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href="#Strict_interpretation_(diatonic_scale)"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Strict interpretation (diatonic scale)</span> </div> </a> <ul id="toc-Strict_interpretation_(diatonic_scale)-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Size_in_different_tuning_systems" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Size_in_different_tuning_systems"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Size in different tuning systems</span> </div> </a> <ul id="toc-Size_in_different_tuning_systems-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Eleventh_harmonic" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Eleventh_harmonic"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Eleventh harmonic</span> </div> </a> <ul id="toc-Eleventh_harmonic-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Dissonance_and_expressiveness" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Dissonance_and_expressiveness"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Dissonance and expressiveness</span> </div> </a> <ul id="toc-Dissonance_and_expressiveness-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Common_uses" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Common_uses"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Common uses</span> </div> </a> <button aria-controls="toc-Common_uses-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 Common uses subsection</span> </button> <ul id="toc-Common_uses-sublist" class="vector-toc-list"> <li id="toc-Occurrences_in_diatonic_scales" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Occurrences_in_diatonic_scales"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Occurrences in diatonic scales</span> </div> </a> <ul id="toc-Occurrences_in_diatonic_scales-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Occurrences_in_chords" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Occurrences_in_chords"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>Occurrences in chords</span> </div> </a> <ul id="toc-Occurrences_in_chords-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Resolution" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Resolution"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3</span> <span>Resolution</span> </div> </a> <ul id="toc-Resolution-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other_uses" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Other_uses"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.4</span> <span>Other uses</span> </div> </a> <ul id="toc-Other_uses-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Historical_uses" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Historical_uses"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Historical uses</span> </div> </a> <ul id="toc-Historical_uses-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">8</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">9</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">10</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">11</span> <span>External links</span> </div> </a> <ul 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Available in 31 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-31" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">31 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A2%D1%80%D1%8B%D1%82%D0%BE%D0%BD_(%D1%96%D0%BD%D1%82%D1%8D%D1%80%D0%B2%D0%B0%D0%BB)" title="Трытон (інтэрвал) – Belarusian" lang="be" hreflang="be" data-title="Трытон (інтэрвал)" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A2%D1%80%D0%B8%D1%82%D0%BE%D0%BD%D1%83%D1%81" title="Тритонус – Bulgarian" lang="bg" hreflang="bg" data-title="Тритонус" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Tr%C3%ADton" title="Tríton – Catalan" lang="ca" hreflang="ca" data-title="Tríton" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Trit%C3%B3n" title="Tritón – Czech" lang="cs" hreflang="cs" data-title="Tritón" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Tritonus" title="Tritonus – Danish" lang="da" hreflang="da" data-title="Tritonus" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Tritonus" title="Tritonus – German" lang="de" hreflang="de" data-title="Tritonus" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Tritoon" title="Tritoon – Estonian" lang="et" hreflang="et" data-title="Tritoon" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Tritono" title="Tritono – Spanish" lang="es" hreflang="es" data-title="Tritono" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Tritonu" title="Tritonu – Basque" lang="eu" hreflang="eu" data-title="Tritonu" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%DA%86%D9%87%D8%A7%D8%B1%D9%85_%D8%A7%D9%81%D8%B2%D9%88%D8%AF%D9%87" title="چهارم افزوده – Persian" lang="fa" hreflang="fa" data-title="چهارم افزوده" 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/Triton_(musique)" title="Triton (musique) – French" lang="fr" hreflang="fr" data-title="Triton (musique)" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%85%8B%EC%98%A8%EC%9D%8C" title="셋온음 – Korean" lang="ko" hreflang="ko" data-title="셋온음" 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%8F%D6%80%D5%AB%D5%BF%D5%B8%D5%B6" title="Տրիտոն – Armenian" lang="hy" hreflang="hy" data-title="Տրիտոն" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Tritonus" title="Tritonus – Croatian" lang="hr" hreflang="hr" data-title="Tritonus" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/T%C3%B3nskratti" title="Tónskratti – Icelandic" lang="is" hreflang="is" data-title="Tónskratti" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Tritono" title="Tritono – Italian" lang="it" hreflang="it" data-title="Tritono" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%98%D7%A8%D7%99%D7%98%D7%95%D7%9F_(%D7%9E%D7%95%D7%96%D7%99%D7%A7%D7%94)" title="טריטון (מוזיקה) – Hebrew" lang="he" hreflang="he" data-title="טריטון (מוזיקה)" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Tritonis" title="Tritonis – Lithuanian" lang="lt" hreflang="lt" data-title="Tritonis" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Tritonus" title="Tritonus – Dutch" lang="nl" hreflang="nl" data-title="Tritonus" 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/%E4%B8%89%E5%85%A8%E9%9F%B3" title="三全音 – Japanese" lang="ja" hreflang="ja" data-title="三全音" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Tritonus" title="Tritonus – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Tritonus" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Tryton_(muzyka)" title="Tryton (muzyka) – Polish" lang="pl" hreflang="pl" data-title="Tryton (muzyka)" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Tr%C3%ADtono" title="Trítono – Portuguese" lang="pt" hreflang="pt" data-title="Trítono" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A2%D1%80%D0%B8%D1%82%D0%BE%D0%BD_(%D0%B8%D0%BD%D1%82%D0%B5%D1%80%D0%B2%D0%B0%D0%BB)" title="Тритон (интервал) – Russian" lang="ru" hreflang="ru" data-title="Тритон (интервал)" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Trit%C3%B3n_(hudba)" title="Tritón (hudba) – Slovak" lang="sk" hreflang="sk" data-title="Tritón (hudba)" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Tritonus" title="Tritonus – Slovenian" lang="sl" hreflang="sl" data-title="Tritonus" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Tritonus" title="Tritonus – Finnish" lang="fi" hreflang="fi" data-title="Tritonus" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Tritonus" title="Tritonus – Swedish" lang="sv" hreflang="sv" data-title="Tritonus" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A2%D1%80%D0%B8%D1%82%D0%BE%D0%BD_(%D1%96%D0%BD%D1%82%D0%B5%D1%80%D0%B2%D0%B0%D0%BB)" title="Тритон (інтервал) – Ukrainian" lang="uk" hreflang="uk" data-title="Тритон (інтервал)" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%A2%9E%E5%9B%9B%E5%BA%A6" title="增四度 – Cantonese" lang="yue" hreflang="yue" data-title="增四度" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%A2%9E%E5%9B%9B%E5%BA%A6" title="增四度 – Chinese" lang="zh" hreflang="zh" data-title="增四度" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a 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data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">For other uses, see <a href="/wiki/Tritone_(disambiguation)" class="mw-disambig" title="Tritone (disambiguation)">Tritone (disambiguation)</a>.</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">"Devil's Chord" redirects here. For the Doctor Who episode, see <a href="/wiki/The_Devil%27s_Chord" title="The Devil's Chord">The Devil's Chord</a>.</div> <div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Musical interval</div><style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox"><caption class="infobox-title">tritone</caption><tbody><tr><th scope="row" class="infobox-label"><a href="/wiki/Inversion_(interval)" class="mw-redirect" title="Inversion (interval)">Inverse</a></th><td class="infobox-data">tritone</td></tr><tr><th colspan="2" class="infobox-header" style="background-color:palegoldenrod;">Name</th></tr><tr><th scope="row" class="infobox-label">Other names</th><td class="infobox-data">augmented fourth, diminished fifth, the Devil’s interval (obscure)</td></tr><tr><th scope="row" class="infobox-label">Abbreviation</th><td class="infobox-data">TT, A4, d5</td></tr><tr><th colspan="2" class="infobox-header" style="background-color:palegoldenrod;">Size</th></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Semitone" title="Semitone">Semitones</a></th><td class="infobox-data">6</td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Interval_class" title="Interval class">Interval class</a></th><td class="infobox-data">6</td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Just_intonation" title="Just intonation">Just interval</a></th><td class="infobox-data"><b>Pythagorean:</b> 729:512, 1024:729<br /> <b>5-limit:</b> 25:18, 36:25; 45:32, 64:45<br /> <b>7-limit:</b> 7:5, 10:7<br /> <b>13-limit:</b> 13:9, 18:13</td></tr><tr><th colspan="2" class="infobox-header" style="background-color:palegoldenrod;"><a href="/wiki/Cent_(music)" title="Cent (music)">Cents</a></th></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Equal_temperament#Twelve-tone_equal_temperament" title="Equal temperament">12-Tone equal temperament</a></th><td class="infobox-data">600</td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Just_intonation" title="Just intonation">Just intonation</a></th><td class="infobox-data"><b>Pythagorean:</b> 612, 588<br /> <b>5-limit:</b> 569, 631; 590, 610<br /> <b>7-limit:</b> 583, 617 <br /> <b>13-limit:</b> 563, 637</td></tr></tbody></table> <p>In <a href="/wiki/Music_theory" title="Music theory">music theory</a>, the <b>tritone</b> is defined as a <a href="/wiki/Interval_(music)" title="Interval (music)">musical interval</a> spanning three adjacent <a href="/wiki/Major_second" title="Major second">whole tones</a> (six <a href="/wiki/Semitone" title="Semitone">semitones</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> For instance, the interval from F up to the B above it (in short, F–B) is a tritone as it can be decomposed into the three adjacent whole tones F–G, G–A, and A–B. </p><p>Narrowly defined, each of these whole tones must be a step in the <a href="/wiki/Scale_(music)" title="Scale (music)">scale</a>, so by this definition, within a <a href="/wiki/Diatonic_scale" title="Diatonic scale">diatonic scale</a> there is only one tritone for each <a href="/wiki/Octave" title="Octave">octave</a>. For instance, the above-mentioned interval F–B is the only tritone formed from the notes of the <a href="/wiki/C_major" title="C major">C major</a> scale. More broadly, a tritone is also commonly defined as any interval with a width of three whole tones (spanning six <a href="/wiki/Semitone" title="Semitone">semitones</a> in the chromatic scale), regardless of <a href="/wiki/Scale_degree" class="mw-redirect" title="Scale degree">scale degrees</a>. According to this definition, a diatonic scale contains two tritones for each octave. For instance, the above-mentioned C major scale contains the tritones F–B (from F to the B above it, also called <b>augmented fourth</b>) and B–F (from B to the F above it, also called <b>diminished fifth</b>, <b>semidiapente</b>, or <b>semitritonus</b>);<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> the latter is decomposed as a semitone B–C, a whole tone C–D, a whole tone D–E, and a semitone E–F, for a total width of three whole tones, but composed as four steps in the scale. In <a href="/wiki/Equal_temperament#Twelve-tone_equal_temperament" title="Equal temperament">twelve-equal temperament</a>, the tritone divides the octave exactly in half as 6 of 12 semitones or 600 of 1,200 <a href="/wiki/Cent_(music)" title="Cent (music)">cents</a>.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>In <a href="/wiki/Classical_music" title="Classical music">classical music</a>, the tritone is a harmonic and melodic <a href="/wiki/Consonance_and_dissonance" title="Consonance and dissonance">dissonance</a> and is important in the study of musical <a href="/wiki/Harmony" title="Harmony">harmony</a>. The tritone can be used to avoid traditional tonality: "Any tendency for a <a href="/wiki/Tonality" title="Tonality">tonality</a> to emerge may be avoided by introducing a note three whole tones distant from the key note of that tonality."<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> The tritone found in the <a href="/wiki/Dominant_seventh_chord" title="Dominant seventh chord">dominant seventh chord</a> can also drive the piece of music towards resolution with its tonic. These various uses exhibit the flexibility, ubiquity, and distinctness of the tritone in music. </p><p>The condition of having tritones is called <a href="/wiki/Anhemitonic_scale" title="Anhemitonic scale">tritonia</a>; that of having no tritones is <a href="/wiki/Anhemitonic_scale" title="Anhemitonic scale">atritonia</a>. A <a href="/wiki/Scale_(music)" title="Scale (music)">musical scale</a> or <a href="/wiki/Chord_(music)" title="Chord (music)">chord</a> containing tritones is called <a href="/wiki/Anhemitonic_scale" title="Anhemitonic scale">tritonic</a>; one without tritones is <a href="/wiki/Anhemitonic_scale" title="Anhemitonic scale">atritonic</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Augmented_fourth_and_diminished_fifth">Augmented fourth and diminished fifth</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Tritone&action=edit&section=1" title="Edit section: Augmented fourth and diminished fifth"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-More_citations_needed_section plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Tritone" title="Special:EditPage/Tritone">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a> in this section. Unsourced material may be challenged and removed.</span> <span class="date-container"><i>(<span class="date">January 2017</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Chromatic_scale_full_octave_ascending_and_descending_on_C.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/Chromatic_scale_full_octave_ascending_and_descending_on_C.svg/400px-Chromatic_scale_full_octave_ascending_and_descending_on_C.svg.png" decoding="async" width="400" height="31" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/Chromatic_scale_full_octave_ascending_and_descending_on_C.svg/600px-Chromatic_scale_full_octave_ascending_and_descending_on_C.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/44/Chromatic_scale_full_octave_ascending_and_descending_on_C.svg/800px-Chromatic_scale_full_octave_ascending_and_descending_on_C.svg.png 2x" data-file-width="673" data-file-height="52" /></a><figcaption>Chromatic scale on C: full octave ascending and descending<figure class="mw-default-size mw-halign-center" typeof="mw:File/Thumb"><span><audio id="mwe_player_1" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-durationhint="17" data-mwtitle="ChromaticScaleUpDown.ogg" data-mwprovider="wikimediacommons" resource="/wiki/File:ChromaticScaleUpDown.ogg"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/f/f0/ChromaticScaleUpDown.ogg/ChromaticScaleUpDown.ogg.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/f/f0/ChromaticScaleUpDown.ogg" type="audio/ogg; codecs="vorbis"" data-width="0" data-height="0" /></audio></span><figcaption>Play in equal temperament</figcaption></figure></figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Chromatic_scale_tritones.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Chromatic_scale_tritones.png/400px-Chromatic_scale_tritones.png" decoding="async" width="400" height="274" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Chromatic_scale_tritones.png/600px-Chromatic_scale_tritones.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Chromatic_scale_tritones.png/800px-Chromatic_scale_tritones.png 2x" data-file-width="1024" data-file-height="702" /></a><figcaption>Full ascending and descending chromatic scale on C, with tritone above each pitch. Pairs of tritones that are <a href="/wiki/Inversion_(music)#Intervals" title="Inversion (music)">inversions</a> of each other are marked below.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Enharmonic_tritone.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7d/Enharmonic_tritone.png/220px-Enharmonic_tritone.png" decoding="async" width="220" height="76" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7d/Enharmonic_tritone.png/330px-Enharmonic_tritone.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7d/Enharmonic_tritone.png/440px-Enharmonic_tritone.png 2x" data-file-width="1411" data-file-height="486" /></a><figcaption>Augmented fourth between C and F<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span> and the diminished fifth between C and G<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span> are <a href="/wiki/Enharmonic" class="mw-redirect" title="Enharmonic">enharmonically equivalent</a> intervals. Both are 600 <a href="/wiki/Cent_(music)" title="Cent (music)">cents</a> wide in <a href="/wiki/Equal_temperament#Twelve-tone_equal_temperament" title="Equal temperament">12-TET</a>.<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="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></figcaption></figure> <p>Since a <a href="/wiki/Chromatic_scale" title="Chromatic scale">chromatic scale</a> is formed by 12 pitches (each a semitone apart from its neighbors), it contains 12 distinct tritones, each starting from a different pitch and spanning six semitones. According to a complex but widely used <a href="/wiki/Interval_(music)#Interval_number_and_quality" title="Interval (music)">naming convention</a>, six of them are classified as <i>augmented fourths</i>, and the other six as <i>diminished fifths</i>. </p><p>Under that convention, a <i>fourth</i> is an interval encompassing four <a href="/wiki/Staff_position" class="mw-redirect" title="Staff position">staff positions</a>, while a <i>fifth</i> encompasses five staff positions (see <a href="/wiki/Interval_(music)#Number" title="Interval (music)">interval number</a> for more details). The augmented fourth (<i>A4</i>) and diminished fifth (<i>d5</i>) are defined as the intervals produced by <a href="/wiki/Augmentation_(music)" title="Augmentation (music)">widening</a> the <a href="/wiki/Perfect_fourth" title="Perfect fourth">perfect fourth</a> and <a href="/wiki/Diminution" title="Diminution">narrowing</a> the <a href="/wiki/Perfect_fifth" title="Perfect fifth">perfect fifth</a> by one <a href="/wiki/Chromatic_semitone" class="mw-redirect" title="Chromatic semitone">chromatic semitone</a>.<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> They both span six semitones, and they are the <a href="/wiki/Inversion_(music)#Intervals" title="Inversion (music)">inverse</a> of each other, meaning that their sum is exactly equal to one <a href="/wiki/Perfect_octave" class="mw-redirect" title="Perfect octave">perfect octave</a> (A4 + d5 = P8). In twelve-tone equal temperament, the most commonly used <a href="/wiki/Tuning_system" class="mw-redirect" title="Tuning system">tuning system</a>, the A4 is <a href="/wiki/Enharmonic" class="mw-redirect" title="Enharmonic">equivalent</a> to a d5, as both have the size of exactly half an <a href="/wiki/Octave" title="Octave">octave</a>. In most other tuning systems, they are not equivalent, and neither is exactly equal to half an octave. </p><p>Any augmented fourth can be decomposed into three whole tones. For instance, the interval F–B is an augmented fourth and can be decomposed into the three adjacent whole tones F–G, G–A, and A–B. </p><p>It is not possible to decompose a diminished fifth into three adjacent whole tones. The reason is that a whole tone is a <a href="/wiki/Major_second" title="Major second">major second</a>, and according to a rule explained elsewhere,<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Naming_conventions_(geographic_names)" title="Wikipedia:Naming conventions (geographic names)"><span title="The geographic scope near this tag is ambiguous. (April 2015)">where?</span></a></i>]</sup> the composition of three seconds is always a fourth (for instance, an A4). To obtain a fifth (for instance, a d5), it is necessary to add another second. For instance, using the notes of the C major scale, the diminished fifth B–F can be decomposed into the four adjacent intervals </p> <dl><dd>B–C (<a href="/wiki/Minor_second" class="mw-redirect" title="Minor second">minor second</a>), C–D (major second), D–E (major second), and E–F (minor second).</dd></dl> <p>Using the notes of a chromatic scale, B–F may be also decomposed into the four adjacent intervals </p> <dl><dd>B–C<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span> (major second), C<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>–D<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span> (major second), 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-sharp">♯</span></span> (major second), and E<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>–F<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-natural">♮</span></span> (<a href="/wiki/Diminished_second" title="Diminished second">diminished second</a>).</dd></dl> <p>Notice that the last diminished second is formed by two <a href="/wiki/Enharmonic" class="mw-redirect" title="Enharmonic">enharmonically equivalent</a> notes (E<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span> and F<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-natural">♮</span></span>). On a <a href="/wiki/Piano_keyboard" class="mw-redirect" title="Piano keyboard">piano keyboard</a>, these notes are produced by the same key. However, in the above-mentioned naming convention, they are considered different notes, as they are written on different <a href="/wiki/Staff_position" class="mw-redirect" title="Staff position">staff positions</a> and have different diatonic functions within music theory. </p> <div class="mw-heading mw-heading2"><h2 id="Definitions">Definitions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Tritone&action=edit&section=2" title="Edit section: Definitions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-More_citations_needed_section plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Tritone" title="Special:EditPage/Tritone">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a> in this section. Unsourced material may be challenged and removed.</span> <span class="date-container"><i>(<span class="date">January 2017</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Tritone_in_the_chromatic_circle.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Tritone_in_the_chromatic_circle.png/220px-Tritone_in_the_chromatic_circle.png" decoding="async" width="220" height="218" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Tritone_in_the_chromatic_circle.png/330px-Tritone_in_the_chromatic_circle.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Tritone_in_the_chromatic_circle.png/440px-Tritone_in_the_chromatic_circle.png 2x" data-file-width="559" data-file-height="553" /></a><figcaption>Tritone drawn in the <a href="/wiki/Chromatic_circle" title="Chromatic circle">chromatic circle</a>.</figcaption></figure> <p>A tritone (abbreviation: <i>TT</i>) is traditionally defined as a musical interval composed of three <a href="/wiki/Major_second" title="Major second">whole tones</a>. As the symbol for whole tone is <i>T</i>, this definition may also be written as follows: </p> <dl><dd><i>TT = T+T+T</i></dd></dl> <p>Only if the three tones are of the same size (which is not the case for many <a href="/wiki/Tuning_system" class="mw-redirect" title="Tuning system">tuning systems</a>) can this formula be simplified to: </p> <dl><dd><i>TT = 3T</i></dd></dl> <p>This definition, however, has two different interpretations (broad and strict). </p> <div class="mw-heading mw-heading3"><h3 id="Broad_interpretation_(chromatic_scale)"><span id="Broad_interpretation_.28chromatic_scale.29"></span>Broad interpretation (chromatic scale)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Tritone&action=edit&section=3" title="Edit section: Broad interpretation (chromatic scale)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In a <a href="/wiki/Chromatic_scale" title="Chromatic scale">chromatic scale</a>, the interval between any note and the previous or next is a semitone. Using the notes of a chromatic scale, each tone can be divided into two semitones: </p> <dl><dd><i>T = S+S</i></dd></dl> <p>For instance, the tone from C to D (in short, C–D) can be decomposed into the two semitones C–C<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span> and C<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>–D by using the note C<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>, which in a chromatic scale lies between C and D. This means that, when a chromatic scale is used, a tritone can be also defined as any musical interval spanning six semitones: </p> <dl><dd><i>TT = T+T+T = S+S+S+S+S+S</i>.</dd></dl> <p>According to this definition, with the twelve notes of a chromatic scale it is possible to define twelve different tritones, each starting from a different note and ending six notes above it. Although all of them span six semitones, six of them are classified as <i>augmented fourth</i>s, and the other six as <i>diminished fifths</i>. </p> <div class="mw-heading mw-heading3"><h3 id="Strict_interpretation_(diatonic_scale)"><span id="Strict_interpretation_.28diatonic_scale.29"></span>Strict interpretation (diatonic scale)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Tritone&action=edit&section=4" title="Edit section: Strict interpretation (diatonic scale)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Within a <a href="/wiki/Diatonic_scale" title="Diatonic scale">diatonic scale</a>, whole tones are always formed by adjacent notes (such as C and D) and therefore they are regarded as <a href="/wiki/Incomposite_interval" title="Incomposite interval">incomposite intervals</a>. In other words, they cannot be divided into smaller intervals. Consequently, in this context the above-mentioned "decomposition" of the tritone into six semitones is typically not allowed. </p><p>If a diatonic scale is used, with its 7 notes it is possible to form only one sequence of three adjacent whole tones (<i>T+T+T</i>). This interval is an A4. For instance, in the <a href="/wiki/C_major" title="C major">C major</a> diatonic scale (C–D–E–F–G–A–B–...), the only tritone is from F to B. It is a tritone because F–G, G–A, and A–B are three adjacent whole tones. It is a <i>fourth</i> because the notes from F to B are four (F, G, A, B). It is <i>augmented</i> (i.e., widened) because it is wider than most of the fourths found in the scale (they are <a href="/wiki/Perfect_fourth" title="Perfect fourth">perfect fourths</a>). </p><p>According to this interpretation, the d5 is not a tritone. Indeed, in a diatonic scale, there is only one d5, and this interval does not meet the strict definition of tritone, as it is formed by one semitone, two whole tones, and another semitone: </p> <dl><dd><i>d5 = S+T+T+S</i>.</dd></dl> <p>For instance, in the C major diatonic scale, the only d5 is from B to F. It is a <i>fifth</i> because the notes from B to F are five (B, C, D, E, F). It is <i>diminished</i> (i.e. narrowed) because it is smaller than most of the fifths found in the scale (they are <a href="/wiki/Perfect_fifth" title="Perfect fifth">perfect fifths</a>). </p> <div class="mw-heading mw-heading2"><h2 id="Size_in_different_tuning_systems">Size in different tuning systems</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Tritone&action=edit&section=5" title="Edit section: Size in different tuning systems"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1237032888/mw-parser-output/.tmulti">.mw-parser-output .tmulti .multiimageinner{display:flex;flex-direction:column}.mw-parser-output .tmulti .trow{display:flex;flex-direction:row;clear:left;flex-wrap:wrap;width:100%;box-sizing:border-box}.mw-parser-output .tmulti .tsingle{margin:1px;float:left}.mw-parser-output .tmulti .theader{clear:both;font-weight:bold;text-align:center;align-self:center;background-color:transparent;width:100%}.mw-parser-output .tmulti .thumbcaption{background-color:transparent}.mw-parser-output .tmulti .text-align-left{text-align:left}.mw-parser-output .tmulti .text-align-right{text-align:right}.mw-parser-output .tmulti .text-align-center{text-align:center}@media all and (max-width:720px){.mw-parser-output .tmulti .thumbinner{width:100%!important;box-sizing:border-box;max-width:none!important;align-items:center}.mw-parser-output .tmulti .trow{justify-content:center}.mw-parser-output .tmulti .tsingle{float:none!important;max-width:100%!important;box-sizing:border-box;text-align:center}.mw-parser-output .tmulti .tsingle .thumbcaption{text-align:left}.mw-parser-output .tmulti .trow>.thumbcaption{text-align:center}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .tmulti .multiimageinner img{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmulti .multiimageinner img{background-color:white}}</style><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:224px;max-width:224px"><div class="trow"><div class="theader">Tritones</div></div><div class="trow"><div class="tsingle" style="width:222px;max-width:222px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Just_augmented_fourth_on_C.png" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/Just_augmented_fourth_on_C.png/220px-Just_augmented_fourth_on_C.png" decoding="async" width="220" height="103" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/Just_augmented_fourth_on_C.png/330px-Just_augmented_fourth_on_C.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/46/Just_augmented_fourth_on_C.png/440px-Just_augmented_fourth_on_C.png 2x" data-file-width="539" data-file-height="252" /></a></span></div><div class="thumbcaption"><a href="/wiki/Major_fourth" class="mw-redirect" title="Major fourth">just augmented fourth</a> between C and F<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>+ – 45:32 (590.22 cents)<span class="mw-default-size" typeof="mw:File"><span><audio id="mwe_player_3" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-mwtitle="Just_augmented_fourth_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/8/80/Just_augmented_fourth_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/80/Just_augmented_fourth_on_C.mid/Just_augmented_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/8/80/Just_augmented_fourth_on_C.mid/Just_augmented_fourth_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span></div></div></div><div class="trow"><div class="tsingle" style="width:222px;max-width:222px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Pythagorean_augmented_fourth_on_C.png" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/55/Pythagorean_augmented_fourth_on_C.png/220px-Pythagorean_augmented_fourth_on_C.png" decoding="async" width="220" height="103" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/55/Pythagorean_augmented_fourth_on_C.png/330px-Pythagorean_augmented_fourth_on_C.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/55/Pythagorean_augmented_fourth_on_C.png/440px-Pythagorean_augmented_fourth_on_C.png 2x" data-file-width="539" data-file-height="252" /></a></span></div><div class="thumbcaption">Pythagorean augmented fourth between C and F<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>++ – 729:512 (611.73 cents)<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-mwtitle="Pythagorean_augmented_fourth_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/c/cf/Pythagorean_augmented_fourth_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/c/cf/Pythagorean_augmented_fourth_on_C.mid/Pythagorean_augmented_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/c/cf/Pythagorean_augmented_fourth_on_C.mid/Pythagorean_augmented_fourth_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span></div></div></div><div class="trow"><div class="tsingle" style="width:222px;max-width:222px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Augmented_fourth_on_C.png" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Augmented_fourth_on_C.png/220px-Augmented_fourth_on_C.png" decoding="async" width="220" height="103" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Augmented_fourth_on_C.png/330px-Augmented_fourth_on_C.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Augmented_fourth_on_C.png/440px-Augmented_fourth_on_C.png 2x" data-file-width="539" data-file-height="252" /></a></span></div><div class="thumbcaption">Classic augmented fourth between C and F<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span> – 25:18 (568.72 cents)<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="Classic_augmented_fourth_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/e/ee/Classic_augmented_fourth_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/ee/Classic_augmented_fourth_on_C.mid/Classic_augmented_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/e/ee/Classic_augmented_fourth_on_C.mid/Classic_augmented_fourth_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span></div></div></div><div class="trow"><div class="tsingle" style="width:222px;max-width:222px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Diminished_fifth_on_C.png" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Diminished_fifth_on_C.png/220px-Diminished_fifth_on_C.png" decoding="async" width="220" height="103" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Diminished_fifth_on_C.png/330px-Diminished_fifth_on_C.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/63/Diminished_fifth_on_C.png/440px-Diminished_fifth_on_C.png 2x" data-file-width="539" data-file-height="252" /></a></span></div><div class="thumbcaption">Classic diminished fifth between C and G<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span> – 36:25 (631.28 cents) <span class="mw-default-size" typeof="mw:File"><span><audio id="mwe_player_6" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-mwtitle="Classic_diminished_fifth_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/2/22/Classic_diminished_fifth_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/2/22/Classic_diminished_fifth_on_C.mid/Classic_diminished_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/2/22/Classic_diminished_fifth_on_C.mid/Classic_diminished_fifth_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span></div></div></div><div class="trow"><div class="tsingle" style="width:222px;max-width:222px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Lesser_septimal_tritone_on_C.png" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Lesser_septimal_tritone_on_C.png/220px-Lesser_septimal_tritone_on_C.png" decoding="async" width="220" height="103" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Lesser_septimal_tritone_on_C.png/330px-Lesser_septimal_tritone_on_C.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Lesser_septimal_tritone_on_C.png/440px-Lesser_septimal_tritone_on_C.png 2x" data-file-width="539" data-file-height="252" /></a></span></div><div class="thumbcaption">Lesser septimal tritone between C and 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: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><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> – 7:5 (582.51 cents)<span class="mw-default-size" typeof="mw:File"><span><audio id="mwe_player_7" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" 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></div></div></div><div class="trow"><div class="tsingle" style="width:222px;max-width:222px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Comparison_of_tritones.png" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Comparison_of_tritones.png/220px-Comparison_of_tritones.png" decoding="async" width="220" height="149" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Comparison_of_tritones.png/330px-Comparison_of_tritones.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Comparison_of_tritones.png/440px-Comparison_of_tritones.png 2x" data-file-width="1417" data-file-height="961" /></a></span></div><div class="thumbcaption">Comparison of intervals near or enharmonic with the tritone</div></div></div></div></div> <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_8" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-mwtitle="Tritone1.mid" data-mwprovider="wikimediacommons" resource="/wiki/File:Tritone1.mid"><source src="//upload.wikimedia.org/wikipedia/commons/1/1b/Tritone1.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/1/1b/Tritone1.mid/Tritone1.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/1/1b/Tritone1.mid/Tritone1.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span><figcaption>Tritone</figcaption></figure></div></div> <p>In twelve-tone equal temperament, the Aug 4 is exactly half an <a href="/wiki/Octave" title="Octave">octave</a> (i.e., a ratio of <a href="/wiki/Square_root_of_2" title="Square root of 2"><span class="nowrap">√<span style="border-top:1px solid; padding:0 0.1em;">2</span></span></a>:1 or 600 <a href="/wiki/Cent_(music)" title="Cent (music)">cents</a>. The inverse of 600 cents is 600 cents. Thus, in this tuning system, the Aug 4 and its inverse (dim 5) are <a href="/wiki/Enharmonic" class="mw-redirect" title="Enharmonic">equivalent</a>. </p><p>The half-octave or equal tempered Aug 4 and dim 5 are unique in being equal to their own inverse (each to the other). In other <a href="/wiki/Meantone_temperament" title="Meantone temperament">meantone</a> tuning systems, besides 12 tone equal temperament, Aug 4 and dim 5 are distinct intervals because neither is exactly half an octave. In any meantone tuning near to <style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="sfrac">⁠<span class="tion"><span class="num">2</span><span class="sr-only">/</span><span class="den">9</span></span>⁠</span>-comma meantone the Aug 4 is near to the ratio 7:5 (582.51) and the dim 5 to 10:7 (617.49), which is what these intervals are in <a href="/wiki/Septimal_meantone_temperament" title="Septimal meantone temperament">septimal meantone temperament</a>. In <a href="/wiki/31_equal_temperament" title="31 equal temperament">31 equal temperament</a>, for example, the Aug 4 is 580.65 cents, whereas the dim 5 is 619.35 cents. This is perceptually indistinguishable from septimal meantone temperament. </p><p>Since they are the inverse of each other, by definition Aug 4 and dim 5 always add up (in cents) to exactly one <a href="/wiki/Octave" title="Octave">perfect octave</a>: </p> <dl><dd><i>Aug 4 + dim 5 = Perf 8</i>.</dd></dl> <p>On the other hand, two Aug 4 add up to six whole tones. In equal temperament, this is equal to exactly one perfect octave: </p> <dl><dd><i>Aug 4 + Aug 4 = Perf 8</i>.</dd></dl> <p>In <a href="/wiki/Quarter-comma_meantone" title="Quarter-comma meantone">quarter-comma meantone</a> temperament, this is a <a href="/wiki/Diesis" title="Diesis">diesis</a> (128:125) less than a perfect octave: </p> <dl><dd><i>Aug 4 + Aug 4 = Perf 8 − <a href="/wiki/Diesis" title="Diesis">diesis</a></i>.</dd></dl> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1034237262"><div class="stack mw-stack stack-right"><div><figure class="mw-default-size" typeof="mw:File/Thumb"><span><audio id="mwe_player_9" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-mwtitle="Just_diminished_fifth_on_C.mid" data-mwprovider="wikimediacommons" resource="/wiki/File:Just_diminished_fifth_on_C.mid"><source src="//upload.wikimedia.org/wikipedia/commons/b/b8/Just_diminished_fifth_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/b8/Just_diminished_fifth_on_C.mid/Just_diminished_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/b/b8/Just_diminished_fifth_on_C.mid/Just_diminished_fifth_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span><figcaption>Just diminished fifth on C</figcaption></figure></div></div> <p>In <a href="/wiki/Just_intonation" title="Just intonation">just intonation</a> several different sizes can be chosen both for the Aug 4 and the dim 5. For instance, in <a href="/wiki/5-limit_tuning" class="mw-redirect" title="5-limit tuning">5-limit tuning</a>, the Aug 4 is either 45:32<sup id="cite_ref-Partch_7-0" class="reference"><a href="#cite_note-Partch-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Renold_8-0" class="reference"><a href="#cite_note-Renold-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Helmholtz_9-0" class="reference"><a href="#cite_note-Helmholtz-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> or 25:18,<sup id="cite_ref-Haluska_24_10-0" class="reference"><a href="#cite_note-Haluska_24-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> and the dim 5 is either 64:45 or 36:25.<sup id="cite_ref-Haluska_25_11-0" class="reference"><a href="#cite_note-Haluska_25-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> The 64:45 just diminished fifth arises in the C <a href="/wiki/Major_scale" title="Major scale">major scale</a> between B and F, consequently the 45:32 augmented fourth arises between F and B.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><p>These ratios are not in all contexts regarded as <a href="/wiki/Five-limit_tuning#The_just_ratios" title="Five-limit tuning">strictly just</a> but they are the justest possible in 5-limit tuning. <a href="/wiki/7-limit" class="mw-redirect" title="7-limit">7-limit</a> tuning allows for the justest possible ratios (ratios with the smallest numerator and denominator), namely 7:5 for the Aug 4 (about 582.5 cents, also known as <a href="/wiki/Septimal_tritone" title="Septimal tritone">septimal tritone</a>) and 10:7 for the dim 5 (about 617.5 cents, also known as Euler's tritone).<sup id="cite_ref-Partch_7-1" class="reference"><a href="#cite_note-Partch-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Haluska_23_13-0" class="reference"><a href="#cite_note-Haluska_23-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Strange_14-0" class="reference"><a href="#cite_note-Strange-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> These ratios are more consonant than 17:12 (about 603.0 <a href="/wiki/Musical_cents" class="mw-redirect" title="Musical cents">cents</a>) and 24:17 (about 597.0 cents), which can be obtained in 17 limit tuning, yet the latter are also fairly common, as they are closer to the equal-tempered value of 600 cents. </p> <div class="mw-heading mw-heading2"><h2 id="Eleventh_harmonic">Eleventh harmonic</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Tritone&action=edit&section=6" title="Edit section: Eleventh harmonic"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1034237262"><div class="stack mw-stack stack-right"><div><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Eleventh_harmonic_on_C.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Eleventh_harmonic_on_C.png/220px-Eleventh_harmonic_on_C.png" decoding="async" width="220" height="103" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Eleventh_harmonic_on_C.png/330px-Eleventh_harmonic_on_C.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Eleventh_harmonic_on_C.png/440px-Eleventh_harmonic_on_C.png 2x" data-file-width="539" data-file-height="252" /></a><figcaption>Eleventh harmonic between C and F<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;">↑</span> – 11:8 (551.32 cents)<span class="mw-default-size" typeof="mw:File"><span><audio id="mwe_player_10" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-mwtitle="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></figcaption></figure></div></div> <p>The ratio of the eleventh harmonic, 11:8 (551.318 cents; approximated as F<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>4 above C1), known as the <b>lesser undecimal tritone</b> or <b>undecimal semi-augmented fourth</b>, is found in some just tunings and on many instruments. For example, very long <a href="/wiki/Alphorn" title="Alphorn">alphorns</a> may reach the twelfth harmonic and transcriptions of their music usually show the eleventh harmonic sharp (F<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span> above C, for example), as in <a href="/wiki/Johannes_Brahms" title="Johannes Brahms">Brahms</a>'s <a href="/wiki/Symphony_No._1_(Brahms)" title="Symphony No. 1 (Brahms)">First Symphony</a>.<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> This note is often corrected to 4:3 on the <a href="/wiki/Natural_horn" title="Natural horn">natural horn</a> in just intonation or Pythagorean tunings, but the pure eleventh harmonic was used in pieces including <a href="/wiki/Benjamin_Britten" title="Benjamin Britten">Britten</a>'s <i><a href="/wiki/Serenade_for_Tenor,_Horn_and_Strings" title="Serenade for Tenor, Horn and Strings">Serenade for tenor, horn and strings</a></i>.<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> <a href="/wiki/Ivan_Wyschnegradsky" title="Ivan Wyschnegradsky">Ivan Wyschnegradsky</a> considered the <a href="/wiki/Major_fourth" class="mw-redirect" title="Major fourth">major fourth</a> a good approximation of the eleventh harmonic. </p> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:Britten_-_Serenade_prologue.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/en/thumb/3/31/Britten_-_Serenade_prologue.png/400px-Britten_-_Serenade_prologue.png" decoding="async" width="400" height="114" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/3/31/Britten_-_Serenade_prologue.png 1.5x" data-file-width="592" data-file-height="168" /></a><figcaption>Use of the eleventh harmonic in the prologue to Britten's <a href="/wiki/Serenade_for_Tenor,_Horn_and_Strings" title="Serenade for Tenor, Horn and Strings">Serenade for Tenor, Horn and Strings</a>.<span class="mw-default-size" typeof="mw:File"><span><audio id="mwe_player_11" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-durationhint="56" data-mwtitle="Britten_-_Serenade_prologue.mid" data-mwprovider="local"><source src="//upload.wikimedia.org/wikipedia/en/transcoded/d/de/Britten_-_Serenade_prologue.mid/Britten_-_Serenade_prologue.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/en/transcoded/d/de/Britten_-_Serenade_prologue.mid/Britten_-_Serenade_prologue.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/en/d/de/Britten_-_Serenade_prologue.mid" type="audio/midi" data-width="0" data-height="0" /></audio></span></span></figcaption></figure> <div class="mw-heading mw-heading2"><h2 id="Dissonance_and_expressiveness">Dissonance and expressiveness</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Tritone&action=edit&section=7" title="Edit section: Dissonance and expressiveness"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ján Haluska wrote: </p> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"><p>The unstable character of the tritone sets it apart, as discussed in [<a href="/wiki/Paul_Hindemith" title="Paul Hindemith">Paul Hindemith</a>. <i>The Craft of Musical Composition</i>, Book I. Associated Music Publishers, New York, 1945]. It can be expressed as a ratio by compounding suitable <a href="/wiki/Superparticular_ratio" title="Superparticular ratio">superparticular ratios</a>. Whether it is assigned the ratio 64/45 or 45/32, depending on the musical context, or indeed some other ratio, it is not superparticular, which is in keeping with its unique role in music.<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></p></blockquote> <p><a href="/wiki/Harry_Partch" title="Harry Partch">Harry Partch</a> has written: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"> <p>Although this ratio [45/32] is composed of numbers which are multiples of 5 or under, they are excessively large for a 5-limit scale, and are sufficient justification, either in this form or as the tempered "tritone", for the epithet "diabolic", which has been used to characterize the interval. This is a case where, because of the largeness of the numbers, none but a <a href="/wiki/Musical_temperament" title="Musical temperament">temperament</a>-perverted ear could possibly prefer 45/32 to a small-number interval of about the same width. </p><p> In the <a href="/wiki/Pythagorean_interval" title="Pythagorean interval">Pythagorean ratio</a> 81/64 both numbers are multiples of 3 or under, yet because of their excessive largeness the ear certainly prefers 5/4 for this approximate degree, even though it involves a prime number higher than 3. In the case of the 45/32 "tritone" our theorists have gone around their elbows to reach their thumbs, which could have been reached simply and directly and non-"diabolically" via the number 7....<sup id="cite_ref-Partch_115_18-0" class="reference"><a href="#cite_note-Partch_115-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup></p></blockquote> <div class="mw-heading mw-heading2"><h2 id="Common_uses">Common uses</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Tritone&action=edit&section=8" title="Edit section: Common uses"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-More_citations_needed_section plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Tritone" title="Special:EditPage/Tritone">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a> in this section. Unsourced material may be challenged and removed.</span> <span class="date-container"><i>(<span class="date">January 2017</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Occurrences_in_diatonic_scales">Occurrences in diatonic scales</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Tritone&action=edit&section=9" title="Edit section: Occurrences in diatonic scales"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The augmented fourth (A4) occurs naturally between the fourth and seventh scale degrees of the <a href="/wiki/Major_scale" title="Major scale">major scale</a> (for example, from F to B in the key of <a href="/wiki/C_major" title="C major">C major</a>). It is also present in the natural <a href="/wiki/Minor_scale" title="Minor scale">minor scale</a> as the interval formed between the second and sixth scale degrees (for example, from D to A<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span> in the key of <a href="/wiki/C_minor" title="C minor">C minor</a>). The melodic minor scale, having two forms, presents a tritone in different locations when ascending and descending (when the scale ascends, the tritone appears between the third and sixth scale degrees and the fourth and seventh scale degrees, and when the scale descends, the tritone appears between the second and sixth scale degrees). <a href="/wiki/Supertonic" title="Supertonic">Supertonic</a> chords using the notes from the natural minor mode thus contain a tritone, regardless of inversion. Containing tritones, these scales are <a href="/wiki/Anhemitonic_scale" title="Anhemitonic scale">tritonic</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Occurrences_in_chords">Occurrences in chords</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Tritone&action=edit&section=10" title="Edit section: Occurrences in chords"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The dominant seventh chord in root position contains a diminished fifth (tritone) within its pitch construction: it occurs between the third and seventh above the <a href="/wiki/Root_(chord)" title="Root (chord)">root</a>. In addition, <a href="/wiki/Augmented_sixth_chord" title="Augmented sixth chord">augmented sixth chords</a>, some of which are enharmonic to dominant seventh chords, contain tritones spelled as augmented fourths (for example, the German sixth, from A to D<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span> in the key of <a href="/wiki/A_minor" title="A minor">A minor</a>); the French sixth chord can be viewed as a superposition of two tritones a major second apart. </p><p>The <a href="/wiki/Diminished_triad" title="Diminished triad">diminished triad</a> also contains a tritone in its construction, deriving its name from the diminished-fifth interval (i.e. a tritone). The <a href="/wiki/Half-diminished_seventh_chord" title="Half-diminished seventh chord">half-diminished seventh chord</a> contains the same tritone, while the fully <a href="/wiki/Diminished_seventh_chord" title="Diminished seventh chord">diminished seventh chord</a> is made up of two superposed tritones a minor third apart. </p><p>Other chords built on these, such as <a href="/wiki/Ninth_chord" title="Ninth chord">ninth chords</a>, often include tritones (as diminished fifths). </p> <div class="mw-heading mw-heading3"><h3 id="Resolution">Resolution</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Tritone&action=edit&section=11" title="Edit section: Resolution"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="thumb tright" style=""><div class="thumbinner" style="width:-moz-fit-content; width:fit-content;"><div class="thumbimage noresize" style="width:auto;"> <div class="mw-ext-score noresize" data-midi="//upload.wikimedia.org/score/g/d/gd9xbp8m99st58t8r1jnbhj9tzirob6/gd9xbp8m.midi"><img src="//upload.wikimedia.org/score/g/d/gd9xbp8m99st58t8r1jnbhj9tzirob6/gd9xbp8m.png" width="198" height="67" alt="
 \new Staff <<
 \new Voice \relative c' {
 \clef treble \key c \major \time 4/4
 \stemUp b'2 c f e
 }
 \new Voice \relative c' {
 \clef treble \key c \major \time 4/4
 \stemDown f2 e \bar "||" b' c \bar "||"
 }
 >>
" /><div style="margin-top: 3px;"><audio controls=""><source src="//upload.wikimedia.org/score/g/d/gd9xbp8m99st58t8r1jnbhj9tzirob6/gd9xbp8m.mp3" type="audio/mpeg" /><div>Audio playback is not supported in your browser. You can <a href="//upload.wikimedia.org/score/g/d/gd9xbp8m99st58t8r1jnbhj9tzirob6/gd9xbp8m.mp3">download the audio file</a>.</div></audio></div></div></div></div></div> <p>In all of the sonorities mentioned above, used in functional harmonic analysis, the tritone pushes towards resolution, generally resolving by <a href="/wiki/Step_(music)" class="mw-redirect" title="Step (music)">step</a> in <a href="/wiki/Contrary_motion" class="mw-redirect" title="Contrary motion">contrary motion</a>. This determines the resolution of chords containing tritones. </p><p>The augmented fourth resolves outward to a minor or major sixth (the first measure below). The inversion of this, a diminished fifth, resolves inward to a major or minor third (the second measure below). The diminished fifth is often called a tritone in modern <a href="/wiki/Tonal_music" class="mw-redirect" title="Tonal music">tonal</a> theory, but functionally and notationally it can only resolve inwards as a diminished fifth and is therefore not reckoned a tritone—that is, an interval composed of three adjacent whole tones—in mid-<a href="/wiki/Renaissance" title="Renaissance">renaissance</a> (early 16th-century) music theory.<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> <div class="mw-heading mw-heading3"><h3 id="Other_uses">Other uses</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Tritone&action=edit&section=12" title="Edit section: Other uses"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The tritone is also one of the defining features of the <a href="/wiki/Locrian_mode" title="Locrian mode">Locrian mode</a>, being featured between the <span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="skin-invert" typeof="mw:File"><a href="/wiki/File:Scale_deg_1.svg" class="mw-file-description" title="scale degree 1"><img alt="scale degree 1" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Scale_deg_1.svg/8px-Scale_deg_1.svg.png" decoding="async" width="8" height="21" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Scale_deg_1.svg/12px-Scale_deg_1.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Scale_deg_1.svg/16px-Scale_deg_1.svg.png 2x" data-file-width="30" data-file-height="80" /></a></span></span> and fifth scale degrees. </p><p>The half-octave tritone interval is used in the musical/auditory illusion known as the <a href="/wiki/Tritone_paradox" title="Tritone paradox">tritone paradox</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Historical_uses">Historical uses</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Tritone&action=edit&section=13" title="Edit section: Historical uses"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="thumb tright" style=""><div class="thumbinner" style="width:532px"><div class="thumbimage noresize" style="width:530px;"> <div class="mw-ext-score noresize" data-midi="//upload.wikimedia.org/score/b/y/by9x9nqe1uzpoew2r6q1pbs2xnxpecy/by9x9nqe.midi"><img src="//upload.wikimedia.org/score/b/y/by9x9nqe1uzpoew2r6q1pbs2xnxpecy/by9x9nqe.png" width="749" height="101" alt=" {
#(set-global-staff-size 14)
\relative c' {
 \clef treble \time 9/8 \key e \major
 \set Score.tempoHideNote = ##t \tempo "Très modéré" 4. = 36
 \override Score.SpacingSpanner #'common-shortest-duration = #(ly:make-moment 1 8)
 \set Staff.midiInstrument = "flute"
 \stemDown cis'4.~(^"Flute"\p cis8~_\markup \italic "doux et expressif" cis16 \set stemRightBeamCount = #1 b \times 2/3 { \set stemLeftBeamCount = #1 ais16 a gis } g8. a16 b bis)
 cis4.~( cis8~ cis16 \set stemRightBeamCount = #1 b \times 2/3 { \set stemLeftBeamCount = #1 ais16 a gis } g8. a16 b bis) \override DynamicLineSpanner.staff-padding = #3
 cis8(\< dis gis e4 gis,8 b4.~\! 
 b8\> b cis ais4)\!
}
}
" /><div style="margin-top: 3px;"><audio controls=""><source src="//upload.wikimedia.org/score/b/y/by9x9nqe1uzpoew2r6q1pbs2xnxpecy/by9x9nqe.mp3" type="audio/mpeg" /><div>Audio playback is not supported in your browser. You can <a href="//upload.wikimedia.org/score/b/y/by9x9nqe1uzpoew2r6q1pbs2xnxpecy/by9x9nqe.mp3">download the audio file</a>.</div></audio></div></div></div><div class="thumbcaption">The theme that opens <a href="/wiki/Claude_Debussy" title="Claude Debussy">Claude Debussy</a>'s <span title="French-language text"><i lang="fr"><a href="/wiki/Pr%C3%A9lude_%C3%A0_l%27apr%C3%A8s-midi_d%27un_faune" title="Prélude à l'après-midi d'un faune">Prélude à l'après-midi d'un faune</a></i></span> outlines the tritone between C<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span> and G.</div></div></div> <p>The tritone is a restless interval, classed as a <a href="/wiki/Consonance_and_dissonance" title="Consonance and dissonance">dissonance</a> in Western music from the early <a href="/wiki/Middle_Ages" title="Middle Ages">Middle Ages</a> through to the end of the <a href="/wiki/Common_practice" class="mw-redirect" title="Common practice">common practice</a> period. This interval was frequently avoided in medieval ecclesiastical singing because of its dissonant quality. The first explicit prohibition of it seems to occur with the development of <a href="/wiki/Guido_of_Arezzo" title="Guido of Arezzo">Guido of Arezzo</a>'s <a href="/wiki/Hexachord" title="Hexachord">hexachordal</a> system, who suggested that rather than make B<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span> a diatonic note, the hexachord be moved and based on C to avoid the F–B tritone altogether. Later theorists such as <a href="/wiki/Ugolino_of_Forl%C3%AC" title="Ugolino of Forlì">Ugolino d'Orvieto</a> and <a href="/wiki/Johannes_Tinctoris" title="Johannes Tinctoris">Tinctoris</a> advocated the inclusion of B<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>.<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> </p><p>From then until the end of the <a href="/wiki/Renaissance" title="Renaissance">Renaissance</a> the tritone was regarded as an unstable interval and rejected as a consonance by most theorists.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p><p>The name <span title="Latin-language text"><i lang="la">diabolus in musica</i></span> (<a href="/wiki/Latin_language" class="mw-redirect" title="Latin language">Latin</a> for 'the <a href="/wiki/Devil" title="Devil">Devil</a> in music') has been applied to the interval from at least the early 18th century, or the late Middle Ages,<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> though its use is not restricted to the tritone, being that the original found example of the term <span title="Latin-language text"><i lang="la">"diabolus en musica"</i></span> is <span title="Latin-language text"><i lang="la">"Mi Contra Fa est diabolus en musica"</i></span> (Mi against Fa is the devil in music). <a href="/wiki/Andreas_Werckmeister" title="Andreas Werckmeister">Andreas Werckmeister</a> cites this term in <a href="/wiki/1702_in_music" title="1702 in music">1702</a> as being used by "the old authorities" for both the tritone and for the clash between chromatically related tones such as F<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-natural">♮</span></span> and F<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>,<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> and five years later likewise calls <span title="Latin-language text"><i lang="la">"diabolus in musica"</i></span> the opposition of "square" and "round" B (B<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-natural">♮</span></span> and B<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>, respectively) because these notes represent the juxtaposition of <span title="Latin-language text"><i lang="la">"mi contra fa"</i></span>.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Johann_Joseph_Fux" title="Johann Joseph Fux">Johann Joseph Fux</a> cites the phrase in his seminal <a href="/wiki/1725_in_music" title="1725 in music">1725</a> work <span title="Latin-language text"><i lang="la"><a href="/wiki/Gradus_ad_Parnassum" title="Gradus ad Parnassum">Gradus ad Parnassum</a></i></span>, <a href="/wiki/Georg_Philipp_Telemann" title="Georg Philipp Telemann">Georg Philipp Telemann</a> in <a href="/wiki/1733_in_music" title="1733 in music">1733</a> describes, "mi against fa", which the ancients called "Satan in music"—and <a href="/wiki/Johann_Mattheson" title="Johann Mattheson">Johann Mattheson</a>, in <a href="/wiki/1739_in_music" title="1739 in music">1739</a>, writes that the "older singers with solmization called this pleasant interval <span title="Latin-language text"><span lang="la" style="font-style: normal;">'mi contra fa'</span></span> or 'the devil in music'."<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> Although the latter two of these authors cite the association with the devil as from the past, there are no known citations of this term from the Middle Ages, as is commonly asserted.<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> However <a href="/wiki/Denis_Arnold" title="Denis Arnold">Denis Arnold</a>, in the <i><a href="/wiki/Oxford_Companion_to_Music#The_New_Oxford_Companion_to_Music" class="mw-redirect" title="Oxford Companion to Music">New Oxford Companion to Music</a></i>, suggests that the nickname was already applied early in the medieval music itself: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>It seems first to have been designated as a "dangerous" interval when <b>Guido of Arezzo</b> developed his system of hexachords and with the introduction of B flat as a diatonic note, at much the same time acquiring its nickname of <span title="Latin-language text"><span lang="la" style="font-style: normal;">"Diabolus in Musica"</span></span> ("the devil in music").<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup></p></blockquote> <p>That original symbolic association with the devil and its avoidance led to Western cultural convention seeing the tritone as suggesting "evil" in music. However, stories that singers were <a href="/wiki/Excommunication" title="Excommunication">excommunicated</a> or otherwise punished by the Church for invoking this interval are likely fanciful. At any rate, avoidance of the interval for musical reasons has a long history, stretching back to the parallel <a href="/wiki/Organum" title="Organum">organum</a> of the <span title="Latin-language text"><i lang="la"><a href="/wiki/Musica_Enchiriadis" class="mw-redirect" title="Musica Enchiriadis">Musica Enchiriadis</a></i></span>. In all these expressions, including the commonly cited <span title="Latin-language text"><i lang="la">"mi contra fa est diabolus in musica"</i></span>, the "mi" and "fa" refer to notes from two adjacent <a href="/wiki/Hexachord" title="Hexachord">hexachords</a>. For instance, in the tritone B–F, B would be "mi", that is the third scale degree in the "hard" hexachord beginning on G, while F would be "fa", that is the fourth scale degree in the "natural" hexachord beginning on C. </p><p>Later, with the rise of the Baroque and Classical music era, composers accepted the tritone, but used it in a specific, controlled way—notably through the principle of the tension-release mechanism of the <a href="/wiki/Tonality" title="Tonality">tonal system</a>. In that system (which is the fundamental musical grammar of Baroque and Classical music), the tritone is one of the defining intervals of the dominant-seventh chord and two tritones separated by a minor third give the fully diminished seventh chord its characteristic sound. In minor, the diminished triad (comprising two minor thirds, which together add up to a tritone) appears on the second scale degree—and thus features prominently in the progression ii<sup>o</sup>–V–i. Often, the <a href="/wiki/Inverted_chord" class="mw-redirect" title="Inverted chord">inversion</a> ii<sup>o6</sup> is used to move the tritone to the inner voices as this allows for stepwise motion in the bass to the dominant root. In three-part counterpoint, free use of the diminished triad in first inversion is permitted, as this eliminates the tritone relation to the bass.<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> </p><p>It is only with the <a href="/wiki/Romantic_music" title="Romantic music">Romantic music</a> and <a href="/wiki/Modern_classical_music" class="mw-redirect" title="Modern classical music">modern classical music</a> that composers started to use it totally freely, without functional limitations notably in an expressive way to exploit the "evil" connotations culturally associated with it, such as <a href="/wiki/Franz_Liszt" title="Franz Liszt">Franz Liszt</a>'s use of the tritone to suggest Hell in his <i><a href="/wiki/Dante_Sonata" title="Dante Sonata">Dante Sonata</a></i>: </p> <div class="center"><div class="thumb tnone" style=""><div class="thumbinner" style="width:-moz-fit-content; width:fit-content;"><div class="thumbimage noresize" style="width:auto;"> <div class="mw-ext-score noresize" data-midi="//upload.wikimedia.org/score/a/m/am1uigv6gp6f9exi3hj88ov4399iws3/am1uigv6.midi"><img src="//upload.wikimedia.org/score/a/m/am1uigv6gp6f9exi3hj88ov4399iws3/am1uigv6.png" width="674" height="187" alt=" {
\relative c' { \new PianoStaff << \set PianoStaff.connectArpeggios = ##t
\new Staff { \key f \major \tempo "Andante maestoso"
 R1 R r2 \clef F << { <a, c fis>2$
 \stemDown <bes des g> <ces ees aes> \stemUp <ees ees'>2..$ q16 s1 } \\
 { \stemNeutral s2*3 <aes bes>2\<_\markup\italic{poco rit.} <g bes>\>
 <ees aes ces ees>1\arpeggio\!^\fermata } >>
}
\new Staff { \clef F \key f \major
 \slashedGrace { <a a'>8 } <a a'>2^^ \slashedGrace { <ees ees'>8 } <ees ees'>2^^
 \slashedGrace { <a, a'>8 } <a a'>4^^ \slashedGrace { <ees ees'>8 } <ees ees'>4^^
 \slashedGrace { <a, a'>8 } <a a'>4^^ \slashedGrace { <ees ees'>8 } <ees ees'>4^^~q1~q~
 q4 <fes fes'>8. ( <ges ges'>16 <fes fes'>4 <ees ees'> )
 <aes ees' aes>1\arpeggio_\fermata %
}
>> } }" /><span class="mw-default-size" typeof="mw:File"><span><audio id="mwe_player_0" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-durationhint="26" data-mwtitle="Liszt,_apres_une_lecture_de_Dante_from_Annees_de_Pelerinage.wav" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/1/14/Liszt%2C_apres_une_lecture_de_Dante_from_Annees_de_Pelerinage.wav/Liszt%2C_apres_une_lecture_de_Dante_from_Annees_de_Pelerinage.wav.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/1/14/Liszt%2C_apres_une_lecture_de_Dante_from_Annees_de_Pelerinage.wav/Liszt%2C_apres_une_lecture_de_Dante_from_Annees_de_Pelerinage.wav.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/1/14/Liszt%2C_apres_une_lecture_de_Dante_from_Annees_de_Pelerinage.wav" type="audio/wav" data-width="0" data-height="0" /></audio></span></span></div></div><div class="thumbcaption">Liszt, <span title="French-language text"><span lang="fr" style="font-style: normal;">"Après une lecture du Dante"</span></span> from <span title="Latin-language text"><i lang="la">Années de Pèlerinage</i></span>.</div></div></div></div> <div style="clear:both;" class=""></div> <div class="thumb tright" style=""><div class="thumbinner" style="width:-moz-fit-content; width:fit-content;"><div class="thumbimage noresize" style="width:auto;"> <span typeof="mw:File"><a href="/wiki/File:Siegfried_Act_2_prelude.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Siegfried_Act_2_prelude.png/400px-Siegfried_Act_2_prelude.png" decoding="async" width="400" height="174" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Siegfried_Act_2_prelude.png/600px-Siegfried_Act_2_prelude.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Siegfried_Act_2_prelude.png/800px-Siegfried_Act_2_prelude.png 2x" data-file-width="2352" data-file-height="1026" /></a></span><span class="mw-default-size" typeof="mw:File"><span><audio id="mwe_player_12" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-durationhint="20" data-mwtitle="Wagner,_Prelude_to_Act_2_of_Siegfried.wav" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/1/14/Wagner%2C_Prelude_to_Act_2_of_Siegfried.wav/Wagner%2C_Prelude_to_Act_2_of_Siegfried.wav.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/1/14/Wagner%2C_Prelude_to_Act_2_of_Siegfried.wav/Wagner%2C_Prelude_to_Act_2_of_Siegfried.wav.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/1/14/Wagner%2C_Prelude_to_Act_2_of_Siegfried.wav" type="audio/wav" data-width="0" data-height="0" /></audio></span></span></div><div class="thumbcaption">Wagner, Prelude to Act 2 of <i>Siegfried</i>.</div></div></div> <p>—or <a href="/wiki/Wagner" class="mw-redirect" title="Wagner">Wagner</a>'s use of timpani tuned to C and F<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span> to convey a brooding atmosphere at the start of the second act of the opera <i><a href="/wiki/Siegfried_(opera)" title="Siegfried (opera)">Siegfried</a></i>. </p> <div class="thumb tright" style=""><div class="thumbinner" style="width:-moz-fit-content; width:fit-content;"><div class="thumbimage noresize" style="width:auto;"> <span typeof="mw:File"><a href="/wiki/File:Debussy_la_Damoiselle_Fig_30.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/Debussy_la_Damoiselle_Fig_30.png/400px-Debussy_la_Damoiselle_Fig_30.png" decoding="async" width="400" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/Debussy_la_Damoiselle_Fig_30.png/600px-Debussy_la_Damoiselle_Fig_30.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/35/Debussy_la_Damoiselle_Fig_30.png/800px-Debussy_la_Damoiselle_Fig_30.png 2x" data-file-width="2430" data-file-height="1001" /></a></span><span class="mw-default-size" typeof="mw:File"><span><audio id="mwe_player_13" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-durationhint="15" data-mwtitle="Debussy,_la_Damoiselle_Elue,_Fig_30.wav" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/7/71/Debussy%2C_la_Damoiselle_Elue%2C_Fig_30.wav/Debussy%2C_la_Damoiselle_Elue%2C_Fig_30.wav.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/7/71/Debussy%2C_la_Damoiselle_Elue%2C_Fig_30.wav/Debussy%2C_la_Damoiselle_Elue%2C_Fig_30.wav.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/7/71/Debussy%2C_la_Damoiselle_Elue%2C_Fig_30.wav" type="audio/wav" data-width="0" data-height="0" /></audio></span></span></div><div class="thumbcaption">Debussy, <span title="French-language text"><i lang="fr">La Damoiselle élue</i></span>, Figure 30.</div></div></div> <p>In his early cantata <span title="French-language text"><i lang="fr"><a href="/wiki/La_Damoiselle_%C3%A9lue" title="La Damoiselle élue">La Damoiselle élue</a></i></span>, <a href="/wiki/Debussy" class="mw-redirect" title="Debussy">Debussy</a> uses a tritone to convey the words of the poem by <a href="/wiki/Dante_Gabriel_Rossetti" title="Dante Gabriel Rossetti">Dante Gabriel Rossetti</a>. </p> <div class="thumb tright" style=""><div class="thumbinner" style="width:-moz-fit-content; width:fit-content;"><div class="thumbimage noresize" style="width:auto;"> <span typeof="mw:File"><a href="/wiki/File:Debussy_Quartet_2nd_movement,_bars_140-7.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Debussy_Quartet_2nd_movement%2C_bars_140-7.png/400px-Debussy_Quartet_2nd_movement%2C_bars_140-7.png" decoding="async" width="400" height="272" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Debussy_Quartet_2nd_movement%2C_bars_140-7.png/600px-Debussy_Quartet_2nd_movement%2C_bars_140-7.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/63/Debussy_Quartet_2nd_movement%2C_bars_140-7.png/800px-Debussy_Quartet_2nd_movement%2C_bars_140-7.png 2x" data-file-width="2380" data-file-height="1617" /></a></span><span class="mw-default-size" typeof="mw:File"><span><audio id="mwe_player_14" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-durationhint="14" data-mwtitle="Debussy_Quartet_2nd_movement,_bars_140-7.wav" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/4/4d/Debussy_Quartet_2nd_movement%2C_bars_140-7.wav/Debussy_Quartet_2nd_movement%2C_bars_140-7.wav.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/4/4d/Debussy_Quartet_2nd_movement%2C_bars_140-7.wav/Debussy_Quartet_2nd_movement%2C_bars_140-7.wav.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/4/4d/Debussy_Quartet_2nd_movement%2C_bars_140-7.wav" type="audio/wav" data-width="0" data-height="0" /></audio></span></span></div><div class="thumbcaption">Debussy, String Quartet, 2nd movement,<br />bars 140–147.</div></div></div> <p><a href="/wiki/Roger_Nichols_(musical_scholar)" title="Roger Nichols (musical scholar)">Roger Nichols</a> (1972, p19) says that "the bare fourths, the wide spacing, the tremolos, all depict the words—'the light thrilled towards her'—with sudden, overwhelming power."<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> Debussy's String Quartet also features passages that emphasize the tritone. </p><p>The tritone was also exploited heavily in that period as an interval of <a href="/wiki/Modulation_(music)" title="Modulation (music)">modulation</a> for its ability to evoke a strong reaction by moving quickly to <a href="/wiki/Distantly_related_key" class="mw-redirect" title="Distantly related key">distantly related keys</a>. For example, the climax of <a href="/wiki/Hector_Berlioz" title="Hector Berlioz">Hector Berlioz</a>'s <span title="French-language text"><i lang="fr"><a href="/wiki/La_damnation_de_Faust" title="La damnation de Faust">La damnation de Faust</a></i></span> (1846) consists of a transition between "huge B and F chords" as Faust arrives in <a href="/wiki/Pand%C3%A6monium_(Paradise_Lost)" title="Pandæmonium (Paradise Lost)">Pandaemonium</a>, the capital of Hell.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> Musicologist <a href="/wiki/Julian_Rushton" title="Julian Rushton">Julian Rushton</a> calls this "a tonal wrench by a tritone".<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> </p><p>Later, in <a href="/wiki/Twelve-tone_music" class="mw-redirect" title="Twelve-tone music">twelve-tone music</a>, <a href="/wiki/Serial_music" class="mw-redirect" title="Serial music">serialism</a>, and other 20th century compositional idioms, composers considered it a neutral interval.<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> In some analyses of the works of 20th century composers, the tritone plays an important structural role; perhaps the most cited is the <a href="/wiki/Axis_system" title="Axis system">axis system</a>, proposed by <a href="/wiki/Ern%C5%91_Lendvai" title="Ernő Lendvai">Ernő Lendvai</a>, in his analysis of the use of tonality in the music of <a href="/wiki/B%C3%A9la_Bart%C3%B3k" title="Béla Bartók">Béla Bartók</a>.<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> Tritone relations are also important in the music of <a href="/wiki/George_Crumb" title="George Crumb">George Crumb</a><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. (March 2016)">citation needed</span></a></i>]</sup> and <a href="/wiki/Benjamin_Britten" title="Benjamin Britten">Benjamin Britten</a>, whose <i><a href="/wiki/War_Requiem" title="War Requiem">War Requiem</a></i> features a tritone between C and F♯ as a recurring motif.<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> John Bridcut (2010, p. 271) describes the power of the interval in creating the sombre and ambiguous opening of the <i>War Requiem</i>:<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> "The idea that the chorus and orchestra are confident in their wrong-headed piety is repeatedly disputed by the music. From the instability of the opening tritone—that unsettling interval between C and F sharp—accompanied by the tolling of warning bells ... eventually resolves into a major chord for the arrival of the boys singing 'Te decet hymnus'."<sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Leonard_Bernstein" title="Leonard Bernstein">Leonard Bernstein</a> uses the tritone harmony as a basis for much of <i><a href="/wiki/West_Side_Story" title="West Side Story">West Side Story</a></i>.<sup id="cite_ref-:0_37-0" class="reference"><a href="#cite_note-:0-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> <a href="/wiki/George_Harrison" title="George Harrison">George Harrison</a> uses tritones on the downbeats of the opening phrases of <a href="/wiki/The_Beatles" title="The Beatles">the Beatles</a> songs "<a href="/wiki/The_Inner_Light_(song)" title="The Inner Light (song)">The Inner Light</a>", "<a href="/wiki/Blue_Jay_Way" title="Blue Jay Way">Blue Jay Way</a>", and "<a href="/wiki/Within_You_Without_You" title="Within You Without You">Within You Without You</a>", creating a prolonged sense of suspended resolution.<sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> Perhaps the most striking use of the interval in rock music of the late 1960s can be found in <a href="/wiki/Jimi_Hendrix" title="Jimi Hendrix">Jimi Hendrix</a>'s song "<a href="/wiki/Purple_Haze" title="Purple Haze">Purple Haze</a>". According to Dave Moskowitz (2010, p. 12), Hendrix "ripped into 'Purple Haze' by beginning the song with the sinister sounding tritone interval creating an opening dissonance, long described as 'The Devil in Music'."<sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> The opening riff of "<a href="/wiki/Black_Sabbath_(song)" title="Black Sabbath (song)">Black Sabbath</a>", the first song on <a href="/wiki/Black_Sabbath" title="Black Sabbath">Black Sabbath</a>'s eponymous debut album, is an inversion of a tritone;<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> the album, and this song in particular, are considered to mark the birth of <a href="/wiki/Heavy_metal_music" title="Heavy metal music">heavy metal music</a>.<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Tritone_substitution.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Tritone_substitution.png/310px-Tritone_substitution.png" decoding="async" width="310" height="131" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Tritone_substitution.png/465px-Tritone_substitution.png 1.5x, //upload.wikimedia.org/wikipedia/commons/1/1b/Tritone_substitution.png 2x" data-file-width="534" data-file-height="225" /></a><figcaption><a href="/wiki/Tritone_substitution" title="Tritone substitution">Tritone substitution</a>: F<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span><sup>7</sup> may substitute for C<sup>7</sup>, and vice versa, because they both share E<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-natural">♮</span></span> and B<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>/A<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span> and due to <a href="/wiki/Voice_leading" title="Voice leading">voice leading</a> considerations.<span class="mw-default-size" typeof="mw:File"><span><audio id="mwe_player_15" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-durationhint="6" data-mwtitle="Tritone_substitution.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/4/4b/Tritone_substitution.mid/Tritone_substitution.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/4/4b/Tritone_substitution.mid/Tritone_substitution.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/4/4b/Tritone_substitution.mid" type="audio/midi" data-width="0" data-height="0" /></audio></span></span></figcaption></figure> <p>Tritones also became important in the development of <a href="/wiki/Jazz" title="Jazz">jazz</a> tertian harmony, where triads and seventh chords are often expanded to become 9th, 11th, or 13th chords, and the tritone often occurs as a substitute for the naturally occurring interval of the perfect 11th. Since the perfect 11th (i.e. an octave plus perfect fourth) is typically perceived as a dissonance requiring a resolution to a major or minor 10th, chords that expand to the 11th or beyond typically raise the 11th a semitone (thus giving us an augmented or sharp 11th, or an octave plus a tritone from the root of the chord) and present it in conjunction with the perfect 5th of the chord. Also in jazz harmony, the tritone is both part of the dominant chord and its substitute dominant (also known as the sub V chord). Because they share the same tritone, they are possible substitutes for one another. This is known as a <a href="/wiki/Tritone_substitution" title="Tritone substitution">tritone substitution</a>. The tritone substitution is one of the most common chord and improvisation devices in jazz. </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"> <p>In the theory of harmony it is known that a diminished interval needs to be resolved inwards, and an augmented interval outwards. ... and with the correct resolution of the <i>true</i> tritones this desire is totally satisfied. However, if one plays a <i>just</i> diminished fifth that is perfectly in tune, for example, there is no wish to resolve it to a major third. Just the opposite—aurally one wants to enlarge it to a minor sixth. The opposite holds true for the <i>just</i> augmented fourth. ... </p><p> These apparently contradictory aural experiences become understandable when the cents of both types of just tritones are compared with those of the true tritones and then read 'crossed-over'. One then notices that the just augmented fourth of 590.224 cents is only 2 cents bigger than the true diminished fifth of 588.270 cents, and that both intervals lie below the middle of the octave of 600.000 cents. It is no wonder that, following the ear, we want to resolve both downwards. The ear only desires the tritone to be resolved upwards when it is bigger than the middle of the octave. Therefore the opposite is the case with the just diminished fifth of 609.776 cents.<sup id="cite_ref-Renold_8-1" class="reference"><a href="#cite_note-Renold-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup></p></blockquote> <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=Tritone&action=edit&section=14" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/List_of_meantone_intervals" title="List of meantone intervals">List of meantone intervals</a></li> <li><a href="/wiki/Interval_(music)" title="Interval (music)">List of musical intervals</a></li> <li><a href="/wiki/List_of_pitch_intervals" title="List of pitch intervals">List of pitch intervals</a></li> <li><a href="/wiki/Ditone" title="Ditone">Ditone</a></li> <li><a href="/wiki/Whole_tone" class="mw-redirect" title="Whole tone">Tone</a></li> <li><a href="/wiki/Hexatonic_scale#Tritone_scale" title="Hexatonic scale">Hexatonic scale § Tritone scale</a></li> <li><a href="/wiki/Consecutive_fifths#Unequal_fifths" title="Consecutive fifths">Consecutive fifths § Unequal fifths</a></li> <li><a href="/wiki/Petrushka_chord" title="Petrushka chord">Petrushka chord</a></li> <li><a href="/wiki/Tritonic_scale" title="Tritonic scale">Tritonic scale</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=Tritone&action=edit&section=15" 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 reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFDrabkin2001" class="citation web cs1">Drabkin, William (20 January 2001). <span class="id-lock-limited" title="Free access subject to limited trial, subscription normally required"><a rel="nofollow" class="external text" href="https://www.oxfordmusiconline.com/grovemusic/view/10.1093/gmo/9781561592630.001.0001/omo-9781561592630-e-0000028403">"Tritone"</a></span>. <i><a href="/wiki/Oxford_Music_Online" class="mw-redirect" title="Oxford Music Online">Oxford Music Online</a></i>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fgmo%2F9781561592630.article.28403">10.1093/gmo/9781561592630.article.28403</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-56159-263-0" title="Special:BookSources/978-1-56159-263-0"><bdi>978-1-56159-263-0</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">August 31,</span> 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Oxford+Music+Online&rft.atitle=Tritone&rft.date=2001-01-20&rft_id=info%3Adoi%2F10.1093%2Fgmo%2F9781561592630.article.28403&rft.isbn=978-1-56159-263-0&rft.aulast=Drabkin&rft.aufirst=William&rft_id=https%3A%2F%2Fwww.oxfordmusiconline.com%2Fgrovemusic%2Fview%2F10.1093%2Fgmo%2F9781561592630.001.0001%2Fomo-9781561592630-e-0000028403&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATritone" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">E.g., <a href="/wiki/Jacobus_Leodiensis" class="mw-redirect" title="Jacobus Leodiensis">Jacobus Leodiensis</a>, <i>Speculum musicae</i>, Liber secundus, in <i>Jacobi Leodiensis Speculum musicae</i>, edited by Roger Bragard, Corpus Scriptorum de Musica 3/2 ([Rome]: <a href="/wiki/American_Institute_of_Musicology" title="American Institute of Musicology">American Institute of Musicology</a>, 1961): 128–31, citations on 192–96, 200, and 229; Jacobus Leodiensis, <i>Speculum musicae</i>, Liber sextus, in <i>Jacobi Leodiensis Speculum musicae</i>, edited by Roger Bragard, Corpus Scriptorum de Musica 3/6 ([Rome]: <a href="/wiki/American_Institute_of_Musicology" title="American Institute of Musicology">American Institute of Musicology</a>, 1973): 1–161, citations on 52 and 68; Johannes Torkesey, <i>Declaratio et expositio</i>, London: British Library, Lansdowne MS 763, ff.89v-94v, citations on f.92r,2–3; <a href="/wiki/Prosdocimus_de_Beldemandis" title="Prosdocimus de Beldemandis">Prosdocimus de Beldemandis</a>, <i>Tractatus musice speculative</i>, in D. Raffaello Baralli and Luigi Torri, "Il Trattato di Prosdocimo de' Beldomandi contro il Lucidario di Marchetto da Padova per la prima volta trascritto e illustrato", <i>Rivista Musicale Italiana</i> 20 (1913): 731–62, citations on 732–34.</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"><a rel="nofollow" class="external text" href="https://books.google.com/books?id=02rFSecPhEsC&q=%22A+prominent+element%22">Randel (2003), p. 911</a>. "A prominent element in the <a href="/wiki/Whole-tone_scale" title="Whole-tone scale">whole-tone scale</a>...its symmetry with respect to the octave gives it a special role in <a href="/wiki/Twelve-tone_music" class="mw-redirect" title="Twelve-tone music">twelve-tone music</a> as well."</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSmith_Brindle1966" class="citation book cs1"><a href="/wiki/Reginald_Smith_Brindle" title="Reginald Smith Brindle">Smith Brindle, Reginald</a> (1966). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=gvNLXHpusw8C"><i>Serial Composition</i></a>. <a href="/wiki/Oxford_University_Press" title="Oxford University Press">Oxford University Press</a>. p. 66. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-19-311906-4" title="Special:BookSources/0-19-311906-4"><bdi>0-19-311906-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Serial+Composition&rft.pages=66&rft.pub=Oxford+University+Press&rft.date=1966&rft.isbn=0-19-311906-4&rft.aulast=Smith+Brindle&rft.aufirst=Reginald&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DgvNLXHpusw8C&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATritone" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">Bruce Benward & Marilyn Nadine Saker (2003). <i>Music: In Theory and Practice, Vol. I</i>, seventh edition (Boston: McGraw-Hill), p. 54. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-294262-0" title="Special:BookSources/978-0-07-294262-0">978-0-07-294262-0</a>.</span> </li> <li id="cite_note-Fonville-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-Fonville_6-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFonville1991" class="citation journal cs1"><a href="/wiki/John_Fonville" title="John Fonville">Fonville, John</a> (1991). "Ben Johnston's Extended Just Intonation: A Guide for Interpreters". <i><a href="/wiki/Perspectives_of_New_Music" title="Perspectives of New Music">Perspectives of New Music</a></i>. <b>29</b> (2): 106–137. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F833435">10.2307/833435</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/833435">833435</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Perspectives+of+New+Music&rft.atitle=Ben+Johnston%27s+Extended+Just+Intonation%3A+A+Guide+for+Interpreters&rft.volume=29&rft.issue=2&rft.pages=106-137&rft.date=1991&rft_id=info%3Adoi%2F10.2307%2F833435&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F833435%23id-name%3DJSTOR&rft.aulast=Fonville&rft.aufirst=John&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATritone" class="Z3988"></span></span> </li> <li id="cite_note-Partch-7"><span class="mw-cite-backlink">^ <a href="#cite_ref-Partch_7-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Partch_7-1"><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="CITEREFPartch1979" class="citation book cs1"><a href="/wiki/Harry_Partch" title="Harry Partch">Partch, H.</a> (1979) [1974]. <a href="/wiki/Genesis_of_a_Music" title="Genesis of a Music"><i>Genesis of a Music: An account of a creative work, its Roots and its fulfillments</i></a> (2nd ed.). New York, NY: Da Capo Press. p. 69. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-306-80106-X" title="Special:BookSources/0-306-80106-X"><bdi>0-306-80106-X</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Genesis+of+a+Music%3A+An+account+of+a+creative+work%2C+its+Roots+and+its+fulfillments&rft.place=New+York%2C+NY&rft.pages=69&rft.edition=2nd&rft.pub=Da+Capo+Press&rft.date=1979&rft.isbn=0-306-80106-X&rft.aulast=Partch&rft.aufirst=H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATritone" class="Z3988"></span> <dl><dd><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1">"<i>Genesis of a Music</i>". <a rel="nofollow" class="external text" href="https://pearl-hifi.com/06_Lit_Archive/02_PEARL_Arch/Vol_16/Sec_51/4555_Genesis_of_a_Music_2nd_Edn.pdf"><i>scanned copy</i></a> <span class="cs1-format">(PDF)</span> (online) (2nd ed.). 1979<span class="reference-accessdate">. Retrieved <span class="nowrap">22 July</span> 2021</span> – via pearl-hifi.com.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Genesis+of+a+Music&rft.btitle=scanned+copy&rft.edition=2nd&rft.date=1979&rft_id=https%3A%2F%2Fpearl-hifi.com%2F06_Lit_Archive%2F02_PEARL_Arch%2FVol_16%2FSec_51%2F4555_Genesis_of_a_Music_2nd_Edn.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATritone" class="Z3988"></span></dd></dl> </span></li> <li id="cite_note-Renold-8"><span class="mw-cite-backlink">^ <a href="#cite_ref-Renold_8-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Renold_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="CITEREFRenold2004" class="citation book cs1">Renold, Maria (2004). <i>Intervals, Scales, Tones, and the Concert Pitch <span class="nowrap">  C = 128 Hz </span></i>. Stevens, Bevis (translator) ; Meuss, Anna R. (additional editing). Forest Row: Temple Lodge. pp. 15–16. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1-902636-46-5" title="Special:BookSources/1-902636-46-5"><bdi>1-902636-46-5</bdi></a>. <q>translated from German</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Intervals%2C+Scales%2C+Tones%2C+and+the+Concert+Pitch+%3Cspan+class%3D%22nowrap%22%3E%26hairsp%3B+C+%3D+128+Hz+%3C%2Fspan%3E&rft.place=Forest+Row&rft.pages=15-16&rft.pub=Temple+Lodge&rft.date=2004&rft.isbn=1-902636-46-5&rft.aulast=Renold&rft.aufirst=Maria&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATritone" class="Z3988"></span></span> </li> <li id="cite_note-Helmholtz-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-Helmholtz_9-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHelmholtz2005" class="citation book cs1"><a href="/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz">Helmholtz, H.</a> (2005) [1875, 1st Engl.]. <a href="/wiki/Alexander_J._Ellis" class="mw-redirect" title="Alexander J. Ellis">Ellis, A.J.</a> (ed.). <a href="/wiki/On_Sensations_of_Tone" class="mw-redirect" title="On Sensations of Tone"><i>On the Sensations of Tone as a Physiological Basis for the Theory of Music</i></a> (reprint ed.). p. 457. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1-4191-7893-8" title="Special:BookSources/1-4191-7893-8"><bdi>1-4191-7893-8</bdi></a>. <q>Name of interval: <i>Just Tritone</i>, cents in interval: 590, number to an octave: 2 ; Name of interval: <i>Pyth. Tritone</i>, cents in interval: 612, number to an octave: 2 </q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=On+the+Sensations+of+Tone+as+a+Physiological+Basis+for+the+Theory+of+Music&rft.pages=457&rft.edition=reprint&rft.date=2005&rft.isbn=1-4191-7893-8&rft.aulast=Helmholtz&rft.aufirst=H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATritone" class="Z3988"></span></span> </li> <li id="cite_note-Haluska_24-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-Haluska_24_10-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHaluska2003" class="citation book cs1">Haluska, Ján (2003). <i>The Mathematical Theory of Tone Systems</i>. Pure and Applied Mathematics Series. Vol. 262. New York, NY / London, UK: Marcel Dekker / Momenta. p. <span class="texhtml mvar" style="font-style:italic;">xxiv</span>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-8247-4714-3" title="Special:BookSources/0-8247-4714-3"><bdi>0-8247-4714-3</bdi></a>. <q>25:18 classic augmented fourth</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Mathematical+Theory+of+Tone+Systems&rft.place=New+York%2C+NY+%2F+London%2C+UK&rft.series=Pure+and+Applied+Mathematics+Series&rft.pages=%3Cspan+class%3D%22texhtml+mvar%22+style%3D%22font-style%3Aitalic%3B%22%3Exxiv%3C%2Fspan%3E&rft.pub=Marcel+Dekker+%2F+Momenta&rft.date=2003&rft.isbn=0-8247-4714-3&rft.aulast=Haluska&rft.aufirst=J%C3%A1n&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATritone" class="Z3988"></span></span> </li> <li id="cite_note-Haluska_25-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-Haluska_25_11-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFHaluska2003">Haluska (2003)</a>, p.  <span class="texhtml mvar" style="font-style:italic;">xxv</span> "36:25 classic diminished fifth".</span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPaul1885" class="citation book cs1">Paul, Oscar (1885). <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_4WEJAQAAMAAJ"><i>A Manual of Harmony for use in Music-Schools and Seminaries, and for Self-Instruction</i></a>. Translated by <a href="/wiki/G._Schirmer,_Inc." title="G. Schirmer, Inc.">Schirmer, Gustav, Sr.</a> Theodore Baker. p. 165 – via archive.org. <q>musical interval 'pythagorean major third'<span class="cs1-kern-right"></span></q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Manual+of+Harmony+for+use+in+Music-Schools+and+Seminaries%2C+and+for+Self-Instruction&rft.pages=165&rft.pub=Theodore+Baker&rft.date=1885&rft.aulast=Paul&rft.aufirst=Oscar&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_4WEJAQAAMAAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATritone" 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: translators list (<a href="/wiki/Category:CS1_maint:_multiple_names:_translators_list" title="Category:CS1 maint: multiple names: translators list">link</a>)</span></span> </li> <li id="cite_note-Haluska_23-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-Haluska_23_13-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFHaluska2003">Haluska (2003)</a>, p. <span class="texhtml mvar" style="font-style:italic;">xxiii</span> "7:5 septimal or Huygens' tritone, Bohlen-Pierce fourth", "10:7 Euler's tritone".</span> </li> <li id="cite_note-Strange-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-Strange_14-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStrangePatricia2001" class="citation book cs1">Strange, Patricia; Patricia, Allen (2001). <i>The Contemporary Violin: Extended performance techniques</i>. p. 147. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-520-22409-4" title="Special:BookSources/0-520-22409-4"><bdi>0-520-22409-4</bdi></a>. <q>... septimal tritone, 10:7; smaller septimal tritone, 7:5; ... This list is not exhaustive, even when limited to the first sixteen partials. Consider the very narrow augmented fourth, 13:9. ... just intonation is not an attempt to generate necessarily consonant intervals.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Contemporary+Violin%3A+Extended+performance+techniques&rft.pages=147&rft.date=2001&rft.isbn=0-520-22409-4&rft.aulast=Strange&rft.aufirst=Patricia&rft.au=Patricia%2C+Allen&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATritone" 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">Monelle, Raymond (2006). <i>The Musical Topic: Hunt, Military And Pastoral</i>, p. 102. <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/9780253347664" title="Special:BookSources/9780253347664">9780253347664</a>.</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">Fauvel, John; Flood, Raymond; and Wilson, Robin J. (2006). <i>Music And Mathematics</i>, pp. 21–22. <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/9780199298938" title="Special:BookSources/9780199298938">9780199298938</a>.</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">Haluska (2003), p. 286.</span> </li> <li id="cite_note-Partch_115-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-Partch_115_18-0">^</a></b></span> <span class="reference-text">Partch (1974), p. 115.</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="CITEREFBent1994" class="citation journal cs1">Bent, Margaret (1994). "Accidentals, Counterpoint and Notation in Aaron's <i>Aggiunta</i> to the <i>Toscanello in Musica</i>". <i>Journal of Musicology</i>. <b>12</b> (3): 306–344 [308]. <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%2F764089">10.2307/764089</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/764089">764089</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+Musicology&rft.atitle=Accidentals%2C+Counterpoint+and+Notation+in+Aaron%27s+Aggiunta+to+the+Toscanello+in+Musica&rft.volume=12&rft.issue=3&rft.pages=306-344+308&rft.date=1994&rft_id=info%3Adoi%2F10.2307%2F764089&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F764089%23id-name%3DJSTOR&rft.aulast=Bent&rft.aufirst=Margaret&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATritone" 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 id="CITEREFGuido_d'Arezzo" class="citation cs2">Guido d'Arezzo, <i>Epistola de ignoto cantu</i>, lines 309–322</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Epistola+de+ignoto+cantu&rft.pages=lines+309-322&rft.au=Guido+d%27Arezzo&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATritone" class="Z3988"></span><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources#What_information_to_include" title="Wikipedia:Citing sources"><span title="A complete citation is needed. (October 2015)">full citation needed</span></a></i>]</sup><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability"><span title="The material near this tag failed verification of its source citation(s). (October 2015)">failed verification</span></a></i>]</sup></span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDrabkin" class="citation web cs1">Drabkin, William. <a rel="nofollow" class="external text" href="http://www.oxfordmusiconline.com/subscriber/article/grove/music/28403">"Tritone"</a>. <i><a href="/wiki/Grove_Music_Online" class="mw-redirect" title="Grove Music Online">Grove Music Online</a> (subscription access)</i>. <a href="/wiki/Grove_Music_Online#Oxford_Music_Online" class="mw-redirect" title="Grove Music Online">Oxford Music Online</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2008-07-21</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Grove+Music+Online+%28subscription+access%29&rft.atitle=Tritone&rft.aulast=Drabkin&rft.aufirst=William&rft_id=http%3A%2F%2Fwww.oxfordmusiconline.com%2Fsubscriber%2Farticle%2Fgrove%2Fmusic%2F28403&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATritone" class="Z3988"></span></span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://books.google.com/books?id=02rFSecPhEsC&q=tritone">Randel (2003), p.239</a>.</span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"><a href="/wiki/Andreas_Werckmeister" title="Andreas Werckmeister">Andreas Werckmeister</a>. <a rel="nofollow" class="external text" href="https://www.digitale-sammlungen.de/de/view/bsb10527826?page=5"><span title="German-language text"><i lang="de">Harmonologia musica, oder kurze Anleitung zur musicalischen Composition</i></span></a> (Frankfurt and Leipzig: Theodor Philipp Calvisius 1702): 6.</span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text"><a href="/wiki/Andreas_Werckmeister" title="Andreas Werckmeister">Andreas Werckmeister</a>, <a rel="nofollow" class="external text" href="https://www.digitale-sammlungen.de/de/view/bsb10527832?page=5"><span title="German-language text"><i lang="de">Musicalische Paradoxal-Discourse, oder allgemeine Vorstellungen</i></span></a> (Quedlinburg: Theodor Philipp Calvisius, 1707): 75–76.</span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFReinhold1974" class="citation book cs1 cs1-prop-foreign-lang-source"><a href="/wiki/Reinhold_Hammerstein" title="Reinhold Hammerstein">Reinhold, Hammerstein</a> (1974). <i>Diabolus in musica: Studien zur Ikonographie der Musik im Mittelalter</i>. Neue Heidelberger Studien zur Musikwissenschaft (in German). Vol. 6. Bern: Francke. p. 7. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/1390982">1390982</a>. <q>... mi contra fa ... welches die alten den Satan in der Music nenneten ... alten Solmisatores dieses angenehme Intervall mi contra fa oder den Teufel in der Music genannt haben.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Diabolus+in+musica%3A+Studien+zur+Ikonographie+der+Musik+im+Mittelalter&rft.place=Bern&rft.series=Neue+Heidelberger+Studien+zur+Musikwissenschaft&rft.pages=7&rft.pub=Francke&rft.date=1974&rft_id=info%3Aoclcnum%2F1390982&rft.aulast=Reinhold&rft.aufirst=Hammerstein&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATritone" class="Z3988"></span></span> </li> <li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSmith1979" class="citation journal cs1">Smith, F. J. (1979). "Some aspects of the tritone and the semitritone in the <i>Speculum Musicae</i>: the non-emergence of the <i>diabolus in musica</i>". <i>Journal of Musicological Research</i>. <b>3</b> (1–2): 63–74 [70]. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F01411897908574507">10.1080/01411897908574507</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+Musicological+Research&rft.atitle=Some+aspects+of+the+tritone+and+the+semitritone+in+the+Speculum+Musicae%3A+the+non-emergence+of+the+diabolus+in+musica&rft.volume=3&rft.issue=1%E2%80%932&rft.pages=63-74+70&rft.date=1979&rft_id=info%3Adoi%2F10.1080%2F01411897908574507&rft.aulast=Smith&rft.aufirst=F.+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATritone" class="Z3988"></span></span> </li> <li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</a></b></span> <span class="reference-text"><a href="/wiki/Denis_Arnold" title="Denis Arnold">Arnold, Denis</a> (1983). "Tritone". in <i>The New Oxford Companion to Music</i>, Volume 1: A–J, Oxford University Press. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-19-311316-3" title="Special:BookSources/0-19-311316-3">0-19-311316-3</a></span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJeppesen1992" class="citation book cs1"><a href="/wiki/Knud_Jeppesen" title="Knud Jeppesen">Jeppesen, Knud</a> (1992) [1939]. <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/counterpointpoly0000jepp"><i>Counterpoint: the polyphonic vocal style of the sixteenth century</i></a></span>. Translated by <a href="/wiki/Glen_Haydon" title="Glen Haydon">Haydon, Glen</a>. foreword by Alfred Mann. New York: Dover. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-486-27036-X" title="Special:BookSources/0-486-27036-X"><bdi>0-486-27036-X</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Counterpoint%3A+the+polyphonic+vocal+style+of+the+sixteenth+century&rft.place=New+York&rft.pub=Dover&rft.date=1992&rft.isbn=0-486-27036-X&rft.aulast=Jeppesen&rft.aufirst=Knud&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fcounterpointpoly0000jepp&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATritone" class="Z3988"></span></span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text">Nichols, R. (1972). <i>Debussy</i>. Oxford University Press.</span> </li> <li id="cite_note-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-30">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRushton1983" class="citation book cs1">Rushton, Julian (1983). <i>The Musical Language of Berlioz</i>. Cambridge University Press. p. 254.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Musical+Language+of+Berlioz&rft.pages=254&rft.pub=Cambridge+University+Press&rft.date=1983&rft.aulast=Rushton&rft.aufirst=Julian&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATritone" class="Z3988"></span></span> </li> <li id="cite_note-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-31">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRushton2001" class="citation book cs1">Rushton, Julian (2001). <i>The Music of Berlioz</i>. Oxford University Press.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Music+of+Berlioz&rft.pub=Oxford+University+Press&rft.date=2001&rft.aulast=Rushton&rft.aufirst=Julian&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATritone" class="Z3988"></span></span> </li> <li id="cite_note-32"><span class="mw-cite-backlink"><b><a href="#cite_ref-32">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPersichetti1961" class="citation book cs1"><a href="/wiki/Vincent_Persichetti" title="Vincent Persichetti">Persichetti, Vincent</a> (1961). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/isbn_9780393095395"><i>Twentieth-century Harmony: Creative Aspects and Practice</i></a></span>. New York: W. W. Norton. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-393-09539-8" title="Special:BookSources/0-393-09539-8"><bdi>0-393-09539-8</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/398434">398434</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Twentieth-century+Harmony%3A+Creative+Aspects+and+Practice&rft.place=New+York&rft.pub=W.+W.+Norton&rft.date=1961&rft_id=info%3Aoclcnum%2F398434&rft.isbn=0-393-09539-8&rft.aulast=Persichetti&rft.aufirst=Vincent&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fisbn_9780393095395&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATritone" class="Z3988"></span></span> </li> <li id="cite_note-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-33">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLendvai1971" class="citation book cs1"><a href="/wiki/Ern%C5%91_Lendvai" title="Ernő Lendvai">Lendvai, Ernő</a> (1971). <i>Béla Bartók: An Analysis of his Music</i>. introd. by <a href="/wiki/Alan_Bush" title="Alan Bush">Alan Bush</a>. London: Kahn & Averill. pp. 1–16. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-900707-04-6" title="Special:BookSources/0-900707-04-6"><bdi>0-900707-04-6</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/240301">240301</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=B%C3%A9la+Bart%C3%B3k%3A+An+Analysis+of+his+Music&rft.place=London&rft.pages=1-16&rft.pub=Kahn+%26+Averill&rft.date=1971&rft_id=info%3Aoclcnum%2F240301&rft.isbn=0-900707-04-6&rft.aulast=Lendvai&rft.aufirst=Ern%C5%91&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATritone" class="Z3988"></span></span> </li> <li id="cite_note-34"><span class="mw-cite-backlink"><b><a href="#cite_ref-34">^</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="http://www.cco.caltech.edu/~tan/Britten/req1.html">"Musical Analysis of the War Requiem"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">16 March</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Musical+Analysis+of+the+War+Requiem&rft_id=http%3A%2F%2Fwww.cco.caltech.edu%2F~tan%2FBritten%2Freq1.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATritone" class="Z3988"></span></span> </li> <li id="cite_note-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-35">^</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://www.youtube.com/watch?v=rsSMCq7pl_k">"Britten: War Requiem"</a>. YouTube. 29 August 2014.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Britten%3A+War+Requiem&rft.pub=YouTube&rft.date=2014-08-29&rft_id=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DrsSMCq7pl_k&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATritone" class="Z3988"></span></span> </li> <li id="cite_note-36"><span class="mw-cite-backlink"><b><a href="#cite_ref-36">^</a></b></span> <span class="reference-text">Bridcut, J. (2010), <i>Essential Britten, a pocket guide for the Britten Centenary</i>. London, Faber.</span> </li> <li id="cite_note-:0-37"><span class="mw-cite-backlink"><b><a href="#cite_ref-:0_37-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKogan2017" class="citation news cs1">Kogan, Judith (2017-10-31). <a rel="nofollow" class="external text" href="https://www.npr.org/2017/10/31/560843189/the-unsettling-sound-of-tritones-the-devils-interval">"The Unsettling Sound Of Tritones, The Devil's Interval"</a>. <i>NPR</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2021-11-11</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=NPR&rft.atitle=The+Unsettling+Sound+Of+Tritones%2C+The+Devil%27s+Interval&rft.date=2017-10-31&rft.aulast=Kogan&rft.aufirst=Judith&rft_id=https%3A%2F%2Fwww.npr.org%2F2017%2F10%2F31%2F560843189%2Fthe-unsettling-sound-of-tritones-the-devils-interval&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATritone" class="Z3988"></span></span> </li> <li id="cite_note-38"><span class="mw-cite-backlink"><b><a href="#cite_ref-38">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRizzi2019" class="citation web cs1">Rizzi, Sofia (2019-03-04). <a rel="nofollow" class="external text" href="https://www.classicfm.com/composers/bernstein-l/bernstein-west-side-story-tritone/">"Why did Bernstein build West Side Story around 'The Devil's Interval'?"</a>. <i>Classic FM</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2021-11-11</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Classic+FM&rft.atitle=Why+did+Bernstein+build+West+Side+Story+around+%27The+Devil%27s+Interval%27%3F&rft.date=2019-03-04&rft.aulast=Rizzi&rft.aufirst=Sofia&rft_id=https%3A%2F%2Fwww.classicfm.com%2Fcomposers%2Fbernstein-l%2Fbernstein-west-side-story-tritone%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATritone" class="Z3988"></span></span> </li> <li id="cite_note-39"><span class="mw-cite-backlink"><b><a href="#cite_ref-39">^</a></b></span> <span class="reference-text">Dominic Pedler. <i>The Songwriting Secrets of the Beatles</i>. Music Sales Ltd. <a href="/wiki/Omnibus_Press" title="Omnibus Press">Omnibus Press</a>. London, 2010 pp. 522–523</span> </li> <li id="cite_note-40"><span class="mw-cite-backlink"><b><a href="#cite_ref-40">^</a></b></span> <span class="reference-text">Moskowitz, D. (2010). <i>The Words and Music of Jimi Hendrix</i>. Praeger.</span> </li> <li id="cite_note-41"><span class="mw-cite-backlink"><b><a href="#cite_ref-41">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChesna2010" class="citation web cs1">Chesna, James (26 February 2010). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110629021833/http://abclocal.go.com/wjrt/story?section=news%2Fentertainment%2Flistening_room&id=7274202">"<span class="cs1-kern-left"></span>'Sleeping (In the Fire)': Listening Room fearless leader faces down fear"</a>. <a href="/wiki/WJRT-TV" title="WJRT-TV">WJRT-TV/DT</a>. Archived from <a rel="nofollow" class="external text" href="http://abclocal.go.com/wjrt/story?section=news/entertainment/listening_room&id=7274202">the original</a> on 29 June 2011<span class="reference-accessdate">. Retrieved <span class="nowrap">28 February</span> 2010</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=%27Sleeping+%28In+the+Fire%29%27%3A+Listening+Room+fearless+leader+faces+down+fear&rft.pub=WJRT-TV%2FDT&rft.date=2010-02-26&rft.aulast=Chesna&rft.aufirst=James&rft_id=http%3A%2F%2Fabclocal.go.com%2Fwjrt%2Fstory%3Fsection%3Dnews%2Fentertainment%2Flistening_room%26id%3D7274202&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATritone" class="Z3988"></span></span> </li> <li id="cite_note-42"><span class="mw-cite-backlink"><b><a href="#cite_ref-42">^</a></b></span> <span class="reference-text">William Irwin, <i>Black Sabbath and Philosophy: Mastering Reality</i> (Hoboken: Wiley-Blackwell, 2012), <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1118397596" title="Special:BookSources/978-1118397596">978-1118397596</a></span> </li> </ol></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=Tritone&action=edit&section=16" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>R., Ken (2012). <i>DOG EAR Tritone Substitution for Jazz Guitar</i>, Amazon Digital Services, Inc., ASIN: B008FRWNIW</li></ul> <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=Tritone&action=edit&section=17" 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="https://web.archive.org/web/20080106220501/http://www.cameron.edu/~lloydd/webdoc1.html">Tritone paradox and Shepard Tones</a> at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> (archived January 6, 2008)</li> <li><a rel="nofollow" class="external text" href="http://news.bbc.co.uk/2/hi/uk_news/magazine/4952646.stm">BBC News Magazine article about the tritone</a></li> <li><a rel="nofollow" class="external text" href="https://www.theguardian.com/music/2007/oct/12/popandrock.classicalmusicandopera">Satan's all-time greatest hit: Will Hodgkinson on the devil's interval</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline 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ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output 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.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 data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar 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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 class="mw-selflink selflink">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 class="mw-selflink selflink">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 href="/wiki/Quarter_tone" title="Quarter tone">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 href="/wiki/Quarter_tone" title="Quarter tone">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><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" 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10.65% 110.251 17 Template:Lang"," 9.52% 98.603 6 Template:Cite_web"," 9.25% 95.800 1 Template:Intervals"," 8.88% 91.955 1 Template:Short_description"]},"scribunto":{"limitreport-timeusage":{"value":"0.477","limit":"10.000"},"limitreport-memusage":{"value":25867699,"limit":52428800},"limitreport-logs":"anchor_id_list = table#1 {\n [\"CITEREFBent1994\"] = 1,\n [\"CITEREFChesna2010\"] = 1,\n [\"CITEREFDrabkin\"] = 1,\n [\"CITEREFDrabkin2001\"] = 1,\n [\"CITEREFFonville1991\"] = 1,\n [\"CITEREFGuido_d\u0026#039;Arezzo\"] = 1,\n [\"CITEREFHaluska2003\"] = 1,\n [\"CITEREFHelmholtz2005\"] = 1,\n [\"CITEREFJeppesen1992\"] = 1,\n [\"CITEREFKogan2017\"] = 1,\n [\"CITEREFLendvai1971\"] = 1,\n [\"CITEREFPartch1979\"] = 1,\n [\"CITEREFPaul1885\"] = 1,\n [\"CITEREFPersichetti1961\"] = 1,\n [\"CITEREFReinhold1974\"] = 1,\n [\"CITEREFRenold2004\"] = 1,\n [\"CITEREFRizzi2019\"] = 1,\n [\"CITEREFRushton1983\"] = 1,\n [\"CITEREFRushton2001\"] = 1,\n [\"CITEREFSmith1979\"] = 1,\n [\"CITEREFSmith_Brindle1966\"] = 1,\n [\"CITEREFStrangePatricia2001\"] = 1,\n}\ntemplate_list = table#1 {\n [\"=\"] = 1,\n [\"Blockquote\"] = 4,\n [\"Citation\"] = 1,\n [\"Citation needed\"] = 1,\n [\"Cite book\"] = 14,\n [\"Cite journal\"] = 3,\n [\"Cite news\"] = 1,\n [\"Cite web\"] = 6,\n [\"Clear\"] = 1,\n [\"Failed verification\"] = 1,\n [\"Full citation needed\"] = 1,\n [\"Harvp\"] = 2,\n [\"ISBN\"] = 5,\n [\"Image frame\"] = 1,\n [\"Infobox Interval\"] = 1,\n [\"Intervals\"] = 1,\n [\"Lang\"] = 17,\n [\"Language with name/for\"] = 1,\n [\"More citations needed section\"] = 3,\n [\"Multiple image\"] = 1,\n [\"Music\"] = 38,\n [\"Mvar\"] = 3,\n [\"Nobr\"] = 1,\n [\"Other uses\"] = 1,\n [\"Redirect\"] = 1,\n [\"Reflist\"] = 1,\n [\"Sfrac\"] = 1,\n [\"Slink\"] = 2,\n [\"Sqrt\"] = 1,\n [\"Stack\"] = 3,\n [\"Thumb\"] = 5,\n [\"Webarchive\"] = 1,\n [\"Where\"] = 1,\n}\narticle_whitelist = table#1 {\n}\n"},"cachereport":{"origin":"mw-web.codfw.canary-67c44fb794-dmq5q","timestamp":"20241128020053","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Tritone","url":"https:\/\/en.wikipedia.org\/wiki\/Tritone","sameAs":"http:\/\/www.wikidata.org\/entity\/Q623939","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q623939","author":{"@type":"Organization","name":"Contributors to Wikimedia projects"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2002-08-11T10:15:59Z","dateModified":"2024-10-18T02:22:00Z","headline":"musical interval of three adjacent whole tones or six semitones; in a diatonic scale each octave contains 1 tritone (e.g. F\u2013B in C major)"}</script> </body> </html>