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vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle In history of Western music subsection</span> </button> <ul id="toc-In_history_of_Western_music-sublist" class="vector-toc-list"> <li id="toc-Antiquity_and_the_middle_ages" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Antiquity_and_the_middle_ages"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Antiquity and the middle ages</span> </div> </a> <ul id="toc-Antiquity_and_the_middle_ages-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Renaissance" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Renaissance"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Renaissance</span> </div> </a> <ul id="toc-Renaissance-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Common_practice_period" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Common_practice_period"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Common practice period</span> </div> </a> <ul id="toc-Common_practice_period-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Neo-classic_harmonic_consonance_theory" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Neo-classic_harmonic_consonance_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Neo-classic harmonic consonance theory</span> </div> </a> <ul id="toc-Neo-classic_harmonic_consonance_theory-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-21st_century" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#21st_century"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.5</span> <span>21st century</span> </div> </a> <ul id="toc-21st_century-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Footnotes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Footnotes"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Footnotes</span> </div> </a> <ul id="toc-Footnotes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sources" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Sources"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Sources</span> </div> </a> <ul id="toc-Sources-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> 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class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Consonance and dissonance</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 23 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-23" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">23 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A1%D1%8A%D0%B7%D0%B2%D1%83%D1%87%D0%B8%D0%B5" title="Съзвучие – Bulgarian" lang="bg" hreflang="bg" data-title="Съзвучие" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Cyseinedd_ac_anghyseinedd" title="Cyseinedd ac anghyseinedd – Welsh" lang="cy" hreflang="cy" data-title="Cyseinedd ac anghyseinedd" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Konsonanz_und_Dissonanz" title="Konsonanz und Dissonanz – German" lang="de" hreflang="de" data-title="Konsonanz und Dissonanz" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Consonancia_y_disonancia" title="Consonancia y disonancia – Spanish" lang="es" hreflang="es" data-title="Consonancia y disonancia" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D8%B7%D8%A8%D9%88%D8%B9%DB%8C%D8%AA_(%D9%85%D9%88%D8%B3%DB%8C%D9%82%DB%8C)" title="مطبوعیت (موسیقی) – Persian" lang="fa" hreflang="fa" data-title="مطبوعیت (موسیقی)" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%98%91%ED%99%94%EC%9D%8C%EA%B3%BC_%EB%B6%88%ED%98%91%ED%99%94%EC%9D%8C" title="협화음과 불협화음 – Korean" lang="ko" hreflang="ko" data-title="협화음과 불협화음" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%BF%D5%B8%D5%B6%D5%BD%D5%B8%D5%B6%D5%A1%D5%B6%D5%BD_%D6%87_%D5%A4%D5%AB%D5%BD%D5%B8%D5%B6%D5%A1%D5%B6%D5%BD" title="Կոնսոնանս և դիսոնանս – Armenian" lang="hy" hreflang="hy" data-title="Կոնսոնանս և դիսոնանս" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Fals" title="Fals – Indonesian" lang="id" hreflang="id" data-title="Fals" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Consonanza_e_dissonanza" title="Consonanza e dissonanza – Italian" lang="it" hreflang="it" data-title="Consonanza e dissonanza" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A7%D7%95%D7%A0%D7%A1%D7%95%D7%A0%D7%A0%D7%A1_%D7%95%D7%93%D7%99%D7%A1%D7%95%D7%A0%D7%A0%D7%A1" title="קונסוננס ודיסוננס – Hebrew" lang="he" hreflang="he" data-title="קונסוננס ודיסוננס" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%94%D0%B8%D1%81%D1%81%D0%BE%D0%BD%D0%B0%D0%BD%D1%81" title="Диссонанс – Kyrgyz" lang="ky" hreflang="ky" data-title="Диссонанс" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Vals_(muziek)" title="Vals (muziek) – Dutch" lang="nl" hreflang="nl" data-title="Vals (muziek)" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%8D%94%E5%92%8C%E9%9F%B3%E3%81%A8%E4%B8%8D%E5%8D%94%E5%92%8C%E9%9F%B3" title="協和音と不協和音 – Japanese" lang="ja" hreflang="ja" data-title="協和音と不協和音" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Conson%C3%A2ncia_e_disson%C3%A2ncia" title="Consonância e dissonância – Portuguese" lang="pt" hreflang="pt" data-title="Consonância e dissonância" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D1%81%D0%BE%D0%BD%D0%B0%D0%BD%D1%81_%D0%B8_%D0%B4%D0%B8%D1%81%D1%81%D0%BE%D0%BD%D0%B0%D0%BD%D1%81" title="Консонанс и диссонанс – Russian" lang="ru" hreflang="ru" data-title="Консонанс и диссонанс" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Konsonanca" title="Konsonanca – Albanian" lang="sq" hreflang="sq" data-title="Konsonanca" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Consonance_and_dissonance" title="Consonance and dissonance – Simple English" lang="en-simple" hreflang="en-simple" data-title="Consonance and dissonance" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Konsonanca_in_disonanca" title="Konsonanca in disonanca – Slovenian" lang="sl" hreflang="sl" data-title="Konsonanca in disonanca" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Konsonanssi_ja_dissonanssi" title="Konsonanssi ja dissonanssi – Finnish" lang="fi" hreflang="fi" data-title="Konsonanssi ja dissonanssi" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Konsonans_ve_disonans" title="Konsonans ve disonans – Turkish" lang="tr" hreflang="tr" data-title="Konsonans ve disonans" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D1%81%D0%BE%D0%BD%D0%B0%D0%BD%D1%81_%D1%96_%D0%B4%D0%B8%D1%81%D0%BE%D0%BD%D0%B0%D0%BD%D1%81" title="Консонанс і дисонанс – Ukrainian" lang="uk" hreflang="uk" data-title="Консонанс і дисонанс" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%8D%94%E5%92%8C%E5%90%8C%E4%B8%8D%E5%8D%94%E5%92%8C" title="協和同不協和 – Cantonese" lang="yue" hreflang="yue" data-title="協和同不協和" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li 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<div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Categorizations of simultaneous or successive sounds</div> <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">For other uses, see <a href="/wiki/Literary_consonance" title="Literary consonance">Literary consonance</a>, <a href="/wiki/North/South_Consonance_Ensemble" title="North/South Consonance Ensemble">North/South Consonance Ensemble</a>, and <a href="/wiki/Dissonance_(disambiguation)" class="mw-redirect mw-disambig" title="Dissonance (disambiguation)">Dissonance (disambiguation)</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:308px;max-width:308px"><div class="trow"><div class="tsingle" style="width:152px;max-width:152px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Perfect_octave_on_C.png" class="mw-file-description"><img alt="A consonance" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Perfect_octave_on_C.png/150px-Perfect_octave_on_C.png" decoding="async" width="150" height="70" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Perfect_octave_on_C.png/225px-Perfect_octave_on_C.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Perfect_octave_on_C.png/300px-Perfect_octave_on_C.png 2x" data-file-width="539" data-file-height="252" /></a></span></div><div class="thumbcaption"><a href="/wiki/Perfect_octave" class="mw-redirect" title="Perfect octave">Perfect octave</a>, a consonant interval<span typeof="mw:File"><span><audio id="mwe_player_0" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="130" style="width:130px;" 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 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 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" /></audio></span></span></div></div><div class="tsingle" style="width:152px;max-width:152px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Minor_second_on_C.png" class="mw-file-description"><img alt="A dissonance" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Minor_second_on_C.png/150px-Minor_second_on_C.png" decoding="async" width="150" height="70" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Minor_second_on_C.png/225px-Minor_second_on_C.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Minor_second_on_C.png/300px-Minor_second_on_C.png 2x" data-file-width="542" data-file-height="252" /></a></span></div><div class="thumbcaption"><a href="/wiki/Minor_second" class="mw-redirect" title="Minor second">Minor second</a>, a dissonance<span typeof="mw:File"><span><audio id="mwe_player_1" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="130" style="width:130px;" 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 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 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" /></audio></span></span></div></div></div></div></div> <p>In music, <b>consonance</b> and <b>dissonance</b> are categorizations of simultaneous or successive <a href="/wiki/Sound" title="Sound">sounds</a>. Within the Western tradition, some listeners associate consonance with sweetness, pleasantness, and acceptability, and dissonance with harshness, unpleasantness, or unacceptability, although there is broad acknowledgement that this depends also on familiarity and musical expertise.<sup id="cite_ref-FOOTNOTELahdelma_and_Eerola2020_1-0" class="reference"><a href="#cite_note-FOOTNOTELahdelma_and_Eerola2020-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> The terms form a structural <a href="/wiki/Dichotomy" title="Dichotomy">dichotomy</a> in which they define each other by mutual exclusion: a consonance is what is not dissonant, and a dissonance is what is not consonant. However, a finer consideration shows that the distinction forms a gradation, from the most consonant to the most dissonant.<sup id="cite_ref-FOOTNOTESchoenberg197821_2-0" class="reference"><a href="#cite_note-FOOTNOTESchoenberg197821-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> In casual discourse, as German composer and <a href="/wiki/Music_theory" title="Music theory">music theorist</a> <a href="/wiki/Paul_Hindemith" title="Paul Hindemith">Paul Hindemith</a> stressed, "The two concepts have never been completely explained, and for a thousand years the definitions have varied".<sup id="cite_ref-FOOTNOTEHindemith194285_3-0" class="reference"><a href="#cite_note-FOOTNOTEHindemith194285-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> The term <i>sonance</i> has been proposed to encompass or refer indistinctly to the terms <i>consonance</i> and <i>dissonance</i>.<sup id="cite_ref-FOOTNOTERenard2016_4-0" class="reference"><a href="#cite_note-FOOTNOTERenard2016-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Definitions">Definitions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Consonance_and_dissonance&action=edit&section=1" title="Edit section: Definitions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The opposition between consonance and dissonance can be made in different contexts: </p> <ul><li>In <a href="/wiki/Acoustics" title="Acoustics">acoustics</a> or <a href="/wiki/Psychophysiology" title="Psychophysiology">psychophysiology</a>, the distinction may be objective. In modern times, it usually is based on the perception of <a href="/wiki/Harmonic" title="Harmonic">harmonic</a> partials of the sounds considered, to such an extent that the distinction really holds only in the case of harmonic sounds (i.e. sounds with <a href="/wiki/Harmonic_partial" class="mw-redirect" title="Harmonic partial">harmonic partials</a>).</li> <li>In music, even if the opposition often is founded on the preceding, objective distinction, it more often is subjective, conventional, cultural, and style- or period-dependent. Dissonance can then be defined as a combination of sounds that does not belong to the style under consideration; in recent music, what is considered stylistically dissonant may even correspond to what is said to be consonant in the context of acoustics (e.g. a major triad in 20th century <a href="/wiki/Atonal_music" class="mw-redirect" title="Atonal music">atonal music</a>). A major second (e.g. the notes C and D played simultaneously) would be considered dissonant if it occurred in a <a href="/wiki/J.S._Bach" class="mw-redirect" title="J.S. Bach">J.S. Bach</a> <a href="/wiki/Prelude_(music)" title="Prelude (music)">prelude</a> from the 1700s; however, the same interval may sound consonant in the context of a <a href="/wiki/Claude_Debussy" title="Claude Debussy">Claude Debussy</a> <a href="/wiki/Musical_composition" title="Musical composition">piece</a> from the early 1900s or an atonal contemporary piece.</li></ul> <p>In both cases, the distinction mainly concerns simultaneous sounds; if successive sounds are considered, their consonance or dissonance depends on the memorial retention of the first sound while the second sound (or pitch) is heard. For this reason, consonance and dissonance have been considered particularly in the case of Western <a href="/wiki/Polyphony" title="Polyphony">polyphonic</a> music, and the present article is concerned mainly with this case. Most historical definitions of consonance and dissonance since about the 16th century have stressed their pleasant/unpleasant, or agreeable/disagreeable character. This may be justifiable in a psychophysiological context, but much less in a musical context properly speaking: dissonances often play a decisive role in making music pleasant, even in a generally consonant context—which is one of the reasons why the musical definition of consonance/dissonance cannot match the psychophysiologic definition. In addition, the oppositions pleasant/unpleasant or agreeable/disagreeable evidence a confusion between the concepts of "dissonance" and of "<a href="/wiki/Noise" title="Noise">noise</a>". (See also <a href="/wiki/Noise_in_music" title="Noise in music">Noise in music</a> and <a href="/wiki/Noise_music" title="Noise music">Noise music</a>.) </p><p>While consonance and dissonance exist only between sounds and therefore necessarily describe intervals (or <a href="/wiki/Chord_(music)" title="Chord (music)">chords</a>), such as the <a href="/wiki/Perfect_interval" class="mw-redirect" title="Perfect interval">perfect intervals</a>, which are often viewed as consonant (e.g., the <a href="/wiki/Unison_(music)" class="mw-redirect" title="Unison (music)">unison</a> and <a href="/wiki/Octave" title="Octave">octave</a>), Occidental <a href="/wiki/Music_theory" title="Music theory">music theory</a> often considers that, in a dissonant chord, one of the tones alone is in itself deemed to be the dissonance: it is this <a href="/wiki/Musical_tone" title="Musical tone">tone</a> in particular that needs "resolution" through a specific <a href="/wiki/Voice_leading" title="Voice leading">voice leading</a> procedure. For example, in the key of C Major, if F is produced as part of the <a href="/wiki/Dominant_seventh" class="mw-redirect" title="Dominant seventh">dominant seventh</a> chord (G<sup>7</sup>, which consists of the pitches G, B, D and F), it is deemed to be "dissonant" and it normally resolves to E during a cadence, with the G<sup>7</sup> chord changing to a C Major chord. </p> <div class="mw-heading mw-heading3"><h3 id="Acoustics_and_psychoacoustics">Acoustics and psychoacoustics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Consonance_and_dissonance&action=edit&section=2" title="Edit section: Acoustics and psychoacoustics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Scientific definitions have been variously based on experience, frequency, and both physical and psychological considerations.<sup id="cite_ref-FOOTNOTEMyers1904315_5-0" class="reference"><a href="#cite_note-FOOTNOTEMyers1904315-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> These include: </p> <dl><dt>Numerical ratios</dt> <dd>In Antiquity, these mainly concerned string-length ratios. From the early 17th century onwards, frequency ratios were more often considered.<sup id="cite_ref-FOOTNOTEChristensen20027–8_6-0" class="reference"><a href="#cite_note-FOOTNOTEChristensen20027–8-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Consonance often is associated with the simplicity of the ratio, i.e. with ratios of lower simple numbers. Many of these definitions do not require <i>exact</i> integer tunings, only approximation.<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Vagueness" title="Wikipedia:Vagueness"><span title="This information is too vague. (July 2014)">vague</span></a></i>]</sup><sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (July 2014)">citation needed</span></a></i>]</sup></dd></dl> <dl><dt>Fusion</dt> <dd>Perception of unity or tonal fusion between different tones and / or their partials.<sup id="cite_ref-FOOTNOTEStumpf1890127–219_7-0" class="reference"><a href="#cite_note-FOOTNOTEStumpf1890127–219-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTEButler_and_Green2002264_8-0" class="reference"><a href="#cite_note-FOOTNOTEButler_and_Green2002264-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup></dd></dl> <dl><dt>Coincidence of partials</dt> <dd>With consonance being a greater coincidence of <a href="/wiki/Harmonic_series_(music)" title="Harmonic series (music)">partials</a>.<sup id="cite_ref-FOOTNOTEHelmholtz1954a[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_9-0" class="reference"><a href="#cite_note-FOOTNOTEHelmholtz1954a[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> By this definition, consonance is dependent not only on the width of the interval between two notes (i.e., the <a href="/wiki/Musical_tuning" title="Musical tuning">musical tuning</a>), but also on the combined spectral distribution and thus sound quality (i.e., the <a href="/wiki/Timbre" title="Timbre">timbre</a>) of the notes (see <a href="/wiki/Critical_band" title="Critical band">Critical band</a>). Thus, a note and the note one octave higher are highly consonant because the partials of the higher note are also partials of the lower note.<sup id="cite_ref-FOOTNOTERoederer1995165_10-0" class="reference"><a href="#cite_note-FOOTNOTERoederer1995165-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup></dd></dl> <dl><dt><a href="/wiki/Dynamic_tonality" title="Dynamic tonality">Dynamic tonality</a></dt> <dd>Like "coincidence of partials" above, <a href="/wiki/Dynamic_tonality" title="Dynamic tonality">dynamic tonality</a> considers consonance to arise from the alignment of partials with notes (as per the video at right; see also <a href="/wiki/Dynamic_tonality#Dynamic_timbres" title="Dynamic tonality">dynamic timbres</a>). <figure class="mw-default-size" typeof="mw:File/Thumb"><span><video id="mwe_player_2" poster="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Mapping_Partials_1080.webm/220px--Mapping_Partials_1080.webm.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" height="124" data-durationhint="141" data-mwtitle="Mapping_Partials_1080.webm" data-mwprovider="wikimediacommons" resource="/wiki/File:Mapping_Partials_1080.webm"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/b9/Mapping_Partials_1080.webm/Mapping_Partials_1080.webm.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="854" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/b9/Mapping_Partials_1080.webm/Mapping_Partials_1080.webm.720p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="720p.vp9.webm" data-width="1280" data-height="720" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/b9/Mapping_Partials_1080.webm/Mapping_Partials_1080.webm.1080p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="1080p.vp9.webm" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/b/b9/Mapping_Partials_1080.webm" type="video/webm; codecs="vp9"" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/b9/Mapping_Partials_1080.webm/Mapping_Partials_1080.webm.144p.mjpeg.mov" type="video/quicktime" data-transcodekey="144p.mjpeg.mov" data-width="256" data-height="144" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/b9/Mapping_Partials_1080.webm/Mapping_Partials_1080.webm.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="426" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/b9/Mapping_Partials_1080.webm/Mapping_Partials_1080.webm.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="640" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/b9/Mapping_Partials_1080.webm/Mapping_Partials_1080.webm.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="640" data-height="360" /></video></span><figcaption>Animation of dynamic tonality's mapping of partials to notes in accordance with the syntonic temperament.</figcaption></figure> Dynamic Tonality explicitly generalizes the relationship between the <a href="/wiki/Harmonic_series_(music)" title="Harmonic series (music)">harmonic series</a> and <a href="/wiki/Just_intonation" title="Just intonation">just intonation</a> to embrace pseudo-harmonic timbres played in related pseudo-just tunings.<sup id="cite_ref-FOOTNOTESethares1992_11-0" class="reference"><a href="#cite_note-FOOTNOTESethares1992-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTESethares2005[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_12-0" class="reference"><a href="#cite_note-FOOTNOTESethares2005[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTEMilneSetharesPlamondon2007_13-0" class="reference"><a href="#cite_note-FOOTNOTEMilneSetharesPlamondon2007-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="This citation requires a reference to the specific page or range of pages in which the material appears. (July 2014)">page needed</span></a></i>]</sup><sup id="cite_ref-FOOTNOTEMilneSetharesPlamondon2008_14-0" class="reference"><a href="#cite_note-FOOTNOTEMilneSetharesPlamondon2008-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="This citation requires a reference to the specific page or range of pages in which the material appears. (July 2014)">page needed</span></a></i>]</sup><sup id="cite_ref-FOOTNOTESetharesMilneTiedjePrechtl2009_15-0" class="reference"><a href="#cite_note-FOOTNOTESetharesMilneTiedjePrechtl2009-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="This citation requires a reference to the specific page or range of pages in which the material appears. (July 2014)">page needed</span></a></i>]</sup> As a result, <a href="/wiki/Dynamic_tonality" title="Dynamic tonality">dynamic tonality</a> enables any musical interval to be made more or less consonant or dissonant in real time (i.e., during composition and/or performance) by controlling the degree to which the partials of the pseudo-harmonic timbre align with the interval's notes in the related pseudo-just tuning. For example, listen to <a href="/wiki/Dynamic_tonality#Example:_C2ShiningC" title="Dynamic tonality">C2ShiningC</a>, which uses a timbre progression and a tuning progression to make the intervals within a single chord more or less consonant.</dd></dl> <div class="mw-heading mw-heading3"><h3 id="Music_theory">Music theory</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Consonance_and_dissonance&action=edit&section=3" title="Edit section: Music theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"><p>A stable tone combination is a consonance; consonances are points of arrival, rest, and resolution.</p><div class="templatequotecite">— <cite><a href="/wiki/Roger_Kamien" title="Roger Kamien">Roger Kamien</a><sup id="cite_ref-FOOTNOTEKamien200841_16-0" class="reference"><a href="#cite_note-FOOTNOTEKamien200841-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup></cite></div></blockquote> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>An unstable tone combination is a dissonance; its tension demands an onward motion to a stable chord. Thus dissonant chords are "active"; traditionally they have been considered harsh and have expressed pain, grief, and conflict.</p><div class="templatequotecite">— <cite>Roger Kamien<sup id="cite_ref-FOOTNOTEKamien200841_16-1" class="reference"><a href="#cite_note-FOOTNOTEKamien200841-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup></cite></div></blockquote> <p>Consonances may include: </p> <ul><li><b>Perfect consonances</b>: <ul><li><a href="/wiki/Unison" title="Unison">unisons</a> and <a href="/wiki/Octave" title="Octave">octaves</a></li> <li><a href="/wiki/Perfect_fourth" title="Perfect fourth">perfect fourths</a> and <a href="/wiki/Perfect_fifth" title="Perfect fifth">perfect fifths</a></li></ul></li> <li><b>Imperfect consonances</b>: <ul><li><a href="/wiki/Major_third" title="Major third">major thirds</a> and <a href="/wiki/Minor_sixth" title="Minor sixth">minor sixths</a></li> <li><a href="/wiki/Minor_third" title="Minor third">minor thirds</a> and <a href="/wiki/Major_sixth" title="Major sixth">major sixths</a></li></ul></li></ul> <p>Dissonances may include: </p> <ul><li><b>Dissonance</b> <ul><li><a href="/wiki/Major_second" title="Major second">major seconds</a> and <a href="/wiki/Minor_seventh" title="Minor seventh">minor seventh</a></li> <li><a href="/wiki/Tritone" title="Tritone">tritones</a></li> <li><a href="/wiki/Minor_second" class="mw-redirect" title="Minor second">minor seconds</a> and <a href="/wiki/Major_seventh" title="Major seventh">major sevenths</a> <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="CITEREFCooper1973" class="citation book cs1">Cooper, Paul (1973). <i>Perspectives in Music Theory</i>. p. 14.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Perspectives+in+Music+Theory&rft.pages=14&rft.date=1973&rft.aulast=Cooper&rft.aufirst=Paul&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConsonance+and+dissonance" class="Z3988"></span></li></ul></li></ul> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Krenek%27s_chord_classification_from_Studies_in_Counterpoint.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/en/thumb/4/47/Krenek%27s_chord_classification_from_Studies_in_Counterpoint.png/310px-Krenek%27s_chord_classification_from_Studies_in_Counterpoint.png" decoding="async" width="310" height="286" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/4/47/Krenek%27s_chord_classification_from_Studies_in_Counterpoint.png 1.5x" data-file-width="328" data-file-height="303" /></a><figcaption><a href="/wiki/Ernst_Krenek" title="Ernst Krenek">Ernst Krenek</a>'s classification, from <i>Studies in Counterpoint</i> (1940), of a triad's overall consonance or dissonance through the consonance or dissonance of the three intervals contained within.<sup id="cite_ref-FOOTNOTESchuijer2008138_17-0" class="reference"><a href="#cite_note-FOOTNOTESchuijer2008138-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> <span class="mw-default-size" typeof="mw:File"><span><audio id="mwe_player_3" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-durationhint="39" data-mwtitle="Krenek's_chord_classification_from_Studies_in_Counterpoint.mid" data-mwprovider="local"><source src="//upload.wikimedia.org/wikipedia/en/transcoded/8/8b/Krenek%27s_chord_classification_from_Studies_in_Counterpoint.mid/Krenek%27s_chord_classification_from_Studies_in_Counterpoint.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/en/transcoded/8/8b/Krenek%27s_chord_classification_from_Studies_in_Counterpoint.mid/Krenek%27s_chord_classification_from_Studies_in_Counterpoint.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/en/8/8b/Krenek%27s_chord_classification_from_Studies_in_Counterpoint.mid" type="audio/midi" data-width="0" data-height="0" /></audio></span></span> For example, C–E–G consists of three consonances (C–E, E–G, C–G) and is ranked 1 while C–D<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>–B consists of one mild dissonance (B–D<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>) and two sharp dissonances (C–D<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>, C–B) and is ranked 6.</figcaption></figure> <div class="mw-heading mw-heading2"><h2 id="Physiological_basis">Physiological basis</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Consonance_and_dissonance&action=edit&section=4" title="Edit section: Physiological basis"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237032888/mw-parser-output/.tmulti"><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:354px;max-width:354px"><div class="trow"><div class="tsingle" style="width:352px;max-width:352px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Line_up_of_harmonics_for_PU_with_P5_and_with_M2.png" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/57/Line_up_of_harmonics_for_PU_with_P5_and_with_M2.png/350px-Line_up_of_harmonics_for_PU_with_P5_and_with_M2.png" decoding="async" width="350" height="139" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/57/Line_up_of_harmonics_for_PU_with_P5_and_with_M2.png/525px-Line_up_of_harmonics_for_PU_with_P5_and_with_M2.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/57/Line_up_of_harmonics_for_PU_with_P5_and_with_M2.png/700px-Line_up_of_harmonics_for_PU_with_P5_and_with_M2.png 2x" data-file-width="972" data-file-height="385" /></a></span></div><div class="thumbcaption">Consonance may be explained as caused by a larger number of aligning harmonics (blue) between two notes.<span class="mw-default-size" typeof="mw:File"><span><audio id="mwe_player_4" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-durationhint="7" data-mwtitle="Just_perfect_fifth_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/5/5c/Just_perfect_fifth_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/5c/Just_perfect_fifth_on_C.mid/Just_perfect_fifth_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/5c/Just_perfect_fifth_on_C.mid/Just_perfect_fifth_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> Dissonance is caused by the beating between close but non-aligned harmonics.<span class="mw-default-size" typeof="mw:File"><span><audio id="mwe_player_5" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-mwtitle="Major_tone_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/7/7b/Major_tone_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/7/7b/Major_tone_on_C.mid/Major_tone_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/7/7b/Major_tone_on_C.mid/Major_tone_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span></div></div></div><div class="trow"><div class="tsingle" style="width:352px;max-width:352px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Interval_wavelength_minor_second.png" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/39/Interval_wavelength_minor_second.png/350px-Interval_wavelength_minor_second.png" decoding="async" width="350" height="141" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/39/Interval_wavelength_minor_second.png/525px-Interval_wavelength_minor_second.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/39/Interval_wavelength_minor_second.png/700px-Interval_wavelength_minor_second.png 2x" data-file-width="1374" data-file-height="553" /></a></span></div><div class="thumbcaption">Dissonance may be the difficulty in determining the relationship between two frequencies, determined by their relative wavelengths. Consonant intervals (low whole number ratios) take less, while dissonant intervals take more time to be determined.<span class="mw-default-size" typeof="mw:File"><span><audio id="mwe_player_6" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-mwtitle="Minor_diatonic_semitone_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/f/fc/Minor_diatonic_semitone_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/f/fc/Minor_diatonic_semitone_on_C.mid/Minor_diatonic_semitone_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/f/fc/Minor_diatonic_semitone_on_C.mid/Minor_diatonic_semitone_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span></div></div></div><div class="trow"><div class="tsingle" style="width:352px;max-width:352px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Dyadic_harmonic_entropy_graph_(optimized_for_low_resolution).png" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Dyadic_harmonic_entropy_graph_%28optimized_for_low_resolution%29.png/350px-Dyadic_harmonic_entropy_graph_%28optimized_for_low_resolution%29.png" decoding="async" width="350" height="173" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Dyadic_harmonic_entropy_graph_%28optimized_for_low_resolution%29.png/525px-Dyadic_harmonic_entropy_graph_%28optimized_for_low_resolution%29.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Dyadic_harmonic_entropy_graph_%28optimized_for_low_resolution%29.png/700px-Dyadic_harmonic_entropy_graph_%28optimized_for_low_resolution%29.png 2x" data-file-width="12000" data-file-height="5918" /></a></span></div><div class="thumbcaption">One component of dissonance—the uncertainty or confusion as to the <a href="/wiki/Virtual_pitch" class="mw-redirect" title="Virtual pitch">virtual pitch</a> evoked by an interval or chord, or the difficulty of fitting its pitches to a harmonic series (discussed by Goldstein and Terhardt, see main text) – is modelled by <a href="/wiki/Harmonic_entropy" class="mw-redirect" title="Harmonic entropy">harmonic entropy</a> theory. Dips in this graph show consonant intervals such as 4:5 and 2:3. Other components not modeled by this theory include critical band roughness, and tonal context (e.g., an augmented second is more dissonant than a minor third although in equal temperament the interval, 300 cents, is the same for both).</div></div></div></div></div> <p>Two notes played simultaneously but with slightly different frequencies produce a <a href="/wiki/Beat_(acoustics)" title="Beat (acoustics)">beating</a> "wah-wah-wah" sound. This phenomenon is used to create the <a href="/wiki/Voix_c%C3%A9leste" title="Voix céleste">Voix céleste</a> stop in organs. Other musical styles such as Bosnian ganga singing, pieces exploring the buzzing sound of the Indian tambura drone, stylized improvisations on the Middle Eastern mijwiz, or Indonesian <a href="/wiki/Gamelan" title="Gamelan">gamelan</a> consider this sound an attractive part of the musical timbre and go to great lengths to create instruments that produce this slight "<a href="/wiki/Roughness_(psychophysics)" title="Roughness (psychophysics)">roughness</a>".<sup id="cite_ref-FOOTNOTEVassilakis2005123_18-0" class="reference"><a href="#cite_note-FOOTNOTEVassilakis2005123-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p><p>Sensory dissonance and its two perceptual manifestations (beating and roughness) are both closely related to a sound signal's amplitude fluctuations. Amplitude fluctuations describe variations in the maximum value (amplitude) of sound signals relative to a reference point and are the result of <a href="/wiki/Interference_(wave_propagation)" class="mw-redirect" title="Interference (wave propagation)">wave interference</a>. The interference principle states that the combined amplitude of two or more vibrations (waves) at any given time may be larger (constructive interference) or smaller (destructive interference) than the amplitude of the individual vibrations (waves), depending on their phase relationship. In the case of two or more waves with different frequencies, their periodically changing phase relationship results in periodic alterations between constructive and destructive interference, giving rise to the phenomenon of amplitude fluctuations.<sup id="cite_ref-FOOTNOTEVassilakis2005121_19-0" class="reference"><a href="#cite_note-FOOTNOTEVassilakis2005121-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p><p>"Amplitude fluctuations can be placed in three overlapping perceptual categories related to the rate of fluctuation: </p> <ol><li>Slow amplitude fluctuations <span class="nowrap">(<span class="texhtml">≲</span> 20 per second)</span> are perceived as loudness fluctuations referred to as <i>beating</i>.</li> <li>As the rate of fluctuation is increased, the loudness appears constant, and the fluctuations are perceived as "fluttering" or roughness (fluctuations between about <span class="nowrap">20 per second</span> and <span class="nowrap">75–150 per second).</span></li> <li>As the amplitude fluctuation rate is increased further, the roughness reaches a maximum strength and then gradually diminishes until it disappears <span class="nowrap">(<span class="texhtml">≳</span> 75–150 fluctuations per second,</span> depending on the frequency of the interfering tones).</li></ol> <p>Assuming the ear performs a frequency analysis on incoming signals, as indicated by <a href="/wiki/Ohm%27s_acoustic_law" title="Ohm's acoustic law">Ohm's acoustic law</a>,<sup id="cite_ref-FOOTNOTEHelmholtz1954b_20-0" class="reference"><a href="#cite_note-FOOTNOTEHelmholtz1954b-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTELevelt_and_Plomp1964[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_21-0" class="reference"><a href="#cite_note-FOOTNOTELevelt_and_Plomp1964[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> the above perceptual categories can be related directly to the bandwidth of the hypothetical analysis filters,<sup id="cite_ref-FOOTNOTEZwickerFlottorpStevens1957[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_22-0" class="reference"><a href="#cite_note-FOOTNOTEZwickerFlottorpStevens1957[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTEZwicker1961[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_23-0" class="reference"><a href="#cite_note-FOOTNOTEZwicker1961[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> For example, in the simplest case of amplitude fluctuations resulting from the addition of two sine signals with frequencies <span class="texhtml mvar" style="font-style:italic;">f</span><sub>1</sub> and <span class="texhtml mvar" style="font-style:italic;">f</span><sub>2</sub>, the fluctuation rate is equal to the frequency difference between the two sines <span class="nowrap"> <span style="font-size:120%">|</span> <span class="texhtml mvar" style="font-style:italic;">f</span><sub>1</sub> − <span class="texhtml mvar" style="font-style:italic;">f</span><sub>2</sub> <span style="font-size:120%">|</span> ,</span> and the following statements represent the general consensus: </p> <ol><li>If the fluctuation rate is smaller than the filter bandwidth, then a single tone is perceived either with fluctuating loudness (beating) or with roughness.</li> <li>If the fluctuation rate is larger than the filter bandwidth, then a complex tone is perceived, to which one or more pitches can be assigned but which, in general, exhibits no beating or roughness.</li></ol> <p>Along with amplitude fluctuation rate, the second most important signal parameter related to the perceptions of beating and roughness is the degree of a signal's amplitude fluctuation, that is, the level difference between peaks and valleys in a signal.<sup id="cite_ref-FOOTNOTETerhardt1974[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_24-0" class="reference"><a href="#cite_note-FOOTNOTETerhardt1974[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTEVassilakis2001[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_25-0" class="reference"><a href="#cite_note-FOOTNOTEVassilakis2001[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> The degree of amplitude fluctuation depends on the relative amplitudes of the components in the signal's spectrum, with interfering tones of equal amplitudes resulting in the highest fluctuation degree and therefore in the highest beating or roughness degree. </p><p>For fluctuation rates comparable to the auditory filter bandwidth, the degree, rate, and shape of a complex signal's amplitude fluctuations are variables that are manipulated by musicians of various cultures to exploit the beating and roughness sensations, making amplitude fluctuation a significant expressive tool in the production of musical sound. Otherwise, when there is no pronounced beating or roughness, the degree, rate, and shape of a complex signal's amplitude fluctuations remain important, through their interaction with the signal's spectral components. This interaction is manifested perceptually in terms of pitch or timbre variations, linked to the introduction of combination tones.<sup id="cite_ref-FOOTNOTEVassilakis2001_26-0" class="reference"><a href="#cite_note-FOOTNOTEVassilakis2001-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTEVassilakis2005_27-0" class="reference"><a href="#cite_note-FOOTNOTEVassilakis2005-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTEVassilakis_and_Fitz2007_28-0" class="reference"><a href="#cite_note-FOOTNOTEVassilakis_and_Fitz2007-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> </p><p>"The beating and roughness sensations associated with certain complex signals are therefore usually understood in terms of sine-component interaction within the same frequency band of the hypothesized auditory filter, called <a href="/wiki/Critical_band" title="Critical band">critical band</a>."<sup id="cite_ref-FOOTNOTEVassilakis2005121–123_29-0" class="reference"><a href="#cite_note-FOOTNOTEVassilakis2005121–123-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> </p> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1096940132">.mw-parser-output .listen .side-box-text{line-height:1.1em}.mw-parser-output .listen-plain{border:none;background:transparent}.mw-parser-output .listen-embedded{width:100%;margin:0;border-width:1px 0 0 0;background:transparent}.mw-parser-output .listen-header{padding:2px}.mw-parser-output .listen-embedded .listen-header{padding:2px 0}.mw-parser-output .listen-file-header{padding:4px 0}.mw-parser-output .listen .description{padding-top:2px}.mw-parser-output .listen .mw-tmh-player{max-width:100%}@media(max-width:719px){.mw-parser-output .listen{clear:both}}@media(min-width:720px){.mw-parser-output .listen:not(.listen-noimage){width:320px}.mw-parser-output .listen-left{overflow:visible;float:left}.mw-parser-output .listen-center{float:none;margin-left:auto;margin-right:auto}}</style><div class="side-box side-box-right listen noprint"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><figure class="mw-halign-center" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Gnome-mime-sound-openclipart.svg/50px-Gnome-mime-sound-openclipart.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Gnome-mime-sound-openclipart.svg/75px-Gnome-mime-sound-openclipart.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/87/Gnome-mime-sound-openclipart.svg/100px-Gnome-mime-sound-openclipart.svg.png 2x" data-file-width="160" data-file-height="160" /></span><figcaption></figcaption></figure></div> <div class="side-box-text plainlist"><div class="haudio"> <div class="listen-file-header"><a href="/wiki/File:Dissonance-M2-to-unison.ogg" title="File:Dissonance-M2-to-unison.ogg">Two pitches moving from the interval of a Minor 2nd to a unison</a></div> <div><span typeof="mw:File"><span><audio id="mwe_player_7" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="232" style="width:232px;" data-durationhint="13" data-mwtitle="Dissonance-M2-to-unison.ogg" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/8/83/Dissonance-M2-to-unison.ogg" type="audio/ogg; codecs="vorbis"" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/83/Dissonance-M2-to-unison.ogg/Dissonance-M2-to-unison.ogg.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span></div> <div class="description">Illustrating the roughness and beat oscillations that gradually reduce as the interval moves towards the unison</div></div></div></div> <div class="side-box-abovebelow"><hr /><i class="selfreference">Problems playing this file? See <a href="/wiki/Help:Media" title="Help:Media">media help</a>.</i></div> </div> <ul><li>Frequency ratios: When harmonic timbres are played in one of the <a href="/wiki/Just_intonation" title="Just intonation">just intonations</a> (or a sufficiently close approximation thereof), ratios of higher simple numbers are more dissonant than lower ones.<sup id="cite_ref-FOOTNOTEPhilip1966[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_30-0" class="reference"><a href="#cite_note-FOOTNOTEPhilip1966[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> However, the farther the timbre departs from the harmonic series, and/or the farther than the tuning departs from a Just Intonation, the less the "frequency ratio" rule applies.<sup id="cite_ref-FOOTNOTESethares2005_31-0" class="reference"><a href="#cite_note-FOOTNOTESethares2005-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup></li></ul> <p>In human hearing, the varying effect of simple ratios may be perceived by one of these mechanisms: </p> <ul><li>Fusion or pattern matching: fundamentals may be perceived through pattern matching of the separately analyzed partials to a best-fit exact-harmonic template,<sup id="cite_ref-FOOTNOTEGerson_and_Goldstein1978[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_32-0" class="reference"><a href="#cite_note-FOOTNOTEGerson_and_Goldstein1978[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> or the best-fit subharmonic,<sup id="cite_ref-FOOTNOTETerhardt1974[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_24-1" class="reference"><a href="#cite_note-FOOTNOTETerhardt1974[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> or harmonics may be perceptually fused into one entity, with dissonances being those intervals less likely mistaken for unisons, the imperfect intervals, because of the multiple estimates, at perfect intervals, of fundamentals, for one harmonic tone.<sup id="cite_ref-FOOTNOTETerhardt1974[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_24-2" class="reference"><a href="#cite_note-FOOTNOTETerhardt1974[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> By these definitions, inharmonic partials of otherwise harmonic spectra are usually processed separately,<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (November 2022)">citation needed</span></a></i>]</sup> unless frequency or amplitude modulated coherently with the harmonic partials.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (November 2022)">citation needed</span></a></i>]</sup> For some of these definitions, neural firing supplies the data for pattern matching; see directly below.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (November 2022)">citation needed</span></a></i>]</sup></li> <li>Period length or neural-firing coincidence: with the length of periodic neural firing created by two or more waveforms, higher simple numbers creating longer periods or lesser coincidence of neural firing and thus dissonance.<sup id="cite_ref-FOOTNOTERoederer1973145–149_33-0" class="reference"><a href="#cite_note-FOOTNOTERoederer1973145–149-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> Purely harmonic tones cause neural firing exactly with the period or some multiple of the pure tone.</li> <li>Dissonance is more generally defined by the amount of beating between <a href="/wiki/Harmonic_series_(music)" title="Harmonic series (music)">partials</a> (called <a href="/wiki/Harmonic" title="Harmonic">harmonics</a> or <a href="/wiki/Overtone" title="Overtone">overtones</a> when occurring in harmonic <a href="/wiki/Timbre" title="Timbre">timbres</a>),(<sup id="cite_ref-FOOTNOTEHelmholtz1954a[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_9-1" class="reference"><a href="#cite_note-FOOTNOTEHelmholtz1954a[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> Terhardt<sup id="cite_ref-FOOTNOTETerhardt1974[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_24-3" class="reference"><a href="#cite_note-FOOTNOTETerhardt1974[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> calls this "sensory dissonance". By this definition, dissonance is dependent not only on the width of the interval between two notes' fundamental frequencies, but also on the widths of the intervals between the two notes' non-fundamental partials. Sensory dissonance (i.e., presence of beating or roughness in a sound) is associated with the inner ear's inability to fully resolve spectral components with excitation patterns whose <a href="/wiki/Critical_bands" class="mw-redirect" title="Critical bands">critical bands</a> overlap. If two pure sine waves, without harmonics, are played together, people tend to perceive maximum dissonance when the frequencies are within the critical band for those frequencies, which is as wide as a minor third for low frequencies and as narrow as a minor second for high frequencies (relative to the range of human hearing).<sup id="cite_ref-FOOTNOTESethares200543_34-0" class="reference"><a href="#cite_note-FOOTNOTESethares200543-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> If harmonic tones with larger intervals are played, the perceived dissonance is due, at least in part, to the presence of intervals between the harmonics of the two notes that fall within the critical band.<sup id="cite_ref-FOOTNOTERoederer1995106_35-0" class="reference"><a href="#cite_note-FOOTNOTERoederer1995106-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> The sensory consonance or dissonance of any given interval, in any given tuning, can be adjusted by adjusting the partials in the timbre to be maximally aligned or mis-aligned, respectively, with the notes of the related tuning.</li> <li>Dissonance sensation is a result of brain's response to unusual or rare sound perceptions.<sup id="cite_ref-FOOTNOTEPankovski_and_Pankovska_E.2017_36-0" class="reference"><a href="#cite_note-FOOTNOTEPankovski_and_Pankovska_E.2017-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> The brain is remembering and ranking the sound patterns that usually enters the ears, and if an unusual (rare occurring) sound is listened to, a well known EEG pattern emerges (<a href="/wiki/P3b" title="P3b">P300/P3b</a>) indicating an oddball event. This causes slight stress in the listener, which is causing the sensation of dissonance. In the same paper, Pankovski and Pankovska show by a software simulated neural network that the brain is capable of such remembering and ranking of the sound patterns, thus perfectly reproducing the well known <a href="/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz">Helmholtz</a>'s list of <a href="/wiki/Dyad_(music)" title="Dyad (music)">two-tone intervals</a> ordered by consonance/dissonance, for the first time in the history of studying these phenomena. As a consequence, Pankovski and Pankovska suggest that the consonance and dissonance are biologically dependent for the more consonant sounds, and culturally dependent for the more dissonant sounds.</li></ul> <p>Generally, the sonance (i.e., a continuum with pure consonance at one end and pure dissonance at the other) of any given interval can be controlled by adjusting the timbre in which it is played, thereby aligning its partials with the current tuning's notes (or <i>vice versa</i>).<sup id="cite_ref-FOOTNOTESethares20051_37-0" class="reference"><a href="#cite_note-FOOTNOTESethares20051-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> The sonance of the interval between two notes can be maximized (producing consonance) by maximizing the alignment of the two notes' partials, whereas it can be minimized (producing dissonance) by mis-aligning each otherwise nearly aligned pair of partials by an amount equal to the width of the critical band at the average of the two partials' frequencies.(<sup id="cite_ref-FOOTNOTESethares20051_37-1" class="reference"><a href="#cite_note-FOOTNOTESethares20051-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTESetharesMilneTiedjePrechtl2009_15-1" class="reference"><a href="#cite_note-FOOTNOTESetharesMilneTiedjePrechtl2009-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p><p>Controlling the sonance of pseudo-harmonic timbres played in pseudo-just tunings in real time is an aspect of <a href="/wiki/Dynamic_tonality" title="Dynamic tonality">dynamic tonality</a>. For example, in <a href="/wiki/William_Sethares" title="William Sethares">William Sethares</a>' piece <i>C to Shining C</i> (discussed at <a href="/wiki/Dynamic_tonality#Example:_C2ShiningC" title="Dynamic tonality">Dynamic tonality § Example: C2ShiningC</a>), the sonance of intervals is affected both by tuning progressions and timbre progressions, introducing tension and release into the playing of a single chord. </p><p>The strongest <a href="/wiki/Homophony" title="Homophony">homophonic</a> (harmonic) <a href="/wiki/Cadence_(music)" class="mw-redirect" title="Cadence (music)">cadence</a>, the authentic cadence, dominant to tonic (D-T, V-I or V<sup>7</sup>-I), is in part created by the dissonant <a href="/wiki/Tritone" title="Tritone">tritone</a><sup id="cite_ref-FOOTNOTEBenward_and_Saker200354_38-0" class="reference"><a href="#cite_note-FOOTNOTEBenward_and_Saker200354-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> created by the seventh, also dissonant, in the dominant seventh chord, which precedes the <a href="/wiki/Tonic_(music)" title="Tonic (music)">tonic</a>. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Dominant_seventh_tritone_resolution.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/95/Dominant_seventh_tritone_resolution.png/220px-Dominant_seventh_tritone_resolution.png" decoding="async" width="220" height="96" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/95/Dominant_seventh_tritone_resolution.png/330px-Dominant_seventh_tritone_resolution.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/95/Dominant_seventh_tritone_resolution.png/440px-Dominant_seventh_tritone_resolution.png 2x" data-file-width="1044" data-file-height="456" /></a><figcaption>Tritone resolution inwards and outwards<figure class="mw-default-size" typeof="mw:File/Thumb"><span><audio id="mwe_player_8" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-durationhint="8" data-mwtitle="Tritone_resolution_inward.ogg" data-mwprovider="wikimediacommons" resource="/wiki/File:Tritone_resolution_inward.ogg"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/4/41/Tritone_resolution_inward.ogg/Tritone_resolution_inward.ogg.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/4/41/Tritone_resolution_inward.ogg" type="audio/ogg; codecs="vorbis"" data-width="0" data-height="0" /></audio></span><figcaption>Inwards</figcaption></figure><figure class="mw-default-size" typeof="mw:File/Thumb"><span><audio id="mwe_player_9" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-durationhint="5" data-mwtitle="Tritone_resolution_outwards.mid" data-mwprovider="wikimediacommons" resource="/wiki/File:Tritone_resolution_outwards.mid"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/83/Tritone_resolution_outwards.mid/Tritone_resolution_outwards.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/83/Tritone_resolution_outwards.mid/Tritone_resolution_outwards.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/8/83/Tritone_resolution_outwards.mid" type="audio/midi" data-width="0" data-height="0" /></audio></span><figcaption>Outwards</figcaption></figure></figcaption></figure> <figure class="mw-default-size mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:Ii-V-I_turnaround_in_C.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Ii-V-I_turnaround_in_C.png/220px-Ii-V-I_turnaround_in_C.png" decoding="async" width="220" height="108" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Ii-V-I_turnaround_in_C.png/330px-Ii-V-I_turnaround_in_C.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/de/Ii-V-I_turnaround_in_C.png/440px-Ii-V-I_turnaround_in_C.png 2x" data-file-width="534" data-file-height="263" /></a><figcaption>Perfect authentic cadence (V–I with roots in the bass and tonic in the highest voice of the final chord): <a href="/wiki/Ii%E2%80%93V%E2%80%93I_progression" title="Ii–V–I progression">ii–V–I progression</a> in C<span class="mw-default-size" typeof="mw:File"><span><audio id="mwe_player_10" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-mwtitle="Ii-V-I_turnaround_in_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/e/e6/Ii-V-I_turnaround_in_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e6/Ii-V-I_turnaround_in_C.mid/Ii-V-I_turnaround_in_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e6/Ii-V-I_turnaround_in_C.mid/Ii-V-I_turnaround_in_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span></figcaption></figure> <div class="mw-heading mw-heading2"><h2 id="Instruments_producing_non-harmonic_overtone_series">Instruments producing non-harmonic overtone series</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Consonance_and_dissonance&action=edit&section=5" title="Edit section: Instruments producing non-harmonic overtone series"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Musical instruments like <a href="/wiki/Bell_(instrument)" class="mw-redirect" title="Bell (instrument)">bells</a> and <a href="/wiki/Xylophone" title="Xylophone">xylophones</a>, called <a href="/wiki/Idiophone" title="Idiophone">Idiophones</a>, are played such that their relatively stiff mass is excited to vibration by means of a striking the instrument. This contrasts with <a href="/wiki/Violin" title="Violin">violins</a>, <a href="/wiki/Flute" title="Flute">flutes</a>, or <a href="/wiki/Drum_(instrument)" class="mw-redirect" title="Drum (instrument)">drums</a>, where the vibrating medium is a light, supple <a href="/wiki/String_(music)" title="String (music)">string</a>, <a href="/wiki/Aerophone" title="Aerophone">column of air</a>, or <a href="/wiki/Drumhead" title="Drumhead">membrane</a>. The <a href="/wiki/Overtone" title="Overtone">overtones</a> of the <a href="/wiki/Harmonic_series_(music)" title="Harmonic series (music)">inharmonic series</a> produced by such instruments may differ greatly from that of the rest of the <a href="/wiki/Orchestra" title="Orchestra">orchestra</a>, and the consonance or dissonance of the harmonic intervals as well.<sup id="cite_ref-FOOTNOTEGouwens20093_39-0" class="reference"><a href="#cite_note-FOOTNOTEGouwens20093-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> </p><p>According to John Gouwens,<sup id="cite_ref-FOOTNOTEGouwens20093_39-1" class="reference"><a href="#cite_note-FOOTNOTEGouwens20093-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> the <a href="/wiki/Carillon" title="Carillon">carillon</a>'s harmony profile is summarized: </p> <ul><li>Consonant: minor third, tritone, minor sixth, perfect fourth, perfect fifth, and possibly minor seventh or even major second</li> <li>Dissonant: major third, major sixth</li> <li>Variable upon individual instrument: major seventh</li> <li><a href="/wiki/Inversion_(interval)" class="mw-redirect" title="Inversion (interval)">Interval inversion</a> does not apply.</li></ul> <div class="mw-heading mw-heading2"><h2 id="In_history_of_Western_music">In history of Western music</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Consonance_and_dissonance&action=edit&section=6" title="Edit section: In history of Western music"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1023981488">@media all and (max-width:720px){.mw-parser-output .rquote{width:auto!important;float:none!important}}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote rquote" style="float: right; width: 33%;"><p>When we consider musical works we find that the triad is ever-present and that the interpolated dissonances have no other purpose than to effect the continuous variation of the triad.</p><div class="templatequotecite">— <cite><a href="/wiki/Lorenz_Mizler" class="mw-redirect" title="Lorenz Mizler">Lorenz Mizler</a> 1739<sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup></cite></div></blockquote> <p>Dissonance has been understood and heard differently in different musical traditions, cultures, styles, and time periods. Relaxation and tension have been used as analogy since the time of Aristotle till the present.<sup id="cite_ref-FOOTNOTEKliewer1975290_41-0" class="reference"><a href="#cite_note-FOOTNOTEKliewer1975290-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> </p><p>The terms dissonance and consonance are often considered equivalent to tension and relaxation. A cadence is (among other things) a place where tension is resolved; hence the long tradition of thinking of a musical phrase as consisting of a <a href="/wiki/Cadence_(music)" class="mw-redirect" title="Cadence (music)">cadence</a> and a passage of gradually accumulating tension leading up to it.<sup id="cite_ref-FOOTNOTEParncutt_and_Hair2011132_42-0" class="reference"><a href="#cite_note-FOOTNOTEParncutt_and_Hair2011132-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> </p><p>Various psychological principles constructed through the audience's general conception of tonal fluidity determine how a listener will distinguish an instance of dissonance within a musical composition. Based on one's developed conception of the general tonal fusion within the piece, an unexpected tone played slightly variant to the overall schema will generate a psychological need for resolve. When the consonant is followed thereafter, the listener will encounter a sense of resolution. Within Western music, these particular instances and psychological effects within a composition have come to possess an ornate connotation.<sup id="cite_ref-FOOTNOTEParncutt_and_Hair2011132_42-1" class="reference"><a href="#cite_note-FOOTNOTEParncutt_and_Hair2011132-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> </p><p>The application of consonance and dissonance "is sometimes regarded as a property of isolated <a href="/wiki/Sonority_(music)" class="mw-redirect" title="Sonority (music)">sonorities</a> that is independent of what precedes or follows them. In most Western music, however, dissonances are held to <i>resolve</i> onto following consonances, and the principle of <a href="/wiki/Resolution_(music)" title="Resolution (music)">resolution</a> is tacitly considered integral to consonance and dissonance".<sup id="cite_ref-FOOTNOTEParncutt_and_Hair2011132_42-2" class="reference"><a href="#cite_note-FOOTNOTEParncutt_and_Hair2011132-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Antiquity_and_the_middle_ages">Antiquity and the middle ages</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Consonance_and_dissonance&action=edit&section=7" title="Edit section: Antiquity and the middle ages"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In Ancient Greece, <i>armonia</i> denoted the production of a unified complex, particularly one expressible in numerical ratios. Applied to music, the concept concerned how sounds in a scale or a melody fit together (in this sense, it could also concern the tuning of a scale).<sup id="cite_ref-FOOTNOTEPhilip1966123–124_43-0" class="reference"><a href="#cite_note-FOOTNOTEPhilip1966123–124-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> The term <i>symphonos</i> was used by Aristoxenus and others to describe the intervals of the fourth, the fifth, the octave and their doublings; other intervals were said <i>diaphonos</i>. This terminology probably referred to the <a href="/wiki/Pythagorean_tuning" title="Pythagorean tuning">Pythagorean tuning</a>, where fourths, fifths and octaves (ratios 4:3, 3:2 and 2:1) were directly tunable, while the other scale degrees (other 3 prime ratios) could only be tuned by combinations of the preceding.<sup id="cite_ref-FOOTNOTEAristoxenus1902188–206_44-0" class="reference"><a href="#cite_note-FOOTNOTEAristoxenus1902188–206-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTETenney198811–12_45-0" class="reference"><a href="#cite_note-FOOTNOTETenney198811–12-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> Until the advent of <a href="/wiki/Polyphony" title="Polyphony">polyphony</a> and even later, this remained the basis of the concept of consonance versus dissonance (<i>symphonia</i> versus <i>diaphonia</i>) in Western music theory. </p><p>In the early Middle Ages, the Latin term <span title="Latin-language text"><i lang="la">consonantia</i></span> translated either <i>armonia</i> or <i>symphonia</i>. Boethius (6th century) characterizes consonance by its sweetness, dissonance by its harshness: "Consonance (<span title="Latin-language text"><i lang="la">consonantia</i></span>) is the blending (<span title="Latin-language text"><i lang="la">mixtura</i></span>) of a high sound with a low one, sweetly and uniformly (<span title="Latin-language text"><i lang="la">suauiter uniformiterque</i></span>) arriving to the ears. Dissonance is the harsh and unhappy percussion (<span title="Latin-language text"><i lang="la">aspera atque iniocunda percussio</i></span>) of two sounds mixed together (<span title="Latin-language text"><i lang="la">sibimet permixtorum</i></span>)".<sup id="cite_ref-FOOTNOTEBoethiusn.d.f._13v._46-0" class="reference"><a href="#cite_note-FOOTNOTEBoethiusn.d.f._13v.-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> It remains unclear, however, whether this could refer to simultaneous sounds. The case becomes clear, however, with Hucbald of Saint Amand (<abbr title="circa">c.</abbr><span style="white-space:nowrap;"> 900 <span class="smallcaps"><span style="font-variant: small-caps; text-transform: lowercase;">CE</span></span></span>), who writes: </p> <dl><dd>"Consonance (<span title="Latin-language text"><i lang="la">consonantia</i></span>) is the measured and concordant blending (<span title="Latin-language text"><i lang="la">rata et concordabilis permixtio</i></span>) of two sounds, which will come about only when two simultaneous sounds from different sources combine into a single musical whole (<span title="Latin-language text"><i lang="la">in unam simul modulationem conveniant</i></span>) ... There are six of these consonances, three simple and three composite, ... octave, fifth, fourth, and octave-plus-fifth, octave-plus-fourth and double octave".<sup id="cite_ref-47" class="reference"><a href="#cite_note-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup></dd></dl> <p>According to <a href="/wiki/Johannes_de_Garlandia_(music_theorist)" title="Johannes de Garlandia (music theorist)">Johannes de Garlandia</a>:<sup id="cite_ref-FOOTNOTEJohannes_de_Garlandia_48-0" class="reference"><a href="#cite_note-FOOTNOTEJohannes_de_Garlandia-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup> </p> <ul><li>Perfect consonance: unisons and octaves.</li></ul> <dl><dd><dl><dd>(<span title="Latin-language text"><i lang="la">Perfecta dicitur, quando due voces junguntur in eodem tempore, ita quod una, secundum auditum, non percipitur ab alia propter concordantiam, et dicitur equisonantiam, ut in unisono et diapason.</i></span></dd> <dd>"[Consonance] is said perfect, when two voices are joined at the same time, so that the one, by audition, cannot be distinguished from the other because of the concordance, and it is called equisonance, as in unison and octave.")</dd></dl></dd></dl> <ul><li>Median consonance: fourths and fifths.</li></ul> <dl><dd><dl><dd>(<span title="Latin-language text"><i lang="la">Medie autem dicuntur, quando duo voces junguntur in eodem tempore; que neque dicuntur perfecte, neque imperfecte, sed partim conveniunt cum perfectis, et partim cum imperfectis. Et sunt due species, scilicet diapente et diatessaron.</i></span></dd> <dd>"Consonances are said median, when two voices are joined at the same time, which neither can be said perfect, nor imperfect, but which partly agree with the perfect, and partly with the imperfect. And they are of two species, namely the fifth and the fourth.")</dd></dl></dd></dl> <ul><li>Imperfect consonance: minor and major thirds. (Imperfect consonances are not formally mentioned in the treatise, but the quotation above concerning median consonances does refer to imperfect consonances, and the section on consonances concludes:</li></ul> <dl><dd><dl><dd><span title="Latin-language text"><i lang="la">Sic apparet quod sex sunt species concordantie, scilicet: unisonus, diapason, diapente, diatessaron, semiditonus, ditonus.</i></span></dd> <dd>"So it appears that there are six species of consonances, that is: unison, octave, fifth, fourth, minor third, major third." The last two are implied to be "imperfect consonances" by deduction.)</dd></dl></dd></dl> <ul><li>Imperfect dissonance: major sixth (tone + fifth) and minor seventh (minor third + fifth).</li></ul> <dl><dd><dl><dd>(<span title="Latin-language text"><i lang="la">Imperfecte dicuntur, quando due voces junguntur ita, quod secundum auditum vel possunt aliquo modo compati, tamen non concordant. Et sunt due species, scilicet tonus cum diapente et semiditonus cum diapente.</i></span></dd> <dd>[Dissonances] are said imperfect, when two voices are joined so that by audition although they can to some extent match, nevertheless they do not concord. And there are two species, namely tone plus fifth and minor third plus fifth.")</dd></dl></dd></dl> <ul><li>Median dissonance: tone and minor sixth (<a href="/wiki/Semitone" title="Semitone">semitone</a> + fifth).</li></ul> <dl><dd><dl><dd>(<span title="Latin-language text"><i lang="la">Medie dicuntur, quando due voces junguntur ita, quod partim conveniunt cum perfectis, partim cum imperfectis. Et iste sunt due species, scilicet tonus et simitonium cum diapente.</i></span></dd> <dd>[Dissonances] are said median when two voices are joined so that they partly match the perfect, partly the imperfect. And they are of two species, namely tone and semitone plus fifth.")</dd></dl></dd></dl> <ul><li>Perfect dissonance: semitone, tritone, major seventh (major third + fifth). (Here again, the perfect dissonances can only be deduced by elimination from this phrase:</li></ul> <dl><dd><dl><dd><span title="Latin-language text"><i lang="la">Iste species dissonantie sunt septem, scilicet: semitonium, tritonus, ditonus cum diapente; tonus cum diapente, semiditonus cum diapente; tonus et semitonium cum diapente.</i></span></dd> <dd>These species of dissonances are seven: semitone, tritone, major third plus fifth; tone plus fifth, minor third plus fifth; tone and semitone plus fifth.")</dd></dl></dd></dl> <p>One example of imperfect consonances previously considered dissonances<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="Are these being treated the same, or differently from the perfect consonances, or the same or differently from dissonances, and how? In other words, how can we tell whether Machaut is treating them as consonances or as dissonances? (July 2014)">clarification needed</span></a></i>]</sup> in <a href="/wiki/Guillaume_de_Machaut" title="Guillaume de Machaut">Guillaume de Machaut</a>'s "Je ne cuit pas qu'onques":<sup id="cite_ref-FOOTNOTEMachaut1926p._13,_Ballade_14,_"Je_ne_cuit_pas_qu'onques_a_creature",_mm._27–31_49-0" class="reference"><a href="#cite_note-FOOTNOTEMachaut1926p._13,_Ballade_14,_"Je_ne_cuit_pas_qu'onques_a_creature",_mm._27–31-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><span><audio id="mwe_player_11" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-durationhint="14" data-mwtitle="Machaut_"Je_ne_cuit_pas_qu'onques".wav" data-mwprovider="wikimediacommons" resource="/wiki/File:Machaut_%22Je_ne_cuit_pas_qu%27onques%22.wav"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/4/48/Machaut_%22Je_ne_cuit_pas_qu%27onques%22.wav/Machaut_%22Je_ne_cuit_pas_qu%27onques%22.wav.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/4/48/Machaut_%22Je_ne_cuit_pas_qu%27onques%22.wav/Machaut_%22Je_ne_cuit_pas_qu%27onques%22.wav.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/4/48/Machaut_%22Je_ne_cuit_pas_qu%27onques%22.wav" type="audio/wav" data-width="0" data-height="0" /></audio></span><figcaption>Machaut "Je ne cuit pas qu'onques"</figcaption></figure> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:Imperfect_consonance_in_Machaut.PNG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/en/thumb/9/94/Imperfect_consonance_in_Machaut.PNG/400px-Imperfect_consonance_in_Machaut.PNG" decoding="async" width="400" height="99" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/94/Imperfect_consonance_in_Machaut.PNG/600px-Imperfect_consonance_in_Machaut.PNG 1.5x, //upload.wikimedia.org/wikipedia/en/9/94/Imperfect_consonance_in_Machaut.PNG 2x" data-file-width="632" data-file-height="157" /></a><figcaption>Xs mark thirds and sixths</figcaption></figure> <p>According to Margo Schulter:<sup id="cite_ref-FOOTNOTESchulter1997a_50-0" class="reference"><a href="#cite_note-FOOTNOTESchulter1997a-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> </p><p>Stable: </p> <ul><li>Purely blending: unisons and octaves</li> <li>Optimally blending: fourths and fifths</li></ul> <p>Unstable: </p> <ul><li>Relatively blending: minor and major thirds</li> <li>Relatively tense: major seconds, minor sevenths, and major sixths</li> <li>Strongly discordant: minor seconds, tritonus<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Template:Typo_help_inline" title="Template:Typo help inline"><span title="similar to tritones (November 2022)">check spelling</span></a></i>]</sup>, and major sevenths, and often minor sixths</li></ul> <p>"Perfect" and "imperfect" and the notion of being (<span title="Latin-language text"><i lang="la">esse</i></span>) must be taken in their contemporaneous <a href="/wiki/Latin" title="Latin">Latin</a> meanings (<i>perfectum</i> [<a href="https://la.wikipedia.org/wiki/Perfectum" class="extiw" title="la:Perfectum">la</a>], <i>imperfectum</i> [<a href="https://la.wikipedia.org/wiki/Imperfectum" class="extiw" title="la:Imperfectum">la</a>]) to understand these terms, such that imperfect is "unfinished" or "incomplete" and thus an imperfect dissonance is "not quite manifestly dissonant" and perfect consonance is "done almost to the point of excess".<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (January 2015)">citation needed</span></a></i>]</sup> Also, <a href="/wiki/Inversion_(interval)" class="mw-redirect" title="Inversion (interval)">inversion of intervals</a> (<a href="/wiki/Major_second" title="Major second">major second</a> in some sense equivalent to <a href="/wiki/Minor_seventh" title="Minor seventh">minor seventh</a>) and <a href="/wiki/Octave" title="Octave">octave</a> <a href="/wiki/Pitch_circularity" title="Pitch circularity">reduction</a> (<a href="/wiki/Minor_ninth" class="mw-redirect" title="Minor ninth">minor ninth</a> in some sense equivalent to minor second) were yet unknown during the Middle Ages.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (January 2015)">citation needed</span></a></i>]</sup> </p><p>Due to the different <a href="/wiki/Just_intonation" title="Just intonation">tuning systems</a> compared to <a href="/wiki/Equal_temperament" title="Equal temperament">modern times</a>, the minor seventh and <a href="/wiki/Major_ninth" class="mw-redirect" title="Major ninth">major ninth</a> were "harmonic consonances", meaning that they correctly reproduced the interval ratios of the <a href="/wiki/Harmonic_series_(music)" title="Harmonic series (music)">harmonic series</a> which softened a bad effect.<sup id="cite_ref-FOOTNOTESchulter1997b_51-0" class="reference"><a href="#cite_note-FOOTNOTESchulter1997b-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="This cannot be true: harmonic partials were unknown in the Middle Ages. (January 2015)">clarification needed</span></a></i>]</sup> They were also often filled in by pairs of perfect fourths and perfect fifths respectively, forming <a href="/wiki/Resonance" title="Resonance">resonant</a> (blending) units characteristic of the musics of the time,<sup id="cite_ref-FOOTNOTESchulter1997c_52-0" class="reference"><a href="#cite_note-FOOTNOTESchulter1997c-52"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup> where "resonance" forms a <a href="/wiki/Three-valued_logic" title="Three-valued logic">complementary trine</a> with the categories of consonance and dissonance.<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="The text near this tag may need clarification or removal of jargon. (January 2015)">clarification needed</span></a></i>]</sup> Conversely, the thirds and <a href="/wiki/Interval_(music)" title="Interval (music)">sixths</a> were <a href="/wiki/Musical_temperament" title="Musical temperament">tempered</a> severely from <a href="/wiki/Pythagorean_tuning" title="Pythagorean tuning">pure ratios</a><sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="The text near this tag may need clarification or removal of jargon. (January 2015)">clarification needed</span></a></i>]</sup>, and in practice usually treated as dissonances in the sense that they had to <a href="/wiki/Resolution_(music)" title="Resolution (music)">resolve</a> to form complete <a href="/wiki/Perfect_cadence" class="mw-redirect" title="Perfect cadence">perfect cadences</a> and stable sonorities.<sup id="cite_ref-FOOTNOTESchulter1997d_53-0" class="reference"><a href="#cite_note-FOOTNOTESchulter1997d-53"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup> </p><p>The salient differences from modern conception:<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (January 2015)">citation needed</span></a></i>]</sup><sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="This all appears to describe Schulter's 'neo-medieval' practice, not true medieval usages. (January 2015)">clarification needed</span></a></i>]</sup> </p> <ul><li>parallel fourths and fifths were acceptable and necessary, open fourths and fifths inside octaves were the characteristic stable sonority in 3 or more voices,</li> <li>minor sevenths and major ninths were fully structural,</li> <li>tritones—as a deponent<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="The text near this tag may need clarification or removal of jargon. (January 2015)">clarification needed</span></a></i>]</sup> sort of fourth or fifth—were sometimes stacked with perfect fourths and fifths,</li> <li>thirds and sixths (and tall <a href="/wiki/Chord_(music)" title="Chord (music)">stacks thereof</a>) were not the sort of intervals upon which stable harmonies were based,</li> <li>final cadential consonances of fourth, fifths, and octaves need not be the target of "resolution" on a beat-to-beat (or similar) time basis: minor sevenths and major ninths may move to octaves forthwith, or sixths to fifths (or minor sevenths), but the fourths and fifths within might become "dissonant" 5:3, 6:3, or 6:4 <a href="/wiki/Chordioid" title="Chordioid">chordioids</a><sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="The text near this tag may need clarification or removal of jargon. (January 2015)">clarification needed</span></a></i>]</sup>, continuing the succession of non-consonant sonorities for timespans limited only by the next cadence.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Renaissance">Renaissance</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Consonance_and_dissonance&action=edit&section=8" title="Edit section: Renaissance"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In <a href="/wiki/Renaissance_music" title="Renaissance music">Renaissance music</a>, the perfect fourth above the bass was considered a dissonance needing immediate resolution. The <i>regola delle terze e seste</i> ("rule of thirds and sixths") required that imperfect consonances should resolve to a perfect one by a half-step progression in one voice and a whole-step progression in another.<sup id="cite_ref-FOOTNOTEDahlhaus1990179_54-0" class="reference"><a href="#cite_note-FOOTNOTEDahlhaus1990179-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> The viewpoint concerning successions of imperfect consonances—perhaps more concerned by a desire to avoid monotony than by their dissonant or consonant character—has been variable. Anonymous XIII (13th century) allowed two or three, Johannes de Garlandia's <i>Optima introductio</i> (13th–14th century) three, four or more, and Anonymous XI (15th century) four or five successive imperfect consonances. <a href="/wiki/Adam_von_Fulda" class="mw-redirect" title="Adam von Fulda">Adam von Fulda</a><sup id="cite_ref-FOOTNOTEGerbert17843:353_55-0" class="reference"><a href="#cite_note-FOOTNOTEGerbert17843:353-55"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup> wrote "Although the ancients formerly would forbid all sequences of more than three or four imperfect consonances, we more modern do not prohibit them." </p> <div class="mw-heading mw-heading3"><h3 id="Common_practice_period">Common practice period</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Consonance_and_dissonance&action=edit&section=9" title="Edit section: Common practice period"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the <a href="/wiki/Common_practice_period" title="Common practice period">common practice period</a>, musical style required <a href="/wiki/Preparation_(music)" title="Preparation (music)">preparation</a> for all dissonances,<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="Unprepared dissonances were an important part of Artusi's objection to Monteverdi's practice; a "prepared dissonance" (the linked article is unreferenced and howlingly inaccurate) is a suspension. (June 2020)">citation needed</span></a></i>]</sup> followed by a <a href="/wiki/Resolution_(music)" title="Resolution (music)">resolution</a> to a consonance. There was also a distinction between <a href="/wiki/Melodic" class="mw-redirect" title="Melodic">melodic</a> and <a href="/wiki/Harmonic" title="Harmonic">harmonic</a> dissonance. Dissonant melodic intervals included the <a href="/wiki/Tritone" title="Tritone">tritone</a> and all <a href="/wiki/Augmentation_(music)" title="Augmentation (music)">augmented</a> and <a href="/wiki/Diminution" title="Diminution">diminished</a> intervals. Dissonant harmonic intervals included: </p> <ul><li><a href="/wiki/Major_second" title="Major second">Major second</a> and <a href="/wiki/Minor_seventh" title="Minor seventh">minor seventh</a></li> <li><a href="/wiki/Minor_second" class="mw-redirect" title="Minor second">Minor second</a> and <a href="/wiki/Major_seventh" title="Major seventh">major seventh</a></li> <li><a href="/wiki/Augmented_fourth" class="mw-redirect" title="Augmented fourth">Augmented fourth</a> and <a href="/wiki/Diminished_fifth" class="mw-redirect" title="Diminished fifth">diminished fifth</a> (<a href="/wiki/Enharmonically" class="mw-redirect" title="Enharmonically">enharmonically</a> equivalent, <a href="/wiki/Tritone" title="Tritone">tritone</a>)</li></ul> <p>Early in history, only intervals low in the <a href="/wiki/Overtone" title="Overtone">overtone series</a> were considered consonant. As time progressed, intervals ever higher on the overtone series were considered as such. The final result of this was the so-called "<a href="/wiki/Emancipation_of_the_dissonance" title="Emancipation of the dissonance">emancipation of the dissonance</a>"<sup id="cite_ref-FOOTNOTESchoenberg1975258–264_56-0" class="reference"><a href="#cite_note-FOOTNOTESchoenberg1975258–264-56"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup> by some 20th-century composers. Early-20th-century American composer <a href="/wiki/Henry_Cowell" title="Henry Cowell">Henry Cowell</a> viewed <a href="/wiki/Tone_cluster" title="Tone cluster">tone clusters</a> as the use of higher and higher overtones.<sup id="cite_ref-57" class="reference"><a href="#cite_note-57"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup> </p><p> Composers in the Baroque era were well aware of the expressive potential of dissonance:</p><figure class="mw-default-size" typeof="mw:File/Thumb"><span><audio id="mwe_player_12" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-durationhint="15" data-mwtitle="Bach_Preludio_XXI_from_Well-tempered_Clavier,_Vol_1.wav" data-mwprovider="wikimediacommons" resource="/wiki/File:Bach_Preludio_XXI_from_Well-tempered_Clavier,_Vol_1.wav"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/84/Bach_Preludio_XXI_from_Well-tempered_Clavier%2C_Vol_1.wav/Bach_Preludio_XXI_from_Well-tempered_Clavier%2C_Vol_1.wav.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/84/Bach_Preludio_XXI_from_Well-tempered_Clavier%2C_Vol_1.wav/Bach_Preludio_XXI_from_Well-tempered_Clavier%2C_Vol_1.wav.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/8/84/Bach_Preludio_XXI_from_Well-tempered_Clavier%2C_Vol_1.wav" type="audio/wav" data-width="0" data-height="0" /></audio></span><figcaption>Bach Preludio XXI from Well-tempered Clavier, Vol 1</figcaption></figure> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:Dissonance_in_Bach.PNG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Dissonance_in_Bach.PNG/300px-Dissonance_in_Bach.PNG" decoding="async" width="300" height="111" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Dissonance_in_Bach.PNG/450px-Dissonance_in_Bach.PNG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Dissonance_in_Bach.PNG/600px-Dissonance_in_Bach.PNG 2x" data-file-width="2065" data-file-height="761" /></a><figcaption>A <a href="/wiki/Major_seventh_chord" title="Major seventh chord">sharply dissonant chord</a> in Bach's <i><a href="/wiki/Well-Tempered_Clavier" class="mw-redirect" title="Well-Tempered Clavier">Well-Tempered Clavier</a></i>, vol. I (Preludio XXI)</figcaption></figure> <p>Bach uses dissonance to communicate religious ideas in his sacred <a href="/wiki/Cantatas" class="mw-redirect" title="Cantatas">cantatas</a> and Passion settings. At the end of the <i><a href="/wiki/St_Matthew_Passion" title="St Matthew Passion">St Matthew Passion</a></i>, where the agony of Christ's betrayal and crucifixion is portrayed, <a href="/wiki/John_Eliot_Gardiner" title="John Eliot Gardiner">John Eliot Gardiner</a><sup id="cite_ref-FOOTNOTEGardiner2013427_58-0" class="reference"><a href="#cite_note-FOOTNOTEGardiner2013427-58"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup> hears that "a final reminder of this comes in the unexpected and almost excruciating dissonance Bach inserts over the very last chord: the melody instruments insist on B natural—the jarring leading tone—before eventually melting in a C minor cadence." </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><span><audio id="mwe_player_13" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-durationhint="11" data-mwtitle="Bach_St_Matthew_Passion_closing_bars_version_for_audio.wav" data-mwprovider="wikimediacommons" resource="/wiki/File:Bach_St_Matthew_Passion_closing_bars_version_for_audio.wav"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e3/Bach_St_Matthew_Passion_closing_bars_version_for_audio.wav/Bach_St_Matthew_Passion_closing_bars_version_for_audio.wav.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e3/Bach_St_Matthew_Passion_closing_bars_version_for_audio.wav/Bach_St_Matthew_Passion_closing_bars_version_for_audio.wav.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/e/e3/Bach_St_Matthew_Passion_closing_bars_version_for_audio.wav" type="audio/wav" data-width="0" data-height="0" /></audio></span><figcaption>Bach <i><a href="/wiki/St_Matthew_Passion" title="St Matthew Passion">St Matthew Passion</a></i> closing bars</figcaption></figure> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:Bach_St_Matthew_Passion_closing_bars.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Bach_St_Matthew_Passion_closing_bars.png/500px-Bach_St_Matthew_Passion_closing_bars.png" decoding="async" width="500" height="307" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Bach_St_Matthew_Passion_closing_bars.png/750px-Bach_St_Matthew_Passion_closing_bars.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/47/Bach_St_Matthew_Passion_closing_bars.png/1000px-Bach_St_Matthew_Passion_closing_bars.png 2x" data-file-width="2430" data-file-height="1493" /></a><figcaption>Closing bars of the final chorus of Bach's <i>St Matthew Passion</i></figcaption></figure> <p>In the opening aria of Cantata <a href="/wiki/BWV_54" class="mw-redirect" title="BWV 54">BWV 54</a>, <i>Widerstehe doch der Sünde</i> ("upon sin oppose resistance"), nearly every strong beat carries a dissonance: </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><span><audio id="mwe_player_14" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-durationhint="29" data-mwtitle="Bach_BWV_54_opening.wav" data-mwprovider="wikimediacommons" resource="/wiki/File:Bach_BWV_54_opening.wav"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/86/Bach_BWV_54_opening.wav/Bach_BWV_54_opening.wav.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/86/Bach_BWV_54_opening.wav/Bach_BWV_54_opening.wav.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/8/86/Bach_BWV_54_opening.wav" type="audio/wav" data-width="0" data-height="0" /></audio></span><figcaption>Bach BWV 54 opening bars</figcaption></figure> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:Bach_BWV_54,_opening_bars.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/36/Bach_BWV_54%2C_opening_bars.png/600px-Bach_BWV_54%2C_opening_bars.png" decoding="async" width="600" height="236" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/36/Bach_BWV_54%2C_opening_bars.png/900px-Bach_BWV_54%2C_opening_bars.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/36/Bach_BWV_54%2C_opening_bars.png/1200px-Bach_BWV_54%2C_opening_bars.png 2x" data-file-width="2468" data-file-height="971" /></a><figcaption>Bach BWV 54, opening bars</figcaption></figure> <p><a href="/wiki/Albert_Schweitzer" title="Albert Schweitzer">Albert Schweitzer</a> says that this aria "begins with an alarming chord of the seventh... It is meant to depict the horror of the curse upon sin that is threatened in the text".<sup id="cite_ref-FOOTNOTESchweitzer190553_59-0" class="reference"><a href="#cite_note-FOOTNOTESchweitzer190553-59"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup> Gillies Whittaker<sup id="cite_ref-FOOTNOTEWhittaker1959368_60-0" class="reference"><a href="#cite_note-FOOTNOTEWhittaker1959368-60"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup> points out that "The thirty-two <a href="/wiki/Basso_continuo" title="Basso continuo">continuo</a> quavers of the initial four bars support four consonances only, all the rest are dissonances, twelve of them being chords containing five different notes. It is a remarkable picture of desperate and unflinching resistance to the Christian to the fell powers of evil." </p><p>According to <a href="/wiki/H._C._Robbins_Landon" title="H. C. Robbins Landon">H. C. Robbins Landon</a>, the opening movement of <a href="/wiki/Joseph_Haydn" title="Joseph Haydn">Haydn</a>'s <a href="/wiki/Symphony_No._82" class="mw-redirect" title="Symphony No. 82">Symphony No. 82</a>, "a brilliant C major work in the best tradition" contains "dissonances of barbaric strength that are succeeded by delicate passages of Mozartean grace":<sup id="cite_ref-FOOTNOTELandon1955415_61-0" class="reference"><a href="#cite_note-FOOTNOTELandon1955415-61"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><span><audio id="mwe_player_15" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-durationhint="21" data-mwtitle="Haydn_Symphony_82_1st_movement_bars_51-63.wav" data-mwprovider="wikimediacommons" resource="/wiki/File:Haydn_Symphony_82_1st_movement_bars_51-63.wav"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/9b/Haydn_Symphony_82_1st_movement_bars_51-63.wav/Haydn_Symphony_82_1st_movement_bars_51-63.wav.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/9b/Haydn_Symphony_82_1st_movement_bars_51-63.wav/Haydn_Symphony_82_1st_movement_bars_51-63.wav.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/9/9b/Haydn_Symphony_82_1st_movement_bars_51-63.wav" type="audio/wav" data-width="0" data-height="0" /></audio></span><figcaption>Haydn Symphony 82 1st movement bars 51–63</figcaption></figure> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:Haydn_Symphony_82_1st_movement_bars_51-64.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Haydn_Symphony_82_1st_movement_bars_51-64.png/500px-Haydn_Symphony_82_1st_movement_bars_51-64.png" decoding="async" width="500" height="234" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Haydn_Symphony_82_1st_movement_bars_51-64.png/750px-Haydn_Symphony_82_1st_movement_bars_51-64.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/Haydn_Symphony_82_1st_movement_bars_51-64.png/1000px-Haydn_Symphony_82_1st_movement_bars_51-64.png 2x" data-file-width="1811" data-file-height="847" /></a><figcaption>Haydn Symphony 82 1st movement bars 51–64</figcaption></figure> <p>The Benedictus from <a href="/wiki/Michael_Haydn" title="Michael Haydn">Michael Haydn</a>'s Missa Quadragesimalis contains a passage of contrapuntal treatment consisting of various dissonances such as a <a href="/wiki/Ninth_chord" title="Ninth chord">ninth chord</a> without its fifth, an <a href="/wiki/Augmented_triad" title="Augmented triad">augmented triad</a>, a <a href="/wiki/Half-diminished_seventh_chord" title="Half-diminished seventh chord">half-diminished seventh chord</a>, and a <a href="/wiki/Minor_seventh_chord" title="Minor seventh chord">minor seventh chord</a>. </p> <style data-mw-deduplicate="TemplateStyles:r1224211176">.mw-parser-output .quotebox{background-color:#F9F9F9;border:1px solid #aaa;box-sizing:border-box;padding:10px;font-size:88%;max-width:100%}.mw-parser-output .quotebox.floatleft{margin:.5em 1.4em .8em 0}.mw-parser-output .quotebox.floatright{margin:.5em 0 .8em 1.4em}.mw-parser-output .quotebox.centered{overflow:hidden;position:relative;margin:.5em auto .8em auto}.mw-parser-output .quotebox.floatleft span,.mw-parser-output .quotebox.floatright span{font-style:inherit}.mw-parser-output .quotebox>blockquote{margin:0;padding:0;border-left:0;font-family:inherit;font-size:inherit}.mw-parser-output .quotebox-title{text-align:center;font-size:110%;font-weight:bold}.mw-parser-output .quotebox-quote>:first-child{margin-top:0}.mw-parser-output .quotebox-quote:last-child>:last-child{margin-bottom:0}.mw-parser-output .quotebox-quote.quoted:before{font-family:"Times New Roman",serif;font-weight:bold;font-size:large;color:gray;content:" “ ";vertical-align:-45%;line-height:0}.mw-parser-output .quotebox-quote.quoted:after{font-family:"Times New Roman",serif;font-weight:bold;font-size:large;color:gray;content:" ” ";line-height:0}.mw-parser-output .quotebox .left-aligned{text-align:left}.mw-parser-output .quotebox .right-aligned{text-align:right}.mw-parser-output .quotebox .center-aligned{text-align:center}.mw-parser-output .quotebox .quote-title,.mw-parser-output .quotebox .quotebox-quote{display:block}.mw-parser-output .quotebox cite{display:block;font-style:normal}@media screen and (max-width:640px){.mw-parser-output .quotebox{width:100%!important;margin:0 0 .8em!important;float:none!important}}</style><div class="quotebox pullquote floatright" style="width:40em; ;"> <blockquote class="quotebox-quote left-aligned" style=""> <p><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=2vD3wHrV6rk"><span class="plainlinks">Benedictus</span></a> on <a href="/wiki/YouTube_video_(identifier)" class="mw-redirect" title="YouTube video (identifier)">YouTube</a> from Michael Haydn's Missa Quadragesimalis, MH 552 performed by Purcell Choir and Orfeo Orchestra conducted by György Vashegyi </p> </blockquote> </div> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:Michael_Haydn_Missa_Quadragesimalis_Benedictus.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Michael_Haydn_Missa_Quadragesimalis_Benedictus.jpg/700px-Michael_Haydn_Missa_Quadragesimalis_Benedictus.jpg" decoding="async" width="700" height="920" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Michael_Haydn_Missa_Quadragesimalis_Benedictus.jpg/1050px-Michael_Haydn_Missa_Quadragesimalis_Benedictus.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/47/Michael_Haydn_Missa_Quadragesimalis_Benedictus.jpg/1400px-Michael_Haydn_Missa_Quadragesimalis_Benedictus.jpg 2x" data-file-width="2480" data-file-height="3260" /></a><figcaption>Benedictus from Michael Haydn's Missa Quadragesimalis</figcaption></figure> <p><a href="/wiki/Wolfgang_Amadeus_Mozart" title="Wolfgang Amadeus Mozart">Mozart's</a> music contains a number of quite radical experiments in dissonance. The following comes from his Adagio and Fugue in C minor, K. 546: </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><span><audio id="mwe_player_16" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-durationhint="17" data-mwtitle="Dissonance_in_Mozart's_Adagio_and_Fugue_in_C_minor,_K546.wav" data-mwprovider="wikimediacommons" resource="/wiki/File:Dissonance_in_Mozart%27s_Adagio_and_Fugue_in_C_minor,_K546.wav"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/d/d9/Dissonance_in_Mozart%27s_Adagio_and_Fugue_in_C_minor%2C_K546.wav/Dissonance_in_Mozart%27s_Adagio_and_Fugue_in_C_minor%2C_K546.wav.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/d/d9/Dissonance_in_Mozart%27s_Adagio_and_Fugue_in_C_minor%2C_K546.wav/Dissonance_in_Mozart%27s_Adagio_and_Fugue_in_C_minor%2C_K546.wav.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/d/d9/Dissonance_in_Mozart%27s_Adagio_and_Fugue_in_C_minor%2C_K546.wav" type="audio/wav" data-width="0" data-height="0" /></audio></span><figcaption>Dissonance in Mozart's Adagio and Fugue in C minor, K. 546</figcaption></figure> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:Dissonance_in_Mozart_counterpoint.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/71/Dissonance_in_Mozart_counterpoint.png/500px-Dissonance_in_Mozart_counterpoint.png" decoding="async" width="500" height="136" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/71/Dissonance_in_Mozart_counterpoint.png/750px-Dissonance_in_Mozart_counterpoint.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/71/Dissonance_in_Mozart_counterpoint.png/1000px-Dissonance_in_Mozart_counterpoint.png 2x" data-file-width="2128" data-file-height="580" /></a><figcaption>Dissonance in Mozart's Adagio and Fugue in C minor, K. 546</figcaption></figure><p> Mozart's <a href="/wiki/String_Quartet_No._19_(Mozart)" title="String Quartet No. 19 (Mozart)">Quartet in C major, K465</a> opens with an adagio introduction that gave the work its nickname, the "Dissonance Quartet":</p><figure class="mw-default-size" typeof="mw:File/Thumb"><span><audio id="mwe_player_17" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-durationhint="28" data-mwtitle="Mozart_Dissonance_Quartet_opening.wav" data-mwprovider="wikimediacommons" resource="/wiki/File:Mozart_Dissonance_Quartet_opening.wav"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/9a/Mozart_Dissonance_Quartet_opening.wav/Mozart_Dissonance_Quartet_opening.wav.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/9a/Mozart_Dissonance_Quartet_opening.wav/Mozart_Dissonance_Quartet_opening.wav.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/9/9a/Mozart_Dissonance_Quartet_opening.wav" type="audio/wav" data-width="0" data-height="0" /></audio></span><figcaption>Mozart Dissonance Quartet opening bars</figcaption></figure><figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:Mozart_Dissonance_Quartet_opening_bars.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Mozart_Dissonance_Quartet_opening_bars.png/600px-Mozart_Dissonance_Quartet_opening_bars.png" decoding="async" width="600" height="181" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Mozart_Dissonance_Quartet_opening_bars.png/900px-Mozart_Dissonance_Quartet_opening_bars.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Mozart_Dissonance_Quartet_opening_bars.png/1200px-Mozart_Dissonance_Quartet_opening_bars.png 2x" data-file-width="2283" data-file-height="690" /></a><figcaption>Mozart Dissonance Quartet opening bars.</figcaption></figure> <p>There are several passing dissonances in this adagio passage, for example on the first beat of bar 3. However the most striking effect here is implied, rather than sounded explicitly. The A flat in the first bar is contradicted by the high A natural in the second bar, but these notes do not sound together as a discord. (See also <a href="/wiki/False_relation" title="False relation">False relation</a>.) </p><p> An even more famous example from Mozart comes in a magical passage from the slow movement of his popular <a href="/wiki/Piano_Concerto_No._21_(Mozart)" title="Piano Concerto No. 21 (Mozart)">"Elvira Madigan"</a> Piano Concerto 21, K467, where the subtle, but quite explicit dissonances on the first beats of each bar are enhanced by exquisite orchestration:</p><figure class="mw-default-size" typeof="mw:File/Thumb"><span><audio id="mwe_player_18" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-durationhint="24" data-mwtitle="Mozart,_from_Piano_Concerto_No._21,_K465.wav" data-mwprovider="wikimediacommons" resource="/wiki/File:Mozart,_from_Piano_Concerto_No._21,_K465.wav"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/1/19/Mozart%2C_from_Piano_Concerto_No._21%2C_K465.wav/Mozart%2C_from_Piano_Concerto_No._21%2C_K465.wav.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/1/19/Mozart%2C_from_Piano_Concerto_No._21%2C_K465.wav/Mozart%2C_from_Piano_Concerto_No._21%2C_K465.wav.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/1/19/Mozart%2C_from_Piano_Concerto_No._21%2C_K465.wav" type="audio/wav" data-width="0" data-height="0" /></audio></span><figcaption>Mozart, from Piano Concerto No. 21, 2nd movement bars 12–17</figcaption></figure><figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:Mozart_Piano_Concerto_21,_2nd_movement_bars_12-17.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/55/Mozart_Piano_Concerto_21%2C_2nd_movement_bars_12-17.png/700px-Mozart_Piano_Concerto_21%2C_2nd_movement_bars_12-17.png" decoding="async" width="700" height="593" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/55/Mozart_Piano_Concerto_21%2C_2nd_movement_bars_12-17.png/1050px-Mozart_Piano_Concerto_21%2C_2nd_movement_bars_12-17.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/55/Mozart_Piano_Concerto_21%2C_2nd_movement_bars_12-17.png/1400px-Mozart_Piano_Concerto_21%2C_2nd_movement_bars_12-17.png 2x" data-file-width="2406" data-file-height="2039" /></a><figcaption>Mozart Piano Concerto 21, 2nd movement bars 12–17.</figcaption></figure> <p>Philip Radcliffe<sup id="cite_ref-FOOTNOTERadcliffe197852_62-0" class="reference"><a href="#cite_note-FOOTNOTERadcliffe197852-62"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup> speaks of this as "a remarkably poignant passage with surprisingly sharp dissonances". Radcliffe says that the dissonances here "have a vivid foretaste of Schumann and the way they gently melt into the major key is equally prophetic of Schubert." <a href="/wiki/Eric_Blom" title="Eric Blom">Eric Blom</a><sup id="cite_ref-FOOTNOTEBlom1935226_63-0" class="reference"><a href="#cite_note-FOOTNOTEBlom1935226-63"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup> says that this movement must have "made Mozart's hearers sit up by its daring modernities... There is a suppressed feeling of discomfort about it." </p><p>The finale of <a href="/wiki/Symphony_No._9_(Beethoven)" title="Symphony No. 9 (Beethoven)">Beethoven's Symphony No. 9</a> opens with a startling discord, consisting of a B flat inserted into a D minor chord: </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><span><audio id="mwe_player_19" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-durationhint="13" data-mwtitle="Beethoven_Symphony_No._9,_finale_opening_bars.wav" data-mwprovider="wikimediacommons" resource="/wiki/File:Beethoven_Symphony_No._9,_finale_opening_bars.wav"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/b4/Beethoven_Symphony_No._9%2C_finale_opening_bars.wav/Beethoven_Symphony_No._9%2C_finale_opening_bars.wav.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/b4/Beethoven_Symphony_No._9%2C_finale_opening_bars.wav/Beethoven_Symphony_No._9%2C_finale_opening_bars.wav.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/b/b4/Beethoven_Symphony_No._9%2C_finale_opening_bars.wav" type="audio/wav" data-width="0" data-height="0" /></audio></span><figcaption>Beethoven Symphony No. 9, finale opening bars</figcaption></figure> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:Grove_Schrekensfanfare_1.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ad/Grove_Schrekensfanfare_1.png/300px-Grove_Schrekensfanfare_1.png" decoding="async" width="300" height="168" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ad/Grove_Schrekensfanfare_1.png/450px-Grove_Schrekensfanfare_1.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ad/Grove_Schrekensfanfare_1.png/600px-Grove_Schrekensfanfare_1.png 2x" data-file-width="1314" data-file-height="734" /></a><figcaption>Beethoven Symphony No. 9, finale, opening bars</figcaption></figure> <p><a href="/wiki/Roger_Scruton" title="Roger Scruton">Roger Scruton</a><sup id="cite_ref-FOOTNOTEScruton2009101_64-0" class="reference"><a href="#cite_note-FOOTNOTEScruton2009101-64"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup> alludes to <a href="/wiki/Richard_Wagner" title="Richard Wagner">Wagner</a>'s description of this chord as introducing "a huge <i>Schreckensfanfare</i>—horror fanfare." When this passage returns later in the same movement (just before the voices enter) the sound is further complicated with the addition of a <a href="/wiki/Diminished_seventh_chord" title="Diminished seventh chord">diminished seventh chord</a>, creating, in Scruton's words "the most atrocious dissonance that Beethoven ever wrote, a <a href="/wiki/First_inversion" title="First inversion">first inversion</a> D-minor triad containing all the notes of the D <a href="/wiki/Minor_scale" title="Minor scale">minor harmonic scale</a>": </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><span><audio id="mwe_player_20" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-durationhint="13" data-mwtitle="Beethoven_Symphony_No._9,_finale_bars_208-215.wav" data-mwprovider="wikimediacommons" resource="/wiki/File:Beethoven_Symphony_No._9,_finale_bars_208-215.wav"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/8d/Beethoven_Symphony_No._9%2C_finale_bars_208-215.wav/Beethoven_Symphony_No._9%2C_finale_bars_208-215.wav.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/8d/Beethoven_Symphony_No._9%2C_finale_bars_208-215.wav/Beethoven_Symphony_No._9%2C_finale_bars_208-215.wav.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/8/8d/Beethoven_Symphony_No._9%2C_finale_bars_208-215.wav" type="audio/wav" data-width="0" data-height="0" /></audio></span><figcaption>Beethoven Symphony No. 9, finale bars 208ff</figcaption></figure> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:Grove_Schrekensfanfare_2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/16/Grove_Schrekensfanfare_2.png/300px-Grove_Schrekensfanfare_2.png" decoding="async" width="300" height="179" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/16/Grove_Schrekensfanfare_2.png/450px-Grove_Schrekensfanfare_2.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/16/Grove_Schrekensfanfare_2.png/600px-Grove_Schrekensfanfare_2.png 2x" data-file-width="1314" data-file-height="783" /></a><figcaption>Beethoven, Symphony No. 9, finale, bars 208-210</figcaption></figure> <p><a href="/wiki/Robert_Schumann" title="Robert Schumann">Robert Schumann</a>'s song "Auf einer Burg" from his cycle <i><a href="/wiki/Liederkreis,_Op._39_(Schumann)" title="Liederkreis, Op. 39 (Schumann)">Liederkreis</a></i>, Op. 39, climaxes on a striking dissonance in the fourteenth bar. As <a href="/wiki/Nicholas_Cook" title="Nicholas Cook">Nicholas Cook</a><sup id="cite_ref-FOOTNOTECook1987242_65-0" class="reference"><a href="#cite_note-FOOTNOTECook1987242-65"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup> points out, this is "the only chord in the whole song that Schumann marks with an accent". Cook goes on to stress that what makes this chord so effective is Schumann's placing of it in its musical context: "in what leads up to it and what comes of it". Cook explains further how the interweaving of lines in both piano and voice parts in the bars leading up to this chord (bars 9–14) "are set on a kind of collision course; hence the feeling of tension rising steadily to a breaking point". </p> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:Schumann_Auf_einer_Burg.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Schumann_Auf_einer_Burg.png/600px-Schumann_Auf_einer_Burg.png" decoding="async" width="600" height="882" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Schumann_Auf_einer_Burg.png/900px-Schumann_Auf_einer_Burg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Schumann_Auf_einer_Burg.png/1200px-Schumann_Auf_einer_Burg.png 2x" data-file-width="2392" data-file-height="3518" /></a><figcaption>Schumann Auf einer Burg. <a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=R-DmyUI1PsQ">Listen</a></figcaption></figure> <p>Wagner made increasing use of dissonance for dramatic effect as his style developed, particularly in his later operas. In the scene known as "Hagen's Watch" from the first act of <i><a href="/wiki/G%C3%B6tterd%C3%A4mmerung" title="Götterdämmerung">Götterdämmerung</a></i>, according to Scruton<sup id="cite_ref-FOOTNOTEScruton2016127_66-0" class="reference"><a href="#cite_note-FOOTNOTEScruton2016127-66"><span class="cite-bracket">[</span>65<span class="cite-bracket">]</span></a></sup> the music conveys a sense of "matchless brooding evil", and the excruciating dissonance in bars 9–10 below it constitute "a semitonal wail of desolation". </p> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:Wagner,_Hagen%27s_Watch_from_Act_1_of_Gotterdamerung.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/55/Wagner%2C_Hagen%27s_Watch_from_Act_1_of_Gotterdamerung.png/500px-Wagner%2C_Hagen%27s_Watch_from_Act_1_of_Gotterdamerung.png" decoding="async" width="500" height="440" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/55/Wagner%2C_Hagen%27s_Watch_from_Act_1_of_Gotterdamerung.png/750px-Wagner%2C_Hagen%27s_Watch_from_Act_1_of_Gotterdamerung.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/55/Wagner%2C_Hagen%27s_Watch_from_Act_1_of_Gotterdamerung.png/1000px-Wagner%2C_Hagen%27s_Watch_from_Act_1_of_Gotterdamerung.png 2x" data-file-width="1811" data-file-height="1592" /></a><figcaption>Wagner, Hagen's Watch from act 1 of <i>Götterdämmerung</i>. <a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=cixC4ovCWNI">Listen</a></figcaption></figure> <p>Another example of a cumulative build-up of dissonance from the early 20th century (1910) can be found in the Adagio that opens <a href="/wiki/Gustav_Mahler" title="Gustav Mahler">Gustav Mahler</a>'s unfinished <a href="/wiki/Symphony_No._10_(Mahler)" title="Symphony No. 10 (Mahler)">10th Symphony</a>: </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><span><audio id="mwe_player_21" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-durationhint="69" data-mwtitle="Mahler_Symphony_No._10_Adagio_bars_201-213.wav" data-mwprovider="wikimediacommons" resource="/wiki/File:Mahler_Symphony_No._10_Adagio_bars_201-213.wav"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/f/ff/Mahler_Symphony_No._10_Adagio_bars_201-213.wav/Mahler_Symphony_No._10_Adagio_bars_201-213.wav.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/f/ff/Mahler_Symphony_No._10_Adagio_bars_201-213.wav/Mahler_Symphony_No._10_Adagio_bars_201-213.wav.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/f/ff/Mahler_Symphony_No._10_Adagio_bars_201-213.wav" type="audio/wav" data-width="0" data-height="0" /></audio></span><figcaption>Mahler Symphony No. 10 Adagio bars 201–213</figcaption></figure> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:Mahler_10_opening_Adagio,_bars_201-213.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Mahler_10_opening_Adagio%2C_bars_201-213.png/500px-Mahler_10_opening_Adagio%2C_bars_201-213.png" decoding="async" width="500" height="393" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Mahler_10_opening_Adagio%2C_bars_201-213.png/750px-Mahler_10_opening_Adagio%2C_bars_201-213.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Mahler_10_opening_Adagio%2C_bars_201-213.png/1000px-Mahler_10_opening_Adagio%2C_bars_201-213.png 2x" data-file-width="2433" data-file-height="1911" /></a><figcaption>Mahler Symphony 10, opening Adagio, bars 201–213</figcaption></figure> <p><a href="/wiki/Richard_Taruskin" title="Richard Taruskin">Richard Taruskin</a><sup id="cite_ref-FOOTNOTETaruskin200523_67-0" class="reference"><a href="#cite_note-FOOTNOTETaruskin200523-67"><span class="cite-bracket">[</span>66<span class="cite-bracket">]</span></a></sup> parsed this chord (in bars 206 and 208) as a "diminished nineteenth ... a searingly dissonant dominant harmony containing nine different pitches. Who knows what <a href="/wiki/Guido_Adler" title="Guido Adler">Guido Adler</a>, for whom the second and Third Symphonies already contained 'unprecedented cacophonies', might have called it?" </p><p>One example of modernist dissonance comes from a work that received its first performance in 1913, three years after the <a href="/wiki/Mahler" class="mw-redirect" title="Mahler">Mahler</a>: </p> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:Stravinsky,_The_Rite_of_Spring,_Sacrificial_Dance.PNG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/en/thumb/a/ae/Stravinsky%2C_The_Rite_of_Spring%2C_Sacrificial_Dance.PNG/500px-Stravinsky%2C_The_Rite_of_Spring%2C_Sacrificial_Dance.PNG" decoding="async" width="500" height="124" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/a/ae/Stravinsky%2C_The_Rite_of_Spring%2C_Sacrificial_Dance.PNG/750px-Stravinsky%2C_The_Rite_of_Spring%2C_Sacrificial_Dance.PNG 1.5x, //upload.wikimedia.org/wikipedia/en/a/ae/Stravinsky%2C_The_Rite_of_Spring%2C_Sacrificial_Dance.PNG 2x" data-file-width="884" data-file-height="220" /></a><figcaption>Igor Stravinsky's <i>The Rite of Spring</i>, "Sacrificial Dance" excerpt<span class="mw-default-size" typeof="mw:File"><span><audio id="mwe_player_22" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-durationhint="4" data-mwtitle="Stravinsky,_The_Rite_of_Spring,_Sacrificial_Dance.mid" data-mwprovider="local"><source src="//upload.wikimedia.org/wikipedia/en/transcoded/0/0a/Stravinsky%2C_The_Rite_of_Spring%2C_Sacrificial_Dance.mid/Stravinsky%2C_The_Rite_of_Spring%2C_Sacrificial_Dance.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/en/transcoded/0/0a/Stravinsky%2C_The_Rite_of_Spring%2C_Sacrificial_Dance.mid/Stravinsky%2C_The_Rite_of_Spring%2C_Sacrificial_Dance.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/en/0/0a/Stravinsky%2C_The_Rite_of_Spring%2C_Sacrificial_Dance.mid" type="audio/midi" data-width="0" data-height="0" /></audio></span></span></figcaption></figure> <p>The West's progressive embrace of increasingly dissonant intervals occurred almost entirely within the context of <a href="/wiki/Harmonic_series_(music)" title="Harmonic series (music)">harmonic</a> <a href="/wiki/Timbre" title="Timbre">timbres</a>, as produced by vibrating strings and columns of air, on which the West's dominant musical instruments are based. By generalizing Helmholtz's notion of consonance (described above as the "coincidence of partials") to embrace non-harmonic timbres and their related tunings, consonance has recently been "emancipated" from harmonic timbres and their related tunings.<sup id="cite_ref-FOOTNOTEMilneSetharesPlamondon2007[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_68-0" class="reference"><a href="#cite_note-FOOTNOTEMilneSetharesPlamondon2007[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>-68"><span class="cite-bracket">[</span>67<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTEMilneSetharesPlamondon2008[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_69-0" class="reference"><a href="#cite_note-FOOTNOTEMilneSetharesPlamondon2008[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>-69"><span class="cite-bracket">[</span>68<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTESetharesMilneTiedjePrechtl2009[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_70-0" class="reference"><a href="#cite_note-FOOTNOTESetharesMilneTiedjePrechtl2009[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>-70"><span class="cite-bracket">[</span>69<span class="cite-bracket">]</span></a></sup> Using electronically controlled pseudo-harmonic timbres, rather than strictly harmonic acoustic timbres, provides tonality with new structural resources such as <a href="/wiki/Dynamic_tonality" title="Dynamic tonality">dynamic tonality</a>. These new resources provide musicians with an alternative to pursuing the musical uses of ever-higher partials of harmonic timbres and, in some people's minds, may resolve what <a href="/wiki/Arnold_Schoenberg" title="Arnold Schoenberg">Arnold Schoenberg</a> described as the "crisis of tonality".(<sup id="cite_ref-FOOTNOTEStein1953[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_71-0" class="reference"><a href="#cite_note-FOOTNOTEStein1953[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>-71"><span class="cite-bracket">[</span>70<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Neo-classic_harmonic_consonance_theory">Neo-classic harmonic consonance theory</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Consonance_and_dissonance&action=edit&section=10" title="Edit section: Neo-classic harmonic consonance theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Thirteenth_chord_CMA13(sharp11).png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Thirteenth_chord_CMA13%28sharp11%29.png/220px-Thirteenth_chord_CMA13%28sharp11%29.png" decoding="async" width="220" height="139" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Thirteenth_chord_CMA13%28sharp11%29.png/330px-Thirteenth_chord_CMA13%28sharp11%29.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Thirteenth_chord_CMA13%28sharp11%29.png/440px-Thirteenth_chord_CMA13%28sharp11%29.png 2x" data-file-width="539" data-file-height="340" /></a><figcaption><a href="/wiki/Thirteenth_chord" class="mw-redirect" title="Thirteenth chord">Thirteenth chord</a> constructed from notes of the Lydian mode<span class="mw-default-size" typeof="mw:File"><span><audio id="mwe_player_23" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-durationhint="5" data-mwtitle="Thirteenth_chord_CMA13(sharp11).mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/8/86/Thirteenth_chord_CMA13%28sharp11%29.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/86/Thirteenth_chord_CMA13%28sharp11%29.mid/Thirteenth_chord_CMA13%28sharp11%29.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/86/Thirteenth_chord_CMA13%28sharp11%29.mid/Thirteenth_chord_CMA13%28sharp11%29.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span></figcaption></figure> <p><a href="/wiki/George_Russell_(composer)" title="George Russell (composer)">George Russell</a>, in his 1953 <i><a href="/wiki/Lydian_Chromatic_Concept_of_Tonal_Organization" title="Lydian Chromatic Concept of Tonal Organization">Lydian Chromatic Concept of Tonal Organization</a></i>, presents a slightly different view from classical practice, one widely taken up in <a href="/wiki/Jazz" title="Jazz">Jazz</a>. He regards the tritone over the tonic as a rather consonant interval due to its derivation from the Lydian dominant thirteenth chord.<sup id="cite_ref-FOOTNOTERussell20081_72-0" class="reference"><a href="#cite_note-FOOTNOTERussell20081-72"><span class="cite-bracket">[</span>71<span class="cite-bracket">]</span></a></sup> </p><p>In effect, he returns to a <a href="#The_Middle_Ages">Medieval</a> consideration of "harmonic consonance"<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="There does not seem to have existed a medieval consideration of "harmonic consonance": what does that mean? (April 2020)">clarification needed</span></a></i>]</sup>: that intervals when not subject to <a href="/wiki/Octave_equivalence" class="mw-redirect" title="Octave equivalence">octave equivalence</a> (at least not by contraction) and correctly reproducing the <a href="/wiki/Just_intonation" title="Just intonation">mathematical ratios</a> of the <a href="/wiki/Harmonic_series_(music)" title="Harmonic series (music)">harmonic series</a><sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="How could just intonation justify a medieval conception? (April 2020)">clarification needed</span></a></i>]</sup> are truly non-dissonant. Thus the harmonic minor seventh, natural major ninth, <a href="/wiki/Quarter_tone" title="Quarter tone">half-sharp</a> (quarter tone) <a href="/wiki/Eleventh" title="Eleventh">eleventh</a> note (<a href="/wiki/Tempered_scale" class="mw-redirect" title="Tempered scale">untempered</a> <a href="/wiki/Tritone" title="Tritone">tritone</a>), <a href="/wiki/Quarter_tone" title="Quarter tone">half-flat</a> <a href="/wiki/Thirteenth" title="Thirteenth">thirteenth</a> note, and <a href="/wiki/Quarter_tone" title="Quarter tone">half-flat</a> <a href="/wiki/Fifteenth" title="Fifteenth">fifteenth</a> note must necessarily be consonant. </p><p>Most of these pitches exist only in a universe of <a href="/wiki/Microtonal_music" class="mw-redirect" title="Microtonal music">microtones</a> smaller than a <a href="/wiki/Semitone" title="Semitone">halfstep</a>; notice also that <a href="/wiki/Dominant_seventh_chord" title="Dominant seventh chord">we already freely take</a> the <a href="/wiki/Flat_(music)" title="Flat (music)">flat</a> (minor) seventh note for the <a href="/wiki/Just_intonation" title="Just intonation">just</a> <a href="/wiki/Harmonic_seventh" title="Harmonic seventh">seventh</a> of the <a href="/wiki/Harmonic_series_(music)" title="Harmonic series (music)">harmonic series</a> in <a href="/wiki/Chord_(music)" title="Chord (music)">chords</a>. Russell extends by approximation the virtual merits of harmonic consonance to the <a href="/wiki/Equal_temperament" title="Equal temperament">12TET</a> tuning system of <a href="/wiki/Jazz" title="Jazz">Jazz</a> and the 12-note octave of the <a href="/wiki/Piano" title="Piano">piano</a>, granting consonance to the <a href="/wiki/Sharp_(music)" title="Sharp (music)">sharp</a> <a href="/wiki/Eleventh" title="Eleventh">eleventh</a> note (approximating the harmonic <a href="/wiki/Eleventh" title="Eleventh">eleventh</a>), that accidental being the sole pitch difference between the <a href="/wiki/Major_scale" title="Major scale">major scale</a> and the <a href="/wiki/Lydian_mode" title="Lydian mode">Lydian mode</a>. </p><p>(In another sense, that <a href="/wiki/Acoustic_scale" title="Acoustic scale">Lydian</a> scale representing the provenance of the <a href="/wiki/Tonic_chord" class="mw-redirect" title="Tonic chord">tonic chord</a> (with major seventh and <a href="/wiki/Tritone" title="Tritone">sharp fourth</a>) replaces or supplements the <a href="/wiki/Mixolydian_mode" title="Mixolydian mode">Mixolydian scale</a> of the <a href="/wiki/Dominant_chord" class="mw-redirect" title="Dominant chord">dominant chord</a> (with minor seventh and <a href="/wiki/Degree_(music)" title="Degree (music)">natural fourth</a>) as the source from which to derive <a href="/wiki/Extended_chord" title="Extended chord">extended tertian harmony</a>.) </p><p>Dan Haerle, in his 1980 <i>The Jazz Language</i>,<sup id="cite_ref-FOOTNOTEHaerle19804_73-0" class="reference"><a href="#cite_note-FOOTNOTEHaerle19804-73"><span class="cite-bracket">[</span>72<span class="cite-bracket">]</span></a></sup> extends the same idea of harmonic consonance and intact <a href="/wiki/Octave" title="Octave">octave</a> displacement to alter <a href="/wiki/Paul_Hindemith" title="Paul Hindemith">Paul Hindemith</a>'s <i>Series 2</i> gradation table from <i>The Craft of Musical Composition</i>.<sup id="cite_ref-FOOTNOTEHindemith1937–701:[[Category:Wikipedia_articles_needing_page_number_citations_from_January_2015]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[Wikipedia:Citing_sources|<span_title="The_volume_number_is_not_sufficient_to_adequately_locate_a_table_in_the_book.&#32;(January_2015)">page&nbsp;needed</span>]]</i>&#93;</sup>_74-0" class="reference"><a href="#cite_note-FOOTNOTEHindemith1937–701:[[Category:Wikipedia_articles_needing_page_number_citations_from_January_2015]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[Wikipedia:Citing_sources|<span_title="The_volume_number_is_not_sufficient_to_adequately_locate_a_table_in_the_book.&#32;(January_2015)">page&nbsp;needed</span>]]</i>&#93;</sup>-74"><span class="cite-bracket">[</span>73<span class="cite-bracket">]</span></a></sup> In contradistinction to Hindemith, whose scale of consonance and dissonance is currently the <i>de facto</i> standard, Haerle places the minor ninth as the most dissonant interval of all, more dissonant than the minor second to which it was once considered by all as octave-equivalent. He also promotes the tritone from most-dissonant position to one just a little less consonant than the perfect fourth and perfect fifth. </p><p>For context: unstated in these theories is that musicians of the <a href="/wiki/Romantic_Era" class="mw-redirect" title="Romantic Era">Romantic Era</a> had effectively promoted the major ninth and minor seventh to a legitimacy of harmonic consonance as well, in their fabrics of 4-note chords.<sup id="cite_ref-FOOTNOTETymoczko2011106_75-0" class="reference"><a href="#cite_note-FOOTNOTETymoczko2011106-75"><span class="cite-bracket">[</span>74<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="21st_century">21st century</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Consonance_and_dissonance&action=edit&section=11" title="Edit section: 21st century"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Dynamic_tonality" title="Dynamic tonality">Dynamic tonality</a> offers a new perspective on consonance and dissonance by enabling a pseudo-just tuning and a pseudo-harmonic timbre to remain related<sup id="cite_ref-Relating_76-0" class="reference"><a href="#cite_note-Relating-76"><span class="cite-bracket">[</span>75<span class="cite-bracket">]</span></a></sup> despite real-time systematic changes to tuning, to timbre, or to both. This enables any musical interval in said tuning to be made more or less consonant in real time by aligning, more or less, the partials of said timbre with the notes of said tuning (or <i>vice versa</i>).<sup id="cite_ref-FOOTNOTEMilneSetharesPlamondon2007[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_68-1" class="reference"><a href="#cite_note-FOOTNOTEMilneSetharesPlamondon2007[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>-68"><span class="cite-bracket">[</span>67<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTEMilneSetharesPlamondon2008[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_69-1" class="reference"><a href="#cite_note-FOOTNOTEMilneSetharesPlamondon2008[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>-69"><span class="cite-bracket">[</span>68<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTESetharesMilneTiedjePrechtl2009[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_70-1" class="reference"><a href="#cite_note-FOOTNOTESetharesMilneTiedjePrechtl2009[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>-70"><span class="cite-bracket">[</span>69<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Consonance_and_dissonance&action=edit&section=12" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Factor_(chord)" title="Factor (chord)">Chord factor</a></li> <li><a href="/wiki/Dissonant_counterpoint" class="mw-redirect" title="Dissonant counterpoint">Dissonant counterpoint</a></li> <li><a href="/wiki/Limit_(music)" title="Limit (music)">Limit (music)</a></li> <li><a href="/wiki/Phonaesthetics" title="Phonaesthetics">Phonaesthetics</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Footnotes">Footnotes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Consonance_and_dissonance&action=edit&section=13" title="Edit section: Footnotes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <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-lower-alpha"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-57"><span class="mw-cite-backlink"><b><a href="#cite_ref-57">^</a></b></span> <span class="reference-text"> ... "the natural spacing of so-called dissonances is as seconds, as in the overtone series, rather than sevenths and ninths ... Groups spaced in seconds may be made to sound euphonious, particularly if played in conjunction with fundamental chord notes taken from lower in the same overtone series. Blends them together and explains them to the ear." — <a href="#CITEREFCowell1969">Cowell (1969)</a>, pp. 111–139</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Consonance_and_dissonance&action=edit&section=14" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist reflist-columns references-column-width" style="column-width: 15em;"> <ol class="references"> <li id="cite_note-FOOTNOTELahdelma_and_Eerola2020-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTELahdelma_and_Eerola2020_1-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFLahdelma_and_Eerola2020">Lahdelma and Eerola 2020</a>.</span> </li> <li id="cite_note-FOOTNOTESchoenberg197821-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTESchoenberg197821_2-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFSchoenberg1978">Schoenberg 1978</a>, p. 21.</span> </li> <li id="cite_note-FOOTNOTEHindemith194285-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEHindemith194285_3-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFHindemith1942">Hindemith 1942</a>, p. 85.</span> </li> <li id="cite_note-FOOTNOTERenard2016-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTERenard2016_4-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFRenard2016">Renard 2016</a>.</span> </li> <li id="cite_note-FOOTNOTEMyers1904315-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEMyers1904315_5-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFMyers1904">Myers 1904</a>, p. 315.</span> </li> <li id="cite_note-FOOTNOTEChristensen20027–8-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEChristensen20027–8_6-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFChristensen2002">Christensen 2002</a>, pp. 7–8.</span> </li> <li id="cite_note-FOOTNOTEStumpf1890127–219-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEStumpf1890127–219_7-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFStumpf1890">Stumpf 1890</a>, pp. 127–219.</span> </li> <li id="cite_note-FOOTNOTEButler_and_Green2002264-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEButler_and_Green2002264_8-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFButler_and_Green2002">Butler and Green 2002</a>, p. 264.</span> </li> <li id="cite_note-FOOTNOTEHelmholtz1954a[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>-9"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTEHelmholtz1954a[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_9-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTEHelmholtz1954a[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_9-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFHelmholtz1954a">Helmholtz 1954a</a>, p. <sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="This citation requires a reference to the specific page or range of pages in which the material appears. (July 2014)">page needed</span></a></i>]</sup>.</span> </li> <li id="cite_note-FOOTNOTERoederer1995165-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTERoederer1995165_10-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFRoederer1995">Roederer 1995</a>, p. 165.</span> </li> <li id="cite_note-FOOTNOTESethares1992-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTESethares1992_11-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFSethares1992">Sethares 1992</a>.</span> </li> <li id="cite_note-FOOTNOTESethares2005[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTESethares2005[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_12-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFSethares2005">Sethares 2005</a>, p. <sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="This citation requires a reference to the specific page or range of pages in which the material appears. (July 2014)">page needed</span></a></i>]</sup>.</span> </li> <li id="cite_note-FOOTNOTEMilneSetharesPlamondon2007-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEMilneSetharesPlamondon2007_13-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFMilneSetharesPlamondon2007">Milne, Sethares & Plamondon 2007</a>.</span> </li> <li id="cite_note-FOOTNOTEMilneSetharesPlamondon2008-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEMilneSetharesPlamondon2008_14-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFMilneSetharesPlamondon2008">Milne, Sethares & Plamondon 2008</a>.</span> </li> <li id="cite_note-FOOTNOTESetharesMilneTiedjePrechtl2009-15"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTESetharesMilneTiedjePrechtl2009_15-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTESetharesMilneTiedjePrechtl2009_15-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFSetharesMilneTiedjePrechtl2009">Sethares et al. 2009</a>.</span> </li> <li id="cite_note-FOOTNOTEKamien200841-16"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTEKamien200841_16-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTEKamien200841_16-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFKamien2008">Kamien 2008</a>, p. 41.</span> </li> <li id="cite_note-FOOTNOTESchuijer2008138-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTESchuijer2008138_17-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFSchuijer2008">Schuijer 2008</a>, p. 138.</span> </li> <li id="cite_note-FOOTNOTEVassilakis2005123-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEVassilakis2005123_18-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFVassilakis2005">Vassilakis 2005</a>, p. 123.</span> </li> <li id="cite_note-FOOTNOTEVassilakis2005121-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEVassilakis2005121_19-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFVassilakis2005">Vassilakis 2005</a>, p. 121.</span> </li> <li id="cite_note-FOOTNOTEHelmholtz1954b-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEHelmholtz1954b_20-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFHelmholtz1954b">Helmholtz 1954b</a>.</span> </li> <li id="cite_note-FOOTNOTELevelt_and_Plomp1964[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTELevelt_and_Plomp1964[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_21-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFLevelt_and_Plomp1964">Levelt and Plomp 1964</a>, p. <sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="This citation requires a reference to the specific page or range of pages in which the material appears. (July 2014)">page needed</span></a></i>]</sup>.</span> </li> <li id="cite_note-FOOTNOTEZwickerFlottorpStevens1957[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEZwickerFlottorpStevens1957[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_22-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFZwickerFlottorpStevens1957">Zwicker, Flottorp & Stevens 1957</a>, p. <sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="This citation requires a reference to the specific page or range of pages in which the material appears. (July 2014)">page needed</span></a></i>]</sup>.</span> </li> <li id="cite_note-FOOTNOTEZwicker1961[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEZwicker1961[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_23-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFZwicker1961">Zwicker 1961</a>, p. <sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="This citation requires a reference to the specific page or range of pages in which the material appears. (July 2014)">page needed</span></a></i>]</sup>.</span> </li> <li id="cite_note-FOOTNOTETerhardt1974[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>-24"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTETerhardt1974[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_24-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTETerhardt1974[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_24-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-FOOTNOTETerhardt1974[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_24-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-FOOTNOTETerhardt1974[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_24-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFTerhardt1974">Terhardt 1974</a>, p. <sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="This citation requires a reference to the specific page or range of pages in which the material appears. (July 2014)">page needed</span></a></i>]</sup>.</span> </li> <li id="cite_note-FOOTNOTEVassilakis2001[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEVassilakis2001[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_25-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFVassilakis2001">Vassilakis 2001</a>, p. <sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="This citation requires a reference to the specific page or range of pages in which the material appears. (July 2014)">page needed</span></a></i>]</sup>.</span> </li> <li id="cite_note-FOOTNOTEVassilakis2001-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEVassilakis2001_26-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFVassilakis2001">Vassilakis 2001</a>.</span> </li> <li id="cite_note-FOOTNOTEVassilakis2005-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEVassilakis2005_27-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFVassilakis2005">Vassilakis 2005</a>.</span> </li> <li id="cite_note-FOOTNOTEVassilakis_and_Fitz2007-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEVassilakis_and_Fitz2007_28-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFVassilakis_and_Fitz2007">Vassilakis and Fitz 2007</a>.</span> </li> <li id="cite_note-FOOTNOTEVassilakis2005121–123-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEVassilakis2005121–123_29-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFVassilakis2005">Vassilakis 2005</a>, pp. 121–123.</span> </li> <li id="cite_note-FOOTNOTEPhilip1966[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEPhilip1966[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_30-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFPhilip1966">Philip 1966</a>, p. <sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="This citation requires a reference to the specific page or range of pages in which the material appears. (July 2014)">page needed</span></a></i>]</sup>.</span> </li> <li id="cite_note-FOOTNOTESethares2005-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTESethares2005_31-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFSethares2005">Sethares 2005</a>.</span> </li> <li id="cite_note-FOOTNOTEGerson_and_Goldstein1978[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>-32"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEGerson_and_Goldstein1978[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_32-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFGerson_and_Goldstein1978">Gerson and Goldstein 1978</a>, p. <sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="This citation requires a reference to the specific page or range of pages in which the material appears. (July 2014)">page needed</span></a></i>]</sup>.</span> </li> <li id="cite_note-FOOTNOTERoederer1973145–149-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTERoederer1973145–149_33-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFRoederer1973">Roederer 1973</a>, pp. 145–149.</span> </li> <li id="cite_note-FOOTNOTESethares200543-34"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTESethares200543_34-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFSethares2005">Sethares 2005</a>, p. 43.</span> </li> <li id="cite_note-FOOTNOTERoederer1995106-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTERoederer1995106_35-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFRoederer1995">Roederer 1995</a>, p. 106.</span> </li> <li id="cite_note-FOOTNOTEPankovski_and_Pankovska_E.2017-36"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEPankovski_and_Pankovska_E.2017_36-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFPankovski_and_Pankovska_E.2017">Pankovski and Pankovska E. 2017</a>.</span> </li> <li id="cite_note-FOOTNOTESethares20051-37"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTESethares20051_37-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTESethares20051_37-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFSethares2005">Sethares 2005</a>, p. 1.</span> </li> <li id="cite_note-FOOTNOTEBenward_and_Saker200354-38"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEBenward_and_Saker200354_38-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFBenward_and_Saker2003">Benward and Saker 2003</a>, p. 54.</span> </li> <li id="cite_note-FOOTNOTEGouwens20093-39"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTEGouwens20093_39-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTEGouwens20093_39-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFGouwens2009">Gouwens 2009</a>, p. 3.</span> </li> <li id="cite_note-40"><span class="mw-cite-backlink"><b><a href="#cite_ref-40">^</a></b></span> <span class="reference-text">Quoted in <a href="#CITEREFForte1979">Forte 1979</a>, p. 136</span> </li> <li id="cite_note-FOOTNOTEKliewer1975290-41"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEKliewer1975290_41-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFKliewer1975">Kliewer 1975</a>, p. 290.</span> </li> <li id="cite_note-FOOTNOTEParncutt_and_Hair2011132-42"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTEParncutt_and_Hair2011132_42-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTEParncutt_and_Hair2011132_42-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-FOOTNOTEParncutt_and_Hair2011132_42-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFParncutt_and_Hair2011">Parncutt and Hair 2011</a>, 132.</span> </li> <li id="cite_note-FOOTNOTEPhilip1966123–124-43"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEPhilip1966123–124_43-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFPhilip1966">Philip 1966</a>, pp. 123–124.</span> </li> <li id="cite_note-FOOTNOTEAristoxenus1902188–206-44"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEAristoxenus1902188–206_44-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFAristoxenus1902">Aristoxenus 1902</a>, pp. 188–206.</span> </li> <li id="cite_note-FOOTNOTETenney198811–12-45"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTETenney198811–12_45-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFTenney1988">Tenney 1988</a>, pp. 11–12.</span> </li> <li id="cite_note-FOOTNOTEBoethiusn.d.f._13v.-46"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEBoethiusn.d.f._13v._46-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFBoethiusn.d.">Boethius n.d.</a>, f. 13v..</span> </li> <li id="cite_note-47"><span class="mw-cite-backlink"><b><a href="#cite_ref-47">^</a></b></span> <span class="reference-text"><a href="#CITEREFHucbaldn.d.">Hucbald n.d.</a>, p. 107; translated in <a href="#CITEREFBabb1978">Babb 1978</a>, p. 19</span> </li> <li id="cite_note-FOOTNOTEJohannes_de_Garlandia-48"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEJohannes_de_Garlandia_48-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFJohannes_de_Garlandia">Johannes de Garlandia</a>.</span> </li> <li id="cite_note-FOOTNOTEMachaut1926p._13,_Ballade_14,_"Je_ne_cuit_pas_qu'onques_a_creature",_mm._27–31-49"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEMachaut1926p._13,_Ballade_14,_"Je_ne_cuit_pas_qu'onques_a_creature",_mm._27–31_49-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFMachaut1926">Machaut 1926</a>, p. 13, Ballade 14, "Je ne cuit pas qu'onques a creature", mm. 27–31.</span> </li> <li id="cite_note-FOOTNOTESchulter1997a-50"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTESchulter1997a_50-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFSchulter1997a">Schulter 1997a</a>.</span> </li> <li id="cite_note-FOOTNOTESchulter1997b-51"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTESchulter1997b_51-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFSchulter1997b">Schulter 1997b</a>.</span> </li> <li id="cite_note-FOOTNOTESchulter1997c-52"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTESchulter1997c_52-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFSchulter1997c">Schulter 1997c</a>.</span> </li> <li id="cite_note-FOOTNOTESchulter1997d-53"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTESchulter1997d_53-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFSchulter1997d">Schulter 1997d</a>.</span> </li> <li id="cite_note-FOOTNOTEDahlhaus1990179-54"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEDahlhaus1990179_54-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFDahlhaus1990">Dahlhaus 1990</a>, p. 179.</span> </li> <li id="cite_note-FOOTNOTEGerbert17843:353-55"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEGerbert17843:353_55-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFGerbert1784">Gerbert 1784</a>, 3:353.</span> </li> <li id="cite_note-FOOTNOTESchoenberg1975258–264-56"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTESchoenberg1975258–264_56-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFSchoenberg1975">Schoenberg 1975</a>, pp. 258–264.</span> </li> <li id="cite_note-FOOTNOTEGardiner2013427-58"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEGardiner2013427_58-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFGardiner2013">Gardiner 2013</a>, 427.</span> </li> <li id="cite_note-FOOTNOTESchweitzer190553-59"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTESchweitzer190553_59-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFSchweitzer1905">Schweitzer 1905</a>, 53.</span> </li> <li id="cite_note-FOOTNOTEWhittaker1959368-60"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEWhittaker1959368_60-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFWhittaker1959">Whittaker 1959</a>, 368.</span> </li> <li id="cite_note-FOOTNOTELandon1955415-61"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTELandon1955415_61-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFLandon1955">Landon 1955</a>, p. 415.</span> </li> <li id="cite_note-FOOTNOTERadcliffe197852-62"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTERadcliffe197852_62-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFRadcliffe1978">Radcliffe 1978</a>, 52.</span> </li> <li id="cite_note-FOOTNOTEBlom1935226-63"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEBlom1935226_63-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFBlom1935">Blom 1935</a>, p. 226.</span> </li> <li id="cite_note-FOOTNOTEScruton2009101-64"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEScruton2009101_64-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFScruton2009">Scruton 2009</a>, 101.</span> </li> <li id="cite_note-FOOTNOTECook1987242-65"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTECook1987242_65-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFCook1987">Cook 1987</a>, p. 242.</span> </li> <li id="cite_note-FOOTNOTEScruton2016127-66"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEScruton2016127_66-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFScruton2016">Scruton 2016</a>, p. 127.</span> </li> <li id="cite_note-FOOTNOTETaruskin200523-67"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTETaruskin200523_67-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFTaruskin2005">Taruskin 2005</a>, 23.</span> </li> <li id="cite_note-FOOTNOTEMilneSetharesPlamondon2007[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>-68"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTEMilneSetharesPlamondon2007[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_68-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTEMilneSetharesPlamondon2007[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_68-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFMilneSetharesPlamondon2007">Milne, Sethares & Plamondon 2007</a>, p. <sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="This citation requires a reference to the specific page or range of pages in which the material appears. (July 2014)">page needed</span></a></i>]</sup>.</span> </li> <li id="cite_note-FOOTNOTEMilneSetharesPlamondon2008[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>-69"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTEMilneSetharesPlamondon2008[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_69-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTEMilneSetharesPlamondon2008[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_69-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFMilneSetharesPlamondon2008">Milne, Sethares & Plamondon 2008</a>, p. <sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="This citation requires a reference to the specific page or range of pages in which the material appears. (July 2014)">page needed</span></a></i>]</sup>.</span> </li> <li id="cite_note-FOOTNOTESetharesMilneTiedjePrechtl2009[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>-70"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTESetharesMilneTiedjePrechtl2009[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_70-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTESetharesMilneTiedjePrechtl2009[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_70-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFSetharesMilneTiedjePrechtl2009">Sethares et al. 2009</a>, p. <sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="This citation requires a reference to the specific page or range of pages in which the material appears. (July 2014)">page needed</span></a></i>]</sup>.</span> </li> <li id="cite_note-FOOTNOTEStein1953[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>-71"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEStein1953[[Category:Wikipedia_articles_needing_page_number_citations_from_July_2014]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[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_2014)">page&nbsp;needed</span>]]</i>&#93;</sup>_71-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFStein1953">Stein 1953</a>, p. <sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="This citation requires a reference to the specific page or range of pages in which the material appears. (July 2014)">page needed</span></a></i>]</sup>.</span> </li> <li id="cite_note-FOOTNOTERussell20081-72"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTERussell20081_72-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFRussell2008">Russell 2008</a>, p. 1.</span> </li> <li id="cite_note-FOOTNOTEHaerle19804-73"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEHaerle19804_73-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFHaerle1980">Haerle 1980</a>, p. 4.</span> </li> <li id="cite_note-FOOTNOTEHindemith1937–701:[[Category:Wikipedia_articles_needing_page_number_citations_from_January_2015]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[Wikipedia:Citing_sources|<span_title="The_volume_number_is_not_sufficient_to_adequately_locate_a_table_in_the_book.&#32;(January_2015)">page&nbsp;needed</span>]]</i>&#93;</sup>-74"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEHindemith1937–701:[[Category:Wikipedia_articles_needing_page_number_citations_from_January_2015]]<sup_class="noprint_Inline-Template_"_style="white-space:nowrap;">&#91;<i>[[Wikipedia:Citing_sources|<span_title="The_volume_number_is_not_sufficient_to_adequately_locate_a_table_in_the_book.&#32;(January_2015)">page&nbsp;needed</span>]]</i>&#93;</sup>_74-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFHindemith1937–70">Hindemith 1937–70</a>, 1:<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="The volume number is not sufficient to adequately locate a table in the book. (January 2015)">page needed</span></a></i>]</sup>.</span> </li> <li id="cite_note-FOOTNOTETymoczko2011106-75"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTETymoczko2011106_75-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFTymoczko2011">Tymoczko 2011</a>, p. 106.</span> </li> <li id="cite_note-Relating-76"><span class="mw-cite-backlink"><b><a href="#cite_ref-Relating_76-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSethares1993" class="citation journal cs1">Sethares, W.A. (1993). <a rel="nofollow" class="external text" href="https://sethares.engr.wisc.edu/consemi.html">"Relating Tuning and Timbre"</a>. <i>Experimental Musical Instruments</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Experimental+Musical+Instruments&rft.atitle=Relating+Tuning+and+Timbre&rft.date=1993&rft.aulast=Sethares&rft.aufirst=W.A.&rft_id=https%3A%2F%2Fsethares.engr.wisc.edu%2Fconsemi.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConsonance+and+dissonance" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Sources">Sources</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Consonance_and_dissonance&action=edit&section=15" title="Edit section: Sources"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin refbegin-columns references-column-width" style="column-width: 25em"> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAristoxenus1902" class="citation book cs1"><a href="/wiki/Aristoxenus" title="Aristoxenus">Aristoxenus</a> (1902). Macran, H. Stewart (ed.). <a rel="nofollow" class="external text" href="https://archive.org/details/harmonicsaristo00arisgoog"><i>Harmonics</i></a>. Oxford, UK: Clarendon Press – via archive.org.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Harmonics&rft.place=Oxford%2C+UK&rft.pub=Clarendon+Press&rft.date=1902&rft.au=Aristoxenus&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fharmonicsaristo00arisgoog&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConsonance+and+dissonance" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBabb1978" class="citation book cs1">Babb, Warren (1978). <i>Hucbald, Guido and John on Music</i>. New Haven, CT / London, UK: 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=Hucbald%2C+Guido+and+John+on+Music&rft.place=New+Haven%2C+CT+%2F+London%2C+UK&rft.pub=Yale+University+Press&rft.date=1978&rft.aulast=Babb&rft.aufirst=Warren&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConsonance+and+dissonance" class="Z3988"></span></li> <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="CITEREFBenward_and_Saker2003">Benward, Bruce, and Marilyn Saker (2003). <i>Music: In Theory and Practice</i>, Vol. I., seventh edition. New York: McGraw-Hill Higher Education. <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:r1238218222"><cite id="CITEREFBlom1935" class="citation book cs1"><a href="/wiki/Eric_Blom" title="Eric Blom">Blom, Eric</a> (1935). <i>Mozart</i>. London, UK: Dent.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mozart&rft.place=London%2C+UK&rft.pub=Dent&rft.date=1935&rft.aulast=Blom&rft.aufirst=Eric&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConsonance+and+dissonance" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFBoethiusn.d."><a href="/wiki/Boethius" title="Boethius">Boethius, Anicius</a> (n.d.). <i>De institutione musica</i>, vol. I, Ms Cambridge, Trinity College, R.15.22 (944), f. 13v. Electronic edition on <a rel="nofollow" class="external text" href="http://www.chmtl.indiana.edu/tml/6th-8th/BOEMUS1C_MCTC944.html">CHTML</a>.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFButler_and_Green2002">Butler, David, and Burdette Green (2002). "From Acoustics to <i>Tonpsychologie</i>". In <i>The Cambridge History of Western Music Theory</i>, edited by Thomas Christensen, 246–271. The Cambridge History of Music 3. 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/9780521623711" title="Special:BookSources/9780521623711">9780521623711</a>.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFChristensen2002">Christensen, Thomas (2002). "Introduction". <i>The Cambridge History of Western Music Theory</i>. Cambridge: 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/9780521623711" title="Special:BookSources/9780521623711">9780521623711</a>.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFCowell1969">Cowell, Henry (1969). <i>New Musical Resources</i>. New York: Something Else Press. [ISBN unspecified].</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFDahlhaus1990">Dahlhaus, Carl (1990). <i>Studies in the Origin of Harmonic Tonality</i>, translated by Robert O. Gjerdigan. 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/0-691-09135-8" title="Special:BookSources/0-691-09135-8">0-691-09135-8</a>.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCook1987" class="citation book cs1">Cook, Nicholas (1987). <i>A Guide to Musical Analysis</i>. London, UK: Dent.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Guide+to+Musical+Analysis&rft.place=London%2C+UK&rft.pub=Dent&rft.date=1987&rft.aulast=Cook&rft.aufirst=Nicholas&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConsonance+and+dissonance" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFForte1979">Forte, Allen. (1979). <i>Tonal Harmony in Concept and Practice</i>, third edition. 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London, UK: Allen Lane.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Music+in+the+Castle+of+Heaven%3A+A+portrait+of+Johann+Sebastian+Bach&rft.place=London%2C+UK&rft.pub=Allen+Lane&rft.date=2013&rft.aulast=Gardiner&rft.aufirst=John+Eliot&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConsonance+and+dissonance" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFGerbert1784">Gerbert, Martin (1784). <i>Scriptores ecclesiastici de musica sacra potissimum: ex variis Italiae, Galliae & Germaniae codicibus manuscriptis</i>, 3 vols. [n.p.]: Typis San-Blasianis. Reprinted, Hildesheim: G. Olms, 1963. [<i>GS</i>]</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFGerson_and_Goldstein1978">Gerson, A., and J. L. Goldstein (1978). "Evidence for a General Template in Central Optimal Processing for Pitch of Complex Tones". <i><a href="/wiki/Journal_of_the_Acoustical_Society_of_America" title="Journal of the Acoustical Society of America">Journal of the Acoustical Society of America</a></i> 63:498–510.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFGouwens2009">Gouwens, John (2009). <i>Composing for the Carillon</i>. Culver IN: Culver Academy Press.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFHaerle1980">Haerle, Dan (1980). <i>The Jazz Language: A Theory Text for Jazz Composition and Improvisation</i>. 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New York, NY: Dover Publications.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Die+Lehre+von+den+Tonempfindungen&rft.place=New+York%2C+NY&rft.edition=2nd+English+%2F+4th+German&rft.pub=Dover+Publications&rft.date=1954&rft.aulast=Helmholtz&rft.aufirst=H.L.F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConsonance+and+dissonance" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHindemith1937–70" class="citation book cs1 cs1-prop-year-range-abbreviated cs1-prop-foreign-lang-source"><a href="/wiki/Paul_Hindemith" title="Paul Hindemith">Hindemith, Paul</a> (1937–70). <i>Unterweisung im Tonsatz</i> (in German). Vol. 1–3. Mainz, DE: B. 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London, UK: Black.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=J.S.+Bach&rft.place=London%2C+UK&rft.pub=Black&rft.date=1905&rft.aulast=Schweitzer&rft.aufirst=A&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConsonance+and+dissonance" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSethares1992" class="citation journal cs1"><a href="/wiki/William_Sethares" title="William Sethares">Sethares, W.A.</a> (September 1992). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20100610092432/http://eceserv0.ece.wisc.edu/~sethares/consemi.html">"Relating tuning and timbre"</a>. <i>Experimental Musical Instruments</i>. Archived from <a rel="nofollow" class="external text" href="http://eceserv0.ece.wisc.edu/~sethares/consemi.html">the original</a> on 10 June 2010<span class="reference-accessdate">. Retrieved <span class="nowrap">29 July</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Experimental+Musical+Instruments&rft.atitle=Relating+tuning+and+timbre&rft.date=1992-09&rft.aulast=Sethares&rft.aufirst=W.A.&rft_id=http%3A%2F%2Feceserv0.ece.wisc.edu%2F~sethares%2Fconsemi.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConsonance+and+dissonance" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSethares2005" class="citation book cs1"><a href="/wiki/William_Sethares" title="William Sethares">Sethares, W.A.</a> (2005). <i>Tuning, Timbre, Spectrum, Scale</i> (2nd ed.). London, UK: Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1-85233-797-4" title="Special:BookSources/1-85233-797-4"><bdi>1-85233-797-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Tuning%2C+Timbre%2C+Spectrum%2C+Scale&rft.place=London%2C+UK&rft.edition=2nd&rft.pub=Springer&rft.date=2005&rft.isbn=1-85233-797-4&rft.aulast=Sethares&rft.aufirst=W.A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConsonance+and+dissonance" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSetharesMilneTiedjePrechtl2009" class="citation journal cs1"><a href="/wiki/William_Sethares" title="William Sethares">Sethares, W.A.</a>; Milne, Andrew; Tiedje, Stefan; Prechtl, Anthony & Plamondon, James (Summer 2009). "Spectral tools for dynamic tonality and audio morphing". <i><a href="/wiki/Computer_Music_Journal" title="Computer Music Journal">Computer Music Journal</a></i>. <b>33</b> (2): 71–84. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1162%2Fcomj.2009.33.2.71">10.1162/comj.2009.33.2.71</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Computer+Music+Journal&rft.atitle=Spectral+tools+for+dynamic+tonality+and+audio+morphing&rft.ssn=summer&rft.volume=33&rft.issue=2&rft.pages=71-84&rft.date=2009&rft_id=info%3Adoi%2F10.1162%2Fcomj.2009.33.2.71&rft.aulast=Sethares&rft.aufirst=W.A.&rft.au=Milne%2C+Andrew&rft.au=Tiedje%2C+Stefan&rft.au=Prechtl%2C+Anthony&rft.au=Plamondon%2C+James&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConsonance+and+dissonance" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFStein1953">Stein, Erwin. 1953. <i>Orpheus in New Guises</i>. London: Rockliff. Reprinted Westport, Conn.: Hyperion Press, 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/978-0-88355-765-5" title="Special:BookSources/978-0-88355-765-5">978-0-88355-765-5</a>.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFStumpf1890">Stumpf, Carl (1890). <i>Tonpsychologie</i>, vol. II. Leipzig: S. Hirzel. Reprinted Hilversum: F. Knuf, 1965.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTaruskin2005" class="citation book cs1 cs1-prop-long-vol">Taruskin, Richard (2005). <i>The Oxford History of Western Music</i>. Vol. 4: Music in the Early Twentieth Century. Oxford, UK and New York, NY: Oxford 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+Oxford+History+of+Western+Music&rft.place=Oxford%2C+UK+and+New+York%2C+NY&rft.pub=Oxford+University+Press&rft.date=2005&rft.aulast=Taruskin&rft.aufirst=Richard&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConsonance+and+dissonance" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFTenney1988">Tenney, James (1988). <i>A History of "Consonance" and "Dissonance"</i>. New York: Excelsior Music Publishing Company.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTerhardt1974" class="citation journal cs1">Terhardt, Ernst (1974). "On the Perception of Periodic Sound Fluctuations (Roughness)". <i>Acustica</i>. <b>30</b> (4): 201–13.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Acustica&rft.atitle=On+the+Perception+of+Periodic+Sound+Fluctuations+%28Roughness%29&rft.volume=30&rft.issue=4&rft.pages=201-13&rft.date=1974&rft.aulast=Terhardt&rft.aufirst=Ernst&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConsonance+and+dissonance" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFTymoczko2011">Tymoczko, Dimitri (2011). <i>A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice</i>. 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/978-0-19-533667-2" title="Special:BookSources/978-0-19-533667-2">978-0-19-533667-2</a>.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFVassilakis2001">Vassilakis, Panteleimon Nestor (2001). <a rel="nofollow" class="external text" href="http://www.acousticslab.org/papers/diss.htm"><i>Perceptual and Physical Properties of Amplitude Fluctuation and their Musical Significance</i></a>. Doctoral dissertation. University of California, Los Angeles.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFVassilakis2005">Vassilakis, Panteleimon Nestor (2005). <a rel="nofollow" class="external text" href="http://www.acousticslab.org/papers/SRE12.htm">"Auditory Roughness as Means of Musical Expression"</a>. <i>Selected Reports in Ethnomusicology</i>, 12: 119–144.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFVassilakis_and_Fitz2007">Vassilakis, Panteleimon Nestor, and K. Fitz (2007). <a rel="nofollow" class="external text" href="http://musicalgorithms.ewu.edu/algorithms/roughness.html">SRA: A web-based research tool for spectral and roughness analysis of sound signals</a>. Supported by a Northwest Academic Computing Consortium grant to J. Middleton, Eastern Washington University.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFWhittaker1959">Whittaker, W.G. (1959). <i>The Cantatas of Johann Sebastian Bach</i>. London and New York: Oxford University Press.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFZwicker1961" class="citation journal cs1"><a href="/wiki/Eberhard_Zwicker" title="Eberhard Zwicker">Zwicker, Eberhard</a> (May 1961). "Subdivision of the Audible Frequency into Critical Bands". <i><a href="/wiki/Journal_of_the_Acoustical_Society_of_America" title="Journal of the Acoustical Society of America">Journal of the Acoustical Society of America</a></i>. <b>33</b> (2): 248–249. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1961ASAJ...33..248Z">1961ASAJ...33..248Z</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1121%2F1.1908630">10.1121/1.1908630</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+the+Acoustical+Society+of+America&rft.atitle=Subdivision+of+the+Audible+Frequency+into+Critical+Bands&rft.volume=33&rft.issue=2&rft.pages=248-249&rft.date=1961-05&rft_id=info%3Adoi%2F10.1121%2F1.1908630&rft_id=info%3Abibcode%2F1961ASAJ...33..248Z&rft.aulast=Zwicker&rft.aufirst=Eberhard&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConsonance+and+dissonance" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFZwickerFlottorpStevens1957" class="citation journal cs1">Zwicker, Eberhard; Flottorp, G.; Stevens, S. S. (1957). "Critical band-width in loudness summation". <i><a href="/wiki/Journal_of_the_Acoustical_Society_of_America" title="Journal of the Acoustical Society of America">Journal of the Acoustical Society of America</a></i>. <b>29</b> (5): 548–557. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1957ASAJ...29..548Z">1957ASAJ...29..548Z</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1121%2F1.1908963">10.1121/1.1908963</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+the+Acoustical+Society+of+America&rft.atitle=Critical+band-width+in+loudness+summation&rft.volume=29&rft.issue=5&rft.pages=548-557&rft.date=1957&rft_id=info%3Adoi%2F10.1121%2F1.1908963&rft_id=info%3Abibcode%2F1957ASAJ...29..548Z&rft.aulast=Zwicker&rft.aufirst=Eberhard&rft.au=Flottorp%2C+G.&rft.au=Stevens%2C+S.+S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConsonance+and+dissonance" class="Z3988"></span></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Consonance_and_dissonance&action=edit&section=16" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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: 25em;"> <ul><li>Anon. (1826). [Untitled]. <i>The Harmonicon: A Journal of Music</i> 4:<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="This citation requires a reference to the specific page or range of pages in which the material appears. (May 2017)">page needed</span></a></i>]</sup></li> <li>Burns, Edward M. (1999). "Intervals, Scales, and Tuning", in <i>The Psychology of Music</i> second edition. Deutsch, Diana, ed. San Diego: Academic 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/0-12-213564-4" title="Special:BookSources/0-12-213564-4">0-12-213564-4</a>.</li> <li><a href="/wiki/Jean-Jacques_Eigeldinger" title="Jean-Jacques Eigeldinger">Eigeldinger, Jean-Jacques</a>, <a href="/wiki/Roy_Howat" title="Roy Howat">Roy Howat</a>, and Naomi Shohet. 1988. <i>Chopin: Pianist and Teacher: As Seen by His Pupils</i>. 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/0-521-36709-3" title="Special:BookSources/0-521-36709-3">0-521-36709-3</a>.</li> <li><a href="/wiki/Oswald_Jonas" title="Oswald Jonas">Jonas, Oswald</a> (1982). <i>Introduction to the Theory of Heinrich Schenker: The Nature of the Musical Work of Art</i>, translated by John Rothgeb. New York: Longman; London: Collier-Macmillan. <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/0-582-28227-6" title="Special:BookSources/0-582-28227-6">0-582-28227-6</a>. [Translated from <i>Einführung in die Lehre Heinrich Schenkers, das Wesen des musikalischen Kunstwerkes</i>, second edition. Vienna: Universal Edition, 1972. First edition as <i>Das Wesen des musikalischen Kunstwerks: Eine Einführung in die Lehre Heinrich Schenkers</i>. Vienna: Saturn-Verlag, 1934.]</li> <li>Kempers, Karel Philippus Bernet, and M. G. Bakker. 1949. <i>Italian Opera</i>, from the Dutch by M. M. Kessler-Button. Symphonia Books. Stockholm: Continental Book Co.</li> <li><a href="/wiki/Knud_Jeppesen" title="Knud Jeppesen">Jeppesen, Knud</a> (1946). <i>The Style of Palestrina and the Dissonance</i>, second revised and enlarged edition, translated by Margaret Hamerik with linguistic alterations and additions by Annie I. Fausboll. Copenhagen: E. Munksgaard; Oxford: Oxford University Press. Reprinted, with corrections, New York: Dover Publications, 1970. <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/9780486223865" title="Special:BookSources/9780486223865">9780486223865</a>.</li> <li>Rice, Timothy (2004). <i>Music in Bulgaria</i>. 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/0-19-514148-2" title="Special:BookSources/0-19-514148-2">0-19-514148-2</a>.</li> <li><a href="/wiki/William_Sethares" title="William Sethares">Sethares, William A.</a> (1993). "Local Consonance and the Relationship between Timbre and Scale". <i><a href="/wiki/Journal_of_the_Acoustical_Society_of_America" title="Journal of the Acoustical Society of America">Journal of the Acoustical Society of America</a></i>, 94(1): 1218. (<a rel="nofollow" class="external text" href="http://eceserv0.ece.wisc.edu/~sethares/papers/consance.html">A non-technical version</a> of the article)</li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Consonance_and_dissonance&action=edit&section=17" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985"><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox 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<span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Consonance_and_dissonance" class="extiw" title="commons:Category:Consonance and dissonance">Consonance and dissonance</a></span>.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20160303203113/http://www.sohl.com/mt/maptone.html">Atlas of Consonance</a></li> <li><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=lsapaauFoUQ">Octave Frequency Sweep, Consonance/Dissonance</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20050313133506/http://dactyl.som.ohio-state.edu/Music829B/notes.html">Consonance and Dissonance—Index to Notes</a> by David Huron at Ohio State University School of Music <ul><li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20050411060050/http://dactyl.som.ohio-state.edu/Music829B/bibliography.html">Bibliography of Consonance and Dissonance</a></li></ul></li> <li><a rel="nofollow" class="external text" href="http://www.johnsankey.ca/consonance.html">The Keyboard Tuning of Domenico Scarlatti</a></li> <li><a rel="nofollow" class="external text" href="http://www.lucytune.com/midi_and_keyboard/dissonance.html">index of Dissonance for any musical scales in LucyTuning and meantone-type tunings</a></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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a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Consonance_and_dissonance" title="Template:Consonance and dissonance"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Consonance_and_dissonance" title="Template talk:Consonance and dissonance"><abbr title="Discuss this 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note">Musical note</a></li> <li><a href="/wiki/Nonchord_tone" title="Nonchord tone">Nonchord tone</a> <ul><li><a href="/wiki/Cambiata" title="Cambiata">Cambiata</a></li> <li><a href="/wiki/Changing_tones" title="Changing tones">Changing tones</a></li> <li><a href="/wiki/Pedal_point" title="Pedal point">Pedal point</a></li> <li><a href="/wiki/Preparation_(music)" title="Preparation (music)">Preparation</a></li> <li><a href="/wiki/Resolution_(music)" title="Resolution (music)">Resolution</a></li></ul></li> <li><a href="/wiki/Harmonic_series_(music)" title="Harmonic series (music)">Spectra</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="3" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Triadic_harmonic_entropy.png/80px-Triadic_harmonic_entropy.png" decoding="async" width="80" height="54" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Triadic_harmonic_entropy.png/120px-Triadic_harmonic_entropy.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Triadic_harmonic_entropy.png/160px-Triadic_harmonic_entropy.png 2x" data-file-width="8814" data-file-height="5932" /></span></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Consonances</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Unison" title="Unison">Unison</a></li> <li><a href="/wiki/Minor_third" title="Minor third">Minor third</a></li> <li><a href="/wiki/Major_third" title="Major third">Major third</a></li> <li><a href="/wiki/Perfect_fourth" title="Perfect fourth">Perfect fourth</a></li> <li><a href="/wiki/Perfect_fifth" title="Perfect fifth">Perfect fifth</a></li> <li><a href="/wiki/Minor_sixth" title="Minor sixth">Minor sixth</a></li> <li><a href="/wiki/Major_sixth" title="Major sixth">Major sixth</a></li> <li><a href="/wiki/Octave" title="Octave">Octave</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Dissonances</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Minor_second" class="mw-redirect" title="Minor second">Minor second</a></li> <li><a href="/wiki/Major_second" title="Major second">Major second</a></li> <li><a href="/wiki/Tritone" title="Tritone">Tritone</a></li> <li><a href="/wiki/Minor_seventh" title="Minor seventh">Minor seventh</a></li> <li><a href="/wiki/Major_seventh" title="Major seventh">Major seventh</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="3"><div> <ul><li><a href="/wiki/List_of_pitch_intervals" title="List of pitch intervals">List of musical intervals</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Music_psychology" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Music_psychology" title="Template:Music psychology"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Music_psychology" title="Template talk:Music psychology"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Music_psychology" title="Special:EditPage/Template:Music psychology"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Music_psychology" style="font-size:114%;margin:0 4em"><a href="/wiki/Music_psychology" title="Music psychology">Music psychology</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Areas</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Biomusicology" title="Biomusicology">Biomusicology</a></li> <li><a href="/wiki/Cognitive_musicology" title="Cognitive musicology">Cognitive musicology</a></li> <li><a href="/wiki/Neuroscience_of_music" title="Neuroscience of music">Cognitive neuroscience of music</a></li> <li><a href="/wiki/Culture_in_music_cognition" title="Culture in music cognition">Culture in music cognition</a></li> <li><a href="/wiki/Evolutionary_musicology" title="Evolutionary musicology">Evolutionary musicology</a></li> <li><a href="/wiki/Psychoacoustics" title="Psychoacoustics">Psychoacoustics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Category:Music_psychology" title="Category:Music psychology">Topics</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Absolute_pitch" title="Absolute pitch">Absolute pitch</a></li> <li><a href="/wiki/Auditory_illusion" title="Auditory illusion">Auditory illusion</a></li> <li><a href="/wiki/Auditory_imagery" title="Auditory imagery">Auditory imagery</a></li> <li><a href="/wiki/Background_music" title="Background music">Background music</a></li> <li><a class="mw-selflink selflink">Consonance and dissonance</a></li> <li><a href="/wiki/Deutsch%27s_scale_illusion" title="Deutsch's scale illusion">Deutsch's scale illusion</a></li> <li><a href="/wiki/Earworm" title="Earworm">Earworm</a></li> <li><a href="/wiki/Embodied_music_cognition" title="Embodied music cognition">Embodied music cognition</a></li> <li><a href="/wiki/Entrainment_(biomusicology)" title="Entrainment (biomusicology)">Entrainment</a></li> <li><a href="/wiki/Exercise_and_music" title="Exercise and music">Exercise and music</a></li> <li><a href="/wiki/Eye_movement_in_music_reading" title="Eye movement in music reading">Eye movement in music reading</a></li> <li><a href="/wiki/Franssen_effect" title="Franssen effect">Franssen effect</a></li> <li><a href="/wiki/Generative_theory_of_tonal_music" title="Generative theory of tonal music">Generative theory of tonal music</a></li> <li><a href="/wiki/Glissando_illusion" title="Glissando illusion">Glissando illusion</a></li> <li><a href="/wiki/Hedonic_music_consumption_model" title="Hedonic music consumption model">Hedonic music consumption model</a></li> <li><a href="/wiki/Illusory_continuity_of_tones" title="Illusory continuity of tones">Illusory continuity of tones</a></li> <li><a href="/wiki/Levitin_effect" title="Levitin effect">Levitin effect</a></li> <li><a href="/wiki/Lipps%E2%80%93Meyer_law" title="Lipps–Meyer law">Lipps–Meyer law</a></li> <li><a href="/wiki/Melodic_expectation" title="Melodic expectation">Melodic expectation</a></li> <li><a href="/wiki/Melodic_fission" title="Melodic fission">Melodic fission</a></li> <li><a href="/wiki/Mozart_effect" title="Mozart effect">Mozart effect</a></li> <li><a href="/wiki/Music_and_emotion" title="Music and emotion">Music and emotion</a></li> <li><a href="/wiki/Dance" title="Dance">Music and movement</a></li> <li><a href="/wiki/Music_in_psychological_operations" title="Music in psychological operations">Music in psychological operations</a></li> <li><a href="/wiki/Psychology_of_music_preference" title="Psychology of music preference">Music preference</a></li> <li><a href="/wiki/Music-related_memory" title="Music-related memory">Music-related memory</a></li> <li><a href="/wiki/Musical_gesture" title="Musical gesture">Musical gesture</a></li> <li><a href="/wiki/Musical_semantics" title="Musical semantics">Musical semantics</a></li> <li><a href="/wiki/Musical_syntax" title="Musical syntax">Musical syntax</a></li> <li><a href="/wiki/Octave_illusion" title="Octave illusion">Octave illusion</a></li> <li><a href="/wiki/Relative_pitch" title="Relative pitch">Relative pitch</a></li> <li><a href="/wiki/Sharawadji_effect" title="Sharawadji effect">Sharawadji effect</a></li> <li><a href="/wiki/Shepard_tone" title="Shepard tone">Shepard tone</a></li> <li><a href="/wiki/Speech-to-song_illusion" title="Speech-to-song illusion">Speech-to-song illusion</a></li> <li><a href="/wiki/Temporal_dynamics_of_music_and_language" title="Temporal dynamics of music and language">Temporal dynamics of music and language</a></li> <li><a href="/wiki/Tonal_memory" title="Tonal memory">Tonal memory</a></li> <li><a href="/wiki/Tritone_paradox" title="Tritone paradox">Tritone paradox</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Music-specific_disorders" title="Music-specific disorders">Disorders</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Amusia" title="Amusia">Amusia</a></li> <li><a href="/wiki/Auditory_arrhythmia" title="Auditory arrhythmia">Auditory arrhythmia</a></li> <li><a href="/wiki/Beat_deafness" title="Beat deafness">Beat deafness</a></li> <li><a href="/wiki/Musical_hallucinations" title="Musical hallucinations">Musical hallucinations</a></li> <li><a href="/wiki/Focal_dystonia" title="Focal dystonia">Musician's dystonia</a></li> <li><a href="/wiki/Music-specific_disorders" title="Music-specific disorders">Music-specific disorders</a></li> <li><a href="/wiki/Tone_deafness" class="mw-redirect" title="Tone deafness">Tone deafness</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related fields</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Aesthetics_of_music" title="Aesthetics of music">Aesthetics of music</a></li> <li><a href="/wiki/Bioacoustics" title="Bioacoustics">Bioacoustics</a></li> <li><a href="/wiki/Ethnomusicology" title="Ethnomusicology">Ethnomusicology</a></li> <li><a href="/wiki/Hearing" title="Hearing">Hearing</a></li> <li><a href="/wiki/Melodic_intonation_therapy" class="mw-redirect" title="Melodic intonation therapy">Melodic intonation therapy</a></li> <li><a href="/wiki/Music_education" title="Music education">Music education</a></li> <li><a href="/wiki/Music_therapy" title="Music therapy">Music therapy</a></li> <li><a href="/wiki/Musical_acoustics" title="Musical acoustics">Musical acoustics</a></li> <li><a href="/wiki/Musicology" title="Musicology">Musicology</a></li> <li><a href="/wiki/Music_therapy" title="Music therapy">Neurologic music therapy</a></li> <li><a href="/wiki/Neuronal_encoding_of_sound" class="mw-redirect" title="Neuronal encoding of sound">Neuronal encoding of sound</a></li> <li><a href="/wiki/Performance_science" title="Performance science">Performance science</a></li> <li><a href="/wiki/Philosophy_of_music" title="Philosophy of music">Philosophy of music</a></li> <li><a href="/wiki/Psychoanalysis_and_music" title="Psychoanalysis and music">Psychoanalysis and music</a></li> <li><a href="/wiki/Sociomusicology" title="Sociomusicology">Sociomusicology</a></li> <li><a href="/wiki/Systematic_musicology" title="Systematic musicology">Systematic musicology</a></li> <li><a href="/wiki/Zoomusicology" title="Zoomusicology">Zoomusicology</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Category:Music_psychologists" title="Category:Music psychologists">Researchers</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Jamshed_Bharucha" title="Jamshed Bharucha">Jamshed Bharucha</a></li> <li><a href="/wiki/Lola_Cuddy" title="Lola Cuddy">Lola Cuddy</a></li> <li><a href="/wiki/Robert_Cutietta" title="Robert Cutietta">Robert Cutietta</a></li> <li><a href="/wiki/Jane_W._Davidson" title="Jane W. Davidson">Jane W. Davidson</a></li> <li><a href="/wiki/Ir%C3%A8ne_Deli%C3%A8ge" title="Irène Deliège">Irène Deliège</a></li> <li><a href="/wiki/Diana_Deutsch" title="Diana Deutsch">Diana Deutsch</a></li> <li><a href="/wiki/Tuomas_Eerola" title="Tuomas Eerola">Tuomas Eerola</a></li> <li><a href="/wiki/Henkjan_Honing" title="Henkjan Honing">Henkjan Honing</a></li> <li><a href="/wiki/David_Huron" title="David Huron">David Huron</a></li> <li><a href="/wiki/Nina_Kraus" title="Nina Kraus">Nina Kraus</a></li> <li><a href="/wiki/Carol_L._Krumhansl" title="Carol L. Krumhansl">Carol L. Krumhansl</a></li> <li><a href="/wiki/Fred_Lerdahl" title="Fred Lerdahl">Fred Lerdahl</a></li> <li><a href="/wiki/Daniel_Levitin" title="Daniel Levitin">Daniel Levitin</a></li> <li><a href="/wiki/Leonard_B._Meyer" title="Leonard B. Meyer">Leonard B. Meyer</a></li> <li><a href="/wiki/Max_Friedrich_Meyer" title="Max Friedrich Meyer">Max Friedrich Meyer</a></li> <li><a href="/wiki/James_Mursell" title="James Mursell">James Mursell</a></li> <li><a href="/wiki/Richard_Parncutt" title="Richard Parncutt">Richard Parncutt</a></li> <li><a href="/wiki/Oliver_Sacks" title="Oliver Sacks">Oliver Sacks</a></li> <li><a href="/wiki/Carl_Seashore" title="Carl Seashore">Carl Seashore</a></li> <li><a href="/wiki/Max_Schoen" title="Max Schoen">Max Schoen</a></li> <li><a href="/wiki/Roger_Shepard" title="Roger Shepard">Roger Shepard</a></li> <li><a href="/wiki/John_Sloboda" title="John Sloboda">John Sloboda</a></li> <li><a href="/wiki/Carl_Stumpf" title="Carl Stumpf">Carl Stumpf</a></li> <li><a href="/wiki/William_Forde_Thompson" title="William Forde Thompson">William Forde Thompson</a></li> <li><a href="/wiki/Sandra_Trehub" title="Sandra Trehub">Sandra Trehub</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Books and journals</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/Music_Perception" title="Music Perception">Music Perception</a></i></li> <li><i><a href="/wiki/Musicae_Scientiae_(journal)" title="Musicae Scientiae (journal)">Musicae Scientiae (journal)</a></i></li> <li><i><a href="/wiki/Musicophilia" title="Musicophilia">Musicophilia</a></i></li> <li><i><a href="/wiki/Music,_Thought,_and_Feeling" title="Music, Thought, and Feeling">Music, Thought, and Feeling</a></i></li> <li><i><a href="/wiki/Psychology_of_Music_(journal)" class="mw-redirect" title="Psychology of Music (journal)">Psychology of Music (journal)</a></i></li> <li><i><a href="/wiki/The_World_in_Six_Songs" title="The World in Six Songs">The World in Six Songs</a></i></li> <li><i><a href="/wiki/This_Is_Your_Brain_on_Music" title="This Is Your Brain on Music">This Is Your Brain on Music</a></i></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Musical_tunings" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Musical_tuning" title="Template:Musical tuning"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Musical_tuning" title="Template talk:Musical tuning"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Musical_tuning" title="Special:EditPage/Template:Musical tuning"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Musical_tunings" style="font-size:114%;margin:0 4em"><a href="/wiki/Musical_tuning" title="Musical tuning">Musical tunings</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Measurement</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Pitch_(music)" title="Pitch (music)">Pitch</a></li> <li><a href="/wiki/Cent_(music)" title="Cent (music)">Cent</a></li> <li><a href="/wiki/Millioctave" title="Millioctave">Millioctave</a></li> <li><a href="/wiki/Savart" title="Savart">Savart</a></li> <li><a href="/wiki/Interval_(music)" title="Interval (music)">Interval</a></li> <li><a href="/wiki/Interval_ratio" title="Interval ratio">Interval ratio</a></li> <li><a href="/wiki/Pitch_class" title="Pitch class">Pitch class</a></li> <li><a class="mw-selflink selflink">Consonance and dissonance</a></li> <li><a href="/wiki/List_of_pitch_intervals" title="List of pitch intervals">List of musical intervals</a></li> <li><a href="/wiki/List_of_intervals_in_5-limit_just_intonation" title="List of intervals in 5-limit just intonation">List of intervals in 5-limit just intonation</a></li> <li><a href="/wiki/List_of_meantone_intervals" title="List of meantone intervals">List of meantone intervals</a></li> <li><a href="/wiki/Microtonal_music" class="mw-redirect" title="Microtonal music">Microtone</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Just_intonation" title="Just intonation">Just intonation</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Euler%E2%80%93Fokker_genus" title="Euler–Fokker genus">Euler–Fokker genus</a></li> <li><a href="/wiki/Harmonic_scale" title="Harmonic scale">Harmonic scale</a></li> <li><a href="/wiki/Harry_Partch%27s_43-tone_scale" title="Harry Partch's 43-tone scale">Harry Partch's 43-tone scale</a></li> <li><a href="/wiki/Hexany" title="Hexany">Hexany</a></li> <li><a href="/wiki/Limit_(music)" title="Limit (music)">Limit</a> <ul><li><a href="/wiki/Five-limit_tuning" title="Five-limit tuning">5-limit</a></li> <li><a href="/wiki/7-limit_tuning" title="7-limit tuning">7-limit</a></li></ul></li> <li><a href="/wiki/List_of_compositions_in_just_intonation" title="List of compositions in just intonation">List of compositions</a></li> <li><a href="/wiki/Otonality_and_Utonality" class="mw-redirect" title="Otonality and Utonality">Otonality</a></li> <li><a href="/wiki/Ptolemy%27s_intense_diatonic_scale" title="Ptolemy's intense diatonic scale">Ptolemy's intense diatonic scale</a></li> <li><a href="/wiki/Pythagorean_tuning" title="Pythagorean tuning">Pythagorean tuning</a></li> <li><a href="/wiki/Scale_of_harmonics" title="Scale of harmonics">Scale of harmonics</a></li> <li><a href="/wiki/Tonality_diamond" title="Tonality diamond">Tonality diamond</a></li> <li><a href="/wiki/Tonality_flux" title="Tonality flux">Tonality flux</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Musical_temperament" title="Musical temperament">Temperaments</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Equal_temperament" title="Equal temperament">Equal</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Whole-tone_scale" title="Whole-tone scale">6-tone</a></li> <li><a href="/wiki/12_equal_temperament" title="12 equal temperament">12-tone</a></li> <li><a href="/wiki/15_equal_temperament" title="15 equal temperament">15-tone</a></li> <li><a href="/wiki/17_equal_temperament" title="17 equal temperament">17-tone</a></li> <li><a href="/wiki/19_equal_temperament" title="19 equal temperament">19-tone</a></li> <li><a href="/wiki/22_equal_temperament" title="22 equal temperament">22-tone</a></li> <li><a href="/wiki/23_equal_temperament" title="23 equal temperament">23-tone</a></li> <li><a href="/wiki/Quarter_tone" title="Quarter tone">24-tone</a> (<a href="/wiki/List_of_quarter_tone_pieces" title="List of quarter tone pieces">pieces</a>)</li> <li><a href="/wiki/31_equal_temperament" title="31 equal temperament">31-tone</a></li> <li><a href="/wiki/34_equal_temperament" title="34 equal temperament">34-tone</a></li> <li><a href="/wiki/41_equal_temperament" title="41 equal temperament">41-tone</a></li> <li><a href="/wiki/53_equal_temperament" title="53 equal temperament">53-tone</a></li> <li><a href="/wiki/58_equal_temperament" title="58 equal temperament">58-tone</a></li> <li><a href="/wiki/72_equal_temperament" title="72 equal temperament">72-tone</a></li> <li><a href="/wiki/96_equal_temperament" title="96 equal temperament">96-tone</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Regular_temperament" title="Regular temperament">Linear</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Meantone_temperament" title="Meantone temperament">Meantone</a> (<a href="/wiki/Quarter-comma_meantone" title="Quarter-comma meantone">quarter-comma</a>, <a href="/wiki/Septimal_meantone_temperament" title="Septimal meantone temperament">septimal</a>)</li> <li><a href="/wiki/Schismatic_temperament" title="Schismatic temperament">Schismatic</a></li> <li><a href="/wiki/Miracle_temperament" class="mw-redirect" title="Miracle temperament">Miracle</a></li> <li><a href="/wiki/Magic_temperament" title="Magic temperament">Magic</a></li> <li><a href="/wiki/Regular_diatonic_tuning" title="Regular diatonic tuning">Regular diatonic</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Irregular</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><a href="/wiki/Well_temperament" title="Well temperament">Well temperament</a>/<a href="/wiki/Temperament_ordinaire" title="Temperament ordinaire">Temperament ordinaire</a> (<a href="/wiki/Kirnberger_temperament" title="Kirnberger temperament">Kirnberger</a>, <a href="/wiki/Vallotti_temperament" title="Vallotti temperament">Vallotti</a>, <a href="/wiki/Werckmeister_temperament" title="Werckmeister temperament">Werckmeister</a>, <a href="/wiki/Young_temperament" title="Young temperament">Young</a>)</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Traditional<br /> non-Western</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chinese_musicology" title="Chinese musicology">Chinese musicology</a></li> <li><a href="/wiki/Sh%C3%AD-%C3%A8r-l%C7%9C" class="mw-redirect" title="Shí-èr-lǜ">Shí-èr-lǜ</a></li> <li><a href="/wiki/Dastgah" class="mw-redirect" title="Dastgah">Dastgah</a></li> <li>Maqam <ul><li><a href="/wiki/Arabic_maqam" title="Arabic maqam">Arabic maqam</a></li> <li><a href="/wiki/Turkish_makam" title="Turkish makam">Turkish makam</a></li> <li><a href="/wiki/Mugham" title="Mugham">Mugham</a></li> <li><a href="/wiki/Muqam" title="Muqam">Muqam</a></li></ul></li> <li><a href="/wiki/Octoechos" title="Octoechos">Octoechos</a></li> <li><a href="/wiki/Pelog" title="Pelog">Pelog</a></li> <li><a href="/wiki/Raga" title="Raga">Raga</a> (<a href="/wiki/Carnatic_raga" title="Carnatic raga">Carnatic raga</a>)</li> <li><a href="/wiki/Slendro" title="Slendro">Slendro</a></li> <li><a href="/wiki/Tetrachord" title="Tetrachord">Tetrachord</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Non-octave</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/833_cents_scale" title="833 cents scale">833 cents scale</a></li> <li><a href="/wiki/A12_scale" title="A12 scale">A12 scale</a></li> <li><a href="/wiki/Alpha_scale" title="Alpha scale">Alpha scale</a></li> <li><a href="/wiki/Beta_scale" title="Beta scale">Beta scale</a></li> <li><a href="/wiki/Gamma_scale" title="Gamma scale">Gamma scale</a></li> <li><a href="/wiki/Delta_scale" title="Delta scale">Delta scale</a></li> <li><a href="/wiki/Bohlen%E2%80%93Pierce_scale" title="Bohlen–Pierce scale">Lambda scale</a> (Bohlen–Pierce)</li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Tonality" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Tonality" title="Template:Tonality"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Tonality" title="Template talk:Tonality"><abbr 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title="Figured bass">Figured bass</a></li> <li><a href="/wiki/Just_intonation" title="Just intonation">Just intonation</a></li> <li><a href="/wiki/Key_(music)" title="Key (music)">Key</a></li> <li><a href="/wiki/Major_and_minor" title="Major and minor">Major and minor</a></li> <li><a href="/wiki/Modulation_(music)" title="Modulation (music)">Modulation</a></li> <li><a href="/wiki/Neotonality" title="Neotonality">Neotonality</a></li> <li><a href="/wiki/Ostinato" title="Ostinato">Ostinato</a></li> <li><a href="/wiki/Otonality_and_utonality" title="Otonality and utonality">Otonality and utonality</a></li> <li><a href="/wiki/Parallel_key" title="Parallel key">Parallel key</a></li> <li><a href="/wiki/Polytonality" title="Polytonality">Polytonality</a></li> <li><a href="/wiki/Progressive_tonality" title="Progressive tonality">Progressive tonality</a></li> <li><a href="/wiki/Schenkerian_analysis" title="Schenkerian analysis">Schenkerian analysis</a></li> <li><a href="/wiki/Sonata_form" 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[\"CITEREFHindemith1937–70\"] = 1,\n [\"CITEREFHindemith1942\"] = 1,\n [\"CITEREFHucbaldn.d.\"] = 1,\n [\"CITEREFJohannes_de_Garlandia\"] = 1,\n [\"CITEREFKamien2008\"] = 1,\n [\"CITEREFKliewer1975\"] = 1,\n [\"CITEREFLahdelma_and_Eerola2020\"] = 1,\n [\"CITEREFLandon1955\"] = 1,\n [\"CITEREFLevelt_and_Plomp1964\"] = 1,\n [\"CITEREFMachaut1926\"] = 1,\n [\"CITEREFMilneSetharesPlamondon2007\"] = 1,\n [\"CITEREFMilneSetharesPlamondon2008\"] = 1,\n [\"CITEREFMyers1904\"] = 1,\n [\"CITEREFPankovski_and_Pankovska_A.2022\"] = 1,\n [\"CITEREFPankovski_and_Pankovska_E.2017\"] = 1,\n [\"CITEREFParncutt_and_Hair2011\"] = 1,\n [\"CITEREFPatterson1986\"] = 1,\n [\"CITEREFPhilip1966\"] = 1,\n [\"CITEREFRadcliffe1978\"] = 1,\n [\"CITEREFRenard2016\"] = 1,\n [\"CITEREFRoederer1973\"] = 1,\n [\"CITEREFRoederer1995\"] = 1,\n [\"CITEREFRussell2008\"] = 1,\n [\"CITEREFSchoenberg1975\"] = 1,\n [\"CITEREFSchoenberg1978\"] = 1,\n [\"CITEREFSchuijer2008\"] = 1,\n [\"CITEREFSchulter1997a\"] = 1,\n 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