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class="vector-toc-list"> <li id="toc-Partial,_harmonic,_fundamental,_inharmonicity,_and_overtone" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Partial,_harmonic,_fundamental,_inharmonicity,_and_overtone"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Partial, harmonic, fundamental, inharmonicity, and overtone</span> </div> </a> <ul id="toc-Partial,_harmonic,_fundamental,_inharmonicity,_and_overtone-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Frequencies,_wavelengths,_and_musical_intervals_in_example_systems" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Frequencies,_wavelengths,_and_musical_intervals_in_example_systems"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Frequencies, wavelengths, and musical intervals in example systems</span> </div> </a> <ul id="toc-Frequencies,_wavelengths,_and_musical_intervals_in_example_systems-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Harmonics_and_tuning" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Harmonics_and_tuning"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Harmonics and tuning</span> </div> </a> <ul id="toc-Harmonics_and_tuning-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Timbre_of_musical_instruments" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Timbre_of_musical_instruments"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Timbre of musical instruments</span> </div> </a> <ul id="toc-Timbre_of_musical_instruments-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Interval_strength" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Interval_strength"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Interval strength</span> </div> </a> <ul id="toc-Interval_strength-sublist" class="vector-toc-list"> </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">6</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-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">8</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " 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class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%93%D0%B0%D1%80%D0%BC%D0%B0%D0%BD%D1%96%D1%87%D0%BD%D1%8B_%D1%88%D1%8D%D1%80%D0%B0%D0%B3_%D0%B3%D1%83%D0%BA%D0%B0%D1%9E" title="Гарманічны шэраг гукаў – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Гарманічны шэраг гукаў" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/S%C3%A8rie_harm%C3%B2nica_(m%C3%BAsica)" title="Sèrie harmònica (música) – Catalan" lang="ca" hreflang="ca" data-title="Sèrie harmònica (música)" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Harmonick%C3%A1_%C5%99ada_(hudba)" title="Harmonická řada (hudba) – Czech" lang="cs" hreflang="cs" data-title="Harmonická řada (hudba)" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Overtone" title="Overtone – Danish" lang="da" hreflang="da" data-title="Overtone" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Naturtonreihe" title="Naturtonreihe – German" lang="de" hreflang="de" data-title="Naturtonreihe" 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/Serie_arm%C3%B3nica_(m%C3%BAsica)" title="Serie armónica (música) – Spanish" lang="es" hreflang="es" data-title="Serie armónica (música)" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Naturtonserio" title="Naturtonserio – Esperanto" lang="eo" hreflang="eo" data-title="Naturtonserio" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B3%D8%B1%DB%8C_%D9%87%D8%A7%D8%B1%D9%85%D9%88%D9%86%DB%8C%DA%A9_(%D9%85%D9%88%D8%B3%DB%8C%D9%82%DB%8C)" title="سری هارمونیک (موسیقی) – Persian" lang="fa" hreflang="fa" data-title="سری هارمونیک (موسیقی)" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr badge-Q70893996 mw-list-item" title=""><a href="https://fr.wikipedia.org/wiki/S%C3%A9rie_harmonique_(musique)" title="Série harmonique (musique) – French" lang="fr" hreflang="fr" data-title="Série harmonique (musique)" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B0%B0%EC%9D%8C%EB%A0%AC" title="배음렬 – Korean" lang="ko" hreflang="ko" data-title="배음렬" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Armonici_naturali" title="Armonici naturali – Italian" lang="it" hreflang="it" data-title="Armonici naturali" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Felhangsor" title="Felhangsor – Hungarian" lang="hu" hreflang="hu" data-title="Felhangsor" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Harmonische_boventoonreeks" title="Harmonische boventoonreeks – Dutch" lang="nl" hreflang="nl" data-title="Harmonische boventoonreeks" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Overtonerekkja" title="Overtonerekkja – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Overtonerekkja" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Szereg_harmoniczny_(muzyka)" title="Szereg harmoniczny (muzyka) – Polish" lang="pl" hreflang="pl" data-title="Szereg harmoniczny (muzyka)" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/S%C3%A9rie_harm%C3%B4nica_(m%C3%BAsica)" title="Série harmônica (música) – Portuguese" lang="pt" hreflang="pt" data-title="Série harmônica (música)" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Spectru_sonor" title="Spectru sonor – Romanian" lang="ro" hreflang="ro" data-title="Spectru sonor" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B%D0%B9_%D0%B7%D0%B2%D1%83%D0%BA%D0%BE%D1%80%D1%8F%D0%B4" title="Натуральный звукоряд – Russian" lang="ru" hreflang="ru" data-title="Натуральный звукоряд" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Harmonic_series_(music)" title="Harmonic series (music) – Simple English" lang="en-simple" hreflang="en-simple" data-title="Harmonic series (music)" 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/Alikvotni_toni" title="Alikvotni toni – Slovenian" lang="sl" hreflang="sl" data-title="Alikvotni toni" 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/Yl%C3%A4s%C3%A4velsarja" title="Yläsävelsarja – Finnish" lang="fi" hreflang="fi" data-title="Yläsävelsarja" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Deltonserien" title="Deltonserien – Swedish" lang="sv" hreflang="sv" data-title="Deltonserien" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-uk badge-Q70893996 mw-list-item" title=""><a href="https://uk.wikipedia.org/wiki/%D0%93%D0%B0%D1%80%D0%BC%D0%BE%D0%BD%D1%96%D1%87%D0%BD%D0%B8%D0%B9_%D1%80%D1%8F%D0%B4_%D0%B7%D0%B2%D1%83%D0%BA%D1%96%D0%B2" title="Гармонічний ряд звуків – Ukrainian" lang="uk" hreflang="uk" data-title="Гармонічний ряд звуків" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E6%B3%9B%E9%9F%B3%E5%88%97" title="泛音列 – Wu" lang="wuu" hreflang="wuu" data-title="泛音列" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%B3%9B%E9%9F%B3%E5%88%97" title="泛音列 – Cantonese" lang="yue" hreflang="yue" data-title="泛音列" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%B3%9B%E9%9F%B3%E5%88%97" title="泛音列 – Chinese" lang="zh" hreflang="zh" data-title="泛音列" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q263961#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> 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class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Sequence of frequencies</div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Harmonic_partials_on_strings.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Harmonic_partials_on_strings.svg/250px-Harmonic_partials_on_strings.svg.png" decoding="async" width="250" height="238" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Harmonic_partials_on_strings.svg/375px-Harmonic_partials_on_strings.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Harmonic_partials_on_strings.svg/500px-Harmonic_partials_on_strings.svg.png 2x" data-file-width="620" data-file-height="590" /></a><figcaption>Harmonics of a string showing the periods of the pure-tone harmonics (period = 1/frequency)</figcaption></figure> <p>The <b>harmonic series</b> (also <b>overtone series</b>) is the sequence of <a href="/wiki/Harmonics" class="mw-redirect" title="Harmonics">harmonics</a>, <a href="/wiki/Musical_tone" title="Musical tone">musical tones</a>, or <a href="/wiki/Pure_tone" title="Pure tone">pure tones</a> whose <a href="/wiki/Frequency" title="Frequency">frequency</a> is an <a href="/wiki/Integer" title="Integer">integer</a> multiple of a <i><a href="/wiki/Fundamental_frequency" title="Fundamental frequency">fundamental frequency</a></i>. </p><p><a href="/wiki/Definite_pitch" class="mw-redirect" title="Definite pitch">Pitched</a> <a href="/wiki/Musical_instrument" title="Musical instrument">musical instruments</a> are often based on an <a href="/wiki/Acoustics" title="Acoustics">acoustic</a> <a href="/wiki/Resonator" title="Resonator">resonator</a> such as a <a href="/wiki/String_(music)" title="String (music)">string</a> or a column of air, which <a href="/wiki/Oscillation" title="Oscillation">oscillates</a> at numerous <a href="/wiki/Normal_mode" title="Normal mode">modes</a> simultaneously. As waves travel in both directions along the string or air column, they reinforce and cancel one another to form <a href="/wiki/Standing_wave" title="Standing wave">standing waves</a>. Interaction with the surrounding air produces audible <a href="/wiki/Sound_waves" class="mw-redirect" title="Sound waves">sound waves</a>, which travel away from the instrument. These frequencies are generally integer multiples, or <a href="/wiki/Harmonic" title="Harmonic">harmonics</a>, of the <a href="/wiki/Fundamental_frequency" title="Fundamental frequency">fundamental</a> and such multiples form the <a href="/wiki/Harmonic_series_(mathematics)" title="Harmonic series (mathematics)">harmonic series</a>. </p><p>The fundamental, which is usually perceived as the lowest <a href="#Partial">partial</a> present, is generally perceived as the <a href="/wiki/Pitch_(music)" title="Pitch (music)">pitch</a> of a musical tone. The musical <a href="/wiki/Timbre" title="Timbre">timbre</a> of a steady tone from such an instrument is strongly affected by the relative strength of each harmonic. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Terminology">Terminology <span class="anchor" id="Partial"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Harmonic_series_(music)&action=edit&section=1" title="Edit section: Terminology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Partial,_harmonic,_fundamental,_inharmonicity,_and_overtone"><span id="Partial.2C_harmonic.2C_fundamental.2C_inharmonicity.2C_and_overtone"></span>Partial, harmonic, fundamental, inharmonicity, and overtone</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Harmonic_series_(music)&action=edit&section=2" title="Edit section: Partial, harmonic, fundamental, inharmonicity, and overtone"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A "complex tone" (the sound of a note with a timbre particular to the instrument playing the note) "can be described as a combination of many simple <a href="/wiki/Wave" title="Wave">periodic waves</a> (i.e., <a href="/wiki/Sine_wave" title="Sine wave">sine waves</a>) or <i>partials,</i> each with its own frequency of <a href="/wiki/Vibration" title="Vibration">vibration</a>, <a href="/wiki/Amplitude" title="Amplitude">amplitude</a>, and <a href="/wiki/Phase_(waves)" title="Phase (waves)">phase</a>".<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> (See also, <a href="/wiki/Fourier_analysis" title="Fourier analysis">Fourier analysis</a>.) </p><p>A <b>partial</b> is any of the <a href="/wiki/Sine_wave" title="Sine wave">sine waves</a> (or "simple tones", as <a href="/wiki/Alexander_John_Ellis" title="Alexander John Ellis">Ellis</a> calls them<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> when translating <a href="/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz">Helmholtz</a>) of which a complex tone is composed, not necessarily with an integer multiple of the lowest harmonic. </p><p>A <b>harmonic</b> is any member of the harmonic series, an ideal set of <a href="/wiki/Frequency" title="Frequency">frequencies</a> that are <a href="/wiki/Natural_number" title="Natural number">positive integer</a> multiples of a common <a href="/wiki/Fundamental_frequency" title="Fundamental frequency">fundamental frequency</a>. The <b>fundamental</b> is a <a href="/wiki/Harmonic" title="Harmonic">harmonic</a> because it is one times itself. A <b>harmonic partial</b> is any real partial component of a complex tone that matches (or nearly matches) an ideal harmonic.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>An <b>inharmonic partial</b> is any partial that does not match an ideal harmonic. <i><a href="/wiki/Inharmonicity" title="Inharmonicity">Inharmonicity</a></i> is a measure of the deviation of a partial from the closest ideal harmonic, typically measured in <a href="/wiki/Cent_(music)" title="Cent (music)">cents</a> for each partial.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>Many <a href="/wiki/Definite_pitch" class="mw-redirect" title="Definite pitch">pitched</a> <a href="/wiki/Acoustic_music" title="Acoustic music">acoustic instruments</a> are designed to have partials that are close to being whole-number ratios with very low inharmonicity; therefore, in <a href="/wiki/Music_theory" title="Music theory">music theory</a>, and in instrument design, it is convenient, although not strictly accurate, to speak of the partials in those instruments' sounds as "harmonics", even though they may have some degree of inharmonicity. The <a href="/wiki/Piano" title="Piano">piano</a>, one of the most important instruments of western tradition, contains a certain degree of inharmonicity among the frequencies generated by each string. Other pitched instruments, especially certain <a href="/wiki/Percussion" class="mw-redirect" title="Percussion">percussion</a> instruments, such as <a href="/wiki/Marimba" title="Marimba">marimba</a>, <a href="/wiki/Vibraphone" title="Vibraphone">vibraphone</a>, <a href="/wiki/Tubular_bell" class="mw-redirect" title="Tubular bell">tubular bells</a>, <a href="/wiki/Timpani" title="Timpani">timpani</a>, and <a href="/wiki/Singing_bowl" class="mw-redirect" title="Singing bowl">singing bowls</a> contain mostly inharmonic partials, yet may give the ear a good sense of pitch because of a few strong partials that resemble harmonics. Unpitched, or indefinite-pitched instruments, such as <a href="/wiki/Cymbal" title="Cymbal">cymbals</a> and <a href="/wiki/Gong#Chau_gong_(tam-tam)" title="Gong">tam-tams</a> make sounds (produce spectra) that are rich in inharmonic partials and may give no impression of implying any particular pitch. </p><p>An <b><a href="/wiki/Overtone" title="Overtone">overtone</a></b> is any partial above the lowest partial. The term overtone does not imply harmonicity or inharmonicity and has no other special meaning other than to exclude the fundamental. It is mostly the relative strength of the different overtones that give an instrument its particular <a href="/wiki/Timbre" title="Timbre">timbre</a>, tone color, or character. When writing or speaking of overtones and partials numerically, care must be taken to designate each correctly to avoid any confusion of one for the other, so the second overtone may not be the third partial, because it is the second sound in a series.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>Some <a href="/wiki/Electronic_musical_instrument" title="Electronic musical instrument">electronic instruments</a>, such as <a href="/wiki/Synthesizer" title="Synthesizer">synthesizers</a>, can play a pure frequency with no <a href="/wiki/Overtone" title="Overtone">overtones</a> (a <a href="/wiki/Sine_wave" title="Sine wave">sine wave</a>). Synthesizers can also combine pure frequencies into more complex tones, such as to simulate other instruments. Certain flutes and ocarinas are very nearly without overtones. </p> <div class="mw-heading mw-heading2"><h2 id="Frequencies,_wavelengths,_and_musical_intervals_in_example_systems"><span id="Frequencies.2C_wavelengths.2C_and_musical_intervals_in_example_systems"></span>Frequencies, wavelengths, and musical intervals in example systems</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Harmonic_series_(music)&action=edit&section=3" title="Edit section: Frequencies, wavelengths, and musical intervals in example systems"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Harmonic_series_to_32.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/Harmonic_series_to_32.png/250px-Harmonic_series_to_32.png" decoding="async" width="250" height="333" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/Harmonic_series_to_32.png/375px-Harmonic_series_to_32.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/72/Harmonic_series_to_32.png/500px-Harmonic_series_to_32.png 2x" data-file-width="1296" data-file-height="1728" /></a><figcaption>Even-numbered string harmonics from 2nd up to the 64th (five octaves)</figcaption></figure> <p>One of the simplest cases to visualise is a <a href="/wiki/String_vibration" title="String vibration">vibrating string</a>, as in the illustration; the string has fixed points at each end, and each harmonic <a href="/wiki/Normal_mode" title="Normal mode">mode</a> divides it into an integer number (1, 2, 3, 4, etc.) of equal-sized sections resonating at increasingly higher frequencies.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability"><span title="The material near this tag failed verification of its source citation(s). (October 2022)">failed verification</span></a></i>]</sup> Similar arguments apply to vibrating air columns in <a href="/wiki/Wind_instrument" title="Wind instrument">wind instruments</a> (for example, "the French <a href="/wiki/Horn_(instrument)" title="Horn (instrument)">horn</a> was originally a valveless instrument that could play only the notes of the harmonic series"<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup>), although these are complicated by having the possibility of anti-nodes (that is, the air column is closed at one end and open at the other), <a href="/wiki/Cone_(geometry)" class="mw-redirect" title="Cone (geometry)">conical</a> as opposed to <a href="/wiki/Cylinder_(geometry)" class="mw-redirect" title="Cylinder (geometry)">cylindrical</a> <a href="/wiki/Bore_(wind_instruments)" title="Bore (wind instruments)">bores</a>, or end-openings that run the <a href="/wiki/Diatonic_and_chromatic" title="Diatonic and chromatic">gamut</a> from no flare, cone flare, or exponentially shaped flares (such as in various bells). </p><p>In most pitched musical instruments, the fundamental (first harmonic) is accompanied by other, higher-frequency harmonics. Thus shorter-wavelength, higher-frequency <a href="/wiki/Wave" title="Wave">waves</a> occur with varying prominence and give each instrument its characteristic tone quality. The fact that a string is fixed at each end means that the longest allowed wavelength on the string (which gives the fundamental frequency) is twice the length of the string (one round trip, with a half cycle fitting between the nodes at the two ends). Other allowed wavelengths are reciprocal multiples (e.g. <style data-mw-deduplicate="TemplateStyles:r1154941027">.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="frac"><span class="num">1</span>⁄<span class="den">2</span></span>, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">1</span>⁄<span class="den">3</span></span>, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">1</span>⁄<span class="den">4</span></span> times) that of the fundamental. </p><p>Theoretically, these shorter wavelengths correspond to <a href="/wiki/Vibration" title="Vibration">vibrations</a> at frequencies that are integer multiples of (e.g. 2, 3, 4 times) the fundamental frequency. Physical characteristics of the vibrating medium and/or the resonator it vibrates against often alter these frequencies. (See <a href="/wiki/Inharmonicity" title="Inharmonicity">inharmonicity</a> and <a href="/wiki/Stretched_tuning" title="Stretched tuning">stretched tuning</a> for alterations specific to wire-stringed instruments and certain <a href="/wiki/Electric_piano" title="Electric piano">electric pianos</a>.) However, those alterations are small, and except for precise, highly specialized tuning, it is reasonable to think of the frequencies of the harmonic series as integer multiples of the fundamental frequency. </p><p>The harmonic series is an <a href="/wiki/Arithmetic_progression" title="Arithmetic progression">arithmetic progression</a> (<i>f</i>, 2<i>f</i>, 3<i>f</i>, 4<i>f</i>, 5<i>f</i>, ...). In terms of frequency (measured in <a href="/wiki/Cycle_per_second" title="Cycle per second">cycles per second</a>, or <a href="/wiki/Hertz" title="Hertz">hertz</a>, where <i>f</i> is the fundamental frequency), the difference between consecutive harmonics is therefore constant and equal to the fundamental. But because human ears respond to sound <a href="/wiki/Nonlinear_system" title="Nonlinear system">nonlinearly</a>, higher harmonics are perceived as "closer together" than lower ones. On the other hand, the <a href="/wiki/Octave" title="Octave">octave</a> series is a <a href="/wiki/Geometric_progression" title="Geometric progression">geometric progression</a> (2<i>f</i>, 4<i>f</i>, 8<i>f</i>, 16<i>f</i>, ...), and people perceive these distances as "<a href="/wiki/Octave#Equivalence" title="Octave">the same</a>" in the sense of <a href="/wiki/Interval_(music)" title="Interval (music)">musical interval</a>. In terms of what one hears, each successively higher <a href="/wiki/Octave" title="Octave">octave</a> in the harmonic series is divided into increasingly "smaller" and more numerous intervals. </p><p>The second harmonic, whose frequency is twice the fundamental, sounds an octave higher; the third harmonic, three times the frequency of the fundamental, sounds a <a href="/wiki/Perfect_fifth" title="Perfect fifth">perfect fifth</a> above the second harmonic. The fourth harmonic vibrates at four times the frequency of the fundamental and sounds a <a href="/wiki/Perfect_fourth" title="Perfect fourth">perfect fourth</a> above the third harmonic (two octaves above the fundamental). Double the harmonic number means double the frequency (which sounds an octave higher). </p> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:Harmonic_Series.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Harmonic_Series.png/650px-Harmonic_Series.png" decoding="async" width="650" height="88" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Harmonic_Series.png/975px-Harmonic_Series.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Harmonic_Series.png/1300px-Harmonic_Series.png 2x" data-file-width="2094" data-file-height="285" /></a><figcaption>An illustration in musical notation of the harmonic series (on C) up to the 20th harmonic. The numbers above the harmonic indicate the difference – in <a href="/wiki/Cent_(music)" title="Cent (music)">cents</a> – from <a href="/wiki/Equal_temperament" title="Equal temperament">equal temperament</a> (rounded to the nearest integer). Blue notes are very flat and red notes are very sharp. Listeners accustomed to more <a href="/wiki/Consonance_and_dissonance" title="Consonance and dissonance">tonal</a> tuning, such as <a href="/wiki/Meantone_temperament" title="Meantone temperament">meantone</a> and <a href="/wiki/Well_temperament" title="Well temperament">well temperaments</a>, notice many other notes are "off".</figcaption></figure> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:Harmonics_to_32.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Harmonics_to_32.png/650px-Harmonics_to_32.png" decoding="async" width="650" height="192" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Harmonics_to_32.png/975px-Harmonics_to_32.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Harmonics_to_32.png/1300px-Harmonics_to_32.png 2x" data-file-width="2152" data-file-height="635" /></a><figcaption>Harmonics on C, from 1st (fundamental) to 32nd harmonic (five octaves higher). Notation used is based on the <a href="/wiki/Ben_Johnston_(composer)#Staff_notation" title="Ben Johnston (composer)">extended just notation</a> by <a href="/wiki/Ben_Johnston_(composer)" title="Ben Johnston (composer)">Ben Johnston</a><span class="mw-default-size" typeof="mw:File"><span><audio id="mwe_player_0" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-mwtitle="Harmonics_to_32.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/9/97/Harmonics_to_32.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/97/Harmonics_to_32.mid/Harmonics_to_32.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/97/Harmonics_to_32.mid/Harmonics_to_32.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span></figcaption></figure> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:Harmonic_series_intervals.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Harmonic_series_intervals.png/550px-Harmonic_series_intervals.png" decoding="async" width="550" height="235" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Harmonic_series_intervals.png/825px-Harmonic_series_intervals.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Harmonic_series_intervals.png/1100px-Harmonic_series_intervals.png 2x" data-file-width="2131" data-file-height="910" /></a><figcaption>Harmonic series as musical notation with intervals between harmonics labeled. Blue notes differ most significantly from equal temperament. One can listen to <a href="//upload.wikimedia.org/wikipedia/commons/9/9d/Harmonics_110x16.ogg" class="internal" title="Harmonics 110x16.ogg">A<sub>2</sub> (110 Hz) and 15 of its partials</a> </figcaption></figure> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:Notation_of_partials_1-19_for_1-1.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Notation_of_partials_1-19_for_1-1.png/400px-Notation_of_partials_1-19_for_1-1.png" decoding="async" width="400" height="103" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Notation_of_partials_1-19_for_1-1.png/600px-Notation_of_partials_1-19_for_1-1.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Notation_of_partials_1-19_for_1-1.png/800px-Notation_of_partials_1-19_for_1-1.png 2x" data-file-width="1030" data-file-height="266" /></a><figcaption>Staff notation of partials 1, 3, 5, 7, 11, 13, 17, and 19 on C. These are "<a href="/wiki/Prime_number" title="Prime number">prime</a> harmonics".<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><span class="mw-default-size" typeof="mw:File"><span><audio id="mwe_player_1" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-mwtitle="Notation_of_partials_1-19_for_1-1.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/a/ad/Notation_of_partials_1-19_for_1-1.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/ad/Notation_of_partials_1-19_for_1-1.mid/Notation_of_partials_1-19_for_1-1.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/ad/Notation_of_partials_1-19_for_1-1.mid/Notation_of_partials_1-19_for_1-1.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span></figcaption></figure> <p><a href="/wiki/Marin_Mersenne" title="Marin Mersenne">Marin Mersenne</a> wrote: "The order of the Consonances is natural, and ... the way we count them, starting from unity up to the number six and beyond is founded in nature."<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> However, to quote <a href="/wiki/Carl_Dahlhaus" title="Carl Dahlhaus">Carl Dahlhaus</a>, "the interval-distance of the natural-tone-row [<a href="/wiki/Overtone" title="Overtone">overtones</a>] [...], counting up to 20, includes everything from the octave to the quarter tone, (and) useful and useless musical tones. The natural-tone-row [harmonic series] justifies everything, that means, nothing."<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Harmonics_and_tuning">Harmonics and tuning</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Harmonic_series_(music)&action=edit&section=4" title="Edit section: Harmonics and tuning"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>If the harmonics are octave displaced and compressed into the span of one <a href="/wiki/Octave" title="Octave">octave</a>, some of them are approximated by the notes of what the <a href="/wiki/Western_world" title="Western world">West</a> has adopted as the chromatic scale based on the fundamental tone. The Western chromatic scale has been modified into twelve equal <a href="/wiki/Minor_second" class="mw-redirect" title="Minor second">semitones</a>, which is slightly out of tune with many of the harmonics, especially the 7th, 11th, and 13th harmonics. In the late 1930s, composer <a href="/wiki/Paul_Hindemith" title="Paul Hindemith">Paul Hindemith</a> ranked musical intervals according to their relative <a href="/wiki/Consonance_and_dissonance" title="Consonance and dissonance">dissonance</a> based on these and similar harmonic relationships.<sup id="cite_ref-Hindemith_11-0" class="reference"><a href="#cite_note-Hindemith-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>Below is a comparison between the first 31 harmonics and the intervals of <a href="/wiki/12-tone_equal_temperament" class="mw-redirect" title="12-tone equal temperament">12-tone equal temperament</a> (12TET), octave displaced and compressed into the span of one octave. Tinted fields highlight differences greater than 5 <a href="/wiki/Cent_(music)" title="Cent (music)">cents</a> (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">1</span>⁄<span class="den">20</span></span> of a semitone), which is the human ear's "<a href="/wiki/Just_noticeable_difference" class="mw-redirect" title="Just noticeable difference">just noticeable difference</a>" for notes played one after the other (smaller differences are noticeable with notes played simultaneously). </p> <table class="wikitable" align="right"> <tbody><tr> <th colspan="5">Harmonic </th> <th>Interval as a ratio </th> <th>Interval in binary </th> <th>12TET interval </th> <th>Note </th> <th>Variance <a href="/wiki/Cent_(music)" title="Cent (music)">cents</a> </th></tr> <tr> <td>1</td> <td>2</td> <td>4</td> <td>8</td> <td>16</td> <td>1, 2</td> <td>1</td> <td>prime (octave)</td> <td>C</td> <td>0 </td></tr> <tr> <td></td> <td></td> <td></td> <td></td> <td>17</td> <td>17/16 (1.0625)</td> <td>1.0001</td> <td>minor second</td> <td>C<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>, D<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span></td> <td>+5 </td></tr> <tr> <td></td> <td></td> <td></td> <td>9</td> <td>18</td> <td>9/8 (1.125)</td> <td>1.001</td> <td>major second</td> <td>D</td> <td>+4 </td></tr> <tr> <td></td> <td></td> <td></td> <td></td> <td>19</td> <td>19/16 (1.1875)</td> <td>1.0011</td> <td>minor third</td> <td>D<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>, E<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span></td> <td>−2 </td></tr> <tr> <td></td> <td></td> <td>5</td> <td>10</td> <td>20</td> <td>5/4 (1.25)</td> <td>1.01</td> <td>major third</td> <td>E</td> <td bgcolor="yellow">−14 </td></tr> <tr> <td></td> <td></td> <td></td> <td></td> <td>21</td> <td>21/16 (1.3125)</td> <td>1.0101</td> <td>fourth</td> <td>F</td> <td bgcolor="yellow">−29 </td></tr> <tr> <td></td> <td></td> <td></td> <td>11</td> <td>22</td> <td>11/8 (1.375)</td> <td>1.011</td> <td rowspan="2">tritone</td> <td rowspan="2">F<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>, G<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span></td> <td bgcolor="yellow">−49 </td></tr> <tr> <td></td> <td></td> <td></td> <td></td> <td>23</td> <td>23/16 (1.4375)</td> <td>1.0111</td> <td bgcolor="yellow">+28 </td></tr> <tr> <td></td> <td>3</td> <td>6</td> <td>12</td> <td>24</td> <td>3/2 (1.5)</td> <td>1.1</td> <td>fifth</td> <td>G</td> <td>+2 </td></tr> <tr> <td></td> <td></td> <td></td> <td></td> <td>25</td> <td>25/16 (1.5625)</td> <td>1.1001</td> <td rowspan="2">minor sixth</td> <td rowspan="2">G<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>, A<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span></td> <td bgcolor="yellow">−27 </td></tr> <tr> <td></td> <td></td> <td></td> <td>13</td> <td>26</td> <td>13/8 (1.625)</td> <td>1.101</td> <td bgcolor="yellow">+41 </td></tr> <tr> <td></td> <td></td> <td></td> <td></td> <td>27</td> <td>27/16 (1.6875)</td> <td>1.1011</td> <td>major sixth</td> <td>A</td> <td bgcolor="yellow">+6 </td></tr> <tr> <td></td> <td></td> <td>7</td> <td>14</td> <td>28</td> <td>7/4 (1.75)</td> <td>1.11</td> <td rowspan="2">minor seventh</td> <td rowspan="2">A<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>, B<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span></td> <td bgcolor="yellow">−31 </td></tr> <tr> <td></td> <td></td> <td></td> <td></td> <td>29</td> <td>29/16 (1.8125)</td> <td>1.1101</td> <td bgcolor="yellow">+30 </td></tr> <tr> <td></td> <td></td> <td></td> <td>15</td> <td>30</td> <td>15/8 (1.875)</td> <td>1.111</td> <td rowspan="2">major seventh</td> <td rowspan="2">B</td> <td bgcolor="yellow">−12 </td></tr> <tr> <td></td> <td></td> <td></td> <td></td> <td>31</td> <td>31/16 (1.9375)</td> <td>1.1111</td> <td bgcolor="yellow">+45 </td></tr></tbody></table> <p>The frequencies of the harmonic series, being integer multiples of the fundamental frequency, are naturally related to each other by whole-numbered ratios and small whole-numbered ratios are likely the basis of the consonance of musical intervals (see <a href="/wiki/Just_intonation" title="Just intonation">just intonation</a>). This objective structure is augmented by psychoacoustic phenomena. For example, a perfect fifth, say 200 and 300 Hz (cycles per second), causes a listener to perceive a <a href="/wiki/Combination_tone" title="Combination tone">combination tone</a> of 100 Hz (the difference between 300 Hz and 200 Hz); that is, an octave below the lower (actual sounding) note. This 100 Hz first-order combination tone then interacts with both notes of the interval to produce second-order combination tones of 200 (300 − 100) and 100 (200 − 100) Hz and all further nth-order combination tones are all the same, being formed from various subtraction of 100, 200, and 300. When one contrasts this with a dissonant interval such as a <a href="/wiki/Tritone" title="Tritone">tritone</a> (not tempered) with a frequency ratio of 7:5 one gets, for example, 700 − 500 = 200 (1st order combination tone) and 500 − 200 = 300 (2nd order). The rest of the combination tones are octaves of 100 Hz so the 7:5 interval actually contains four notes: 100 Hz (and its octaves), 300 Hz, 500 Hz and 700 Hz. The lowest combination tone (100 Hz) is a seventeenth (two octaves and a <a href="/wiki/Major_third" title="Major third">major third</a>) below the lower (actual sounding) note of the <a href="/wiki/Tritone" title="Tritone">tritone</a>. All the intervals succumb to similar analysis as has been demonstrated by <a href="/wiki/Paul_Hindemith" title="Paul Hindemith">Paul Hindemith</a> in his book <i>The Craft of Musical Composition</i>, although he rejected the use of harmonics from the seventh and beyond.<sup id="cite_ref-Hindemith_11-1" class="reference"><a href="#cite_note-Hindemith-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>The <a href="/wiki/Mixolydian_mode" title="Mixolydian mode">Mixolydian mode</a> is consonant with the first 10 harmonics of the harmonic series (the 11th harmonic, a tritone, is not in the Mixolydian mode). The <a href="/wiki/Ionian_mode" title="Ionian mode">Ionian mode</a> is consonant with only the first 6 harmonics of the series (the seventh harmonic, a minor seventh, is not in the Ionian mode). The <a href="/wiki/Rishabhapriya" title="Rishabhapriya">Rishabhapriya ragam</a> is consonant with the first 14 harmonics of the series. </p> <div class="mw-heading mw-heading2"><h2 id="Timbre_of_musical_instruments">Timbre of musical instruments</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Harmonic_series_(music)&action=edit&section=5" title="Edit section: Timbre of musical instruments"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-More_citations_needed_section plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Harmonic_series_(music)" title="Special:EditPage/Harmonic series (music)">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a> in this section. Unsourced material may be challenged and removed.</span> <span class="date-container"><i>(<span class="date">November 2011</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>The relative <a href="/wiki/Amplitude" title="Amplitude">amplitudes</a> (strengths) of the various harmonics primarily determine the <a href="/wiki/Timbre" title="Timbre">timbre</a> of different instruments and sounds, though onset <a href="/wiki/Transient_(acoustics)" title="Transient (acoustics)">transients</a>, <a href="/wiki/Formant" title="Formant">formants</a>, <a href="/wiki/Noise" title="Noise">noises</a>, and inharmonicities also play a role. For example, the <a href="/wiki/Clarinet" title="Clarinet">clarinet</a> and <a href="/wiki/Saxophone" title="Saxophone">saxophone</a> have similar <a href="/wiki/Mouthpiece_(woodwind)" title="Mouthpiece (woodwind)">mouthpieces</a> and <a href="/wiki/Reed_(music)" class="mw-redirect" title="Reed (music)">reeds</a>, and both produce sound through <a href="/wiki/Resonance" title="Resonance">resonance</a> of air inside a chamber whose mouthpiece end is considered closed. Because the clarinet's resonator is cylindrical, the <i>even</i>-numbered harmonics are less present. The saxophone's resonator is conical, which allows the even-numbered harmonics to sound more strongly and thus produces a more complex tone. The <a href="/wiki/Inharmonicity" title="Inharmonicity">inharmonic</a> ringing of the instrument's metal resonator is even more prominent in the sounds of brass instruments. </p><p>Human ears tend to group phase-coherent, harmonically-related frequency components into a single sensation. Rather than perceiving the individual partials–harmonic and inharmonic, of a musical tone, humans perceive them together as a tone color or timbre, and the overall <a href="/wiki/Pitch_(music)" title="Pitch (music)">pitch</a> is heard as the fundamental of the harmonic series being experienced. If a sound is heard that is made up of even just a few simultaneous sine tones, and if the intervals among those tones form part of a harmonic series, the brain tends to group this input into a sensation of the pitch of the fundamental of that series, <a href="/wiki/Missing_fundamental" title="Missing fundamental">even if the fundamental is not present</a>. </p><p>Variations in the frequency of harmonics can also affect the <i>perceived</i> fundamental pitch. These variations, most clearly documented in the piano and other stringed instruments but also apparent in <a href="/wiki/Brass_instrument" title="Brass instrument">brass instruments</a>, are caused by a combination of metal stiffness and the interaction of the vibrating air or string with the resonating body of the instrument. </p> <div class="mw-heading mw-heading2"><h2 id="Interval_strength">Interval strength</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Harmonic_series_(music)&action=edit&section=6" title="Edit section: Interval strength"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/David_Cope" title="David Cope">David Cope</a> (1997) suggests the concept of <a href="/wiki/Interval_(music)#Consonant_and_dissonant" title="Interval (music)">interval strength</a>,<sup id="cite_ref-Cope_12-0" class="reference"><a href="#cite_note-Cope-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> in which an interval's strength, consonance, or stability (see <a href="/wiki/Consonance_and_dissonance" title="Consonance and dissonance">consonance and dissonance</a>) is determined by its approximation to a lower and stronger, or higher and weaker, position in the harmonic series. See also: <a href="/wiki/Lipps%E2%80%93Meyer_law" title="Lipps–Meyer law">Lipps–Meyer law</a>. </p><p>Thus, an equal-tempered perfect fifth (<span class="noprint"><span class="ext-phonos"><span data-nosnippet="" id="ooui-php-1" class="ext-phonos-PhonosButton noexcerpt oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-ooui="{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/2\/20\/Perfect_fifth_on_C.mid\/Perfect_fifth_on_C.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"play"},"data":{"ipa":"","text":"","lang":"en","wikibase":"","file":"Perfect fifth on C.mid"},"classes":["ext-phonos-PhonosButton","noexcerpt"]}"><a role="button" tabindex="0" href="//upload.wikimedia.org/wikipedia/commons/transcoded/2/20/Perfect_fifth_on_C.mid/Perfect_fifth_on_C.mid.mp3" rel="nofollow" aria-label="Play audio" title="Play audio" class="oo-ui-buttonElement-button"><span class="oo-ui-iconElement-icon oo-ui-icon-volumeUp"></span><span class="oo-ui-labelElement-label">play</span><span class="oo-ui-indicatorElement-indicator oo-ui-indicatorElement-noIndicator"></span></a></span><sup class="ext-phonos-attribution noexcerpt navigation-not-searchable"><a href="/wiki/File:Perfect_fifth_on_C.mid" title="File:Perfect fifth on C.mid">ⓘ</a></sup></span></span>) is stronger than an equal-tempered <a href="/wiki/Minor_third" title="Minor third">minor third</a> (<span class="noprint"><span class="ext-phonos"><span data-nosnippet="" id="ooui-php-2" class="ext-phonos-PhonosButton noexcerpt oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-ooui="{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/3\/31\/Minor_third_on_C.mid\/Minor_third_on_C.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"play"},"data":{"ipa":"","text":"","lang":"en","wikibase":"","file":"Minor third on C.mid"},"classes":["ext-phonos-PhonosButton","noexcerpt"]}"><a role="button" tabindex="0" href="//upload.wikimedia.org/wikipedia/commons/transcoded/3/31/Minor_third_on_C.mid/Minor_third_on_C.mid.mp3" rel="nofollow" aria-label="Play audio" title="Play audio" class="oo-ui-buttonElement-button"><span class="oo-ui-iconElement-icon oo-ui-icon-volumeUp"></span><span class="oo-ui-labelElement-label">play</span><span class="oo-ui-indicatorElement-indicator oo-ui-indicatorElement-noIndicator"></span></a></span><sup class="ext-phonos-attribution noexcerpt navigation-not-searchable"><a href="/wiki/File:Minor_third_on_C.mid" title="File:Minor third on C.mid">ⓘ</a></sup></span></span>), since they approximate a just perfect fifth (<span class="noprint"><span class="ext-phonos"><span data-nosnippet="" id="ooui-php-3" class="ext-phonos-PhonosButton noexcerpt oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-ooui="{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/5\/5c\/Just_perfect_fifth_on_C.mid\/Just_perfect_fifth_on_C.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"play"},"data":{"ipa":"","text":"","lang":"en","wikibase":"","file":"Just perfect fifth on C.mid"},"classes":["ext-phonos-PhonosButton","noexcerpt"]}"><a role="button" tabindex="0" href="//upload.wikimedia.org/wikipedia/commons/transcoded/5/5c/Just_perfect_fifth_on_C.mid/Just_perfect_fifth_on_C.mid.mp3" rel="nofollow" aria-label="Play audio" title="Play audio" class="oo-ui-buttonElement-button"><span class="oo-ui-iconElement-icon oo-ui-icon-volumeUp"></span><span class="oo-ui-labelElement-label">play</span><span class="oo-ui-indicatorElement-indicator oo-ui-indicatorElement-noIndicator"></span></a></span><sup class="ext-phonos-attribution noexcerpt navigation-not-searchable"><a href="/wiki/File:Just_perfect_fifth_on_C.mid" title="File:Just perfect fifth on C.mid">ⓘ</a></sup></span></span>) and just minor third (<span class="noprint"><span class="ext-phonos"><span data-nosnippet="" id="ooui-php-4" class="ext-phonos-PhonosButton noexcerpt oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-ooui="{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/4\/42\/Just_minor_third_on_C.mid\/Just_minor_third_on_C.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"play"},"data":{"ipa":"","text":"","lang":"en","wikibase":"","file":"Just minor third on C.mid"},"classes":["ext-phonos-PhonosButton","noexcerpt"]}"><a role="button" tabindex="0" href="//upload.wikimedia.org/wikipedia/commons/transcoded/4/42/Just_minor_third_on_C.mid/Just_minor_third_on_C.mid.mp3" rel="nofollow" aria-label="Play audio" title="Play audio" class="oo-ui-buttonElement-button"><span class="oo-ui-iconElement-icon oo-ui-icon-volumeUp"></span><span class="oo-ui-labelElement-label">play</span><span class="oo-ui-indicatorElement-indicator oo-ui-indicatorElement-noIndicator"></span></a></span><sup class="ext-phonos-attribution noexcerpt navigation-not-searchable"><a href="/wiki/File:Just_minor_third_on_C.mid" title="File:Just minor third on C.mid">ⓘ</a></sup></span></span>), respectively. The just minor third appears between harmonics 5 and 6 while the just fifth appears lower, between harmonics 2 and 3. </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=Harmonic_series_(music)&action=edit&section=7" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <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: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 img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><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"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Harmonic_series_(music)" class="extiw" title="commons:Category:Harmonic series (music)">Harmonic series (music)</a></span>.</div></div> </div> <ul><li><a href="/wiki/Fourier_series" title="Fourier series">Fourier series</a></li> <li><a href="/wiki/Klang_(music)" title="Klang (music)">Klang (music)</a></li> <li><a href="/wiki/Otonality_and_Utonality" class="mw-redirect" title="Otonality and Utonality">Otonality and Utonality</a></li> <li><a href="/wiki/Piano_acoustics" title="Piano acoustics">Piano acoustics</a></li> <li><a href="/wiki/Scale_of_harmonics" title="Scale of harmonics">Scale of harmonics</a></li> <li><a href="/wiki/Undertone_series" title="Undertone series">Undertone series</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Harmonic_series_(music)&action=edit&section=8" title="Edit section: Notes"><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"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><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="CITEREFWilliam_Forde_Thompson2008" class="citation book cs1"><a href="/wiki/William_Forde_Thompson" title="William Forde Thompson">William Forde Thompson</a> (2008). <a rel="nofollow" class="external text" href="http://www.oup.com/us/catalog/general/subject/Psychology/CognitivePsychology/?view=usa&ci=9780195377071"><i>Music, Thought, and Feeling: Understanding the Psychology of Music</i></a>. Oxford University Press. p. 46. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-537707-1" title="Special:BookSources/978-0-19-537707-1"><bdi>978-0-19-537707-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Music%2C+Thought%2C+and+Feeling%3A+Understanding+the+Psychology+of+Music&rft.pages=46&rft.pub=Oxford+University+Press&rft.date=2008&rft.isbn=978-0-19-537707-1&rft.au=William+Forde+Thompson&rft_id=http%3A%2F%2Fwww.oup.com%2Fus%2Fcatalog%2Fgeneral%2Fsubject%2FPsychology%2FCognitivePsychology%2F%3Fview%3Dusa%26ci%3D9780195377071&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHarmonic+series+%28music%29" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHermann_von_Helmholtz1885" class="citation book cs1"><a href="/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz">Hermann von Helmholtz</a> (1885). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=GwE6AAAAIAAJ&q=%22musical+tone%22+simple+compound&pg=PA23"><i>On the Sensations of Tone as a Physiological Basis for the Theory of Music</i></a>. Translated by <a href="/wiki/Alexander_John_Ellis" title="Alexander John Ellis">Alexander John Ellis</a> (2nd ed.). Longmans, Green. p. 23.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=On+the+Sensations+of+Tone+as+a+Physiological+Basis+for+the+Theory+of+Music&rft.pages=23&rft.edition=2nd&rft.pub=Longmans%2C+Green&rft.date=1885&rft.au=Hermann+von+Helmholtz&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DGwE6AAAAIAAJ%26q%3D%2522musical%2Btone%2522%2Bsimple%2Bcompound%26pg%3DPA23&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHarmonic+series+%28music%29" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJohn_R._Pierce2001" class="citation book cs1"><a href="/wiki/John_R._Pierce" title="John R. Pierce">John R. Pierce</a> (2001). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=L04W8ADtpQ4C&q=musical+tone+harmonic+partial+fundamental+integer&pg=PA169">"Consonance and Scales"</a>. In Perry R. Cook (ed.). <i>Music, Cognition, and Computerized Sound</i>. MIT Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-262-53190-0" title="Special:BookSources/978-0-262-53190-0"><bdi>978-0-262-53190-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Consonance+and+Scales&rft.btitle=Music%2C+Cognition%2C+and+Computerized+Sound&rft.pub=MIT+Press&rft.date=2001&rft.isbn=978-0-262-53190-0&rft.au=John+R.+Pierce&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DL04W8ADtpQ4C%26q%3Dmusical%2Btone%2Bharmonic%2Bpartial%2Bfundamental%2Binteger%26pg%3DPA169&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHarmonic+series+%28music%29" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMartha_Goodway_and_Jay_Scott_Odell1987" class="citation book cs1"><a href="/wiki/Martha_Goodway" title="Martha Goodway">Martha Goodway</a> and Jay Scott Odell (1987). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=sE1mk8ed1dkC&q=inharmonicity+defined+partial+frequencies&pg=PA93"><i>The Historical Harpsichord Volume Two: The Metallurgy of 17th- and 18th- Century Music Wire</i></a>. Pendragon Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-918728-54-8" title="Special:BookSources/978-0-918728-54-8"><bdi>978-0-918728-54-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Historical+Harpsichord+Volume+Two%3A+The+Metallurgy+of+17th-+and+18th-+Century+Music+Wire&rft.pub=Pendragon+Press&rft.date=1987&rft.isbn=978-0-918728-54-8&rft.au=Martha+Goodway+and+Jay+Scott+Odell&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DsE1mk8ed1dkC%26q%3Dinharmonicity%2Bdefined%2Bpartial%2Bfrequencies%26pg%3DPA93&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHarmonic+series+%28music%29" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><a href="#CITEREFRiemann1896">Riemann 1896</a>, p. 143: "let it be understood, the second overtone is not the third tone of the series, but the second"</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRoederer1995" class="citation book cs1">Roederer, Juan G. (1995). <i>The Physics and Psychophysics of Music</i>. Springer. p. 106. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-387-94366-8" title="Special:BookSources/0-387-94366-8"><bdi>0-387-94366-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Physics+and+Psychophysics+of+Music&rft.pages=106&rft.pub=Springer&rft.date=1995&rft.isbn=0-387-94366-8&rft.aulast=Roederer&rft.aufirst=Juan+G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHarmonic+series+%28music%29" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKostkaPayne1995" class="citation book cs1"><a href="/wiki/Stefan_Kostka" title="Stefan Kostka">Kostka, Stefan</a>; Payne, Dorothy (1995). <i>Tonal Harmony</i> (3rd ed.). McGraw-Hill. p. 102. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-07-035874-5" title="Special:BookSources/0-07-035874-5"><bdi>0-07-035874-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Tonal+Harmony&rft.pages=102&rft.edition=3rd&rft.pub=McGraw-Hill&rft.date=1995&rft.isbn=0-07-035874-5&rft.aulast=Kostka&rft.aufirst=Stefan&rft.au=Payne%2C+Dorothy&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHarmonic+series+%28music%29" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFonville1991" class="citation journal cs1"><a href="/wiki/John_Fonville" title="John Fonville">Fonville, John</a> (Summer 1991). "Ben Johnston's Extended Just Intonation: A guide for interpreters". <i><a href="/wiki/Perspectives_of_New_Music" title="Perspectives of New Music">Perspectives of New Music</a></i>. <b>29</b> (2): 106–137 (121). <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F833435">10.2307/833435</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/833435">833435</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Perspectives+of+New+Music&rft.atitle=Ben+Johnston%27s+Extended+Just+Intonation%3A+A+guide+for+interpreters&rft.ssn=summer&rft.volume=29&rft.issue=2&rft.pages=106-137+%28121%29&rft.date=1991&rft_id=info%3Adoi%2F10.2307%2F833435&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F833435%23id-name%3DJSTOR&rft.aulast=Fonville&rft.aufirst=John&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHarmonic+series+%28music%29" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCohen2013" class="citation book cs1"><a href="/wiki/Floris_Cohen" title="Floris Cohen">Cohen, H. F.</a> (2013). <i>Quantifying Music: The science of music at the first stage of scientific revolution 1580–1650</i>. Springer. p. 103. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9789401576864" title="Special:BookSources/9789401576864"><bdi>9789401576864</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantifying+Music%3A+The+science+of+music+at+the+first+stage+of+scientific+revolution+1580%E2%80%931650&rft.pages=103&rft.pub=Springer&rft.date=2013&rft.isbn=9789401576864&rft.aulast=Cohen&rft.aufirst=H.+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHarmonic+series+%28music%29" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text">Sabbagh, Peter (2003). <i>The Development of Harmony in <a href="/wiki/Alexander_Scriabin" title="Alexander Scriabin">Scriabin</a>'s Works</i>, p. 12. Universal. <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/9781581125955" title="Special:BookSources/9781581125955">9781581125955</a>. Cites: <a href="/wiki/Carl_Dahlhaus" title="Carl Dahlhaus">Dahlhaus, Carl</a> (1972). "Struktur und Expression bei Alexander Skrjabin", <i>Musik des Ostens</i>, Vol. 6, p. 229.</span> </li> <li id="cite_note-Hindemith-11"><span class="mw-cite-backlink">^ <a href="#cite_ref-Hindemith_11-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Hindemith_11-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="/wiki/Paul_Hindemith" title="Paul Hindemith">Hindemith, Paul</a> (1942). <a rel="nofollow" class="external text" href="http://noty-naputi.info/sites/default/files/Musical%20Composition-Hindemit.pdf"><i>The Craft of Musical Composition: Book 1 – Theoretical Part</i></a>, pp. 15ff. Translated by <a href="/wiki/Arthur_Mendel" title="Arthur Mendel">Arthur Mendel</a> (London: Schott & Co; New York: Associated Music Publishers. <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/0901938300" title="Special:BookSources/0901938300">0901938300</a>). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20140701100137/http://noty-naputi.info/sites/default/files/Musical%20Composition-Hindemit.pdf">Archived</a> 2014-07-01 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>.</span> </li> <li id="cite_note-Cope-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-Cope_12-0">^</a></b></span> <span class="reference-text"><a href="/wiki/David_Cope" title="David Cope">Cope, David</a> (1997). <i>Techniques of the Contemporary Composer</i>, p. 40–41. New York, New York: Schirmer Books. <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/0-02-864737-8" title="Special:BookSources/0-02-864737-8">0-02-864737-8</a>.</span> </li> </ol></div></div> <p><b>Sources</b> </p> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRiemann1896" class="citation book cs1"><a href="/wiki/Hugo_Riemann" title="Hugo Riemann">Riemann, Hugo</a> (1896). <i><a href="https://imslp.org/wiki/Musiklexikon_(Riemann,_Hugo)" class="extiw" title="scores:Musiklexikon (Riemann, Hugo)">Dictionary of Music</a></i>. Translated by John South Shedlock. London: Augener & Co.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Dictionary+of+Music&rft.place=London&rft.pub=Augener+%26+Co&rft.date=1896&rft.aulast=Riemann&rft.aufirst=Hugo&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHarmonic+series+%28music%29" class="Z3988"></span></li></ul> <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=Harmonic_series_(music)&action=edit&section=9" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1">Coul, Manuel Op de. <a rel="nofollow" class="external text" href="http://www.huygens-fokker.org/docs/intervals.html">"List of intervals (Compiled)"</a>. Huygens-Fokker Foundation centre for microtonal music<span class="reference-accessdate">. Retrieved <span class="nowrap">2016-06-15</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=List+of+intervals+%28Compiled%29&rft.pub=Huygens-Fokker+Foundation+centre+for+microtonal+music&rft.aulast=Coul&rft.aufirst=Manuel+Op+de&rft_id=http%3A%2F%2Fwww.huygens-fokker.org%2Fdocs%2Fintervals.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHarmonic+series+%28music%29" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1">Datta, A. K.; Sengupta, R.; Dey, N.; Nag, D. (2006). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120118091305/http://www.itcsra.org/sra_story/sra_story_research/sra_story_resrch_links/sra_story_resrch_pubs/hindustani_music.html"><i>Experimental Analysis of Shrutis from Performances in Hindustani Music</i></a>. Kolkata, India: SRD ITC SRA. pp. I–X, 1–103. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/81-903818-0-6" title="Special:BookSources/81-903818-0-6"><bdi>81-903818-0-6</bdi></a>. Archived from <a rel="nofollow" class="external text" href="http://www.itcsra.org/sra_story/sra_story_research/sra_story_resrch_links/sra_story_resrch_pubs/hindustani_music.html">the original</a> on 2012-01-18.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Experimental+Analysis+of+Shrutis+from+Performances+in+Hindustani+Music&rft.place=Kolkata%2C+India&rft.pages=I-X%2C+1-103&rft.pub=SRD+ITC+SRA&rft.date=2006&rft.isbn=81-903818-0-6&rft.au=Datta%2C+A.+K.&rft.au=Sengupta%2C+R.&rft.au=Dey%2C+N.&rft.au=Nag%2C+D.&rft_id=http%3A%2F%2Fwww.itcsra.org%2Fsra_story%2Fsra_story_research%2Fsra_story_resrch_links%2Fsra_story_resrch_pubs%2Fhindustani_music.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHarmonic+series+%28music%29" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1 cs1-prop-foreign-lang-source"><a href="/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz">Helmholtz, H.</a> (1865). <a rel="nofollow" class="external text" href="https://archive.org/details/b21717114"><i>Die Lehre von dem Tonempfindungen. Zweite ausgabe</i></a> (in German). Braunschweig: Vieweg und Sohn. pp. I–XII, 1–606<span class="reference-accessdate">. Retrieved <span class="nowrap">2016-10-12</span></span>.</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+dem+Tonempfindungen.+Zweite+ausgabe&rft.place=Braunschweig&rft.pages=I-XII%2C+1-606&rft.pub=Vieweg+und+Sohn&rft.date=1865&rft.aulast=Helmholtz&rft.aufirst=H.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fb21717114&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHarmonic+series+%28music%29" class="Z3988"></span> (see <i><a href="/wiki/Sensations_of_Tone" title="Sensations of Tone">Sensations of Tone</a></i>)</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1">IEV (1994). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160619074202/http://www.electropedia.org/iev/iev.nsf/d253fda6386f3a52c1257af700281ce6?OpenForm">"Electropedia: The World's Online Electrotechnical Vocabulary"</a>. <a href="/wiki/International_Electrotechnical_Commission" title="International Electrotechnical Commission">International Electrotechnical Commission</a>. Archived from <a rel="nofollow" class="external text" href="http://www.electropedia.org/iev/iev.nsf/d253fda6386f3a52c1257af700281ce6?OpenForm">the original</a> on 2016-06-19<span class="reference-accessdate">. Retrieved <span class="nowrap">2016-06-15</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Electropedia%3A+The+World%27s+Online+Electrotechnical+Vocabulary&rft.pub=International+Electrotechnical+Commission&rft.date=1994&rft.au=IEV&rft_id=http%3A%2F%2Fwww.electropedia.org%2Fiev%2Fiev.nsf%2Fd253fda6386f3a52c1257af700281ce6%3FOpenForm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHarmonic+series+%28music%29" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation encyclopaedia cs1"><a href="/wiki/Horace_Lamb" title="Horace Lamb">Lamb, Horace</a> (1911). <span class="cs1-ws-icon" title="s:1911 Encyclopædia Britannica/Harmonic Analysis"><a class="external text" href="https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Harmonic_Analysis">"Harmonic Analysis" </a></span>. In <a href="/wiki/Hugh_Chisholm" title="Hugh Chisholm">Chisholm, Hugh</a> (ed.). <i><a href="/wiki/Encyclop%C3%A6dia_Britannica_Eleventh_Edition" title="Encyclopædia Britannica Eleventh Edition">Encyclopædia Britannica</a></i>. Vol. 12 (11th ed.). Cambridge University Press. pp. 956, 958.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Harmonic+Analysis&rft.btitle=Encyclop%C3%A6dia+Britannica&rft.pages=956%2C+958&rft.edition=11th&rft.pub=Cambridge+University+Press&rft.date=1911&rft.aulast=Lamb&rft.aufirst=Horace&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHarmonic+series+%28music%29" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><a href="/wiki/Harry_Partch" title="Harry Partch">Partch, Harry</a> (1974). <a rel="nofollow" class="external text" href="https://monoskop.org/File:Partch_Harry_Genesis_of_a_Music_2nd_ed.pdf"><i>Genesis of a Music: An Account of a Creative Work, Its Roots, and Its Fulfillments</i></a> <span class="cs1-format">(PDF)</span> (2nd enlarged ed.). New York: Da Capo Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-306-80106-X" title="Special:BookSources/0-306-80106-X"><bdi>0-306-80106-X</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">2016-06-15</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Genesis+of+a+Music%3A+An+Account+of+a+Creative+Work%2C+Its+Roots%2C+and+Its+Fulfillments&rft.place=New+York&rft.edition=2nd+enlarged&rft.pub=Da+Capo+Press&rft.date=1974&rft.isbn=0-306-80106-X&rft.aulast=Partch&rft.aufirst=Harry&rft_id=http%3A%2F%2Fmonoskop.org%2FFile%3APartch_Harry_Genesis_of_a_Music_2nd_ed.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHarmonic+series+%28music%29" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1">Schouten, J. F. (February 24, 1940). <a rel="nofollow" class="external text" href="http://www.dwc.knaw.nl/DL/publications/PU00017418.pdf"><i>The residue, a new component in subjective sound analysis</i></a> <span class="cs1-format">(PDF)</span>. Eindhoven, Holland: Natuurkundig Laboratorium der N. V. Philips' Gloeilampenfabrieken (communicated by Prof. G. Holst at the meeting). pp. 356–65<span class="reference-accessdate">. Retrieved <span class="nowrap">2016-09-26</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+residue%2C+a+new+component+in+subjective+sound+analysis&rft.place=Eindhoven%2C+Holland&rft.pages=356-65&rft.pub=Natuurkundig+Laboratorium+der+N.+V.+Philips%27+Gloeilampenfabrieken+%28communicated+by+Prof.+G.+Holst+at+the+meeting%29&rft.date=1940-02-24&rft.au=Schouten%2C+J.+F.&rft_id=http%3A%2F%2Fwww.dwc.knaw.nl%2FDL%2Fpublications%2FPU00017418.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHarmonic+series+%28music%29" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1 cs1-prop-script cs1-prop-foreign-lang-source">Волконский, Андрей Михайлович (1998). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20230418120914/http://maxima-library.org/avtory/avtorskie-serii/b/291722"><bdi lang="ru">Основы темперации</bdi></a> (in Russian). Композитор, Москва. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/5-85285-184-1" title="Special:BookSources/5-85285-184-1"><bdi>5-85285-184-1</bdi></a>. Archived from <a rel="nofollow" class="external text" href="http://maxima-library.org/avtory/avtorskie-serii/b/291722">the original</a> on 2023-04-18<span class="reference-accessdate">. Retrieved <span class="nowrap">2016-06-15</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%D0%9E%D1%81%D0%BD%D0%BE%D0%B2%D1%8B+%D1%82%D0%B5%D0%BC%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B8&rft.pub=%D0%9A%D0%BE%D0%BC%D0%BF%D0%BE%D0%B7%D0%B8%D1%82%D0%BE%D1%80%2C+%D0%9C%D0%BE%D1%81%D0%BA%D0%B2%D0%B0&rft.date=1998&rft.isbn=5-85285-184-1&rft.au=%D0%92%D0%BE%D0%BB%D0%BA%D0%BE%D0%BD%D1%81%D0%BA%D0%B8%D0%B9%2C+%D0%90%D0%BD%D0%B4%D1%80%D0%B5%D0%B9+%D0%9C%D0%B8%D1%85%D0%B0%D0%B9%D0%BB%D0%BE%D0%B2%D0%B8%D1%87&rft_id=http%3A%2F%2Fmaxima-library.org%2Favtory%2Favtorskie-serii%2Fb%2F291722&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHarmonic+series+%28music%29" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1 cs1-prop-script cs1-prop-foreign-lang-source">Тюлин, Юрий Николаевич (1966). Беспалова, Н. (ed.). <bdi lang="ru">Учение о гармонии</bdi> [<i>The teaching on harmony</i>] (in Russian) (Издание Третье, Исправленное и Дополненное = Third Edition, Revised and Enlarged ed.). Moscow: Музыка.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%D0%A3%D1%87%D0%B5%D0%BD%D0%B8%D0%B5+%D0%BE+%D0%B3%D0%B0%D1%80%D0%BC%D0%BE%D0%BD%D0%B8%D0%B8&rft.place=Moscow&rft.edition=%D0%98%D0%B7%D0%B4%D0%B0%D0%BD%D0%B8%D0%B5+%D0%A2%D1%80%D0%B5%D1%82%D1%8C%D0%B5%2C+%D0%98%D1%81%D0%BF%D1%80%D0%B0%D0%B2%D0%BB%D0%B5%D0%BD%D0%BD%D0%BE%D0%B5+%D0%B8+%D0%94%D0%BE%D0%BF%D0%BE%D0%BB%D0%BD%D0%B5%D0%BD%D0%BD%D0%BE%D0%B5+%3D+Third+Edition%2C+Revised+and+Enlarged&rft.pub=%D0%9C%D1%83%D0%B7%D1%8B%D0%BA%D0%B0&rft.date=1966&rft.aulast=%D0%A2%D1%8E%D0%BB%D0%B8%D0%BD&rft.aufirst=%D0%AE%D1%80%D0%B8%D0%B9+%D0%9D%D0%B8%D0%BA%D0%BE%D0%BB%D0%B0%D0%B5%D0%B2%D0%B8%D1%87&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHarmonic+series+%28music%29" class="Z3988"></span></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 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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:Acoustics" title="Template:Acoustics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Acoustics" title="Template talk:Acoustics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Acoustics" title="Special:EditPage/Template:Acoustics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Acoustics" style="font-size:114%;margin:0 4em"><a href="/wiki/Acoustics" title="Acoustics">Acoustics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Acoustical_engineering" title="Acoustical engineering">Acoustical engineering</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/Architectural_acoustics" title="Architectural acoustics">Architectural acoustics</a></li> <li><a href="/wiki/Monochord" title="Monochord">Monochord</a></li> <li><a href="/wiki/Reverberation" title="Reverberation">Reverberation</a></li> <li><a href="/wiki/Soundproofing" title="Soundproofing">Soundproofing</a></li> <li><a href="/wiki/String_vibration" title="String vibration">String vibration</a></li> <li><a href="/wiki/Sympathetic_resonance" title="Sympathetic resonance">Sympathetic resonance</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="5" style="width:1px;padding:0 0 0 2px"><div><div class="plainlist"><ul><li><span typeof="mw:File"><a href="/wiki/File:Spectrogram_showing_shared_partials.png" class="mw-file-description"><img alt="A spectrogram of a violin playing a note and then a perfect fifth above it. The shared partials are highlighted by the white dashes." src="//upload.wikimedia.org/wikipedia/commons/thumb/2/26/Spectrogram_showing_shared_partials.png/80px-Spectrogram_showing_shared_partials.png" decoding="async" width="80" height="67" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/26/Spectrogram_showing_shared_partials.png/120px-Spectrogram_showing_shared_partials.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/26/Spectrogram_showing_shared_partials.png/160px-Spectrogram_showing_shared_partials.png 2x" data-file-width="300" data-file-height="250" /></a></span></li><li><span style="font-size:85%;"><a href="/wiki/Spectrogram" title="Spectrogram">Spectrogram</a></span></li></ul></div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Psychoacoustics" title="Psychoacoustics">Psychoacoustics</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/Pitch_(music)" title="Pitch (music)">Pitch</a> <ul><li><a href="/wiki/Bark_scale" title="Bark scale">Bark scale</a></li> <li><a href="/wiki/Mel_scale" title="Mel scale">Mel scale</a></li></ul></li> <li><a href="/wiki/Equal-loudness_contour" title="Equal-loudness contour">Equal-loudness contour</a> <ul><li><a href="/wiki/Fletcher%E2%80%93Munson_curves" class="mw-redirect" title="Fletcher–Munson curves">Fletcher–Munson curves</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Audio_frequency" title="Audio frequency">Audio frequency</a> and <a href="/wiki/Pitch_(music)" title="Pitch (music)">pitch</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/Beat_(acoustics)" title="Beat (acoustics)">Beat</a></li> <li><a href="/wiki/Formant" title="Formant">Formant</a></li> <li><a href="/wiki/Fundamental_frequency" title="Fundamental frequency">Fundamental frequency</a></li> <li><a href="/wiki/Frequency_spectrum" class="mw-redirect" title="Frequency spectrum">Frequency spectrum</a> <ul><li><a href="/wiki/Harmonic_spectrum" title="Harmonic spectrum">harmonic spectrum</a></li></ul></li> <li><a href="/wiki/Harmonic" title="Harmonic">Harmonic</a> <ul><li><a class="mw-selflink selflink">Series</a></li> <li><a href="/wiki/Inharmonicity" title="Inharmonicity">Inharmonicity</a></li> <li><a href="/wiki/Missing_fundamental" title="Missing fundamental">Missing fundamental</a></li></ul></li> <li><a href="/wiki/Combination_tone" title="Combination tone">Combination tone</a></li> <li><a href="/wiki/Mersenne%27s_laws" title="Mersenne's laws">Mersenne's laws</a></li> <li><a href="/wiki/Overtone" title="Overtone">Overtone</a></li> <li><a href="/wiki/Acoustic_resonance" title="Acoustic resonance">Resonance</a></li> <li><a href="/wiki/Standing_wave" title="Standing wave">Standing wave</a> <ul><li><a href="/wiki/Node_(physics)" title="Node (physics)">Node</a></li></ul></li> <li><a href="/wiki/Undertone_series" title="Undertone series">Subharmonic</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Acousticians</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/John_Backus_(acoustician)" title="John Backus (acoustician)">John Backus</a></li> <li><a href="/wiki/Jens_Blauert" title="Jens Blauert">Jens Blauert</a></li> <li><a href="/wiki/Ernst_Chladni" title="Ernst Chladni">Ernst Chladni</a></li> <li><a href="/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz">Hermann von Helmholtz</a></li> <li><a href="/wiki/Carleen_Hutchins" title="Carleen Hutchins">Carleen Hutchins</a></li> <li><a href="/wiki/Franz_Melde" title="Franz Melde">Franz Melde</a></li> <li><a href="/wiki/Marin_Mersenne" title="Marin Mersenne">Marin Mersenne</a></li> <li><a href="/wiki/Werner_Meyer-Eppler" title="Werner Meyer-Eppler">Werner Meyer-Eppler</a></li> <li><a href="/wiki/John_William_Strutt,_3rd_Baron_Rayleigh" title="John William Strutt, 3rd Baron Rayleigh">Lord Rayleigh</a></li> <li><a href="/wiki/Joseph_Sauveur" title="Joseph Sauveur">Joseph Sauveur</a></li> <li><a href="/wiki/D._Van_Holliday" title="D. Van Holliday">D. Van Holliday</a></li> <li><a href="/wiki/Thomas_Young_(scientist)" title="Thomas Young (scientist)">Thomas Young</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related topics</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/Echo" title="Echo">Echo</a></li> <li><a href="/wiki/Infrasound" title="Infrasound">Infrasound</a></li> <li><a href="/wiki/Sound" title="Sound">Sound</a></li> <li><a href="/wiki/Ultrasound" title="Ultrasound">Ultrasound</a></li> <li><a href="/wiki/Musical_acoustics" title="Musical acoustics">Musical acoustics</a> <ul><li><a href="/wiki/Piano_acoustics" title="Piano acoustics">Piano</a></li> <li><a href="/wiki/Violin_acoustics" title="Violin acoustics">Violin</a></li></ul></li></ul> </div></td></tr><tr><td class="navbox-abovebelow hlist" colspan="3"><div> <ul><li><span class="noviewer" typeof="mw:File"><span 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navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3"><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: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 template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Consonance_and_dissonance" title="Special:EditPage/Template:Consonance and dissonance"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Consonance_and_dissonance" style="font-size:114%;margin:0 4em"><a href="/wiki/Consonance_and_dissonance" title="Consonance and dissonance">Consonance and dissonance</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Musical_argument" title="Musical argument">Argument</a></li> <li><a href="/wiki/Avoid_note" title="Avoid note">Avoid note</a></li> <li><a href="/wiki/Beat_(acoustics)" title="Beat (acoustics)">Beating</a></li> <li><a href="/wiki/Cadence" title="Cadence">Cadence</a></li> <li><a href="/wiki/Chord_(music)" title="Chord (music)">Chord</a></li> <li><a href="/wiki/Interval_(music)" title="Interval (music)">Interval</a></li> <li><a href="/wiki/Musical_note" title="Musical 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 class="mw-selflink selflink">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="Musical_strings,_wires,_and_instruments" 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:Strings_(music)" title="Template:Strings (music)"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Strings_(music)" title="Template talk:Strings (music)"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Strings_(music)" title="Special:EditPage/Template:Strings (music)"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Musical_strings,_wires,_and_instruments" style="font-size:114%;margin:0 4em">Musical <a href="/wiki/String_(music)" title="String (music)">strings</a>, <a href="/wiki/Piano_wire" title="Piano wire">wires</a>, and <a href="/wiki/String_instrument" title="String instrument">instruments</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div><a href="/wiki/List_of_string_instruments" title="List of string instruments">List</a> (<a href="/wiki/List_of_chordophones_by_Hornbostel%E2%80%93Sachs_number" title="List of chordophones by Hornbostel–Sachs number"> Hornbostel–Sachs numbers</a>)</div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bow_(music)" title="Bow (music)">Bow</a></li> <li><a href="/wiki/Bridge_(instrument)" title="Bridge (instrument)">Bridge</a> <ul><li><a href="/wiki/3rd_bridge" title="3rd bridge">Third bridge</a></li></ul></li> <li><a href="/wiki/Chordophone" class="mw-redirect" title="Chordophone">Chordophone</a></li> <li><a href="/wiki/Course_(music)" title="Course (music)">Course</a></li> <li><a href="/wiki/Drone_(music)" class="mw-redirect" title="Drone (music)">Drone</a></li> <li><a href="/wiki/Enharmonic" class="mw-redirect" title="Enharmonic">Enharmonic</a></li> <li><a href="/wiki/Fingerboard" title="Fingerboard">Fingerboard</a></li> <li><a href="/wiki/Fret" title="Fret">Fret</a></li> <li><a href="/wiki/Fundamental_frequency" title="Fundamental frequency">Fundamental</a>/<a class="mw-selflink selflink">Harmonics</a>/<a href="/wiki/Overtone" title="Overtone">Overtones</a>/<a href="/wiki/String_harmonic" title="String harmonic">String harmonic</a></li> <li><a href="/wiki/Longitudinal_wave" title="Longitudinal wave">Longitudinal wave</a> <ul><li><a href="/wiki/Long-string_instrument" title="Long-string instrument">Long-string instrument</a></li></ul></li> <li><a href="/wiki/Melde%27s_experiment" title="Melde's experiment">Melde's experiment</a></li> <li><a href="/wiki/Mersenne%27s_laws" title="Mersenne's laws">Mersenne's laws</a></li> <li><a href="/wiki/Monochord" title="Monochord">Monochord</a></li> <li><i><a href="/wiki/Music_On_A_Long_Thin_Wire" title="Music On A Long Thin Wire">Music On A Long Thin Wire</a></i></li> <li><a href="/wiki/Node_(physics)" title="Node (physics)">Node</a></li> <li><a href="/wiki/Nut_(string_instrument)" title="Nut (string instrument)">Nut</a></li> <li><a href="/wiki/Reentrant_tuning" title="Reentrant tuning">Re-entry</a></li> <li><a href="/wiki/Scale_length_(string_instruments)" title="Scale length (string instruments)">Scale length</a></li> <li><a href="/wiki/Sound_board_(music)" title="Sound board (music)">Soundboard</a></li> <li><a href="/wiki/Standing_wave" title="Standing wave">Standing wave</a></li> <li><a href="/wiki/String_vibration" title="String vibration">String vibration</a></li> <li><a href="/wiki/Transverse_wave" title="Transverse wave">Transverse wave</a></li> <li><a href="/wiki/Tuning_mechanisms_for_stringed_instruments" title="Tuning mechanisms for stringed instruments">Tuning peg</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Monochord" title="Monochord">Monochords</a> and<br /> <a href="/wiki/Musical_bow" title="Musical bow">musical bows</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/Ahardin" title="Ahardin">Ahardin</a></li> <li><a href="/wiki/Berimbau" title="Berimbau">Berimbau</a></li> <li><a href="/wiki/Bladder_fiddle" title="Bladder fiddle">Bladder fiddle</a> <ul><li><a href="/wiki/Boom-ba" class="mw-redirect" title="Boom-ba">Boom-ba</a></li></ul></li> <li><a href="/wiki/%C4%90%C3%A0n_b%E1%BA%A7u" title="Đàn bầu">Đàn bầu</a></li> <li><a href="/wiki/Diddley_bow" title="Diddley bow">Diddley bow</a></li> <li><a href="/wiki/Duxianqin" title="Duxianqin">Duxianqin</a></li> <li><a href="/wiki/Ektara" title="Ektara">Ektara</a></li> <li><a href="/wiki/Ground_bow" title="Ground bow">Ground bow</a></li> <li><a href="/wiki/Ichigenkin" title="Ichigenkin">Ichigenkin</a></li> <li><a href="/wiki/Jap_fiddle" title="Jap fiddle">Japanese fiddle</a></li> <li><a href="/wiki/Jew%27s_harp" title="Jew's harp">Jaw harp</a> <ul><li><a href="/wiki/Genggong" title="Genggong">Genggong</a></li> <li><a href="/wiki/Gogona" title="Gogona">Gogona</a></li> <li><a href="/wiki/Temir_komuz" title="Temir komuz">Khomuz</a></li> <li><a href="/wiki/Kubing" title="Kubing">Kubing</a></li> <li><a href="/wiki/Morsing" title="Morsing">Morsing</a></li> <li><a href="/wiki/Mukkuri" title="Mukkuri">Mukkuri</a></li></ul></li> <li><a href="/wiki/Langeleik" title="Langeleik">Langeleik</a></li> <li><a href="/wiki/Lesiba" title="Lesiba">Lesiba</a></li> <li><a href="/wiki/Masenqo" title="Masenqo">Masenqo</a></li> <li><a href="/wiki/Onavillu" title="Onavillu">Onavillu</a></li> <li><a href="/wiki/Psalmodicon" title="Psalmodicon">Psalmodicon</a></li> <li><a href="/wiki/Tromba_marina" title="Tromba marina">Tromba marina</a></li> <li><a href="/wiki/Tumbi" title="Tumbi">Tumbi</a></li> <li><a href="/wiki/Umuduri" title="Umuduri">Umuduri</a></li> <li><a href="/wiki/Unitar_(instrument)" title="Unitar (instrument)">Unitar</a></li> <li><a href="/wiki/Washtub_bass" title="Washtub bass">Washtub bass</a></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Harmonic_series_(music)&oldid=1251044682">https://en.wikipedia.org/w/index.php?title=Harmonic_series_(music)&oldid=1251044682</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Category</a>: <ul><li><a href="/wiki/Category:Harmonic_series_(music)" 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