Maninka and Mandinka of Western Africa. 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African Rhythm and African Sensibility: Aesthetics and Social Action in African Musical Idioms. Chicago: University of Chicago Press. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-226-10345-7" title="Special:BookSources/978-0-226-10345-7">978-0-226-10345-7</a>.</li> <li>Civil, Miguel (2010). "The Lexical Texts in the Schøyen Collection". Cornell University Studies in Assyriology and Sumerology 12:203–214.</li> <li><a href="/wiki/Confucius" title="Confucius">Confucius</a> (1999). The Analects of Confucius, edited by <a href="/wiki/Roger_T._Ames" title="Roger T. Ames">Roger T. 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(1997). "Articulation". Essential Dictionary of Music: Definitions, Composers, Theory, Instrument and Vocal Ranges, second edition. The Essential Dictionary Series. Los Angeles: Alfred Publishing. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-88284-728-7" title="Special:BookSources/0-88284-728-7">0-88284-728-7</a>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHewitt2008" class="citation book cs1">Hewitt, Michael (2008). Music Theory for Computer Musicians. Boston, MA: Course Technology Ptr. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-59863-503-4" title="Special:BookSources/978-1-59863-503-4"><bdi>978-1-59863-503-4</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/185033110">185033110</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Music+Theory+for+Computer+Musicians&rft.place=Boston%2C+MA&rft.pub=Course+Technology+Ptr&rft.date=2008&rft_id=info%3Aoclcnum%2F185033110&rft.isbn=978-1-59863-503-4&rft.aulast=Hewitt&rft.aufirst=Michael&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusic+theory" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHoutsma1995" class="citation book cs1">Houtsma, Adrianus JM. 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(1967). The Physics of Musical Sound. Princeton, Toronto, and London: D. Van Nostrand Company.</li> <li><a href="/wiki/Stefan_Kostka" title="Stefan Kostka">Kostka, Stefan</a>, and Dorothy Payne (2004). Tonal Harmony, fifth edition. New York: McGraw-Hill.</li> <li><a href="/wiki/Gerhard_Kubik" title="Gerhard Kubik">Kubik, Gerhard</a> (1998). Kalimba—Nsansi—Mbira. Lamellophone in Afrika. Berlin: Museum fur Volkerkunde. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/3886094391" title="Special:BookSources/3886094391">3886094391</a>.</li> <li><a href="/wiki/Emmanuel_Laroche" title="Emmanuel Laroche">Laroche, Emmanuel</a> (1955). Le palais royal d' Ugarit 3: Textes accadiens et hourrites des archives est, ouest et centrales. Paris: C. Klincksieck</li> <li>Lawn, Richard J., and Jeffrey L. Hellmer (1996). Jazz Theory and Practice. 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Kenneth Wilson, and Peter Urquhart. n.d. "Canon (i)." <a href="/wiki/Grove_Music_Online" class="mw-redirect" title="Grove Music Online">Grove Music Online</a>. Oxford Music Online (Accessed 2 January 2011) (subscription required).</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1">Mazzola, Guerino (1985). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=ktPuAAAAMAAJ">Gruppen und Kategorien in der Musik: Entwurf einer mathematischen Musiktheorie</a>. Heldermann. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-88538-210-2" title="Special:BookSources/978-3-88538-210-2"><bdi>978-3-88538-210-2</bdi></a>. 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"Jiahu guiling gudi yu Zhongguo yinyue wenming zhi yuan (贾湖龟铃骨笛与中国音乐文明之源)" [The relation of Jiahu bone flutes and turtle shell shakers to the origin of Chinese music]. Wenwu (文物) [Cultural Relics], no. 3: 50–55.</li> <li>Wu, Zhongzian, and Karin Taylor Wu (2014). Heavenly Stems and Earthly Branches: Tian Gan Dizhi, The Heart of Chinese Wisdom Traditions. London and Philadelphia: Singing Dragon (Jessica Kingsley Publishers).</li> <li>Yamaguchi, Masaya (2006). The Complete Thesaurus of Musical Scales, revised edition. New York: Masaya Music Services. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-9676353-0-6" title="Special:BookSources/0-9676353-0-6">0-9676353-0-6</a>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFZhangHarbottleWangKong1999" class="citation journal cs1">Zhang, Juzhong; Harbottle, Garman; Wang, Changsui; Kong, Zhaochen (23 September 1999). <a rel="nofollow" class="external text" href="http://www.nature.com/nature/journal/v401/n6751/pdf/401366a0.pdf">"Oldest playable musical instruments found at Jiahu early Neolithic site in China"</a> (PDF). Nature. 401 (6751). Springer Science and Business Media LLC: 366–368. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F43865">10.1038/43865</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0028-0836">0028-0836</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/16862110">16862110</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=Oldest+playable+musical+instruments+found+at+Jiahu+early+Neolithic+site+in+China&rft.volume=401&rft.issue=6751&rft.pages=366-368&rft.date=1999-09-23&rft.issn=0028-0836&rft_id=info%3Apmid%2F16862110&rft_id=info%3Adoi%2F10.1038%2F43865&rft.aulast=Zhang&rft.aufirst=Juzhong&rft.au=Harbottle%2C+Garman&rft.au=Wang%2C+Changsui&rft.au=Kong%2C+Zhaochen&rft_id=http%3A%2F%2Fwww.nature.com%2Fnature%2Fjournal%2Fv401%2Fn6751%2Fpdf%2F401366a0.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusic+theory" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJuzhongKuen2005" class="citation journal cs1">Juzhong, Zhang; Kuen, Lee Yun (2005). "The Magic Flutes". Natural History. 114 (7). American Museum of natural history: 43–47. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0028-0712">0028-0712</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Natural+History&rft.atitle=The+Magic+Flutes.&rft.volume=114&rft.issue=7&rft.pages=43-47&rft.date=2005&rft.issn=0028-0712&rft.aulast=Juzhong&rft.aufirst=Zhang&rft.au=Kuen%2C+Lee+Yun&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusic+theory" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFZhangXiaoLee2004" class="citation journal cs1">Zhang, Juzhong; Xiao, Xinghua; Lee, Yun Kuen (2004). <a rel="nofollow" class="external text" href="https://www.cambridge.org/core/services/aop-cambridge-core/content/view/B3F09EEC1AFB5D16C96C0DF8301BC877/S0003598X00113432a.pdf/the-early-development-of-music-analysis-of-the-jiahu-bone-flutes.pdf">"The early development of music. Analysis of the Jiahu bone flutes"</a> (PDF). Antiquity. 78 (302). Cambridge University Press (CUP): 769–778. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1017%2Fs0003598x00113432">10.1017/s0003598x00113432</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0003-598X">0003-598X</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Antiquity&rft.atitle=The+early+development+of+music.+Analysis+of+the+Jiahu+bone+flutes&rft.volume=78&rft.issue=302&rft.pages=769-778&rft.date=2004&rft_id=info%3Adoi%2F10.1017%2Fs0003598x00113432&rft.issn=0003-598X&rft.aulast=Zhang&rft.aufirst=Juzhong&rft.au=Xiao%2C+Xinghua&rft.au=Lee%2C+Yun+Kuen&rft_id=https%3A%2F%2Fwww.cambridge.org%2Fcore%2Fservices%2Faop-cambridge-core%2Fcontent%2Fview%2FB3F09EEC1AFB5D16C96C0DF8301BC877%2FS0003598X00113432a.pdf%2Fthe-early-development-of-music-analysis-of-the-jiahu-bone-flutes.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusic+theory" class="Z3988"></li></ul> </div> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(8)"><h2 id="External_links">External links</h2> <a role="button" href="/w/index.php?title=Music_theory&action=edit&section=43" title="Edit section: External links" class="cdx-button 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rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237033735"><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><noscript><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/40px-Wikibooks-logo-en-noslogan.svg.png" decoding="async" width="40" height="40" class="mw-file-element" data-file-width="400" data-file-height="400"></noscript><span class="lazy-image-placeholder" style="width: 40px;height: 40px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/40px-Wikibooks-logo-en-noslogan.svg.png" data-alt="" data-width="40" data-height="40" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/60px-Wikibooks-logo-en-noslogan.svg.png 1.5x, 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class="external text" href="https://ftl.toolforge.org/cgi-bin/ftl?st=wp&su=Music+theory">Resources in your library</a></li> </ul></div></div> </div> <ul><li><a href="/wiki/Oscar_van_Dillen" title="Oscar van Dillen">Dillen, Oscar van</a>, <a rel="nofollow" class="external text" href="http://www.oscarvandillen.com/Outline_of_basic_music_theory">Outline of basic music theory</a> (2011)</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output 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edited on 20 November 2024, at 18:09 </div> </a> <div class="post-content footer-content"> <div id='mw-data-after-content'> <div class="read-more-container"></div> </div> <div id="p-lang"> <h4>Languages</h4> <section> <ul id="p-variants" class="minerva-languages"></ul> <ul class="minerva-languages"><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Musiktheorie" title="Musiktheorie – Alemannic" lang="gsw" hreflang="gsw" data-title="Musiktheorie" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" class="interlanguage-link-target">Alemannisch</a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%86%D8%B8%D8%B1%D9%8A%D8%A9_%D8%A7%D9%84%D9%85%D9%88%D8%B3%D9%8A%D9%82%D9%89" title="نظرية الموسيقى – Arabic" lang="ar" hreflang="ar" data-title="نظرية الموسيقى" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target">العربية</a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Teor%C3%ADa_musical" title="Teoría musical – Asturian" lang="ast" hreflang="ast" data-title="Teoría musical" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target">Asturianu</a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Musiqi_n%C9%99z%C9%99riyy%C9%99si" title="Musiqi nəzəriyyəsi – Azerbaijani" lang="az" hreflang="az" data-title="Musiqi nəzəriyyəsi" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target">Azərbaycanca</a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B8%E0%A6%99%E0%A7%8D%E0%A6%97%E0%A7%80%E0%A6%A4_%E0%A6%A4%E0%A6%A4%E0%A7%8D%E0%A6%A4%E0%A7%8D%E0%A6%AC" title="সঙ্গীত তত্ত্ব – Bangla" lang="bn" hreflang="bn" data-title="সঙ্গীত তত্ত্ব" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target">বাংলা</a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%8F_%D0%BD%D0%B0_%D0%BC%D1%83%D0%B7%D0%B8%D0%BA%D0%B0%D1%82%D0%B0" title="Теория на музиката – Bulgarian" lang="bg" hreflang="bg" data-title="Теория на музиката" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target">Български</a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Teoria_de_la_m%C3%BAsica" title="Teoria de la música – Catalan" lang="ca" hreflang="ca" data-title="Teoria de la música" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target">Català</a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Hudebn%C3%AD_teorie" title="Hudební teorie – Czech" lang="cs" hreflang="cs" data-title="Hudební teorie" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target">Čeština</a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Musikteori" title="Musikteori – Danish" lang="da" hreflang="da" data-title="Musikteori" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target">Dansk</a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Musiktheorie" title="Musiktheorie – German" lang="de" hreflang="de" data-title="Musiktheorie" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target">Deutsch</a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Muusikateooria" title="Muusikateooria – Estonian" lang="et" hreflang="et" data-title="Muusikateooria" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target">Eesti</a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Teor%C3%ADa_musical" title="Teoría musical – Spanish" lang="es" hreflang="es" data-title="Teoría musical" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target">Español</a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Muzikteorio" title="Muzikteorio – Esperanto" lang="eo" hreflang="eo" data-title="Muzikteorio" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target">Esperanto</a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Teoria_musikal" title="Teoria musikal – Basque" lang="eu" hreflang="eu" data-title="Teoria musikal" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target">Euskara</a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AA%D8%A6%D9%88%D8%B1%DB%8C_%D9%85%D9%88%D8%B3%DB%8C%D9%82%DB%8C" title="تئوری موسیقی – Persian" lang="fa" hreflang="fa" data-title="تئوری موسیقی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target">فارسی</a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Th%C3%A9orie_de_la_musique" title="Théorie de la musique – French" lang="fr" hreflang="fr" data-title="Théorie de la musique" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target">Français</a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9D%8C%EC%95%85_%EC%9D%B4%EB%A1%A0" title="음악 이론 – Korean" lang="ko" hreflang="ko" data-title="음악 이론" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target">한국어</a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B8%E0%A4%82%E0%A4%97%E0%A5%80%E0%A4%A4_%E0%A4%B8%E0%A4%BF%E0%A4%A6%E0%A5%8D%E0%A4%A7%E0%A4%BE%E0%A4%82%E0%A4%A4" title="संगीत सिद्धांत – Hindi" lang="hi" hreflang="hi" data-title="संगीत सिद्धांत" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target">हिन्दी</a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Teorija_glazbe" title="Teorija glazbe – Croatian" lang="hr" hreflang="hr" data-title="Teorija glazbe" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target">Hrvatski</a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Teori_musik" title="Teori musik – Indonesian" lang="id" hreflang="id" data-title="Teori musik" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target">Bahasa Indonesia</a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/T%C3%B3nfr%C3%A6%C3%B0i" title="Tónfræði – Icelandic" lang="is" hreflang="is" data-title="Tónfræði" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target">Íslenska</a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Teoria_musicale" title="Teoria musicale – Italian" lang="it" hreflang="it" data-title="Teoria musicale" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target">Italiano</a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%AA%D7%95%D7%A8%D7%AA_%D7%94%D7%9E%D7%95%D7%96%D7%99%D7%A7%D7%94" title="תורת המוזיקה – Hebrew" lang="he" hreflang="he" data-title="תורת המוזיקה" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target">עברית</a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9B%E1%83%A3%E1%83%A1%E1%83%98%E1%83%99%E1%83%98%E1%83%A1_%E1%83%97%E1%83%94%E1%83%9D%E1%83%A0%E1%83%98%E1%83%90" title="მუსიკის თეორია – Georgian" lang="ka" hreflang="ka" data-title="მუსიკის თეორია" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target">ქართული</a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Theoria_musicae" title="Theoria musicae – Latin" lang="la" hreflang="la" data-title="Theoria musicae" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target">Latina</a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Zeneelm%C3%A9let" title="Zeneelmélet – Hungarian" lang="hu" hreflang="hu" data-title="Zeneelmélet" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target">Magyar</a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%98%D0%B0_%D0%BD%D0%B0_%D0%BC%D1%83%D0%B7%D0%B8%D0%BA%D0%B0%D1%82%D0%B0" title="Теорија на музиката – Macedonian" lang="mk" hreflang="mk" data-title="Теорија на музиката" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target">Македонски</a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Muziektheorie" title="Muziektheorie – Dutch" lang="nl" hreflang="nl" data-title="Muziektheorie" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target">Nederlands</a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E9%9F%B3%E6%A5%BD%E7%90%86%E8%AB%96" title="音楽理論 – Japanese" lang="ja" hreflang="ja" data-title="音楽理論" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target">日本語</a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Musikkteori" title="Musikkteori – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Musikkteori" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target">Norsk bokmål</a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Musikkteori" title="Musikkteori – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Musikkteori" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target">Norsk nynorsk</a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Teoria_muzyki" title="Teoria muzyki – Polish" lang="pl" hreflang="pl" data-title="Teoria muzyki" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target">Polski</a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Teoria_musical" title="Teoria musical – Portuguese" lang="pt" hreflang="pt" data-title="Teoria musical" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target">Português</a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Teoria_muzical%C4%83" title="Teoria muzicală – Romanian" lang="ro" hreflang="ro" data-title="Teoria muzicală" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target">Română</a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%8F_%D0%BC%D1%83%D0%B7%D1%8B%D0%BA%D0%B8" title="Теория музыки – Russian" lang="ru" hreflang="ru" data-title="Теория музыки" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target">Русский</a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Muisic_theory" title="Muisic theory – Scots" lang="sco" hreflang="sco" data-title="Muisic theory" data-language-autonym="Scots" data-language-local-name="Scots" class="interlanguage-link-target">Scots</a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Tiur%C3%ACa_musicali" title="Tiurìa musicali – Sicilian" lang="scn" hreflang="scn" data-title="Tiurìa musicali" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target">Sicilianu</a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Music_theory" title="Music theory – Simple English" lang="en-simple" hreflang="en-simple" data-title="Music theory" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target">Simple English</a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Hudobn%C3%A1_te%C3%B3ria" title="Hudobná teória – Slovak" lang="sk" hreflang="sk" data-title="Hudobná teória" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target">Slovenčina</a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%AA%DB%8C%DB%86%D8%B1%DB%8C%DB%8C_%D9%85%DB%86%D8%B3%DB%8C%D9%82%D8%A7" title="تیۆریی مۆسیقا – Central Kurdish" lang="ckb" hreflang="ckb" data-title="تیۆریی مۆسیقا" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target">کوردی</a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%98%D0%B0_%D0%BC%D1%83%D0%B7%D0%B8%D0%BA%D0%B5" title="Теорија музике – Serbian" lang="sr" hreflang="sr" data-title="Теорија музике" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target">Српски / srpski</a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Teorija_muzike" title="Teorija muzike – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Teorija muzike" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target">Srpskohrvatski / српскохрватски</a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Musiikinteoria" title="Musiikinteoria – Finnish" lang="fi" hreflang="fi" data-title="Musiikinteoria" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target">Suomi</a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Musikteori" title="Musikteori – Swedish" lang="sv" hreflang="sv" data-title="Musikteori" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target">Svenska</a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Teorya_ng_tugtugin" title="Teorya ng tugtugin – Tagalog" lang="tl" hreflang="tl" data-title="Teorya ng tugtugin" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target">Tagalog</a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%B8%E0%B0%82%E0%B0%97%E0%B1%80%E0%B0%A4_%E0%B0%B8%E0%B0%BF%E0%B0%A6%E0%B1%8D%E0%B0%A7%E0%B0%BE%E0%B0%82%E0%B0%A4%E0%B0%82" title="సంగీత సిద్ధాంతం – Telugu" lang="te" hreflang="te" data-title="సంగీత సిద్ధాంతం" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target">తెలుగు</a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/M%C3%BCzik_teorisi" title="Müzik teorisi – Turkish" lang="tr" hreflang="tr" data-title="Müzik teorisi" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target">Türkçe</a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D1%96%D1%8F_%D0%BC%D1%83%D0%B7%D0%B8%D0%BA%D0%B8" title="Теорія музики – Ukrainian" lang="uk" hreflang="uk" data-title="Теорія музики" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target">Українська</a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%86%D8%B8%D8%B1%DB%8C%DB%81_%D9%85%D9%88%D8%B3%DB%8C%D9%82%DB%8C" title="نظریہ موسیقی – Urdu" lang="ur" hreflang="ur" data-title="نظریہ موسیقی" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target">اردو</a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/L%C3%BD_thuy%E1%BA%BFt_%C3%A2m_nh%E1%BA%A1c" title="Lý thuyết âm nhạc – Vietnamese" lang="vi" hreflang="vi" data-title="Lý thuyết âm nhạc" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target">Tiếng Việt</a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%A8%82%E7%90%86" title="樂理 – Cantonese" lang="yue" hreflang="yue" data-title="樂理" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target">粵語</a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%A8%82%E7%90%86" title="樂理 – Chinese" lang="zh" hreflang="zh" data-title="樂理" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target">中文</a></li><li class="interlanguage-link interwiki-rsk mw-list-item"><a href="https://rsk.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%8F_%D0%BC%D1%83%D0%B7%D0%B8%D0%BA%D0%B8" title="Теория музики – Pannonian Rusyn" lang="rsk" hreflang="rsk" data-title="Теория музики" data-language-autonym="Руски" data-language-local-name="Pannonian Rusyn" class="interlanguage-link-target">Руски</a></li></ul> </section> </div> <div class="minerva-footer-logo"><img src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" alt="Wikipedia" width="120" height="18" style="width: 7.5em; height: 1.125em;"/> </div> <ul id="footer-info" class="footer-info hlist hlist-separated"> <li id="footer-info-lastmod"> This page was last edited on 20 November 2024, at 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