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id="toc-Equal-tempered_tuning_systems" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Equal-tempered_tuning_systems"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Equal-tempered tuning systems</span> </div> </a> <ul id="toc-Equal-tempered_tuning_systems-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Just_intonation_tuning_systems" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Just_intonation_tuning_systems"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Just intonation tuning systems</span> </div> </a> <ul id="toc-Just_intonation_tuning_systems-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Playing_quarter_tones" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Playing_quarter_tones"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Playing quarter tones</span> </div> </a> <ul id="toc-Playing_quarter_tones-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Music_of_the_Middle_East" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Music_of_the_Middle_East"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Music of the Middle East</span> </div> </a> <button aria-controls="toc-Music_of_the_Middle_East-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Music of the Middle East subsection</span> </button> <ul id="toc-Music_of_the_Middle_East-sublist" class="vector-toc-list"> <li id="toc-Quarter-tone_scale" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Quarter-tone_scale"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Quarter-tone scale</span> </div> </a> <ul id="toc-Quarter-tone_scale-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-In_popular_Western_music" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#In_popular_Western_music"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>In popular Western music</span> </div> </a> <ul id="toc-In_popular_Western_music-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ancient_Greek_tetrachords" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ancient_Greek_tetrachords"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Ancient Greek tetrachords</span> </div> </a> <ul id="toc-Ancient_Greek_tetrachords-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Interval_size_in_equal_temperament" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Interval_size_in_equal_temperament"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Interval size in equal temperament</span> </div> </a> <ul id="toc-Interval_size_in_equal_temperament-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">7</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </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 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mw-list-item"><a href="https://ca.wikipedia.org/wiki/Quart_de_to" title="Quart de to – Catalan" lang="ca" hreflang="ca" data-title="Quart de to" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Cuarto_de_tono" title="Cuarto de tono – Spanish" lang="es" hreflang="es" data-title="Cuarto de tono" 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/Kvarontono" title="Kvarontono – Esperanto" lang="eo" hreflang="eo" data-title="Kvarontono" 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%B1%D8%A8%D8%B9_%D9%BE%D8%B1%D8%AF%D9%87" title="ربع پرده – Persian" lang="fa" hreflang="fa" data-title="ربع پرده" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Quart_de_ton" title="Quart de ton – French" lang="fr" hreflang="fr" data-title="Quart de ton" 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/%EC%82%AC%EB%B6%84%EC%9D%8C" title="사분음 – Korean" lang="ko" hreflang="ko" data-title="사분음" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%94%D5%A1%D5%BC%D5%B8%D6%80%D5%A4%D5%BF%D5%B8%D5%B6%D5%A1%D5%B5%D5%AB%D5%B6_%D5%B0%D5%A1%D5%B4%D5%A1%D5%AF%D5%A1%D6%80%D5%A3" title="Քառորդտոնային համակարգ – Armenian" lang="hy" hreflang="hy" data-title="Քառորդտոնային համակարգ" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Kwarttoonverdeling" title="Kwarttoonverdeling – Dutch" lang="nl" hreflang="nl" data-title="Kwarttoonverdeling" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%9B%9B%E5%88%86%E9%9F%B3" title="四分音 – Japanese" lang="ja" hreflang="ja" data-title="四分音" data-language-autonym="日本語" data-language-local-name="Japanese" 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</div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Musical interval</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">"24 equal temperament" redirects here. For other uses, see <a href="/wiki/Arab_tone_system" title="Arab tone system">Arab tone system</a>.</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><span><audio id="mwe_player_3" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-mwtitle="Quarter_tone_on_C.mid" data-mwprovider="wikimediacommons" resource="/wiki/File:Quarter_tone_on_C.mid"><source src="//upload.wikimedia.org/wikipedia/commons/b/b8/Quarter_tone_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/b8/Quarter_tone_on_C.mid/Quarter_tone_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/b8/Quarter_tone_on_C.mid/Quarter_tone_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span><figcaption>Quarter tone on C</figcaption></figure> <p>A <b>quarter tone</b> is a pitch halfway between the usual notes of a <a href="/wiki/Chromatic_scale" title="Chromatic scale">chromatic scale</a> or an <a href="/wiki/Interval_(music)" title="Interval (music)">interval</a> about half as wide (orally, or logarithmically) as a <a href="/wiki/Semitone" title="Semitone">semitone</a>, which itself is half a <a href="/wiki/Major_second" title="Major second">whole tone</a>. Quarter tones divide the octave by 50 <a href="/wiki/Cent_(music)" title="Cent (music)">cents</a> each, and have 24 different pitches. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Heckel_ViertelTonTRP_C.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a7/Heckel_ViertelTonTRP_C.jpg/330px-Heckel_ViertelTonTRP_C.jpg" decoding="async" width="330" height="137" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a7/Heckel_ViertelTonTRP_C.jpg/495px-Heckel_ViertelTonTRP_C.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a7/Heckel_ViertelTonTRP_C.jpg/660px-Heckel_ViertelTonTRP_C.jpg 2x" data-file-width="1747" data-file-height="723" /></a><figcaption><a href="/wiki/Trumpet" title="Trumpet">Trumpet</a> with 3 normal valves and a quartering on the extension valve (right)</figcaption></figure> <p>Quarter tones have their roots in the music of the Middle East and more specifically in <a href="/wiki/Persian_traditional_music" title="Persian traditional music">Persian traditional music</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> However, the first evidenced proposal of the <a href="/wiki/Equal_temperament" title="Equal temperament">equally-tempered</a> quarter tone scale, or <b>24 equal temperament</b>, was made by 19th-century music theorists Heinrich Richter in 1823<sup id="cite_ref-JR_2-0" class="reference"><a href="#cite_note-JR-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/Mikhail_Mishaqa" title="Mikhail Mishaqa">Mikhail Mishaqa</a> about 1840.<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> Composers who have written music using this scale include: <a href="/wiki/Pierre_Boulez" title="Pierre Boulez">Pierre Boulez</a>, <a href="/wiki/Juli%C3%A1n_Carrillo" title="Julián Carrillo">Julián Carrillo</a>, <a href="/wiki/Mildred_Couper" title="Mildred Couper">Mildred Couper</a>, <a href="/wiki/George_Enescu" title="George Enescu">George Enescu</a>, <a href="/wiki/Alberto_Ginastera" title="Alberto Ginastera">Alberto Ginastera</a>, <a href="/wiki/G%C3%A9rard_Grisey" title="Gérard Grisey">Gérard Grisey</a>, <a href="/wiki/Alois_H%C3%A1ba" title="Alois Hába">Alois Hába</a>, <a href="/wiki/Ljubica_Mari%C4%87" title="Ljubica Marić">Ljubica Marić</a>, <a href="/wiki/Charles_Ives" title="Charles Ives">Charles Ives</a>, <a href="/wiki/Tristan_Murail" title="Tristan Murail">Tristan Murail</a>, <a href="/wiki/Krzysztof_Penderecki" title="Krzysztof Penderecki">Krzysztof Penderecki</a>, <a href="/wiki/Giacinto_Scelsi" title="Giacinto Scelsi">Giacinto Scelsi</a>, <a href="/wiki/Ammar_El_Sherei" title="Ammar El Sherei">Ammar El Sherei</a>, <a href="/wiki/Karlheinz_Stockhausen" title="Karlheinz Stockhausen">Karlheinz Stockhausen</a>, <a href="/wiki/Tui_St._George_Tucker" title="Tui St. George Tucker">Tui St. George Tucker</a>, <a href="/wiki/Ivan_Wyschnegradsky" title="Ivan Wyschnegradsky">Ivan Wyschnegradsky</a>, <a href="/wiki/Iannis_Xenakis" title="Iannis Xenakis">Iannis Xenakis</a>, and <a href="/wiki/Seppe_Gebruers" title="Seppe Gebruers">Seppe Gebruers</a> (See <a href="/wiki/List_of_quarter_tone_pieces" title="List of quarter tone pieces">List of quarter tone pieces</a>.) </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Types">Types<span class="anchor" id="Undecimal_quarter_tone"></span><span class="anchor" id="Thirty-third_harmonic"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quarter_tone&action=edit&section=1" title="Edit section: Types"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Equal-tempered_tuning_systems">Equal-tempered tuning systems</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quarter_tone&action=edit&section=2" title="Edit section: Equal-tempered tuning systems"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Ives_quarter_tone_fundamental_chord.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Ives_quarter_tone_fundamental_chord.png/290px-Ives_quarter_tone_fundamental_chord.png" decoding="async" width="290" height="184" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Ives_quarter_tone_fundamental_chord.png/435px-Ives_quarter_tone_fundamental_chord.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Ives_quarter_tone_fundamental_chord.png/580px-Ives_quarter_tone_fundamental_chord.png 2x" data-file-width="581" data-file-height="368" /></a><figcaption>Composer Charles Ives chose the four-note chord above (C–D<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="mw-default-size skin-invert" typeof="mw:File"><a href="/wiki/File:Llpd%2B1%C2%BD.svg" class="mw-file-description" title="three quarter sharp"><img alt="three quarter sharp" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/Llpd%2B1%C2%BD.svg/8px-Llpd%2B1%C2%BD.svg.png" decoding="async" width="8" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/Llpd%2B1%C2%BD.svg/12px-Llpd%2B1%C2%BD.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/54/Llpd%2B1%C2%BD.svg/16px-Llpd%2B1%C2%BD.svg.png 2x" data-file-width="137" data-file-height="200" /></a></span></span>–G–A<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="mw-default-size skin-invert" typeof="mw:File"><a href="/wiki/File:Llpd%2B1%C2%BD.svg" class="mw-file-description" title="three quarter sharp"><img alt="three quarter sharp" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/Llpd%2B1%C2%BD.svg/8px-Llpd%2B1%C2%BD.svg.png" decoding="async" width="8" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/Llpd%2B1%C2%BD.svg/12px-Llpd%2B1%C2%BD.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/54/Llpd%2B1%C2%BD.svg/16px-Llpd%2B1%C2%BD.svg.png 2x" data-file-width="137" data-file-height="200" /></a></span></span>) as good possibility for a "fundamental" chord in the quarter-tone scale, akin not to the tonic but to the major chord of traditional tonality.<sup id="cite_ref-Boatwright_4-0" class="reference"><a href="#cite_note-Boatwright-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><span class="mw-default-size" typeof="mw:File"><span><audio id="mwe_player_4" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-durationhint="7" data-mwtitle="Ives_fundamental_chord_(quarter_tones).ogg" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/b/b9/Ives_fundamental_chord_%28quarter_tones%29.ogg" type="audio/ogg; codecs="vorbis"" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/b9/Ives_fundamental_chord_%28quarter_tones%29.ogg/Ives_fundamental_chord_%28quarter_tones%29.ogg.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span><span class="mw-default-size" typeof="mw:File"><span><audio id="mwe_player_5" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-mwtitle="Ives_quarter_tone_fundamental_chord_arp.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/5/55/Ives_quarter_tone_fundamental_chord_arp.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/55/Ives_quarter_tone_fundamental_chord_arp.mid/Ives_quarter_tone_fundamental_chord_arp.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/55/Ives_quarter_tone_fundamental_chord_arp.mid/Ives_quarter_tone_fundamental_chord_arp.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span></figcaption></figure> <style data-mw-deduplicate="TemplateStyles:r1034237262">.mw-parser-output .stack{box-sizing:border-box}.mw-parser-output .stack>div{margin:1px;overflow:hidden}@media all and (min-width:720px){.mw-parser-output .stack-clear-left{float:left;clear:left}.mw-parser-output .stack-clear-right{float:right;clear:right}.mw-parser-output .stack-left{float:left}.mw-parser-output .stack-right{float:right}.mw-parser-output .stack-margin-clear-left{float:left;clear:left;margin-right:1em}.mw-parser-output .stack-margin-clear-right{float:right;clear:right;margin-left:1em}.mw-parser-output .stack-margin-left{float:left;margin-right:1em}.mw-parser-output .stack-margin-right{float:right;margin-left:1em}}</style><div class="stack mw-stack stack-right"><div><figure class="mw-default-size" typeof="mw:File/Thumb"><span><audio id="mwe_player_6" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-mwtitle="Neutral_second_on_C.mid" data-mwprovider="wikimediacommons" resource="/wiki/File:Neutral_second_on_C.mid"><source src="//upload.wikimedia.org/wikipedia/commons/2/2d/Neutral_second_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/2/2d/Neutral_second_on_C.mid/Neutral_second_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/2/2d/Neutral_second_on_C.mid/Neutral_second_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span><figcaption>Neutral second on C</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><span><audio id="mwe_player_7" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-durationhint="7" data-mwtitle="8-tet_scale_on_C.mid" data-mwprovider="wikimediacommons" resource="/wiki/File:8-tet_scale_on_C.mid"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/7/7f/8-tet_scale_on_C.mid/8-tet_scale_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/7/7f/8-tet_scale_on_C.mid/8-tet_scale_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/7/7f/8-tet_scale_on_C.mid" type="audio/midi" data-width="0" data-height="0" /></audio></span><figcaption>8-tet scale on C</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><span><audio id="mwe_player_8" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-mwtitle="Major_second_on_C.mid" data-mwprovider="wikimediacommons" resource="/wiki/File:Major_second_on_C.mid"><source src="//upload.wikimedia.org/wikipedia/commons/b/b9/Major_second_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/b9/Major_second_on_C.mid/Major_second_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/b9/Major_second_on_C.mid/Major_second_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span><figcaption>Major second on C</figcaption></figure></div></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Subminor_seventh_on_C.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/Subminor_seventh_on_C.png/220px-Subminor_seventh_on_C.png" decoding="async" width="220" height="93" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/Subminor_seventh_on_C.png/330px-Subminor_seventh_on_C.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/54/Subminor_seventh_on_C.png/440px-Subminor_seventh_on_C.png 2x" data-file-width="6532" data-file-height="2762" /></a><figcaption>The "subminor seventh": <span class="nowrap">B<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="mw-default-size skin-invert" typeof="mw:File"><a href="/wiki/File:Three_quarter_flat.svg" class="mw-file-description" title="three quarter flat"><img alt="three quarter flat" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Three_quarter_flat.svg/10px-Three_quarter_flat.svg.png" decoding="async" width="10" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Three_quarter_flat.svg/15px-Three_quarter_flat.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Three_quarter_flat.svg/20px-Three_quarter_flat.svg.png 2x" data-file-width="166" data-file-height="200" /></a></span></span></span>=<span class="nowrap">A<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="mw-default-size skin-invert" typeof="mw:File"><a href="/wiki/File:Arabic_music_notation_half_sharp.svg" class="mw-file-description" title="half sharp"><img alt="half sharp" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Arabic_music_notation_half_sharp.svg/6px-Arabic_music_notation_half_sharp.svg.png" decoding="async" width="6" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Arabic_music_notation_half_sharp.svg/9px-Arabic_music_notation_half_sharp.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Arabic_music_notation_half_sharp.svg/12px-Arabic_music_notation_half_sharp.svg.png 2x" data-file-width="106" data-file-height="200" /></a></span></span></span>, 19 quarter tones. It approximates the <a href="/wiki/Harmonic_seventh" title="Harmonic seventh">harmonic seventh</a>, <span class="nowrap">B<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="mw-default-size skin-invert" typeof="mw:File"><a href="/wiki/File:7_rightside_up.png" class="mw-file-description" title="7"><img alt="7" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/7_rightside_up.png/8px-7_rightside_up.png" decoding="async" width="8" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/7_rightside_up.png/13px-7_rightside_up.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1c/7_rightside_up.png/17px-7_rightside_up.png 2x" data-file-width="84" data-file-height="158" /></a></span></span><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span></span>. Maneri-Sims notation: <span class="nowrap">B<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="mw-default-size skin-invert" typeof="mw:File"><a href="/wiki/File:Sims_flagged_arrow_up.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Sims_flagged_arrow_up.svg/7px-Sims_flagged_arrow_up.svg.png" decoding="async" width="7" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Sims_flagged_arrow_up.svg/10px-Sims_flagged_arrow_up.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Sims_flagged_arrow_up.svg/13px-Sims_flagged_arrow_up.svg.png 2x" data-file-width="348" data-file-height="712" /></a></span></span><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span></span></figcaption></figure> <p>The term <i>quarter tone</i> can refer to a number of different intervals, all very close in size. For example, some 17th- and 18th-century theorists used the term to describe the distance between a sharp and enharmonically distinct flat in mean-tone temperaments (e.g., 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>).<sup id="cite_ref-JR_2-1" class="reference"><a href="#cite_note-JR-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> In the quarter-tone scale, also called <b>24-tone equal temperament</b> (24-TET), the quarter tone is 50 <a href="/wiki/Cent_(music)" title="Cent (music)">cents</a>, or a frequency ratio of <span class="nowrap"><sup style="margin-right: -0.5em; vertical-align: 0.8em;">24</sup>√<span style="border-top:1px solid; padding:0 0.1em;">2</span></span> or approximately 1.0293, and divides the octave into 24 equal steps (<a href="/wiki/Equal_temperament" title="Equal temperament">equal temperament</a>). In this scale the quarter tone is the smallest <a href="/wiki/Step_(music)" class="mw-redirect" title="Step (music)">step</a>. A semitone is thus made of two steps, and three steps make a <b>three-quarter tone</b> or <a href="/wiki/Neutral_second" class="mw-redirect" title="Neutral second">neutral second</a>, half of a <a href="/wiki/Minor_third" title="Minor third">minor third</a>. The 8-TET scale is composed of three-quarter tones. Four steps make a whole tone. </p><p>Quarter tones and intervals close to them also occur in a number of other equally tempered tuning systems. <a href="/wiki/22_equal_temperament" title="22 equal temperament">22-TET</a> contains an interval of 54.55 cents, slightly wider than a quarter-tone, whereas <a href="/wiki/53_equal_temperament" title="53 equal temperament">53-TET</a> has an interval of 45.28 cents, slightly smaller. <a href="/wiki/72_equal_temperament" title="72 equal temperament">72-TET</a> also has equally tempered quarter-tones, and indeed contains three quarter-tone scales, since 72 is divisible by 24. The smallest interval in <a href="/wiki/31_equal_temperament" title="31 equal temperament">31 equal temperament</a> (the "diesis" of 38.71 cents) is half a <a href="/wiki/Chromatic_semitone" class="mw-redirect" title="Chromatic semitone">chromatic semitone</a>, one-third of a <a href="/wiki/Diatonic_semitone" class="mw-redirect" title="Diatonic semitone">diatonic semitone</a> and one-fifth of a whole tone, so it may function as a quarter tone, a fifth-tone <i>or</i> a sixth-tone. </p> <div class="mw-heading mw-heading3"><h3 id="Just_intonation_tuning_systems">Just intonation tuning systems</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quarter_tone&action=edit&section=3" title="Edit section: Just intonation tuning systems"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In <a href="/wiki/Just_intonation" title="Just intonation">just intonation</a> the quarter tone can be represented by the <a href="/wiki/Septimal_quarter_tone" title="Septimal quarter tone">septimal quarter tone</a>, 36:35 (48.77 cents), or by the <b>undecimal quarter tone</b> (i.e. the <b>thirty-third harmonic</b>), 33:32 (53.27 cents), approximately half the semitone of 16:15 or 25:24. The ratio of 36:35 is only 1.23 cents narrower than a 24-TET quarter tone. This just ratio is also the difference between a <a href="/wiki/Minor_third" title="Minor third">minor third</a> (6:5) and <a href="/wiki/Septimal_minor_third" title="Septimal minor third">septimal minor third</a> (7:6). </p><p>Composer <a href="/wiki/Ben_Johnston_(composer)" title="Ben Johnston (composer)">Ben Johnston</a>, to accommodate the <a href="/wiki/Just_interval" class="mw-redirect" title="Just interval">just</a> septimal quarter tone, uses a small "7" (<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="mw-default-size skin-invert" typeof="mw:File"><a href="/wiki/File:7_rightside_up.png" class="mw-file-description" title="7"><img alt="7" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/7_rightside_up.png/8px-7_rightside_up.png" decoding="async" width="8" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/7_rightside_up.png/13px-7_rightside_up.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1c/7_rightside_up.png/17px-7_rightside_up.png 2x" data-file-width="84" data-file-height="158" /></a></span></span>) as an accidental to indicate a note is lowered 49 cents, or an upside down "<span style="display:inline-block;top:0.5em;transform:matrix(-1, 0, 0, -1, 0, 0);">7</span>" (<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="mw-default-size skin-invert" typeof="mw:File"><a href="/wiki/File:7_upside_down.png" class="mw-file-description" title="7 upside-down"><img alt="7 upside-down" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/7_upside_down.png/8px-7_upside_down.png" decoding="async" width="8" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/7_upside_down.png/13px-7_upside_down.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4b/7_upside_down.png/17px-7_upside_down.png 2x" data-file-width="84" data-file-height="158" /></a></span></span>) to indicate a note is raised 49 cents,<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> or a ratio of 36:35.<sup id="cite_ref-Fonville_6-0" class="reference"><a href="#cite_note-Fonville-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Johnston uses an upward and downward arrow to indicate a note is raised or lowered by a ratio of 33:32, or 53 cents.<sup id="cite_ref-Fonville_6-1" class="reference"><a href="#cite_note-Fonville-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> The <a href="/wiki/Maneri-Sims_notation" class="mw-redirect" title="Maneri-Sims notation">Maneri-Sims notation</a> system designed for <a href="/wiki/72-et" class="mw-redirect" title="72-et">72-et</a> uses the accidentals <span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="mw-default-size skin-invert" typeof="mw:File"><a href="/wiki/File:Sims_flagged_arrow_down.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Sims_flagged_arrow_down.svg/10px-Sims_flagged_arrow_down.svg.png" decoding="async" width="10" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Sims_flagged_arrow_down.svg/15px-Sims_flagged_arrow_down.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Sims_flagged_arrow_down.svg/21px-Sims_flagged_arrow_down.svg.png 2x" data-file-width="525" data-file-height="712" /></a></span></span> and <span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="mw-default-size skin-invert" typeof="mw:File"><a href="/wiki/File:Sims_flagged_arrow_up.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Sims_flagged_arrow_up.svg/7px-Sims_flagged_arrow_up.svg.png" decoding="async" width="7" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Sims_flagged_arrow_up.svg/10px-Sims_flagged_arrow_up.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Sims_flagged_arrow_up.svg/13px-Sims_flagged_arrow_up.svg.png 2x" data-file-width="348" data-file-height="712" /></a></span></span> for a quarter tone (36:35 or 48.77 cents) up and down. </p> <div class="mw-heading mw-heading2"><h2 id="Playing_quarter_tones">Playing quarter tones</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quarter_tone&action=edit&section=4" title="Edit section: Playing quarter tones"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:QuartertoneClarinet.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/58/QuartertoneClarinet.jpg/220px-QuartertoneClarinet.jpg" decoding="async" width="220" height="313" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/58/QuartertoneClarinet.jpg/330px-QuartertoneClarinet.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/5/58/QuartertoneClarinet.jpg 2x" data-file-width="422" data-file-height="600" /></a><figcaption><a href="/wiki/Quarter_tone_clarinet" title="Quarter tone clarinet">Quarter tone clarinet</a> by Fritz Schüller viewed from four sides.</figcaption></figure> <p>Any tunable musical instrument can be used to perform quarter tones, if two players and two identical instruments, with one tuned a quarter tone higher, are used. As this requires neither a special instrument nor special techniques, much quarter toned music is written for pairs of pianos, violins, harps, etc. The retuning of the instrument, and then returning it to its former pitch, is easy for violins, harder for harps, and slow and relatively expensive for pianos. </p><p>The following deals with the ability of single instruments to produce quarter tones. In Western instruments, this means "in addition to the usual 12-tone system". Because many musical instruments manufactured today (2018) are designed for the 12-tone scale, not all are usable for playing quarter tones. Sometimes special playing techniques must be used. </p><p>Conventional musical instruments that <i>cannot</i> play quarter tones (except by using special techniques—see below) include: </p> <ul><li>Most standard or unmodified non-electronic keyboard instruments, such as <a href="/wiki/Piano" title="Piano">pianos</a>, <a href="/wiki/Organ_(instrument)" class="mw-redirect" title="Organ (instrument)">organs</a>, and <a href="/wiki/Accordion" title="Accordion">accordions</a></li> <li><a href="/wiki/Fret" title="Fret">Fretted</a> <a href="/wiki/String_instruments" class="mw-redirect" title="String instruments">string instruments</a> such as <a href="/wiki/Guitars" class="mw-redirect" title="Guitars">guitars</a>, <a href="/wiki/Bass_guitars" class="mw-redirect" title="Bass guitars">bass guitars</a>, and <a href="/wiki/Ukulele" title="Ukulele">ukuleles</a> (though on these it is possible to play quarter tones by <a href="/wiki/Bend_(guitar)" class="mw-redirect" title="Bend (guitar)">pitch-bending</a>, with special tunings, or with customized necks)</li> <li><a href="/wiki/Percussion_instrument#Definite_pitch" title="Percussion instrument">Pitched percussion instruments</a>, if standard techniques are used, and if the instruments are not tunable</li> <li>Western <a href="/wiki/Wind_instruments" class="mw-redirect" title="Wind instruments">wind instruments</a> that use keys or valves <ul><li><a href="/wiki/Woodwind_instruments" class="mw-redirect" title="Woodwind instruments">Woodwind instruments</a>, such as clarinets, saxophones, flutes, and oboes (though with many of these, it is still possible using non-standard techniques such as special fingerings or by the player manipulating their <a href="/wiki/Embouchure" title="Embouchure">embouchure</a>, to play at least <i>some</i> quarter tones, if not a whole <a href="/wiki/Scale_(music)" title="Scale (music)">scale</a>)</li> <li>Valved brass instruments (<a href="/wiki/Trumpet" title="Trumpet">trumpet</a>, <a href="/wiki/Tuba" title="Tuba">tuba</a>) (though, as with woodwinds, embouchure manipulation, as well as <a href="/wiki/Harmonic_series_(music)" title="Harmonic series (music)">harmonic</a> tones that fall closer to quarter-tones than half-tones, make quarter-tone scales possible; the <a href="/wiki/Horn_(instrument)" title="Horn (instrument)">horn</a> technique of adjusting pitch with the right hand in the bell makes this instrument an exception)</li></ul></li> <li><a href="/wiki/Harmonica" title="Harmonica">Harmonica</a> (although note bending is a common technique)</li></ul> <p>Conventional musical instruments that <i>can</i> play quarter tones include </p> <ul><li>Electronic instruments: <ul><li><a href="/wiki/Synthesizer" title="Synthesizer">Synthesizers</a>, using either special keyboard controllers or continuous-pitch controllers such as <a href="/wiki/Synthesizer#Fingerboard_controller" title="Synthesizer">fingerboard controllers</a>, or when controlled by a <a href="/wiki/Music_sequencer" title="Music sequencer">sequencer</a> capable of outputting quarter-tone control signals.</li> <li><a href="/wiki/Theremin" title="Theremin">Theremins</a> and other <a href="/wiki/Category:Continuous_pitch_instruments" title="Category:Continuous pitch instruments">continuously pitched instruments</a></li></ul></li> <li>Fretless <a href="/wiki/String_instrument" title="String instrument">string instruments</a>, such as the <a href="/wiki/Violin_family" title="Violin family">violin family</a>, <a href="/wiki/Fretless_guitar" title="Fretless guitar">fretless guitars</a>, fretless electric basses, <a href="/wiki/Oud" title="Oud">ouds</a>, and members of the <a href="/wiki/Huqin" title="Huqin">huqin</a> family of instruments.</li> <li>String instruments with movable frets (such as the <a href="/wiki/Sitar" title="Sitar">sitar</a>)</li> <li>Specially fretted string instruments (such as the Turkish <a href="/wiki/Ba%C4%9Flama" title="Bağlama">bağlama</a>).</li> <li>Fretted string instruments <a href="/wiki/Guitar_tunings" title="Guitar tunings">specially tuned</a> to quarter tones</li> <li><a href="/wiki/Pedal_steel_guitar" title="Pedal steel guitar">Pedal steel guitar</a></li> <li>Wind instruments whose main means of tone-control is a slide, such as <a href="/wiki/Trombone" title="Trombone">trombones</a>, the <a href="/wiki/P._D._Q._Bach#Tromboon" title="P. D. Q. Bach">tromboon</a> invented by <a href="/wiki/P._D._Q._Bach" title="P. D. Q. Bach">P. D. Q. Bach</a>, the <a href="/wiki/Slide_trumpet" title="Slide trumpet">slide trumpet</a> and the <a href="/wiki/Slide_whistle" title="Slide whistle">slide whistle</a></li> <li>Specially keyed woodwind instruments. A <a href="/wiki/Quarter_tone_clarinet" title="Quarter tone clarinet">quarter tone clarinet</a> was built by Fritz Schüller (1883–1977) of <a href="/wiki/Markneukirchen" title="Markneukirchen">Markneukirchen</a>, and a quarter tone mechanism for flutes by Eva Kingma.<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></li> <li>Valved brass instruments with extra, quarter-tone valves, and natural brass instruments that play through the <a href="/wiki/Harmonic_series_(music)#Harmonics_and_tuning" title="Harmonic series (music)">11th and 13th partials of the harmonic series</a></li> <li><a href="/wiki/Voice" class="mw-redirect" title="Voice">Voice</a></li> <li><a href="/wiki/Kazoo" title="Kazoo">Kazoo</a></li> <li><a href="/wiki/Percussion_instrument#Definite_pitch" title="Percussion instrument">Pitched percussion instruments</a>, when tuning permits (e.g., timpani), or using special techniques</li></ul> <p>Other instruments can be used to play quarter tones when using <a href="/wiki/Audio_signal_processing" title="Audio signal processing">audio signal processing</a> effects such as <a href="/wiki/Pitch_shifter_(audio_processor)" class="mw-redirect" title="Pitch shifter (audio processor)">pitch shifting</a>. </p><p>Quarter-tone pianos have been built, which consist essentially of two pianos with two keyboards stacked one above the other in a single case, one tuned a quarter tone higher than the other.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (June 2013)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading2"><h2 id="Music_of_the_Middle_East">Music of the Middle East</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quarter_tone&action=edit&section=5" title="Edit section: Music of the Middle East"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Persian_traditional_music" title="Persian traditional music">Persian traditional music</a>, <a href="/wiki/Arabic_music" title="Arabic music">Arabic music</a>, and <a href="/wiki/Arab_tone_system" title="Arab tone system">Arab tone system</a></div> <p>Many Persian <a href="/wiki/Dastgah" class="mw-redirect" title="Dastgah">dastgah</a> and Arabic <a href="/wiki/Arabic_maqam" title="Arabic maqam"><i>maqamat</i></a> contain intervals of three-quarter tone size; a short list of these follows.<sup id="cite_ref-Spector_8-0" class="reference"><a href="#cite_note-Spector-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <ol><li><a href="/wiki/Bayati_(maqam)" title="Bayati (maqam)">Bayati</a> (<span title="Arabic-language text"><span lang="ar" dir="rtl">بیاتی</span></span>): D E<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="mw-default-size skin-invert" typeof="mw:File"><a href="/wiki/File:Llpd-%C2%BD.svg" class="mw-file-description" title="half flat"><img alt="half flat" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Llpd-%C2%BD.svg/4px-Llpd-%C2%BD.svg.png" decoding="async" width="4" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Llpd-%C2%BD.svg/7px-Llpd-%C2%BD.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Llpd-%C2%BD.svg/9px-Llpd-%C2%BD.svg.png 2x" data-file-width="77" data-file-height="200" /></a></span></span> F G A B<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span> C D <dl><dd><div class="mw-ext-score noresize" data-midi="//upload.wikimedia.org/score/a/l/aly4oxgblbn0hmwlj206tgugzpx1zhx/aly4oxgb.midi"><img src="//upload.wikimedia.org/score/a/l/aly4oxgblbn0hmwlj206tgugzpx1zhx/aly4oxgb.png" width="212" height="52" alt="
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" /><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-durationhint="11" data-mwtitle="Arabic-scale_rast.ogg" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/8/88/Arabic-scale_rast.ogg" type="audio/ogg; codecs="vorbis"" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/88/Arabic-scale_rast.ogg/Arabic-scale_rast.ogg.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span></div></dd></dl></li> <li><a href="/wiki/Saba_(music)" title="Saba (music)">Saba</a> (<span title="Arabic-language text"><span lang="ar" dir="rtl">صبا</span></span>): D E<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="mw-default-size skin-invert" typeof="mw:File"><a href="/wiki/File:Llpd-%C2%BD.svg" class="mw-file-description" title="half flat"><img alt="half flat" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Llpd-%C2%BD.svg/4px-Llpd-%C2%BD.svg.png" decoding="async" width="4" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Llpd-%C2%BD.svg/7px-Llpd-%C2%BD.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Llpd-%C2%BD.svg/9px-Llpd-%C2%BD.svg.png 2x" data-file-width="77" data-file-height="200" /></a></span></span> F G<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span> A B<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span> C D <dl><dd><div class="mw-ext-score noresize" data-midi="//upload.wikimedia.org/score/n/y/nym4j5mmzqhwp4uwydhqwpunnisciyq/nym4j5mm.midi"><img src="//upload.wikimedia.org/score/n/y/nym4j5mmzqhwp4uwydhqwpunnisciyq/nym4j5mm.png" width="213" height="52" alt="
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d4 eeh f ges a bes c d \bar "|"
}
" /><span class="mw-default-size" typeof="mw:File"><span><audio id="mwe_player_2" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-durationhint="11" data-mwtitle="Arabic-scale_saba.ogg" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/9/98/Arabic-scale_saba.ogg" type="audio/ogg; codecs="vorbis"" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/98/Arabic-scale_saba.ogg/Arabic-scale_saba.ogg.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span></div></dd></dl></li> <li><a href="/wiki/Sigah" title="Sigah">Sigah</a> (<span title="Arabic-language text"><span lang="ar" dir="rtl">سه گاه</span></span>): E<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="mw-default-size skin-invert" typeof="mw:File"><a href="/wiki/File:Llpd-%C2%BD.svg" class="mw-file-description" title="half flat"><img alt="half flat" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Llpd-%C2%BD.svg/4px-Llpd-%C2%BD.svg.png" decoding="async" width="4" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Llpd-%C2%BD.svg/7px-Llpd-%C2%BD.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Llpd-%C2%BD.svg/9px-Llpd-%C2%BD.svg.png 2x" data-file-width="77" data-file-height="200" /></a></span></span> F G A B<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="mw-default-size skin-invert" typeof="mw:File"><a href="/wiki/File:Llpd-%C2%BD.svg" class="mw-file-description" title="half flat"><img alt="half flat" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Llpd-%C2%BD.svg/4px-Llpd-%C2%BD.svg.png" decoding="async" width="4" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Llpd-%C2%BD.svg/7px-Llpd-%C2%BD.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Llpd-%C2%BD.svg/9px-Llpd-%C2%BD.svg.png 2x" data-file-width="77" data-file-height="200" /></a></span></span> C D E<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="mw-default-size skin-invert" typeof="mw:File"><a href="/wiki/File:Llpd-%C2%BD.svg" class="mw-file-description" title="half flat"><img alt="half flat" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Llpd-%C2%BD.svg/4px-Llpd-%C2%BD.svg.png" decoding="async" width="4" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Llpd-%C2%BD.svg/7px-Llpd-%C2%BD.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Llpd-%C2%BD.svg/9px-Llpd-%C2%BD.svg.png 2x" data-file-width="77" data-file-height="200" /></a></span></span> <dl><dd><div class="mw-ext-score noresize" data-midi="//upload.wikimedia.org/score/j/0/j0coimkxejm8crfmfmaf5ywflxubxzs/j0coimkx.midi"><img src="//upload.wikimedia.org/score/j/0/j0coimkxejm8crfmfmaf5ywflxubxzs/j0coimkx.png" width="211" height="52" alt="
\relative c' {
\time 8/4 \omit Staff.TimeSignature
eeh f g a beh c d eeh \bar "|"
}
" /><div style="margin-top: 3px;"><audio controls=""><source src="//upload.wikimedia.org/score/j/0/j0coimkxejm8crfmfmaf5ywflxubxzs/j0coimkx.mp3" type="audio/mpeg" /><div>Audio playback is not supported in your browser. You can <a href="//upload.wikimedia.org/score/j/0/j0coimkxejm8crfmfmaf5ywflxubxzs/j0coimkx.mp3">download the audio file</a>.</div></audio></div></div></dd></dl></li> <li><a href="/wiki/Ajam_(maqam)" title="Ajam (maqam)">‘Ajam</a> (<span title="Arabic-language text"><span lang="ar" dir="rtl">عجم</span></span>)</li> <li>Hoseyni</li></ol> <p>The Islamic philosopher and scientist <a href="/wiki/Al-Farabi" title="Al-Farabi">Al-Farabi</a> described a number of intervals in his work in music, including a number of quarter tones. </p><p>Assyrian/Syriac Church Music Scale:<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> </p> <ol><li>Qadmoyo (Bayati)</li> <li>Trayono (Hussayni)</li> <li>Tlithoyo (Segah)</li> <li>Rbiʿoyo (Rast)</li> <li>Hmishoyo</li> <li>Shtithoyo (ʿAjam)</li> <li>Shbiʿoyo</li> <li>Tminoyo</li></ol> <div class="mw-heading mw-heading3"><h3 id="Quarter-tone_scale">Quarter-tone scale</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quarter_tone&action=edit&section=6" title="Edit section: Quarter-tone scale"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Known as <i>gadwal</i> in Arabic,<sup id="cite_ref-Spector_8-1" class="reference"><a href="#cite_note-Spector-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> the <b>quarter-tone scale</b> was developed in the Middle East in the eighteenth century and many of the first detailed writings in the nineteenth century Syria describe the scale as being of 24 equal tones.<sup id="cite_ref-Marcus_10-0" class="reference"><a href="#cite_note-Marcus-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> The invention of the scale is attributed to <a href="/wiki/Mikhail_Mishaqa" title="Mikhail Mishaqa">Mishaqa</a> who wrote a book devoted to the topic<sup id="cite_ref-Mishaqa_11-0" class="reference"><a href="#cite_note-Mishaqa-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> but made clear that his teacher, Sheikh Muhammad al-Attar (1764–1828), was one among many already familiar with the concept.<sup id="cite_ref-Maalouf_12-0" class="reference"><a href="#cite_note-Maalouf-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-ext-score noresize" data-midi="//upload.wikimedia.org/score/4/q/4qps83u9qqz1la8hf045wpnwn5b5u7v/4qps83u9.midi"><img src="//upload.wikimedia.org/score/4/q/4qps83u9qqz1la8hf045wpnwn5b5u7v/4qps83u9.png" width="757" height="143" alt="
\relative c' {
\cadenzaOn \omit Staff.TimeSignature
\tempo 1 = 90 \set Score.tempoHideNote = ##t
c1 cih cis cisih d dih dis disih e eih f fih fis fisih g gih gis gisih a aih ais aisih b bih \bar "|" c \bar "|." \break
c1 ceh b beh bes beseh a aeh aes aeseh g geh ges geseh f feh e eeh ees eeseh d deh des deseh \bar "|" c \bar "|."
}
" /><div style="margin-top: 3px;"><audio controls=""><source src="//upload.wikimedia.org/score/4/q/4qps83u9qqz1la8hf045wpnwn5b5u7v/4qps83u9.mp3" type="audio/mpeg" /><div>Audio playback is not supported in your browser. You can <a href="//upload.wikimedia.org/score/4/q/4qps83u9qqz1la8hf045wpnwn5b5u7v/4qps83u9.mp3">download the audio file</a>.</div></audio></div></div> <p>The quarter tone scale may be primarily a <a href="/wiki/Music_theory" title="Music theory">theoretical</a> construct in Arabic music. The quarter tone gives musicians a "conceptual map" they can use to discuss and compare intervals by number of quarter tones, and this may be one of the reasons it accompanies a renewed interest in theory, with instruction in music theory a mainstream requirement since that period.<sup id="cite_ref-Marcus_10-1" class="reference"><a href="#cite_note-Marcus-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>Previously, pitches of a mode were chosen from a scale consisting of seventeen tones, developed by <a href="/wiki/Safi_al-Din_al-Urmawi" title="Safi al-Din al-Urmawi">Safi al-Din al-Urmawi</a> in the thirteenth century.<sup id="cite_ref-Maalouf_12-1" class="reference"><a href="#cite_note-Maalouf-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:24ed2.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/24ed2.svg/250px-24ed2.svg.png" decoding="async" width="250" height="660" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/24ed2.svg/375px-24ed2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0e/24ed2.svg/500px-24ed2.svg.png 2x" data-file-width="500" data-file-height="1320" /></a><figcaption>19-Limit just intonation intervals approximated in 24 <span class="smallcaps"><span style="font-variant: small-caps; text-transform: lowercase;">TET</span></span></figcaption></figure> <p>Composer <a href="/wiki/Charles_Ives" title="Charles Ives">Charles Ives</a> chose the chord C–D<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="mw-default-size skin-invert" typeof="mw:File"><a href="/wiki/File:Arabic_music_notation_half_sharp.svg" class="mw-file-description" title="half sharp"><img alt="half sharp" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Arabic_music_notation_half_sharp.svg/6px-Arabic_music_notation_half_sharp.svg.png" decoding="async" width="6" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Arabic_music_notation_half_sharp.svg/9px-Arabic_music_notation_half_sharp.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Arabic_music_notation_half_sharp.svg/12px-Arabic_music_notation_half_sharp.svg.png 2x" data-file-width="106" data-file-height="200" /></a></span></span>–F–G<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="mw-default-size skin-invert" typeof="mw:File"><a href="/wiki/File:Arabic_music_notation_half_sharp.svg" class="mw-file-description" title="half sharp"><img alt="half sharp" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Arabic_music_notation_half_sharp.svg/6px-Arabic_music_notation_half_sharp.svg.png" decoding="async" width="6" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Arabic_music_notation_half_sharp.svg/9px-Arabic_music_notation_half_sharp.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Arabic_music_notation_half_sharp.svg/12px-Arabic_music_notation_half_sharp.svg.png 2x" data-file-width="106" data-file-height="200" /></a></span></span>–B<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span> as good possibility for a "secondary" chord in the quarter-tone scale, akin to the minor chord of traditional tonality. He considered that it may be built upon any degree of the quarter tone scale<sup id="cite_ref-Boatwright_4-1" class="reference"><a href="#cite_note-Boatwright-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Here is the secondary "minor" and its "first inversion": </p> <div class="mw-ext-score noresize" data-midi="//upload.wikimedia.org/score/5/n/5no7setqwoywf5xn0rbil3sydr2va3s/5no7setq.midi"><img src="//upload.wikimedia.org/score/5/n/5no7setqwoywf5xn0rbil3sydr2va3s/5no7setq.png" width="159" height="55" alt="
\relative c' {
\omit Staff.TimeSignature
\set Score.tempoHideNote = ##t
<c dih f gih bes>1 \bar "|" <c f gih bes dih>1 \bar "|."
}
" /></div> <div class="mw-heading mw-heading2"><h2 id="In_popular_Western_music">In popular Western music</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quarter_tone&action=edit&section=7" title="Edit section: In popular Western music"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Seppe_Gebruer_%27Playing_with_standards%27.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Seppe_Gebruer_%27Playing_with_standards%27.jpg/220px-Seppe_Gebruer_%27Playing_with_standards%27.jpg" decoding="async" width="220" height="124" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Seppe_Gebruer_%27Playing_with_standards%27.jpg/330px-Seppe_Gebruer_%27Playing_with_standards%27.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Seppe_Gebruer_%27Playing_with_standards%27.jpg/440px-Seppe_Gebruer_%27Playing_with_standards%27.jpg 2x" data-file-width="1920" data-file-height="1080" /></a><figcaption></figcaption></figure> <p>The bass descent of <a href="/wiki/Nancy_Sinatra" title="Nancy Sinatra">Nancy Sinatra</a>'s version of "<a href="/wiki/These_Boots_Are_Made_for_Walkin%27" title="These Boots Are Made for Walkin'">These Boots Are Made for Walkin'</a><span style="padding-left:.15em;">"</span> includes quarter tone descents.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> Several quarter-tone albums have been recorded by Jute Gyte, a one-man avantgarde black metal band from Missouri, USA.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> Another quartertone metal album was issued by the Swedish band Massive Audio Nerve.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> Australian <a href="/wiki/Psychedelic_rock" title="Psychedelic rock">psychedelic rock</a> band <a href="/wiki/King_Gizzard_%26_the_Lizard_Wizard" title="King Gizzard & the Lizard Wizard">King Gizzard & the Lizard Wizard</a>'s albums <i><a href="/wiki/Flying_Microtonal_Banana" title="Flying Microtonal Banana">Flying Microtonal Banana</a></i>, <a href="/wiki/K.G._(album)" title="K.G. (album)">K.G.</a>, and <a href="/wiki/L.W._(album)" title="L.W. (album)">L.W.</a> heavily emphasize quarter-tones and used a custom-built guitar in 24 <span class="smallcaps"><span style="font-variant: small-caps; text-transform: lowercase;">TET</span></span> tuning.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> Jazz violinist / violist <a href="/wiki/Mat_Maneri" title="Mat Maneri">Mat Maneri</a>, in conjunction with his father <a href="/wiki/Joe_Maneri" title="Joe Maneri">Joe Maneri</a>, made a crossover fusion album, <i>Pentagon</i> (2005),<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> that featured experiments in hip hop with quarter tone pianos, as well as electric organ and <a href="/wiki/Mellotron" title="Mellotron">mellotron</a> textures, along with distorted trombone, in a post-Bitches Brew type of mixed <a href="/wiki/Jazz" title="Jazz">jazz</a> / <a href="/wiki/Rock_music" title="Rock music">rock</a>.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p><p>Later, <a href="/wiki/Seppe_Gebruers" title="Seppe Gebruers">Seppe Gebruers</a> started playing and improvising with two pianos tuned a quarter-tone apart. In 2019 he started a research project at the <a href="/wiki/Royal_Conservatory_of_Ghent" title="Royal Conservatory of Ghent">Royal Conservatory of Ghent</a>, titled 'Unexplored possibilities of contemporary improvisation and the influence of microtonality in the creation process'.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> With two pianos tuned a quarter tone apart Gebruers recorded 'The Room: Time & Space' (2018) in a trio formation with drummer <a href="/wiki/Paul_Lovens" title="Paul Lovens">Paul Lovens</a> and bassist <a href="/w/index.php?title=Hugo_Anthunes&action=edit&redlink=1" class="new" title="Hugo Anthunes (page does not exist)">Hugo Anthunes</a>. In his solo project 'Playing with standards' (album release January 2023), Gebruers plays with famous songs including jazz standards. With <a href="/wiki/Paul_Lytton" title="Paul Lytton">Paul Lytton</a> and <a href="/w/index.php?title=Nils_Vermeulen&action=edit&redlink=1" class="new" title="Nils Vermeulen (page does not exist)">Nils Vermeulen</a> he forms a 'Playing with standards' trio. </p> <div class="mw-heading mw-heading2"><h2 id="Ancient_Greek_tetrachords">Ancient Greek tetrachords</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quarter_tone&action=edit&section=8" title="Edit section: Ancient Greek tetrachords"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Genus_(music)#Enharmonic" title="Genus (music)">enharmonic genus</a> of the <a href="/wiki/Ancient_Greece" title="Ancient Greece">Greek</a> <a href="/wiki/Tetrachord" title="Tetrachord">tetrachord</a> consisted of a <a href="/wiki/Ditone" title="Ditone">ditone</a> or an approximate <a href="/wiki/Major_third" title="Major third">major third</a>, and a <a href="/wiki/Semitone" title="Semitone">semitone</a>, which was divided into two <a href="/wiki/Microtones" class="mw-redirect" title="Microtones">microtones</a>. <a href="/wiki/Aristoxenos" class="mw-redirect" title="Aristoxenos">Aristoxenos</a>, <a href="/wiki/Didymos_(music_theorist)" class="mw-redirect" title="Didymos (music theorist)">Didymos</a> and others presented the semitone as being divided into two approximate quarter tone intervals of about the same size, while other ancient Greek theorists described the microtones resulting from dividing the semitone of the enharmonic genus as unequal in size (i.e., one smaller than a quarter tone and one larger).<sup id="cite_ref-Chalmers-Divisions-5-49_21-0" class="reference"><a href="#cite_note-Chalmers-Divisions-5-49-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-West1992_22-0" class="reference"><a href="#cite_note-West1992-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Greek_Dorian_enharmonic_genus.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Greek_Dorian_enharmonic_genus.png/290px-Greek_Dorian_enharmonic_genus.png" decoding="async" width="290" height="63" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Greek_Dorian_enharmonic_genus.png/435px-Greek_Dorian_enharmonic_genus.png 1.5x, //upload.wikimedia.org/wikipedia/commons/8/8a/Greek_Dorian_enharmonic_genus.png 2x" data-file-width="513" data-file-height="111" /></a><figcaption>Greek Dorian enharmonic genus: two disjunct tetrachords each of a quarter tone, quarter tone, and major third.<span class="mw-default-size" typeof="mw:File"><span><audio id="mwe_player_9" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-mwtitle="Greek_Dorian_mode_on_E,_enharmonic_genus.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/8/8e/Greek_Dorian_mode_on_E%2C_enharmonic_genus.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/8e/Greek_Dorian_mode_on_E%2C_enharmonic_genus.mid/Greek_Dorian_mode_on_E%2C_enharmonic_genus.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/8e/Greek_Dorian_mode_on_E%2C_enharmonic_genus.mid/Greek_Dorian_mode_on_E%2C_enharmonic_genus.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </figcaption></figure> <div style="clear:both;" class=""></div> <div class="mw-heading mw-heading2"><h2 id="Interval_size_in_equal_temperament">Interval size in equal temperament</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quarter_tone&action=edit&section=9" title="Edit section: Interval size in equal temperament"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Here are the sizes of some common intervals in a 24-note equally tempered scale, with the interval names proposed by <a href="/wiki/Alois_H%C3%A1ba" title="Alois Hába">Alois Hába</a> (neutral third, etc.) and <a href="/wiki/Ivan_Wyschnegradsky" title="Ivan Wyschnegradsky">Ivan Wyschnegradsky</a> (major fourth, etc.): </p> <dl><dd><table class="wikitable"> <tbody><tr> <th>Interval name </th> <th>Size<br />(steps) </th> <th>Size<br />(cents) </th> <th>MIDI </th> <th>Just ratio </th> <th>Just<br />(cents) </th> <th>MIDI </th> <th>Error<br />(cents) </th></tr> <tr> <td><a href="/wiki/Octave" title="Octave">octave</a> </td> <td align="center">24 </td> <td align="center">1200 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_10" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-durationhint="7" data-mwtitle="Perfect_octave_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/f/f0/Perfect_octave_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/f/f0/Perfect_octave_on_C.mid/Perfect_octave_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/f/f0/Perfect_octave_on_C.mid/Perfect_octave_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">2:1 </td> <td align="center">1200.00 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_11" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-durationhint="7" data-mwtitle="Perfect_octave_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/f/f0/Perfect_octave_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/f/f0/Perfect_octave_on_C.mid/Perfect_octave_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/f/f0/Perfect_octave_on_C.mid/Perfect_octave_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center"><span style="visibility:hidden;color:transparent;">+0</span>0.00 </td></tr> <tr> <td><a href="/wiki/Semidiminished_octave" class="mw-redirect" title="Semidiminished octave">semidiminished octave</a> </td> <td align="center">23 </td> <td align="center">1150 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_12" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Supermajor_seventh_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/a/a6/Supermajor_seventh_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/a6/Supermajor_seventh_on_C.mid/Supermajor_seventh_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/a6/Supermajor_seventh_on_C.mid/Supermajor_seventh_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">35:18 </td> <td align="center">1151.23 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_13" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Septimal_supermajor_seventh_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/8/84/Septimal_supermajor_seventh_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/84/Septimal_supermajor_seventh_on_C.mid/Septimal_supermajor_seventh_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/84/Septimal_supermajor_seventh_on_C.mid/Septimal_supermajor_seventh_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">−<span style="visibility:hidden;color:transparent;">0</span>1.23 </td></tr> <tr> <td><a href="/wiki/Supermajor_seventh" class="mw-redirect" title="Supermajor seventh">supermajor seventh</a> </td> <td align="center">23 </td> <td align="center">1150 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_14" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Supermajor_seventh_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/a/a6/Supermajor_seventh_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/a6/Supermajor_seventh_on_C.mid/Supermajor_seventh_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/a6/Supermajor_seventh_on_C.mid/Supermajor_seventh_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">27:14 </td> <td align="center">1137.04 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_15" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Septimal_major_seventh_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/5/52/Septimal_major_seventh_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/52/Septimal_major_seventh_on_C.mid/Septimal_major_seventh_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/52/Septimal_major_seventh_on_C.mid/Septimal_major_seventh_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">+12.96 </td></tr> <tr> <td><a href="/wiki/Major_seventh" title="Major seventh">major seventh</a> </td> <td align="center">22 </td> <td align="center">1100 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_16" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Major_seventh_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/c/cb/Major_seventh_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/c/cb/Major_seventh_on_C.mid/Major_seventh_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/c/cb/Major_seventh_on_C.mid/Major_seventh_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">15:8<span style="visibility:hidden;color:transparent;">0</span> </td> <td align="center">1088.27 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_17" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Just_major_seventh_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/a/a4/Just_major_seventh_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/a4/Just_major_seventh_on_C.mid/Just_major_seventh_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/a4/Just_major_seventh_on_C.mid/Just_major_seventh_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">+11.73 </td></tr> <tr> <td><a href="/wiki/Neutral_seventh" class="mw-redirect" title="Neutral seventh">neutral seventh</a>, <a href="/wiki/Major_tone" class="mw-redirect" title="Major tone">major tone</a> </td> <td align="center">21 </td> <td align="center">1050 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_18" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Neutral_seventh_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/6/60/Neutral_seventh_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/6/60/Neutral_seventh_on_C.mid/Neutral_seventh_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/6/60/Neutral_seventh_on_C.mid/Neutral_seventh_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">11:6<span style="visibility:hidden;color:transparent;">0</span> </td> <td align="center">1049.36 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_19" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Undecimal_neutral_seventh_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/4/4e/Undecimal_neutral_seventh_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/4/4e/Undecimal_neutral_seventh_on_C.mid/Undecimal_neutral_seventh_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/4/4e/Undecimal_neutral_seventh_on_C.mid/Undecimal_neutral_seventh_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">+<span style="visibility:hidden;color:transparent;">0</span>0.64 </td></tr> <tr> <td><a href="/wiki/Neutral_seventh" class="mw-redirect" title="Neutral seventh">neutral seventh</a>, <a href="/wiki/Minor_tone" class="mw-redirect" title="Minor tone">minor tone</a> </td> <td align="center">21 </td> <td align="center">1050 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_20" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Neutral_seventh_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/6/60/Neutral_seventh_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/6/60/Neutral_seventh_on_C.mid/Neutral_seventh_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/6/60/Neutral_seventh_on_C.mid/Neutral_seventh_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">20:11 </td> <td align="center">1035.00 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_21" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Lesser_undecimal_neutral_seventh_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/d/d5/Lesser_undecimal_neutral_seventh_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/d/d5/Lesser_undecimal_neutral_seventh_on_C.mid/Lesser_undecimal_neutral_seventh_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/d/d5/Lesser_undecimal_neutral_seventh_on_C.mid/Lesser_undecimal_neutral_seventh_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">+15.00 </td></tr> <tr> <td>large just <a href="/wiki/Minor_seventh" title="Minor seventh">minor seventh</a> </td> <td align="center">20 </td> <td align="center">1000 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_22" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Minor_seventh_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/a/a5/Minor_seventh_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/a5/Minor_seventh_on_C.mid/Minor_seventh_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/a5/Minor_seventh_on_C.mid/Minor_seventh_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">9:5 </td> <td align="center">1017.60 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_23" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Greater_just_minor_seventh_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/e/e2/Greater_just_minor_seventh_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e2/Greater_just_minor_seventh_on_C.mid/Greater_just_minor_seventh_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e2/Greater_just_minor_seventh_on_C.mid/Greater_just_minor_seventh_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">−17.60 </td></tr> <tr> <td>small just <a href="/wiki/Minor_seventh" title="Minor seventh">minor seventh</a> </td> <td align="center">20 </td> <td align="center">1000 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_24" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Minor_seventh_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/a/a5/Minor_seventh_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/a5/Minor_seventh_on_C.mid/Minor_seventh_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/a5/Minor_seventh_on_C.mid/Minor_seventh_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">16:9<span style="visibility:hidden;color:transparent;">0</span> </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>996.09 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_25" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Lesser_just_minor_seventh_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/e/e9/Lesser_just_minor_seventh_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e9/Lesser_just_minor_seventh_on_C.mid/Lesser_just_minor_seventh_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e9/Lesser_just_minor_seventh_on_C.mid/Lesser_just_minor_seventh_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">+<span style="visibility:hidden;color:transparent;">0</span>3.91 </td></tr> <tr> <td><a href="/wiki/Supermajor_sixth" class="mw-redirect" title="Supermajor sixth">supermajor sixth</a>/<a href="/wiki/Subminor_seventh" class="mw-redirect" title="Subminor seventh">subminor seventh</a> </td> <td align="center">19 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>950 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_26" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Subminor_seventh_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/8/8b/Subminor_seventh_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/8b/Subminor_seventh_on_C.mid/Subminor_seventh_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/8b/Subminor_seventh_on_C.mid/Subminor_seventh_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">7:4 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>968.83 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_27" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Harmonic_seventh_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/d/dd/Harmonic_seventh_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/d/dd/Harmonic_seventh_on_C.mid/Harmonic_seventh_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/d/dd/Harmonic_seventh_on_C.mid/Harmonic_seventh_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">−18.83 </td></tr> <tr> <td><a href="/wiki/Major_sixth" title="Major sixth">major sixth</a> </td> <td align="center">18 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>900 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_28" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Major_sixth_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/d/df/Major_sixth_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/d/df/Major_sixth_on_C.mid/Major_sixth_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/d/df/Major_sixth_on_C.mid/Major_sixth_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">5:3 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>884.36 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_29" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Just_major_sixth_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/9/98/Just_major_sixth_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/98/Just_major_sixth_on_C.mid/Just_major_sixth_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/98/Just_major_sixth_on_C.mid/Just_major_sixth_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">+15.64 </td></tr> <tr> <td><a href="/wiki/Neutral_sixth" title="Neutral sixth">neutral sixth</a> </td> <td align="center">17 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>850 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_30" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Neutral_sixth_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/5/5d/Neutral_sixth_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/5d/Neutral_sixth_on_C.mid/Neutral_sixth_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/5d/Neutral_sixth_on_C.mid/Neutral_sixth_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">18:11 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>852.59 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_31" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Undecimal_neutral_sixth_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/3/3b/Undecimal_neutral_sixth_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/3/3b/Undecimal_neutral_sixth_on_C.mid/Undecimal_neutral_sixth_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/3/3b/Undecimal_neutral_sixth_on_C.mid/Undecimal_neutral_sixth_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">−<span style="visibility:hidden;color:transparent;">0</span>2.59 </td></tr> <tr> <td><a href="/wiki/Minor_sixth" title="Minor sixth">minor sixth</a> </td> <td align="center">16 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>800 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_32" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Minor_sixth_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/9/9a/Minor_sixth_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/9a/Minor_sixth_on_C.mid/Minor_sixth_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/9a/Minor_sixth_on_C.mid/Minor_sixth_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">8:5 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>813.69 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_33" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Just_minor_sixth_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/4/41/Just_minor_sixth_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/4/41/Just_minor_sixth_on_C.mid/Just_minor_sixth_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/4/41/Just_minor_sixth_on_C.mid/Just_minor_sixth_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">−13.69 </td></tr> <tr> <td><a href="/wiki/Subminor_sixth" class="mw-redirect" title="Subminor sixth">subminor sixth</a> </td> <td align="center">15 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>750 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_34" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Subminor_sixth_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/a/a8/Subminor_sixth_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/a8/Subminor_sixth_on_C.mid/Subminor_sixth_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/a8/Subminor_sixth_on_C.mid/Subminor_sixth_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">14:9<span style="visibility:hidden;color:transparent;">0</span> </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>764.92 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_35" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Septimal_minor_sixth_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/3/3a/Septimal_minor_sixth_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/3/3a/Septimal_minor_sixth_on_C.mid/Septimal_minor_sixth_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/3/3a/Septimal_minor_sixth_on_C.mid/Septimal_minor_sixth_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">−14.92 </td></tr> <tr> <td><a href="/wiki/Perfect_fifth" title="Perfect fifth">perfect fifth</a> </td> <td align="center">14 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>700 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_36" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Perfect_fifth_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/2/20/Perfect_fifth_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/2/20/Perfect_fifth_on_C.mid/Perfect_fifth_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/2/20/Perfect_fifth_on_C.mid/Perfect_fifth_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">3:2 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>701.96 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_37" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-durationhint="7" data-mwtitle="Just_perfect_fifth_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/5/5c/Just_perfect_fifth_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/5c/Just_perfect_fifth_on_C.mid/Just_perfect_fifth_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/5c/Just_perfect_fifth_on_C.mid/Just_perfect_fifth_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">−<span style="visibility:hidden;color:transparent;">0</span>1.96 </td></tr> <tr> <td><a href="/wiki/Minor_fifth" class="mw-redirect" title="Minor fifth">minor fifth</a> </td> <td align="center">13 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>650 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_38" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Thirteen_quarter_tones_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/6/6f/Thirteen_quarter_tones_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/6/6f/Thirteen_quarter_tones_on_C.mid/Thirteen_quarter_tones_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/6/6f/Thirteen_quarter_tones_on_C.mid/Thirteen_quarter_tones_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">16:11 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>648.68 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_39" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Eleventh_harmonic_inverse_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/9/92/Eleventh_harmonic_inverse_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/92/Eleventh_harmonic_inverse_on_C.mid/Eleventh_harmonic_inverse_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/92/Eleventh_harmonic_inverse_on_C.mid/Eleventh_harmonic_inverse_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">+<span style="visibility:hidden;color:transparent;">0</span>1.32 </td></tr> <tr> <td>lesser <a href="/wiki/Septimal_tritone" title="Septimal tritone">septimal tritone</a> </td> <td align="center">12 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>600 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_40" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-durationhint="7" data-mwtitle="Tritone_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/58/Tritone_on_C.mid/Tritone_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/58/Tritone_on_C.mid/Tritone_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/5/58/Tritone_on_C.mid" type="audio/midi" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">7:5 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>582.51 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_41" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Lesser_septimal_tritone_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/2/24/Lesser_septimal_tritone_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/2/24/Lesser_septimal_tritone_on_C.mid/Lesser_septimal_tritone_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/2/24/Lesser_septimal_tritone_on_C.mid/Lesser_septimal_tritone_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">+17.49 </td></tr> <tr> <td><a href="/wiki/Major_fourth" class="mw-redirect" title="Major fourth">major fourth</a> </td> <td align="center">11 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>550 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_42" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Eleven_quarter_tones_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/c/cb/Eleven_quarter_tones_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/c/cb/Eleven_quarter_tones_on_C.mid/Eleven_quarter_tones_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/c/cb/Eleven_quarter_tones_on_C.mid/Eleven_quarter_tones_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">11:8<span style="visibility:hidden;color:transparent;">0</span> </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>551.32 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_43" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Eleventh_harmonic_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/2/2a/Eleventh_harmonic_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/2/2a/Eleventh_harmonic_on_C.mid/Eleventh_harmonic_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/2/2a/Eleventh_harmonic_on_C.mid/Eleventh_harmonic_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">−<span style="visibility:hidden;color:transparent;">0</span>1.32 </td></tr> <tr> <td><a href="/wiki/Perfect_fourth" title="Perfect fourth">perfect fourth</a> </td> <td align="center">10 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>500 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_44" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Perfect_fourth_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/8/87/Perfect_fourth_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/87/Perfect_fourth_on_C.mid/Perfect_fourth_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/87/Perfect_fourth_on_C.mid/Perfect_fourth_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">4:3 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>498.04 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_45" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Just_perfect_fourth_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/b/be/Just_perfect_fourth_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/be/Just_perfect_fourth_on_C.mid/Just_perfect_fourth_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/be/Just_perfect_fourth_on_C.mid/Just_perfect_fourth_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">+<span style="visibility:hidden;color:transparent;">0</span>1.96 </td></tr> <tr> <td>tridecimal <a href="/wiki/Major_third" title="Major third">major third</a> </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>9 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>450 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_46" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Nine_quarter_tones_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/b/b7/Nine_quarter_tones_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/b7/Nine_quarter_tones_on_C.mid/Nine_quarter_tones_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/b7/Nine_quarter_tones_on_C.mid/Nine_quarter_tones_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">13:10 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>454.21 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_47" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-durationhint="7" data-mwtitle="Tridecimal_major_third_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/4/41/Tridecimal_major_third_on_C.mid/Tridecimal_major_third_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/4/41/Tridecimal_major_third_on_C.mid/Tridecimal_major_third_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/4/41/Tridecimal_major_third_on_C.mid" type="audio/midi" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">−<span style="visibility:hidden;color:transparent;">0</span>4.21 </td></tr> <tr> <td><a href="/wiki/Septimal_major_third" title="Septimal major third">septimal major third</a> </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>9 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>450 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_48" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Nine_quarter_tones_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/b/b7/Nine_quarter_tones_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/b7/Nine_quarter_tones_on_C.mid/Nine_quarter_tones_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/b7/Nine_quarter_tones_on_C.mid/Nine_quarter_tones_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">9:7 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>435.08 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_49" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Septimal_major_third_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/5/55/Septimal_major_third_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/55/Septimal_major_third_on_C.mid/Septimal_major_third_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/55/Septimal_major_third_on_C.mid/Septimal_major_third_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">+14.92 </td></tr> <tr> <td><a href="/wiki/Major_third" title="Major third">major third</a> </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>8 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>400 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_50" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Major_third_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/9/91/Major_third_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/91/Major_third_on_C.mid/Major_third_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/91/Major_third_on_C.mid/Major_third_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">5:4 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>386.31 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_51" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-durationhint="7" data-mwtitle="Just_major_third_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/2/2a/Just_major_third_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/2/2a/Just_major_third_on_C.mid/Just_major_third_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/2/2a/Just_major_third_on_C.mid/Just_major_third_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">+13.69 </td></tr> <tr> <td>undecimal <a href="/wiki/Neutral_third" title="Neutral third">neutral third</a> </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>7 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>350 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_52" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Neutral_third_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/7/77/Neutral_third_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/7/77/Neutral_third_on_C.mid/Neutral_third_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/7/77/Neutral_third_on_C.mid/Neutral_third_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">11:9<span style="visibility:hidden;color:transparent;">0</span> </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>347.41 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_53" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Undecimal_neutral_third_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/f/ff/Undecimal_neutral_third_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/f/ff/Undecimal_neutral_third_on_C.mid/Undecimal_neutral_third_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/f/ff/Undecimal_neutral_third_on_C.mid/Undecimal_neutral_third_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">+<span style="visibility:hidden;color:transparent;">0</span>2.59 </td></tr> <tr> <td><a href="/wiki/Minor_third" title="Minor third">minor third</a> </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>6 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>300 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_54" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Minor_third_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/3/31/Minor_third_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/3/31/Minor_third_on_C.mid/Minor_third_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/3/31/Minor_third_on_C.mid/Minor_third_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">6:5 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>315.64 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_55" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Just_minor_third_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/4/42/Just_minor_third_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/4/42/Just_minor_third_on_C.mid/Just_minor_third_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/4/42/Just_minor_third_on_C.mid/Just_minor_third_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">−15.64 </td></tr> <tr> <td><a href="/wiki/Septimal_minor_third" title="Septimal minor third">septimal minor third</a> </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>5 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>250 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_56" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Five_quarter_tones_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/a/a0/Five_quarter_tones_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/a0/Five_quarter_tones_on_C.mid/Five_quarter_tones_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/a0/Five_quarter_tones_on_C.mid/Five_quarter_tones_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">7:6 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>266.87 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_57" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Septimal_minor_third_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/7/73/Septimal_minor_third_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/7/73/Septimal_minor_third_on_C.mid/Septimal_minor_third_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/7/73/Septimal_minor_third_on_C.mid/Septimal_minor_third_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">−16.87 </td></tr> <tr> <td>tridecimal five-quarter tone </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>5 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>250 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_58" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Five_quarter_tones_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/a/a0/Five_quarter_tones_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/a0/Five_quarter_tones_on_C.mid/Five_quarter_tones_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/a0/Five_quarter_tones_on_C.mid/Five_quarter_tones_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">15:13 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>247.74 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_59" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-durationhint="7" data-mwtitle="Tridecimal_five-quarter_tone_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/9d/Tridecimal_five-quarter_tone_on_C.mid/Tridecimal_five-quarter_tone_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/9d/Tridecimal_five-quarter_tone_on_C.mid/Tridecimal_five-quarter_tone_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/9/9d/Tridecimal_five-quarter_tone_on_C.mid" type="audio/midi" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">+<span style="visibility:hidden;color:transparent;">0</span>2.26 </td></tr> <tr> <td><a href="/wiki/Septimal_whole_tone" title="Septimal whole tone">septimal whole tone</a> </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>5 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>250 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_60" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Five_quarter_tones_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/a/a0/Five_quarter_tones_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/a0/Five_quarter_tones_on_C.mid/Five_quarter_tones_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/a0/Five_quarter_tones_on_C.mid/Five_quarter_tones_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">8:7 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>231.17 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_61" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Septimal_major_second_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/4/4f/Septimal_major_second_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/4/4f/Septimal_major_second_on_C.mid/Septimal_major_second_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/4/4f/Septimal_major_second_on_C.mid/Septimal_major_second_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">+18.83 </td></tr> <tr> <td><a href="/wiki/Major_second" title="Major second">major second</a>, <a href="/wiki/Major_tone" class="mw-redirect" title="Major tone">major tone</a> </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>4 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>200 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_62" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Major_second_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/b/b9/Major_second_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/b9/Major_second_on_C.mid/Major_second_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/b9/Major_second_on_C.mid/Major_second_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">9:8 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>203.91 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_63" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Major_tone_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/7/7b/Major_tone_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/7/7b/Major_tone_on_C.mid/Major_tone_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/7/7b/Major_tone_on_C.mid/Major_tone_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">−<span style="visibility:hidden;color:transparent;">0</span>3.91 </td></tr> <tr> <td><a href="/wiki/Major_second" title="Major second">major second</a>, <a href="/wiki/Minor_tone" class="mw-redirect" title="Minor tone">minor tone</a> </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>4 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>200 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_64" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Major_second_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/b/b9/Major_second_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/b9/Major_second_on_C.mid/Major_second_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/b9/Major_second_on_C.mid/Major_second_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">10:9<span style="visibility:hidden;color:transparent;">0</span> </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>182.40 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_65" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Minor_tone_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/8/89/Minor_tone_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/89/Minor_tone_on_C.mid/Minor_tone_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/89/Minor_tone_on_C.mid/Minor_tone_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">+17.60 </td></tr> <tr> <td><a href="/wiki/Neutral_second" class="mw-redirect" title="Neutral second">neutral second</a>, greater undecimal </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>3 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>150 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_66" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Neutral_second_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/2/2d/Neutral_second_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/2/2d/Neutral_second_on_C.mid/Neutral_second_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/2/2d/Neutral_second_on_C.mid/Neutral_second_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">11:10 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>165.00 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_67" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Greater_undecimal_neutral_second_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/7/79/Greater_undecimal_neutral_second_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/7/79/Greater_undecimal_neutral_second_on_C.mid/Greater_undecimal_neutral_second_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/7/79/Greater_undecimal_neutral_second_on_C.mid/Greater_undecimal_neutral_second_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">−15.00 </td></tr> <tr> <td><a href="/wiki/Neutral_second" class="mw-redirect" title="Neutral second">neutral second</a>, lesser undecimal </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>3 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>150 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_68" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Neutral_second_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/2/2d/Neutral_second_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/2/2d/Neutral_second_on_C.mid/Neutral_second_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/2/2d/Neutral_second_on_C.mid/Neutral_second_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">12:11 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>150.64 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_69" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Lesser_undecimal_neutral_second_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/3/30/Lesser_undecimal_neutral_second_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/3/30/Lesser_undecimal_neutral_second_on_C.mid/Lesser_undecimal_neutral_second_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/3/30/Lesser_undecimal_neutral_second_on_C.mid/Lesser_undecimal_neutral_second_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">−<span style="visibility:hidden;color:transparent;">0</span>0.64 </td></tr> <tr> <td>15:14 semitone </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>2 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>100 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_70" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Minor_second_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/8/8a/Minor_second_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/8a/Minor_second_on_C.mid/Minor_second_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/8a/Minor_second_on_C.mid/Minor_second_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">15:14 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>119.44 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_71" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Septimal_diatonic_semitone_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/6/69/Septimal_diatonic_semitone_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/6/69/Septimal_diatonic_semitone_on_C.mid/Septimal_diatonic_semitone_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/6/69/Septimal_diatonic_semitone_on_C.mid/Septimal_diatonic_semitone_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">−19.44 </td></tr> <tr> <td><a href="/wiki/Diatonic_semitone" class="mw-redirect" title="Diatonic semitone">diatonic semitone</a>, <a href="/wiki/Just_intonation" title="Just intonation">just</a> </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>2 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>100 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_72" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Minor_second_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/8/8a/Minor_second_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/8a/Minor_second_on_C.mid/Minor_second_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/8a/Minor_second_on_C.mid/Minor_second_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">16:15 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>111.73 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_73" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Just_diatonic_semitone_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/b/be/Just_diatonic_semitone_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/be/Just_diatonic_semitone_on_C.mid/Just_diatonic_semitone_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/be/Just_diatonic_semitone_on_C.mid/Just_diatonic_semitone_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">−11.73 </td></tr> <tr> <td>21:20 semitone </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>2 </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>100 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_74" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Minor_second_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/8/8a/Minor_second_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/8a/Minor_second_on_C.mid/Minor_second_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/8a/Minor_second_on_C.mid/Minor_second_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">21:20 </td> <td align="center"><span style="visibility:hidden;color:transparent;">00</span>84.47 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_75" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Septimal_chromatic_semitone_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/b/ba/Septimal_chromatic_semitone_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/ba/Septimal_chromatic_semitone_on_C.mid/Septimal_chromatic_semitone_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/ba/Septimal_chromatic_semitone_on_C.mid/Septimal_chromatic_semitone_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">+15.53 </td></tr> <tr> <td>28:27 semitone </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>1 </td> <td align="center"><span style="visibility:hidden;color:transparent;">00</span>50 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_76" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Quarter_tone_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/b/b8/Quarter_tone_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/b8/Quarter_tone_on_C.mid/Quarter_tone_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/b8/Quarter_tone_on_C.mid/Quarter_tone_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">28:27 </td> <td align="center"><span style="visibility:hidden;color:transparent;">00</span>62.96 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_77" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Septimal_minor_second_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/6/60/Septimal_minor_second_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/6/60/Septimal_minor_second_on_C.mid/Septimal_minor_second_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/6/60/Septimal_minor_second_on_C.mid/Septimal_minor_second_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">−12.96 </td></tr> <tr> <td>33:32 semitone </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>1 </td> <td align="center"><span style="visibility:hidden;color:transparent;">00</span>50 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_78" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Quarter_tone_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/b/b8/Quarter_tone_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/b8/Quarter_tone_on_C.mid/Quarter_tone_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/b8/Quarter_tone_on_C.mid/Quarter_tone_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">33:32 </td> <td align="center"><span style="visibility:hidden;color:transparent;">00</span>53.27 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_79" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Thirty-third_harmonic_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/6/69/Thirty-third_harmonic_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/6/69/Thirty-third_harmonic_on_C.mid/Thirty-third_harmonic_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/6/69/Thirty-third_harmonic_on_C.mid/Thirty-third_harmonic_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">−3.27 </td></tr> <tr> <td><a href="/wiki/Unison" title="Unison">unison</a> </td> <td align="center"><span style="visibility:hidden;color:transparent;">0</span>0 </td> <td align="center"><span style="visibility:hidden;color:transparent;">000</span>0 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_80" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Middle_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/e/e2/Middle_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e2/Middle_C.mid/Middle_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e2/Middle_C.mid/Middle_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center">1:1 </td> <td align="center"><span style="visibility:hidden;color:transparent;">000</span>0.00 </td> <td><span typeof="mw:File"><span><audio id="mwe_player_81" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="120" style="width:120px;" data-mwtitle="Middle_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/e/e2/Middle_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e2/Middle_C.mid/Middle_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e2/Middle_C.mid/Middle_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span> </td> <td align="center"><span style="visibility:hidden;color:transparent;">+0</span>0.00 </td></tr></tbody></table></dd></dl> <p>Moving from <a href="/wiki/Equal_temperament" title="Equal temperament">12-TET</a> to 24-TET allows the better approximation of a number of intervals. Intervals matched particularly closely include the <a href="/wiki/Neutral_second" class="mw-redirect" title="Neutral second">neutral second</a>, <a href="/wiki/Neutral_third" title="Neutral third">neutral third</a>, and (11:8) ratio, or the 11th harmonic. The <a href="/wiki/Septimal_minor_third" title="Septimal minor third">septimal minor third</a> and <a href="/wiki/Septimal_major_third" title="Septimal major third">septimal major third</a> are approximated rather poorly; the (13:10) and (15:13) ratios, involving the 13th harmonic, are matched very closely. Overall, 24-TET can be viewed as matching the 11th and 13th harmonics more closely than the 7th. </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=Quarter_tone&action=edit&section=10" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Musical_temperament" title="Musical temperament">Musical temperament</a></li> <li><a href="/wiki/List_of_quarter_tone_pieces" title="List of quarter tone pieces">List of quarter tone pieces</a></li> <li><a href="/wiki/List_of_meantone_intervals" title="List of meantone intervals">List of meantone intervals</a></li> <li><a href="/wiki/53_equal_temperament#Holdrian_comma" title="53 equal temperament">Holdrian Comma</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quarter_tone&action=edit&section=11" title="Edit section: References"><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"><a href="/wiki/Hormoz_Farhat" title="Hormoz Farhat">Hormoz Farhat</a> (2004). The Dastgah Concept in Persian Music. Cambridge University Press. <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><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-54206-5" title="Special:BookSources/0-521-54206-5">0-521-54206-5</a></span> </li> <li id="cite_note-JR-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-JR_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-JR_2-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="/wiki/Julian_Rushton" title="Julian Rushton">Julian Rushton</a>, "Quarter-Tone", <i><a href="/wiki/The_New_Grove_Dictionary_of_Music_and_Musicians" title="The New Grove Dictionary of Music and Musicians">The New Grove Dictionary of Music and Musicians</a></i>, second edition, edited by <a href="/wiki/Stanley_Sadie" title="Stanley Sadie">Stanley Sadie</a> and <a href="/wiki/John_Tyrrell_(musicologist)" title="John Tyrrell (musicologist)">John Tyrrell</a> (London: Macmillan, 2001).</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">Touma, Habib Hassan (1996). <i>The Music of the Arabs</i>, p. 16. Translator: Laurie Schwartz. Portland, Oregon: Amadeus Press. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-931340-88-8" title="Special:BookSources/0-931340-88-8">0-931340-88-8</a>.</span> </li> <li id="cite_note-Boatwright-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-Boatwright_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Boatwright_4-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="/wiki/Howard_Boatwright" title="Howard Boatwright">Boatwright, Howard</a> (1965). "Ives' Quarter-Tone Impressions", <i><a href="/wiki/Perspectives_of_New_Music" title="Perspectives of New Music">Perspectives of New Music</a></i> 3, no. 2 (Spring–Summer): pp. 22–31; citations on pp. 27–28; reprinted in <i>Perspectives on American Composers</i>, edited by <a href="/wiki/Benjamin_Boretz" title="Benjamin Boretz">Benjamin Boretz</a> and <a href="/wiki/Edward_T._Cone" title="Edward T. Cone">Edward T. Cone</a>, pp. 3–12, New York: W. W. Norton, 1971, citation on pp. 8–9. "These two chords outlined above might be termed major and minor."</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">Douglas Keislar; <a href="/wiki/Easley_Blackwood_Jr." title="Easley Blackwood Jr.">Easley Blackwood</a>; <a href="/wiki/John_Eaton_(composer)" title="John Eaton (composer)">John Eaton</a>; <a href="/wiki/Lou_Harrison" title="Lou Harrison">Lou Harrison</a>; <a href="/wiki/Ben_Johnston_(composer)" title="Ben Johnston (composer)">Ben Johnston</a>; <a href="/wiki/Joel_Mandelbaum" title="Joel Mandelbaum">Joel Mandelbaum</a>; William Schottstaedt. p.193. "Six American Composers on Nonstandard Tunnings", <i><a href="/wiki/Perspectives_of_New_Music" title="Perspectives of New Music">Perspectives of New Music</a></i>, vol. 29, no. 1. (Winter 1991), pp. 176–211.</span> </li> <li id="cite_note-Fonville-6"><span class="mw-cite-backlink">^ <a href="#cite_ref-Fonville_6-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Fonville_6-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="/wiki/John_Fonville" title="John Fonville">Fonville, John</a> (Summer, 1991). "Ben Johnston's Extended Just Intonation: A Guide for Interpreters", p. 114, <i><a href="/wiki/Perspectives_of_New_Music" title="Perspectives of New Music">Perspectives of New Music</a></i>, vol. 29, no. 2, pp. 106–137.</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"><a rel="nofollow" class="external text" href="https://kingmaflutes.com/wpfk/kingma-system/">Kingma System</a></span> </li> <li id="cite_note-Spector-8"><span class="mw-cite-backlink">^ <a href="#cite_ref-Spector_8-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Spector_8-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSpector1970" class="citation journal cs1">Spector, Johanna (May 1970). "Classical ʿUd Music in Egypt with Special Reference to Maqamat". <i><a href="/wiki/Ethnomusicology_(journal)" class="mw-redirect" title="Ethnomusicology (journal)">Ethnomusicology</a></i>. <b>14</b> (2): 243–257. <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%2F849799">10.2307/849799</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/849799">849799</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Ethnomusicology&rft.atitle=Classical+%CA%BFUd+Music+in+Egypt+with+Special+Reference+to+Maqamat&rft.volume=14&rft.issue=2&rft.pages=243-257&rft.date=1970-05&rft_id=info%3Adoi%2F10.2307%2F849799&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F849799%23id-name%3DJSTOR&rft.aulast=Spector&rft.aufirst=Johanna&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuarter+tone" 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">Asaad, Gabriel (1990). <i>Syria's Music Throughout History</i></span> </li> <li id="cite_note-Marcus-10"><span class="mw-cite-backlink">^ <a href="#cite_ref-Marcus_10-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Marcus_10-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMarcus1993" class="citation journal cs1">Marcus, Scott (Spring–Summer 1993). "The interface between theory and practice: Intonation in Arab music". <i><a href="/wiki/Asian_Music_(journal)" class="mw-redirect" title="Asian Music (journal)">Asian Music</a></i>. <b>24</b> (2): 39–58. <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%2F834466">10.2307/834466</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/834466">834466</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Asian+Music&rft.atitle=The+interface+between+theory+and+practice%3A+Intonation+in+Arab+music&rft.chron=spring%E2%80%93summer&rft.volume=24&rft.issue=2&rft.pages=39-58&rft.date=1993&rft_id=info%3Adoi%2F10.2307%2F834466&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F834466%23id-name%3DJSTOR&rft.aulast=Marcus&rft.aufirst=Scott&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuarter+tone" class="Z3988"></span></span> </li> <li id="cite_note-Mishaqa-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-Mishaqa_11-0">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMishaqac._1840" class="citation book cs1 cs1-prop-foreign-lang-source"><a href="/wiki/Mikhail_Mishaqa" title="Mikhail Mishaqa">Mishaqa, Mikhiiʾil</a> (c. 1840). <i>al-Risāla al-shihābiyya fi 'l-ṣināʿa al-mūsīqiyya</i> [<i>Essay on the Art of Music for the Emir Shihāb</i>] (in Arabic).</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=al-Ris%C4%81la+al-shih%C4%81biyya+fi+%27l-%E1%B9%A3in%C4%81%CA%BFa+al-m%C5%ABs%C4%ABqiyya&rft.aulast=Mishaqa&rft.aufirst=Mikhii%CA%BEil&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuarter+tone" class="Z3988"></span></span> </li> <li id="cite_note-Maalouf-12"><span class="mw-cite-backlink">^ <a href="#cite_ref-Maalouf_12-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Maalouf_12-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMaalouf2003" class="citation journal cs1">Maalouf, Shireen (October–December 2003). "Mikhiiʾil Mishiiqa: Virtual founder of the twenty-four equal quartertone scale". <i><a href="/wiki/Journal_of_the_American_Oriental_Society" title="Journal of the American Oriental Society">Journal of the American Oriental Society</a></i>. <b>123</b> (4): 835–840. <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%2F3589971">10.2307/3589971</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/3589971">3589971</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+the+American+Oriental+Society&rft.atitle=Mikhii%CA%BEil+Mishiiqa%3A+Virtual+founder+of+the+twenty-four+equal+quartertone+scale&rft.volume=123&rft.issue=4&rft.pages=835-840&rft.date=2003-10%2F2003-12&rft_id=info%3Adoi%2F10.2307%2F3589971&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F3589971%23id-name%3DJSTOR&rft.aulast=Maalouf&rft.aufirst=Shireen&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuarter+tone" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEverett2009" class="citation book cs1"><a href="/wiki/Walter_Everett_(musicologist)" title="Walter Everett (musicologist)">Everett, Walter</a> (2009). <i>The Foundations of Rock</i>. Oxford University Press. p. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=PH88DwAAQBAJ&pg=PA32">32</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780195310238" title="Special:BookSources/9780195310238"><bdi>9780195310238</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+Foundations+of+Rock&rft.pages=32&rft.pub=Oxford+University+Press&rft.date=2009&rft.isbn=9780195310238&rft.aulast=Everett&rft.aufirst=Walter&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuarter+tone" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTremblay2014" class="citation news cs1">Tremblay, Dæv (3 September 2014). <a rel="nofollow" class="external text" href="https://canthisevenbecalledmusic.com/jute-gyte-ressentiment/">"Jute Gyte – <i>Ressentiment</i>"</a>. <i>canthisbecalledmusic.com</i> (album review).</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=canthisbecalledmusic.com&rft.atitle=Jute+Gyte+%E2%80%93+Ressentiment&rft.date=2014-09-03&rft.aulast=Tremblay&rft.aufirst=D%C3%A6v&rft_id=https%3A%2F%2Fcanthisevenbecalledmusic.com%2Fjute-gyte-ressentiment%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuarter+tone" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGyte" class="citation audio-visual cs1">Gyte, Jute. <a rel="nofollow" class="external text" href="https://jutegyte.bandcamp.com/album/discontinuities"><i><span></span></i>Discontinuities<i><span></span></i></a>. <i>jutegyte.bandcamp.com</i> (music album). (commercial site).</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Discontinuities&rft.series=%28commercial+site%29&rft.aulast=Gyte&rft.aufirst=Jute&rft_id=https%3A%2F%2Fjutegyte.bandcamp.com%2Falbum%2Fdiscontinuities&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuarter+tone" class="Z3988"></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation news cs1"><a rel="nofollow" class="external text" href="http://www.blabbermouth.net/news/massive-audio-nerve-to-release-cancer-vulgaris-in-july">"Massive Audio Nerve's album <i>Cancer Vulgaris</i> in July"</a>. <i>blabbermouth.net</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=blabbermouth.net&rft.atitle=Massive+Audio+Nerve%27s+album+Cancer+Vulgaris+in+July&rft_id=http%3A%2F%2Fwww.blabbermouth.net%2Fnews%2Fmassive-audio-nerve-to-release-cancer-vulgaris-in-july&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuarter+tone" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHuguenor2017" class="citation news cs1">Huguenor, Mike (21 August 2017). <a rel="nofollow" class="external text" href="https://www.guitarworld.com/artists/king-gizzard-lizard-wizard-talk-new-album-flying-microtonal-banana">"King Gizzard & the Lizard Wizard talk new album <i>Flying Microtonal Banana</i>"</a>. <i>Guitar World (guitarworld.com)</i> (interview)<span class="reference-accessdate">. Retrieved <span class="nowrap">2021-01-27</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Guitar+World+%28guitarworld.com%29&rft.atitle=King+Gizzard+%26+the+Lizard+Wizard+talk+new+album+Flying+Microtonal+Banana&rft.date=2017-08-21&rft.aulast=Huguenor&rft.aufirst=Mike&rft_id=https%3A%2F%2Fwww.guitarworld.com%2Fartists%2Fking-gizzard-lizard-wizard-talk-new-album-flying-microtonal-banana&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuarter+tone" class="Z3988"></span></span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFManeriManeri2005" class="citation audio-visual cs1"><a href="/wiki/Mat_Maneri" title="Mat Maneri">Maneri, M.</a>; <a href="/wiki/Joe_Maneri" title="Joe Maneri">Maneri, J.</a> (2005). <i>Pentagon</i> (music album).</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Pentagon&rft.date=2005&rft.aulast=Maneri&rft.aufirst=M.&rft.au=Maneri%2C+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuarter+tone" class="Z3988"></span></span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFManeri2005" class="citation magazine cs1">Maneri, Mat (1 December 2005). <a rel="nofollow" class="external text" href="https://www.popmatters.com/manerimat-pentagon-2495996795.html">"<i>Pentagon</i> by Will Layman"</a>. <i><a href="/wiki/PopMatters" title="PopMatters">PopMatters</a></i> (album review).</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=PopMatters&rft.atitle=Pentagon+by+Will+Layman&rft.date=2005-12-01&rft.aulast=Maneri&rft.aufirst=Mat&rft_id=https%3A%2F%2Fwww.popmatters.com%2Fmanerimat-pentagon-2495996795.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuarter+tone" class="Z3988"></span></span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://troikavzw.com/playingwithstandards/">"Seppe Gebruers - Playing with Standards"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Seppe+Gebruers+-+Playing+with+Standards&rft_id=https%3A%2F%2Ftroikavzw.com%2Fplayingwithstandards%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuarter+tone" class="Z3988"></span></span> </li> <li id="cite_note-Chalmers-Divisions-5-49-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-Chalmers-Divisions-5-49_21-0">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChalmers1993" class="citation book cs1">Chalmers, John H., Jr. (1993). <i>Divisions of the Tetrachord</i>. Hanover, NH: Frog Peak Music. Chapter 5, page 49. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-945996-04-7" title="Special:BookSources/0-945996-04-7"><bdi>0-945996-04-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Divisions+of+the+Tetrachord&rft.place=Hanover%2C+NH&rft.pages=Chapter-5%2C+page-49&rft.pub=Frog+Peak+Music&rft.date=1993&rft.isbn=0-945996-04-7&rft.aulast=Chalmers&rft.aufirst=John+H.%2C+Jr.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuarter+tone" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: CS1 maint: multiple names: authors list (<a href="/wiki/Category:CS1_maint:_multiple_names:_authors_list" title="Category:CS1 maint: multiple names: authors list">link</a>)</span></span> </li> <li id="cite_note-West1992-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-West1992_22-0">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWest1992" class="citation book cs1"><a href="/wiki/Martin_Litchfield_West" title="Martin Litchfield West">West, Martin L.</a> (1992). <i>Ancient Greek Music</i>. Oxford, UK: Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-19-814975-1" title="Special:BookSources/0-19-814975-1"><bdi>0-19-814975-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Ancient+Greek+Music&rft.place=Oxford%2C+UK&rft.pub=Oxford+University+Press&rft.date=1992&rft.isbn=0-19-814975-1&rft.aulast=West&rft.aufirst=Martin+L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuarter+tone" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quarter_tone&action=edit&section=12" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin refbegin-columns references-column-width" style="column-width: 25em"> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBartolozzi1967" class="citation book cs1">Bartolozzi, Bruno (1967). <i>New Sounds for Woodwind</i>. London, UK / New York, NY: Oxford University Press.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=New+Sounds+for+Woodwind&rft.place=London%2C+UK+%2F+New+York%2C+NY&rft.pub=Oxford+University+Press&rft.date=1967&rft.aulast=Bartolozzi&rft.aufirst=Bruno&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuarter+tone" class="Z3988"></span></li></ul> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBousted2002" class="citation magazine cs1">Bousted, Donald (Fall 2002). "Microtonality, the recorder and the quarter-tone recorder manual". <i>The Recorder Magazine</i>. Vol. 22, no. 3. pp. 99–102.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Recorder+Magazine&rft.atitle=Microtonality%2C+the+recorder+and+the+quarter-tone+recorder+manual&rft.ssn=fall&rft.volume=22&rft.issue=3&rft.pages=99-102&rft.date=2002&rft.aulast=Bousted&rft.aufirst=Donald&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuarter+tone" class="Z3988"></span></li></ul> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBousted2005" class="citation magazine cs1">Bousted, Donald (Fall 2005). "Next step quarter-tone resources: Melody". <i>The Recorder Magazine</i>. Vol. 25, no. 3. pp. 88–91.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Recorder+Magazine&rft.atitle=Next+step+quarter-tone+resources%3A+Melody&rft.ssn=fall&rft.volume=25&rft.issue=3&rft.pages=88-91&rft.date=2005&rft.aulast=Bousted&rft.aufirst=Donald&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuarter+tone" class="Z3988"></span></li></ul> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCaravan1979" class="citation book cs1">Caravan, Ronald R. (1979). <i>Preliminary Exercises and Etudes in Contemporary Techniques for Clarinet: Introductory material for the study of multiphonics, quarter tones, and timbre variation</i>. Oswego, NY: Ethos Publications.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Preliminary+Exercises+and+Etudes+in+Contemporary+Techniques+for+Clarinet%3A+Introductory+material+for+the+study+of+multiphonics%2C+quarter+tones%2C+and+timbre+variation&rft.place=Oswego%2C+NY&rft.pub=Ethos+Publications&rft.date=1979&rft.aulast=Caravan&rft.aufirst=Ronald+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuarter+tone" class="Z3988"></span></li></ul> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEllis1975" class="citation book cs1"><a href="/wiki/Don_Ellis" title="Don Ellis">Ellis, Don</a> (1975). <i>Quarter Tones: A text with musical examples, exercises, and etudes</i>. Plainview, NY: Harold Branch.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quarter+Tones%3A+A+text+with+musical+examples%2C+exercises%2C+and+etudes&rft.place=Plainview%2C+NY&rft.pub=Harold+Branch&rft.date=1975&rft.aulast=Ellis&rft.aufirst=Don&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuarter+tone" class="Z3988"></span></li></ul> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMacDonald1822" class="citation book cs1">MacDonald, John (1822). <i>A Treatise on the Harmonic System Arising from the Vibrations of the Aliquot Divisions of Strings</i>. London, UK: T. Preston.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Treatise+on+the+Harmonic+System+Arising+from+the+Vibrations+of+the+Aliquot+Divisions+of+Strings&rft.place=London%2C+UK&rft.pub=T.+Preston&rft.date=1822&rft.aulast=MacDonald&rft.aufirst=John&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuarter+tone" class="Z3988"></span></li></ul> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMöllendorffMonzo2001" class="citation book cs1">Möllendorff, Willi; Monzo, Joe (2001). <i>Music with Quarter-Tones: Experiences at the bichromatic harmonium</i>. U.S.: J. Monzo.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Music+with+Quarter-Tones%3A+Experiences+at+the+bichromatic+harmonium&rft.place=U.S.&rft.pub=J.+Monzo&rft.date=2001&rft.aulast=M%C3%B6llendorff&rft.aufirst=Willi&rft.au=Monzo%2C+Joe&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuarter+tone" class="Z3988"></span></li></ul> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRees2007" class="citation journal cs1">Rees, Carla (2007). "Eva Kingma and the quarter-tone flute". <i>Pan: The Flute Magazine</i>. <b>26</b> (4): 23–29.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Pan%3A+The+Flute+Magazine&rft.atitle=Eva+Kingma+and+the+quarter-tone+flute&rft.volume=26&rft.issue=4&rft.pages=23-29&rft.date=2007&rft.aulast=Rees&rft.aufirst=Carla&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuarter+tone" class="Z3988"></span></li></ul> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRewoldt2000" class="citation journal cs1">Rewoldt, Todd (2000). "Altissimo quarter-tones for the alto saxophone". <i>Saxophone Symposium</i>. <b>25</b>: 56–69.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Saxophone+Symposium&rft.atitle=Altissimo+quarter-tones+for+the+alto+saxophone&rft.volume=25&rft.pages=56-69&rft.date=2000&rft.aulast=Rewoldt&rft.aufirst=Todd&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuarter+tone" class="Z3988"></span></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quarter_tone&action=edit&section=13" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>"<a rel="nofollow" class="external text" href="http://www.tonalsoft.com/enc/q/quarter-tone.aspx">quarter-tone / 24-edo</a>", <i>TonalSoft.com</i></li></ul> <div class="navbox-styles"><style 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.navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Intervals" style="padding:3px"><table class="nowraplinks hlist mw-collapsible mw-collapsed 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"><style 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abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Intervals" title="Template:Intervals"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Intervals" title="Template talk:Intervals"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Intervals" title="Special:EditPage/Template:Intervals"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Intervals" style="font-size:114%;margin:0 4em"><a href="/wiki/Interval_(music)" title="Interval (music)">Intervals</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Equal_temperament" title="Equal temperament">Twelve-<br />semitone</a><br />(post-Bach<br />Western)</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="(Numbers_in_bracketsare_the_number_ofsemitones_in_theinterval.)" scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><i>(Numbers in brackets<br />are the number of<br /><a href="/wiki/Semitone" title="Semitone">semitones</a> in the<br />interval.)</i></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:6em;font-weight:normal;">Perfect</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Unison" title="Unison">unison</a> (0)</li> <li><a href="/wiki/Perfect_fourth" title="Perfect fourth">fourth</a> (5)</li> <li><a href="/wiki/Perfect_fifth" title="Perfect fifth">fifth</a> (7)</li> <li><a href="/wiki/Octave" title="Octave">octave</a> (12)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;font-weight:normal;"><a href="/wiki/Major_and_minor#Intervals_and_chords" title="Major and minor">Major</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Major_second" title="Major second">second</a> (2)</li> <li><a href="/wiki/Major_third" title="Major third">third</a> (4)</li> <li><a href="/wiki/Major_sixth" title="Major sixth">sixth</a> (9)</li> <li><a href="/wiki/Major_seventh" title="Major seventh">seventh</a> (11)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;font-weight:normal;"><a href="/wiki/Major_and_minor#Intervals_and_chords" title="Major and minor">Minor</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Minor_second" class="mw-redirect" title="Minor second">second</a> (1)</li> <li><a href="/wiki/Minor_third" title="Minor third">third</a> (3)</li> <li><a href="/wiki/Minor_sixth" title="Minor sixth">sixth</a> (8)</li> <li><a href="/wiki/Minor_seventh" title="Minor seventh">seventh</a> (10)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;font-weight:normal;"><a href="/wiki/Augmentation_(music)#Augmentation_of_intervals" title="Augmentation (music)">Augmented</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Augmented_unison" title="Augmented unison">unison</a> (1)</li> <li><a href="/wiki/Augmented_second" title="Augmented second">second</a> (3)</li> <li><a href="/wiki/Augmented_third" title="Augmented third">third</a> (5)</li> <li><a href="/wiki/Tritone" title="Tritone">fourth</a> (6)</li> <li><a href="/wiki/Augmented_fifth" title="Augmented fifth">fifth</a> (8)</li> <li><a href="/wiki/Augmented_sixth" title="Augmented sixth">sixth</a> (10)</li> <li><a href="/wiki/Augmented_seventh" title="Augmented seventh">seventh</a> (12)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;font-weight:normal;"><a href="/wiki/Diminution#Diminution_of_intervals" title="Diminution">Diminished</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Diminished_second" title="Diminished second">second</a> (0)</li> <li><a href="/wiki/Diminished_third" title="Diminished third">third</a> (2)</li> <li><a href="/wiki/Diminished_fourth" title="Diminished fourth">fourth</a> (4)</li> <li><a href="/wiki/Tritone" title="Tritone">fifth</a> (6)</li> <li><a href="/wiki/Diminished_sixth" title="Diminished sixth">sixth</a> (7)</li> <li><a href="/wiki/Diminished_seventh" title="Diminished seventh">seventh</a> (9)</li> <li><a href="/wiki/Diminished_octave" title="Diminished octave">octave</a> (11)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;font-weight:normal;"><a href="/wiki/Interval_(music)#Simple_and_compound" title="Interval (music)">Compound</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ninth" title="Ninth">ninth</a> (13 or 14)</li> <li><a href="/wiki/Third_(chord)" title="Third (chord)">tenth</a> (15 or 16)</li> <li><a href="/wiki/Eleventh" title="Eleventh">eleventh</a> (17 or 18)</li> <li><a href="/wiki/Fifth_(chord)" title="Fifth (chord)">twelfth</a> (18 or 19)</li> <li><a href="/wiki/Thirteenth" title="Thirteenth">thirteenth</a> (20 or 21)</li> <li><a href="/wiki/Seventh_(chord)" title="Seventh (chord)">fourteenth</a> (22 or 23)</li> <li><a href="/wiki/Fifteenth" title="Fifteenth">fifteenth</a> (24)</li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other<br />tuning<br />systems</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><b><a href="/wiki/24-tone_equal_temperament" class="mw-redirect" title="24-tone equal temperament">24-tone equal temperament</a></b><br /><i>(Numbers in brackets refer<br />to fractional semitones.)</i></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Neutral" scope="row" class="navbox-group" style="width:5em;font-weight:normal;"><div><br /><a href="/wiki/Neutral_interval" title="Neutral interval">Neutral</a><br /><br /></div></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a class="mw-selflink selflink">quarter tone</a> (<span class="frac"><span class="num">1</span>⁄<span class="den">2</span></span>)</li> <li><a href="/wiki/Neutral_interval" title="Neutral interval">second</a> (<span class="frac">1<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">2</span></span>)</li> <li><a href="/wiki/Neutral_third" title="Neutral third">third</a> (<span class="frac">3<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">2</span></span>)</li> <li><a href="/wiki/Major_fourth_and_minor_fifth" title="Major fourth and minor fifth">major fourth</a> (<span class="frac">5<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">2</span></span>)</li> <li><a href="/wiki/Major_fourth_and_minor_fifth" title="Major fourth and minor fifth">minor fifth</a> (<span class="frac">6<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">2</span></span>)</li> <li><a href="/wiki/Neutral_sixth" title="Neutral sixth">sixth</a> (<span class="frac">8<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">2</span></span>)</li> <li><a href="/wiki/Neutral_interval" title="Neutral interval">seventh</a> (<span class="frac">10<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">2</span></span>)</li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><b><a href="/wiki/Just_intonation" title="Just intonation">Just intonations</a></b><br /><i>(Numbers in brackets<br />refer to pitch ratios.)</i></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/7-limit_tuning" title="7-limit tuning">7-limit</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Septimal_quarter_tone" title="Septimal quarter tone">septimal quarter tone</a> (36:35)</li> <li><a href="/wiki/Septimal_third_tone" title="Septimal third tone">septimal third tone</a> (28:27)</li> <li><a href="/wiki/Septimal_chromatic_semitone" title="Septimal chromatic semitone">septimal chromatic semitone</a> (21:20)</li> <li><a href="/wiki/Septimal_diatonic_semitone" title="Septimal diatonic semitone">septimal diatonic semitone</a> (15:14)</li> <li><a href="/wiki/Septimal_whole_tone" title="Septimal whole tone">supermajor second</a> (8:7)</li> <li><a href="/wiki/Septimal_minor_third" title="Septimal minor third">subminor third</a> (7:6)</li> <li><a href="/wiki/Septimal_major_third" title="Septimal major third">supermajor third</a> (9:7)</li> <li><a href="/wiki/Septimal_tritone" title="Septimal tritone">subminor fifth</a> (7:5)</li> <li><a href="/wiki/Septimal_tritone" title="Septimal tritone">supermajor fourth</a> (10:7)</li> <li><a href="/wiki/Harmonic_seventh" title="Harmonic seventh">subminor seventh</a> (7:4)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Limit_(music)" title="Limit (music)">Higher-limit</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Minor_diatonic_semitone" title="Minor diatonic semitone">minor diatonic semitone</a> (17-limit)</li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other<br />intervals</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:6em;font-weight:normal;"><b>Groups</b></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Microtonal_music" class="mw-redirect" title="Microtonal music">Microtone</a></li> <li><a href="/wiki/List_of_intervals_in_5-limit_just_intonation" title="List of intervals in 5-limit just intonation">5-limit</a></li> <li><a href="/wiki/Comma_(music)" title="Comma (music)">Comma</a></li> <li><a href="/wiki/Pseudo-octave" title="Pseudo-octave">Pseudo-octave</a></li> <li><a href="/wiki/Pythagorean_interval" title="Pythagorean interval">Pythagorean interval</a></li> <li><a href="/wiki/Subminor_and_supermajor" title="Subminor and supermajor">Subminor and supermajor</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;font-weight:normal;"><i><b>Semitones</b></i></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Pythagorean_limma" class="mw-redirect" title="Pythagorean limma">Pythagorean limma</a></li> <li><a href="/wiki/Pythagorean_apotome" class="mw-redirect" title="Pythagorean apotome">Pythagorean apotome</a></li> <li><a href="/wiki/Major_limma" title="Major limma">Major limma</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;font-weight:normal;"><i><b>Quarter tones</b></i></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a class="mw-selflink selflink">Quarter tone</a></li> <li><a href="/wiki/Septimal_quarter_tone" title="Septimal quarter tone">Septimal quarter tone</a></li> <li><a href="/wiki/Undecimal_quarter_tone" class="mw-redirect" title="Undecimal quarter tone">Undecimal quarter tone</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;font-weight:normal;"><b><a href="/wiki/Comma_(music)" title="Comma (music)">Commas</a></b></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Pythagorean_comma" title="Pythagorean comma">Pythagorean comma</a> (23.5 cents)</li> <li><a href="/wiki/Syntonic_comma" title="Syntonic comma">Syntonic comma</a> (21.5 cents)</li> <li><a href="/wiki/Holdrian_comma" class="mw-redirect" title="Holdrian comma">Holdrian comma</a> (22.6 cents)</li> <li><a href="/wiki/Septimal_comma" title="Septimal comma">Septimal comma</a> (27.3 cents)</li></ul> <ul><li><a href="/wiki/Diesis" title="Diesis">Lesser diesis</a> (41.1 cents)</li> <li><a href="/wiki/Diesis" title="Diesis">Greater diesis</a> (62.6 cents)</li> <li><a href="/wiki/Septimal_diesis" title="Septimal diesis">Septimal diesis</a> (35.7 cents)</li></ul> <ul><li><a href="/wiki/Diaschisma" title="Diaschisma">Diaschisma</a> (19.5 cents)</li> <li><a href="/wiki/Semicomma" title="Semicomma">Semicomma</a> (10.1 cents)</li> <li><a href="/wiki/Septimal_semicomma" title="Septimal semicomma">Septimal semicomma</a> (13.8 cents)</li> <li><a href="/wiki/Kleisma" title="Kleisma">Kleisma</a> (8.1 cents)</li> <li><a href="/wiki/Septimal_kleisma" title="Septimal kleisma">Septimal kleisma</a> (7.7 cents)</li></ul> <ul><li><a href="/wiki/Schisma" title="Schisma">Schisma</a> (1.95 cents)</li> <li><a href="/wiki/Breedsma" title="Breedsma">Breedsma</a> (0.72 cents)</li> <li><a href="/wiki/Ragisma" title="Ragisma">Ragisma</a> (0.4 cents)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;font-weight:normal;"><b>Measurement</b></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cent_(music)" title="Cent (music)">Cent</a></li> <li><a href="/wiki/Cent_(music)#Centitones" title="Cent (music)">Centitone</a></li> <li><a href="/wiki/Millioctave" title="Millioctave">Millioctave</a></li> <li><a href="/wiki/Savart" title="Savart">Savart</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;font-weight:normal;"><b>Others</b></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Wolf_interval" title="Wolf interval">Wolf</a></li> <li><a href="/wiki/Ditone" title="Ditone">Ditone</a></li> <li><a href="/wiki/Semiditone" class="mw-redirect" title="Semiditone">Semiditone</a></li> <li><a href="/wiki/George_Secor#Secor" title="George Secor">Secor</a></li> <li><a href="/wiki/Incomposite_interval" title="Incomposite interval">Incomposite interval</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><span class="noviewer" typeof="mw:File"><span title="List-Class article"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/d/db/Symbol_list_class.svg/16px-Symbol_list_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/d/db/Symbol_list_class.svg/23px-Symbol_list_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/d/db/Symbol_list_class.svg/31px-Symbol_list_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/List_of_pitch_intervals" title="List of pitch intervals">List of pitch intervals</a></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="Microtonal_music" 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="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:Microtonal_music" title="Template:Microtonal music"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Microtonal_music" title="Template talk:Microtonal music"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Microtonal_music" title="Special:EditPage/Template:Microtonal music"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Microtonal_music" style="font-size:114%;margin:0 4em"><a href="/wiki/Microtonality" title="Microtonality">Microtonal music</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Composers</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/Richard_Barrett_(composer)" title="Richard Barrett (composer)">Richard Barrett</a></li> <li><a href="/wiki/B%C3%A9la_Bart%C3%B3k" title="Béla Bartók">Béla Bartók</a></li> <li><a href="/wiki/Easley_Blackwood_Jr." title="Easley Blackwood Jr.">Easley Blackwood Jr.</a></li> <li><a href="/wiki/Heinz_Bohlen" title="Heinz Bohlen">Heinz Bohlen</a></li> <li><a href="/wiki/Juli%C3%A1n_Carrillo" title="Julián Carrillo">Julián Carrillo</a></li> <li><a href="/wiki/Franklin_Cox" title="Franklin Cox">Franklin Cox</a></li> <li><a href="/wiki/Mildred_Couper" title="Mildred Couper">Mildred Couper</a></li> <li><a href="/wiki/John_Eaton_(composer)" title="John Eaton (composer)">John Eaton</a></li> <li><a href="/wiki/Brian_Ferneyhough" title="Brian Ferneyhough">Brian Ferneyhough</a></li> <li><a href="/wiki/Michael_Finnissy" title="Michael Finnissy">Michael Finnissy</a></li> <li><a href="/wiki/Bj%C3%B8rn_Fongaard" title="Bjørn Fongaard">Bjørn Fongaard</a></li> <li><a href="/wiki/Alois_H%C3%A1ba" title="Alois Hába">Alois Hába</a></li> <li><a href="/wiki/Christiaan_Huygens" title="Christiaan Huygens">Christiaan Huygens</a></li> <li><a href="/wiki/Charles_Ives" title="Charles Ives">Charles Ives</a></li> <li><a href="/wiki/Ben_Johnston_(composer)" title="Ben Johnston (composer)">Ben Johnston</a></li> <li><a href="/wiki/Gy%C3%B6rgy_Ligeti" title="György Ligeti">György Ligeti</a></li> <li><a href="/wiki/King_Gizzard_%26_the_Lizard_Wizard" title="King Gizzard & the Lizard Wizard">Stu Mackenzie</a></li> <li><a href="/wiki/Claus-Steffen_Mahnkopf" title="Claus-Steffen Mahnkopf">Claus-Steffen Mahnkopf</a></li> <li><a href="/wiki/Joel_Mandelbaum" title="Joel Mandelbaum">Joel Mandelbaum</a></li> <li><a href="/wiki/Joe_Maneri" title="Joe Maneri">Joe Maneri</a></li> <li><a href="/wiki/Roger_Redgate" title="Roger Redgate">Roger Redgate</a></li> <li><a href="/wiki/John_Schneider_(guitarist)" title="John Schneider (guitarist)">John Schneider</a></li> <li><a href="/wiki/Sevish" title="Sevish">Sevish</a></li> <li><a href="/wiki/Ezra_Sims" title="Ezra Sims">Ezra Sims</a></li> <li><a href="/wiki/Nicola_Vicentino" title="Nicola Vicentino">Nicola Vicentino</a></li> <li><a href="/wiki/Claude_Vivier" title="Claude Vivier">Claude Vivier</a></li> <li><a href="/wiki/Elaine_Walker_(composer)" title="Elaine Walker (composer)">Elaine Walker</a></li> <li><a href="/wiki/Ivan_Wyschnegradsky" title="Ivan Wyschnegradsky">Ivan Wyschnegradsky</a></li> <li><a href="/wiki/La_Monte_Young" title="La Monte Young">La Monte Young</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="7" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/Three_quarter_flat" title="Three quarter flat"><img alt="Three quarter flat." src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Three_quarter_flat.svg/55px-Three_quarter_flat.svg.png" decoding="async" width="55" height="66" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Three_quarter_flat.svg/83px-Three_quarter_flat.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Three_quarter_flat.svg/110px-Three_quarter_flat.svg.png 2x" data-file-width="166" data-file-height="200" /></a></span><div style="clear:both;" class=""></div><div style="clear:both;" class=""></div><div style="clear:both;" class=""></div><div style="clear:both;" class=""></div><div style="clear:both;" class=""></div><div style="clear:both;" class=""></div><span typeof="mw:File"><a href="/wiki/Three-quarter_sharp" title="Three-quarter sharp"><img alt="Three-quarter sharp." src="//upload.wikimedia.org/wikipedia/commons/thumb/d/dc/Three-quarter_sharp.svg/40px-Three-quarter_sharp.svg.png" decoding="async" width="40" height="86" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/dc/Three-quarter_sharp.svg/60px-Three-quarter_sharp.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/dc/Three-quarter_sharp.svg/80px-Three-quarter_sharp.svg.png 2x" data-file-width="70" data-file-height="150" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Inventors</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/Glenn_Branca" title="Glenn Branca">Glenn Branca</a></li> <li><a href="/wiki/Wendy_Carlos" title="Wendy Carlos">Wendy Carlos</a></li> <li><a href="/wiki/Ivor_Darreg" title="Ivor Darreg">Ivor Darreg</a></li> <li><a href="/wiki/Adriaan_Fokker" title="Adriaan Fokker">Adriaan Fokker</a></li> <li><a href="/wiki/Lou_Harrison" title="Lou Harrison">Lou Harrison</a></li> <li><a href="/wiki/Yuri_Landman" title="Yuri Landman">Yuri Landman</a></li> <li><a href="/wiki/Harry_Partch" title="Harry Partch">Harry Partch</a></li> <li><a href="/wiki/Tui_St._George_Tucker" title="Tui St. George Tucker">Tui St. George Tucker</a></li> <li><a href="/wiki/Nicola_Vicentino" title="Nicola Vicentino">Nicola Vicentino</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Tunings and<br />scales</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Non-octave-repeating_scale" class="mw-redirect" title="Non-octave-repeating scale">Non-octave-<br />repeating scales</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Alpha_scale" title="Alpha scale">Alpha scale</a></li> <li><a href="/wiki/Beta_scale" title="Beta scale">Beta scale</a></li> <li><a href="/wiki/Gamma_scale" title="Gamma scale">Gamma scale</a></li> <li><a href="/wiki/Delta_scale" title="Delta scale">Delta scale</a></li> <li><a href="/wiki/Bohlen%E2%80%93Pierce_scale" title="Bohlen–Pierce scale">Lambda scale</a> (Bohlen–Pierce scale)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Equal_temperament" title="Equal temperament">Equal temperament</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/15_equal_temperament" title="15 equal temperament">15</a></li> <li><a href="/wiki/17_equal_temperament" title="17 equal temperament">17</a></li> <li><a href="/wiki/19_equal_temperament" title="19 equal temperament">19</a></li> <li><a href="/wiki/22_equal_temperament" title="22 equal temperament">22</a></li> <li><a href="/wiki/23_equal_temperament" title="23 equal temperament">23</a></li> <li><a class="mw-selflink selflink">24</a></li> <li><a href="/wiki/31_equal_temperament" title="31 equal temperament">31</a></li> <li><a href="/wiki/34_equal_temperament" title="34 equal temperament">34</a></li> <li><a href="/wiki/41_equal_temperament" title="41 equal temperament">41</a></li> <li><a href="/wiki/53_equal_temperament" title="53 equal temperament">53</a></li> <li><a href="/wiki/58_equal_temperament" title="58 equal temperament">58</a></li> <li><a href="/wiki/72_equal_temperament" title="72 equal temperament">72</a></li> <li><a href="/wiki/96_equal_temperament" title="96 equal temperament">96</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Just_intonation" title="Just intonation">Just intonation</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Harry_Partch%27s_43-tone_scale" title="Harry Partch's 43-tone scale">Harry Partch's 43-tone scale</a></li> <li><a href="/wiki/Henry_Ward_Poole" title="Henry Ward Poole">Double diatonic</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts and<br />techniques</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/Limit_(music)" title="Limit (music)">Limit</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/Semitone" title="Semitone">Semitone</a></li> <li><a href="/wiki/Sonido_13" title="Sonido 13">Sonido 13</a></li> <li><a href="/wiki/Xenharmonic_music" title="Xenharmonic music">Xenharmonicity</a></li> <li><a href="/wiki/Tonality_diamond" title="Tonality diamond">Tonality diamond</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Groups and<br />publications</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/Boston_Microtonal_Society" class="mw-redirect" title="Boston Microtonal Society">Boston Microtonal Society</a></li> <li><i><a href="/wiki/Genesis_of_a_Music" title="Genesis of a Music">Genesis of a Music</a></i></li> <li><a href="/wiki/Huygens-Fokker_Foundation" title="Huygens-Fokker Foundation">Huygens-Fokker Foundation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Compositions</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/Beauty_in_the_Beast" title="Beauty in the Beast">Beauty in the Beast</a></i></li> <li><a href="/wiki/List_of_quarter_tone_pieces" title="List of quarter tone pieces">quarter tone pieces</a></li> <li><a href="/wiki/List_of_compositions_in_just_intonation" title="List of compositions in just intonation">just pieces</a></li> <li><i><a href="/wiki/Mother_(opera)" title="Mother (opera)">Mother</a></i></li> <li><i><a href="/wiki/Sonata_for_Microtonal_Piano_(Ben_Johnston)" title="Sonata for Microtonal Piano (Ben Johnston)">Sonata for Microtonal Piano</a></i></li> <li><i><a href="/wiki/Suite_for_Microtonal_Piano" title="Suite for Microtonal Piano">Suite for Microtonal Piano</a></i></li> <li><i><a href="/wiki/Twelve_Microtonal_Etudes_for_Electronic_Music_Media" title="Twelve Microtonal Etudes for Electronic Music Media">Twelve Microtonal Etudes for Electronic Music Media</a></i></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other 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/Enharmonic_keyboard" title="Enharmonic keyboard">Enharmonic keyboard</a></li> <li><a href="/wiki/Generalized_keyboard" title="Generalized keyboard">Generalized keyboard</a></li> <li><a href="/wiki/Modernism_(music)" title="Modernism (music)">Modernism (music)</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_tunings" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Musical_tuning" title="Template:Musical tuning"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Musical_tuning" title="Template talk:Musical tuning"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Musical_tuning" title="Special:EditPage/Template:Musical tuning"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Musical_tunings" style="font-size:114%;margin:0 4em"><a href="/wiki/Musical_tuning" title="Musical tuning">Musical tunings</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Measurement</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Pitch_(music)" title="Pitch (music)">Pitch</a></li> <li><a href="/wiki/Cent_(music)" title="Cent (music)">Cent</a></li> <li><a href="/wiki/Millioctave" title="Millioctave">Millioctave</a></li> <li><a href="/wiki/Savart" title="Savart">Savart</a></li> <li><a href="/wiki/Interval_(music)" title="Interval (music)">Interval</a></li> <li><a href="/wiki/Interval_ratio" title="Interval ratio">Interval ratio</a></li> <li><a href="/wiki/Pitch_class" title="Pitch class">Pitch class</a></li> <li><a href="/wiki/Consonance_and_dissonance" title="Consonance and dissonance">Consonance and dissonance</a></li> <li><a href="/wiki/List_of_pitch_intervals" title="List of pitch intervals">List of musical intervals</a></li> <li><a href="/wiki/List_of_intervals_in_5-limit_just_intonation" title="List of intervals in 5-limit just intonation">List of intervals in 5-limit just intonation</a></li> <li><a href="/wiki/List_of_meantone_intervals" title="List of meantone intervals">List of meantone intervals</a></li> <li><a href="/wiki/Microtonal_music" class="mw-redirect" title="Microtonal music">Microtone</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Just_intonation" title="Just intonation">Just intonation</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Euler%E2%80%93Fokker_genus" title="Euler–Fokker genus">Euler–Fokker genus</a></li> <li><a href="/wiki/Harmonic_scale" title="Harmonic scale">Harmonic scale</a></li> <li><a href="/wiki/Harry_Partch%27s_43-tone_scale" title="Harry Partch's 43-tone scale">Harry Partch's 43-tone scale</a></li> <li><a href="/wiki/Hexany" title="Hexany">Hexany</a></li> <li><a href="/wiki/Limit_(music)" title="Limit (music)">Limit</a> <ul><li><a href="/wiki/Five-limit_tuning" title="Five-limit tuning">5-limit</a></li> <li><a href="/wiki/7-limit_tuning" title="7-limit tuning">7-limit</a></li></ul></li> <li><a href="/wiki/List_of_compositions_in_just_intonation" title="List of compositions in just intonation">List of compositions</a></li> <li><a href="/wiki/Otonality_and_Utonality" class="mw-redirect" title="Otonality and Utonality">Otonality</a></li> <li><a href="/wiki/Ptolemy%27s_intense_diatonic_scale" title="Ptolemy's intense diatonic scale">Ptolemy's intense diatonic scale</a></li> <li><a href="/wiki/Pythagorean_tuning" title="Pythagorean tuning">Pythagorean tuning</a></li> <li><a href="/wiki/Scale_of_harmonics" title="Scale of harmonics">Scale of harmonics</a></li> <li><a href="/wiki/Tonality_diamond" title="Tonality diamond">Tonality diamond</a></li> <li><a href="/wiki/Tonality_flux" title="Tonality flux">Tonality flux</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Musical_temperament" title="Musical temperament">Temperaments</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Equal_temperament" title="Equal temperament">Equal</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Whole-tone_scale" title="Whole-tone scale">6-tone</a></li> <li><a href="/wiki/12_equal_temperament" title="12 equal temperament">12-tone</a></li> <li><a href="/wiki/15_equal_temperament" title="15 equal temperament">15-tone</a></li> <li><a href="/wiki/17_equal_temperament" title="17 equal temperament">17-tone</a></li> <li><a href="/wiki/19_equal_temperament" title="19 equal temperament">19-tone</a></li> <li><a href="/wiki/22_equal_temperament" title="22 equal temperament">22-tone</a></li> <li><a href="/wiki/23_equal_temperament" title="23 equal temperament">23-tone</a></li> <li><a class="mw-selflink selflink">24-tone</a> (<a href="/wiki/List_of_quarter_tone_pieces" title="List of quarter tone pieces">pieces</a>)</li> <li><a href="/wiki/31_equal_temperament" title="31 equal temperament">31-tone</a></li> <li><a href="/wiki/34_equal_temperament" title="34 equal temperament">34-tone</a></li> <li><a href="/wiki/41_equal_temperament" title="41 equal temperament">41-tone</a></li> <li><a href="/wiki/53_equal_temperament" title="53 equal temperament">53-tone</a></li> <li><a href="/wiki/58_equal_temperament" title="58 equal temperament">58-tone</a></li> <li><a href="/wiki/72_equal_temperament" title="72 equal temperament">72-tone</a></li> <li><a href="/wiki/96_equal_temperament" title="96 equal temperament">96-tone</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Regular_temperament" title="Regular temperament">Linear</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Meantone_temperament" title="Meantone temperament">Meantone</a> (<a href="/wiki/Quarter-comma_meantone" title="Quarter-comma meantone">quarter-comma</a>, <a href="/wiki/Septimal_meantone_temperament" title="Septimal meantone temperament">septimal</a>)</li> <li><a href="/wiki/Schismatic_temperament" title="Schismatic temperament">Schismatic</a></li> <li><a href="/wiki/Miracle_temperament" class="mw-redirect" title="Miracle temperament">Miracle</a></li> <li><a href="/wiki/Magic_temperament" title="Magic temperament">Magic</a></li> <li><a href="/wiki/Regular_diatonic_tuning" title="Regular diatonic tuning">Regular diatonic</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Irregular</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><a href="/wiki/Well_temperament" title="Well temperament">Well temperament</a>/<a href="/wiki/Temperament_ordinaire" title="Temperament ordinaire">Temperament ordinaire</a> (<a href="/wiki/Kirnberger_temperament" title="Kirnberger temperament">Kirnberger</a>, <a href="/wiki/Vallotti_temperament" title="Vallotti temperament">Vallotti</a>, <a href="/wiki/Werckmeister_temperament" title="Werckmeister temperament">Werckmeister</a>, <a href="/wiki/Young_temperament" title="Young temperament">Young</a>)</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Traditional<br /> non-Western</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chinese_musicology" title="Chinese musicology">Chinese musicology</a></li> <li><a href="/wiki/Sh%C3%AD-%C3%A8r-l%C7%9C" class="mw-redirect" title="Shí-èr-lǜ">Shí-èr-lǜ</a></li> <li><a href="/wiki/Dastgah" class="mw-redirect" title="Dastgah">Dastgah</a></li> <li>Maqam <ul><li><a href="/wiki/Arabic_maqam" title="Arabic maqam">Arabic maqam</a></li> <li><a href="/wiki/Turkish_makam" title="Turkish makam">Turkish makam</a></li> <li><a href="/wiki/Mugham" title="Mugham">Mugham</a></li> <li><a href="/wiki/Muqam" title="Muqam">Muqam</a></li></ul></li> <li><a href="/wiki/Octoechos" title="Octoechos">Octoechos</a></li> <li><a href="/wiki/Pelog" title="Pelog">Pelog</a></li> <li><a href="/wiki/Raga" title="Raga">Raga</a> (<a href="/wiki/Carnatic_raga" title="Carnatic raga">Carnatic raga</a>)</li> <li><a href="/wiki/Slendro" title="Slendro">Slendro</a></li> <li><a href="/wiki/Tetrachord" title="Tetrachord">Tetrachord</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Non-octave</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/833_cents_scale" title="833 cents scale">833 cents scale</a></li> <li><a href="/wiki/A12_scale" title="A12 scale">A12 scale</a></li> <li><a href="/wiki/Alpha_scale" title="Alpha scale">Alpha scale</a></li> <li><a href="/wiki/Beta_scale" title="Beta scale">Beta scale</a></li> <li><a href="/wiki/Gamma_scale" title="Gamma scale">Gamma scale</a></li> <li><a href="/wiki/Delta_scale" title="Delta scale">Delta scale</a></li> <li><a href="/wiki/Bohlen%E2%80%93Pierce_scale" title="Bohlen–Pierce scale">Lambda scale</a> (Bohlen–Pierce)</li></ul> </div></td></tr></tbody></table></div>    </div><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=Quarter_tone&oldid=1240749784">https://en.wikipedia.org/w/index.php?title=Quarter_tone&oldid=1240749784</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a 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