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<div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Musical interval</div><style data-mw-deduplicate="TemplateStyles: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">Major fourth</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">Minor fifth</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">Eleventh harmonic<br />Paramajor fourth</td></tr><tr><th scope="row" class="infobox-label">Abbreviation</th><td class="infobox-data">M4</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">~5½</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">~5½</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">11:8</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/Quarter_tone" title="Quarter tone">24-Tone equal temperament</a></th><td class="infobox-data">550</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">551.32</td></tr></tbody></table> <div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Musical interval</div><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546"><table class="infobox"><caption class="infobox-title">Minor fifth</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">Major fourth</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">Eleventh subharmonic<br />Paraminor fifth</td></tr><tr><th scope="row" class="infobox-label">Abbreviation</th><td class="infobox-data">m5</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">~6½</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">~5½</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">16:11</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/Quarter_tone" title="Quarter tone">24-Tone equal temperament</a></th><td class="infobox-data">650</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">648.68</td></tr></tbody></table> <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>The eleventh harmonic <span class="noprint"><span class="ext-phonos"><span data-nosnippet="" id="ooui-php-1" class="ext-phonos-PhonosButton noexcerpt oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-ooui="{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/2\/2a\/Eleventh_harmonic_on_C.mid\/Eleventh_harmonic_on_C.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"Play"},"data":{"ipa":"","text":"","lang":"en","wikibase":"","file":"Eleventh harmonic on C.mid"},"classes":["ext-phonos-PhonosButton","noexcerpt"]}"><a role="button" tabindex="0" href="//upload.wikimedia.org/wikipedia/commons/transcoded/2/2a/Eleventh_harmonic_on_C.mid/Eleventh_harmonic_on_C.mid.mp3" rel="nofollow" aria-label="Play audio" title="Play audio" class="oo-ui-buttonElement-button"><span class="oo-ui-iconElement-icon oo-ui-icon-volumeUp"></span><span class="oo-ui-labelElement-label">Play</span><span class="oo-ui-indicatorElement-indicator oo-ui-indicatorElement-noIndicator"></span></a></span><sup class="ext-phonos-attribution noexcerpt navigation-not-searchable"><a href="/wiki/File:Eleventh_harmonic_on_C.mid" title="File:Eleventh harmonic on C.mid">ⓘ</a></sup></span></span> – shown using the <a href="/wiki/Ben_Johnston_notation" class="mw-redirect" title="Ben Johnston notation">Ben Johnston notation</a> – can be approximated by the major fourth.</figcaption></figure> <style data-mw-deduplicate="TemplateStyles:r1237032888/mw-parser-output/.tmulti">.mw-parser-output .tmulti .multiimageinner{display:flex;flex-direction:column}.mw-parser-output .tmulti .trow{display:flex;flex-direction:row;clear:left;flex-wrap:wrap;width:100%;box-sizing:border-box}.mw-parser-output .tmulti .tsingle{margin:1px;float:left}.mw-parser-output .tmulti .theader{clear:both;font-weight:bold;text-align:center;align-self:center;background-color:transparent;width:100%}.mw-parser-output .tmulti .thumbcaption{background-color:transparent}.mw-parser-output .tmulti .text-align-left{text-align:left}.mw-parser-output .tmulti .text-align-right{text-align:right}.mw-parser-output .tmulti .text-align-center{text-align:center}@media all and (max-width:720px){.mw-parser-output .tmulti .thumbinner{width:100%!important;box-sizing:border-box;max-width:none!important;align-items:center}.mw-parser-output .tmulti .trow{justify-content:center}.mw-parser-output .tmulti .tsingle{float:none!important;max-width:100%!important;box-sizing:border-box;text-align:center}.mw-parser-output .tmulti .tsingle .thumbcaption{text-align:left}.mw-parser-output .tmulti .trow>.thumbcaption{text-align:center}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .tmulti .multiimageinner img{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmulti .multiimageinner img{background-color:white}}</style><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:308px;max-width:308px"><div class="trow"><div class="tsingle" style="width:152px;max-width:152px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File: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/150px-Just_augmented_fourth_on_C.png" decoding="async" width="150" height="70" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/Just_augmented_fourth_on_C.png/225px-Just_augmented_fourth_on_C.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/46/Just_augmented_fourth_on_C.png/300px-Just_augmented_fourth_on_C.png 2x" data-file-width="539" data-file-height="252" /></a></span></div></div><div class="tsingle" style="width:152px;max-width:152px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Just_tritone_on_C.png" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/59/Just_tritone_on_C.png/150px-Just_tritone_on_C.png" decoding="async" width="150" height="84" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/59/Just_tritone_on_C.png/225px-Just_tritone_on_C.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/59/Just_tritone_on_C.png/300px-Just_tritone_on_C.png 2x" data-file-width="3895" data-file-height="2190" /></a></span></div></div></div><div class="trow" style="display:flex"><div class="thumbcaption">Just augmented fourth on C <span class="noprint"><span class="ext-phonos"><span data-nosnippet="" id="ooui-php-2" class="ext-phonos-PhonosButton noexcerpt oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-ooui="{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/8\/80\/Just_augmented_fourth_on_C.mid\/Just_augmented_fourth_on_C.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"Play"},"data":{"ipa":"","text":"","lang":"en","wikibase":"","file":"Just augmented fourth on C.mid"},"classes":["ext-phonos-PhonosButton","noexcerpt"]}"><a role="button" tabindex="0" href="//upload.wikimedia.org/wikipedia/commons/transcoded/8/80/Just_augmented_fourth_on_C.mid/Just_augmented_fourth_on_C.mid.mp3" rel="nofollow" aria-label="Play audio" title="Play audio" class="oo-ui-buttonElement-button"><span class="oo-ui-iconElement-icon oo-ui-icon-volumeUp"></span><span class="oo-ui-labelElement-label">Play</span><span class="oo-ui-indicatorElement-indicator oo-ui-indicatorElement-noIndicator"></span></a></span><sup class="ext-phonos-attribution noexcerpt navigation-not-searchable"><a href="/wiki/File:Just_augmented_fourth_on_C.mid" title="File:Just augmented fourth on C.mid">ⓘ</a></sup></span></span> and its inverse, the just tritone on C <span class="noprint"><span class="ext-phonos"><span data-nosnippet="" id="ooui-php-3" class="ext-phonos-PhonosButton noexcerpt oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-ooui="{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/f\/f7\/Just_tritone_on_C.mid\/Just_tritone_on_C.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"Play"},"data":{"ipa":"","text":"","lang":"en","wikibase":"","file":"Just tritone on C.mid"},"classes":["ext-phonos-PhonosButton","noexcerpt"]}"><a role="button" tabindex="0" href="//upload.wikimedia.org/wikipedia/commons/transcoded/f/f7/Just_tritone_on_C.mid/Just_tritone_on_C.mid.mp3" rel="nofollow" aria-label="Play audio" title="Play audio" class="oo-ui-buttonElement-button"><span class="oo-ui-iconElement-icon oo-ui-icon-volumeUp"></span><span class="oo-ui-labelElement-label">Play</span><span class="oo-ui-indicatorElement-indicator oo-ui-indicatorElement-noIndicator"></span></a></span><sup class="ext-phonos-attribution noexcerpt navigation-not-searchable"><a href="/wiki/File:Just_tritone_on_C.mid" title="File:Just tritone on C.mid">ⓘ</a></sup></span></span></div></div></div></div> <p>In <a href="/wiki/Music" title="Music">music</a>, the <b>major fourth</b> and <b>minor fifth</b>, also known as the <b>paramajor fourth</b> and <b>paraminor fifth</b>, are <a href="/wiki/Interval_(music)" title="Interval (music)">intervals</a> from the <a href="/wiki/Quarter-tone_scale" class="mw-redirect" title="Quarter-tone scale">quarter-tone scale</a>, named by <a href="/wiki/Ivan_Wyschnegradsky" title="Ivan Wyschnegradsky">Ivan Wyschnegradsky</a> to describe the tones surrounding the <a href="/wiki/Tritone" title="Tritone">tritone</a> (F<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>/G<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>) found in the more familiar <a href="/wiki/Twelve-tone_scale" class="mw-redirect" title="Twelve-tone scale">twelve-tone scale</a>,<sup id="cite_ref-Skinner_1-0" class="reference"><a href="#cite_note-Skinner-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> as shown in the table below: </p> <table class="wikitable" width="60%" style="text-align:center"> <tbody><tr> <th width="5%"> </th> <th width="11%">perfect fourth </th> <th width="11%">(para)major fourth </th> <th width="11%">tritone </th> <th width="11%">(para)minor fifth </th> <th width="11%">perfect fifth </th></tr> <tr> <th>In C: </th> <td>F </td> <td>≊ 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> </td> <td>F<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>/G<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span> </td> <td>≊ 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:Llpd-%C2%BD.svg" class="mw-file-description" title="half flat"><img alt="half flat" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Llpd-%C2%BD.svg/4px-Llpd-%C2%BD.svg.png" decoding="async" width="4" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Llpd-%C2%BD.svg/7px-Llpd-%C2%BD.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Llpd-%C2%BD.svg/9px-Llpd-%C2%BD.svg.png 2x" data-file-width="77" data-file-height="200" /></a></span></span> </td> <td>G </td></tr> <tr> <th>In cents: </th> <td>500 </td> <td>550 </td> <td>600 </td> <td>650 </td> <td>700 </td></tr></tbody></table> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Major_fourth">Major fourth</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Major_fourth_and_minor_fifth&action=edit&section=1" title="Edit section: Major fourth"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A major fourth (<span class="noprint"><span class="ext-phonos"><span data-nosnippet="" id="ooui-php-4" class="ext-phonos-PhonosButton noexcerpt oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-ooui="{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/c\/cb\/Eleven_quarter_tones_on_C.mid\/Eleven_quarter_tones_on_C.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"Play"},"data":{"ipa":"","text":"","lang":"en","wikibase":"","file":"Eleven quarter tones on C.mid"},"classes":["ext-phonos-PhonosButton","noexcerpt"]}"><a role="button" tabindex="0" href="//upload.wikimedia.org/wikipedia/commons/transcoded/c/cb/Eleven_quarter_tones_on_C.mid/Eleven_quarter_tones_on_C.mid.mp3" rel="nofollow" aria-label="Play audio" title="Play audio" class="oo-ui-buttonElement-button"><span class="oo-ui-iconElement-icon oo-ui-icon-volumeUp"></span><span class="oo-ui-labelElement-label">Play</span><span class="oo-ui-indicatorElement-indicator oo-ui-indicatorElement-noIndicator"></span></a></span><sup class="ext-phonos-attribution noexcerpt navigation-not-searchable"><a href="/wiki/File:Eleven_quarter_tones_on_C.mid" title="File:Eleven quarter tones on C.mid">ⓘ</a></sup></span></span>) is the interval that lies midway between the <a href="/wiki/Perfect_fourth" title="Perfect fourth">perfect fourth</a> (500 <a href="/wiki/Cent_(music)" title="Cent (music)">cents</a>) and the <a href="/wiki/Augmented_fourth" class="mw-redirect" title="Augmented fourth">augmented fourth</a> (600 cents) and is thus 550 cents (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>). It <a href="/wiki/Inversion_(interval)" class="mw-redirect" title="Inversion (interval)">inverts</a> to a minor fifth. Wyschnegradsky considered it a good approximation of the <a href="/wiki/Eleventh_harmonic" class="mw-redirect" title="Eleventh harmonic">eleventh harmonic</a><sup id="cite_ref-Skinner_1-1" class="reference"><a href="#cite_note-Skinner-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> (11:8 or 551.32 cents).<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> A narrower undecimal major fourth is found at 537 cents (the ratio 15:11). <a href="/wiki/31_equal_temperament" title="31 equal temperament">31 equal temperament</a> has an interval of 542 cents, which lies in between the two types of undecimal major fourth. </p><p>The term may also be applied to the "comma-deficient major fourth" (or "chromatic major fourth"<sup id="cite_ref-Bacon_3-0" class="reference"><a href="#cite_note-Bacon-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>), which is the ratio 25:18, or 568.72 cents (F<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>).<sup id="cite_ref-Edinburgh_4-0" class="reference"><a href="#cite_note-Edinburgh-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Minor_fifth">Minor fifth</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Major_fourth_and_minor_fifth&action=edit&section=2" title="Edit section: Minor fifth"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A minor fifth (<span class="noprint"><span class="ext-phonos"><span data-nosnippet="" id="ooui-php-5" class="ext-phonos-PhonosButton noexcerpt oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-ooui="{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/6\/6f\/Thirteen_quarter_tones_on_C.mid\/Thirteen_quarter_tones_on_C.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"Play"},"data":{"ipa":"","text":"","lang":"en","wikibase":"","file":"Thirteen quarter tones on C.mid"},"classes":["ext-phonos-PhonosButton","noexcerpt"]}"><a role="button" tabindex="0" href="//upload.wikimedia.org/wikipedia/commons/transcoded/6/6f/Thirteen_quarter_tones_on_C.mid/Thirteen_quarter_tones_on_C.mid.mp3" rel="nofollow" aria-label="Play audio" title="Play audio" class="oo-ui-buttonElement-button"><span class="oo-ui-iconElement-icon oo-ui-icon-volumeUp"></span><span class="oo-ui-labelElement-label">Play</span><span class="oo-ui-indicatorElement-indicator oo-ui-indicatorElement-noIndicator"></span></a></span><sup class="ext-phonos-attribution noexcerpt navigation-not-searchable"><a href="/wiki/File:Thirteen_quarter_tones_on_C.mid" title="File:Thirteen quarter tones on C.mid">ⓘ</a></sup></span></span>) is the interval midway between the <a href="/wiki/Diminished_fifth" class="mw-redirect" title="Diminished fifth">diminished fifth</a> (600 cents) and the <a href="/wiki/Perfect_fifth" title="Perfect fifth">perfect fifth</a> (700 cents) and thus 650 cents (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:Llpd-%C2%BD.svg" class="mw-file-description" title="half flat"><img alt="half flat" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Llpd-%C2%BD.svg/4px-Llpd-%C2%BD.svg.png" decoding="async" width="4" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Llpd-%C2%BD.svg/7px-Llpd-%C2%BD.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Llpd-%C2%BD.svg/9px-Llpd-%C2%BD.svg.png 2x" data-file-width="77" data-file-height="200" /></a></span></span>). It <a href="/wiki/Inversion_(interval)" class="mw-redirect" title="Inversion (interval)">inverts</a> to a major fourth. It approximates the eleventh subharmonic (G<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;">↓</span>), 16:11 (648.68 cents). </p><p>The term may also be applied to the ratio 64:45 (G<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>-) or 609.77 cents (<span class="noprint"><span class="ext-phonos"><span data-nosnippet="" id="ooui-php-6" class="ext-phonos-PhonosButton noexcerpt oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-ooui="{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/f\/f7\/Just_tritone_on_C.mid\/Just_tritone_on_C.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"Play"},"data":{"ipa":"","text":"","lang":"en","wikibase":"","file":"Just tritone on C.mid"},"classes":["ext-phonos-PhonosButton","noexcerpt"]}"><a role="button" tabindex="0" href="//upload.wikimedia.org/wikipedia/commons/transcoded/f/f7/Just_tritone_on_C.mid/Just_tritone_on_C.mid.mp3" rel="nofollow" aria-label="Play audio" title="Play audio" class="oo-ui-buttonElement-button"><span class="oo-ui-iconElement-icon oo-ui-icon-volumeUp"></span><span class="oo-ui-labelElement-label">Play</span><span class="oo-ui-indicatorElement-indicator oo-ui-indicatorElement-noIndicator"></span></a></span><sup class="ext-phonos-attribution noexcerpt navigation-not-searchable"><a href="/wiki/File:Just_tritone_on_C.mid" title="File:Just tritone on C.mid">ⓘ</a></sup></span></span>), formed from the perfect fourth (4/3 = 498.04) and the major semitone (16/15 = 111.73),<sup id="cite_ref-Bacon_3-1" class="reference"><a href="#cite_note-Bacon-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> which is sharp of the G<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span> tritone. The "comma-redundant minor fifth" has the ratio 36:25 (G<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>), or 631.28 cents, and is formed from two minor thirds.<sup id="cite_ref-Edinburgh_4-1" class="reference"><a href="#cite_note-Edinburgh-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> The tridecimal minor fifth (13:9), or tridecimal <a href="/wiki/Tritone" title="Tritone">tritone</a>, is slightly larger at 636.6 cents. </p> <div class="mw-heading mw-heading2"><h2 id="Other">Other</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Major_fourth_and_minor_fifth&action=edit&section=3" title="Edit section: Other"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The term major fourth may also be applied to the follow, as minor fifth may be applied to their inversions (in the sense of augmented and diminished): </p> <ul><li>The "comma-deficient major fourth" (or "chromatic major fourth"<sup id="cite_ref-Bacon_3-2" class="reference"><a href="#cite_note-Bacon-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>) is the ratio 25:18, or 568.72 cents (F<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>).<sup id="cite_ref-Edinburgh_4-2" class="reference"><a href="#cite_note-Edinburgh-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></li> <li>45:32 (F<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>+) or 590.22 cents (<span class="noprint"><span class="ext-phonos"><span data-nosnippet="" id="ooui-php-7" class="ext-phonos-PhonosButton noexcerpt oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-ooui="{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/8\/80\/Just_augmented_fourth_on_C.mid\/Just_augmented_fourth_on_C.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"Play"},"data":{"ipa":"","text":"","lang":"en","wikibase":"","file":"Just augmented fourth on C.mid"},"classes":["ext-phonos-PhonosButton","noexcerpt"]}"><a role="button" tabindex="0" href="//upload.wikimedia.org/wikipedia/commons/transcoded/8/80/Just_augmented_fourth_on_C.mid/Just_augmented_fourth_on_C.mid.mp3" rel="nofollow" aria-label="Play audio" title="Play audio" class="oo-ui-buttonElement-button"><span class="oo-ui-iconElement-icon oo-ui-icon-volumeUp"></span><span class="oo-ui-labelElement-label">Play</span><span class="oo-ui-indicatorElement-indicator oo-ui-indicatorElement-noIndicator"></span></a></span><sup class="ext-phonos-attribution noexcerpt navigation-not-searchable"><a href="/wiki/File:Just_augmented_fourth_on_C.mid" title="File:Just augmented fourth on C.mid">ⓘ</a></sup></span></span>), formed from the major third (5/4 = 386.31) and the major tone (9/8 = 203.91) or two major tones (9:8) and one minor tone (10:9)<sup id="cite_ref-Bacon_3-3" class="reference"><a href="#cite_note-Bacon-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup></li> <li>729:512 (F<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span>++) or 611.73 cents (<span class="noprint"><span class="ext-phonos"><span data-nosnippet="" id="ooui-php-8" class="ext-phonos-PhonosButton noexcerpt oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-ooui="{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/c\/cf\/Pythagorean_augmented_fourth_on_C.mid\/Pythagorean_augmented_fourth_on_C.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"Play"},"data":{"ipa":"","text":"","lang":"en","wikibase":"","file":"Pythagorean augmented fourth on C.mid"},"classes":["ext-phonos-PhonosButton","noexcerpt"]}"><a role="button" tabindex="0" href="//upload.wikimedia.org/wikipedia/commons/transcoded/c/cf/Pythagorean_augmented_fourth_on_C.mid/Pythagorean_augmented_fourth_on_C.mid.mp3" rel="nofollow" aria-label="Play audio" title="Play audio" class="oo-ui-buttonElement-button"><span class="oo-ui-iconElement-icon oo-ui-icon-volumeUp"></span><span class="oo-ui-labelElement-label">Play</span><span class="oo-ui-indicatorElement-indicator oo-ui-indicatorElement-noIndicator"></span></a></span><sup class="ext-phonos-attribution noexcerpt navigation-not-searchable"><a href="/wiki/File:Pythagorean_augmented_fourth_on_C.mid" title="File:Pythagorean augmented fourth on C.mid">ⓘ</a></sup></span></span>), formed from the perfect fourth and the <a href="/wiki/Apotome_(music)" class="mw-redirect" title="Apotome (music)">apotome</a>.<sup id="cite_ref-Bacon_3-4" class="reference"><a href="#cite_note-Bacon-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup></li></ul> <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=Major_fourth_and_minor_fifth&action=edit&section=4" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Subminor_and_supermajor" title="Subminor and supermajor">Subminor and supermajor</a></li> <li><a href="/wiki/Neutral_interval" title="Neutral interval">Neutral interval</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=Major_fourth_and_minor_fifth&action=edit&section=5" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-Skinner-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-Skinner_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Skinner_1-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Skinner, Miles Leigh (2007). <i>Toward a Quarter-tone Syntax: Analyses of Selected Works by Blackwood, Haba, Ives, and Wyschnegradsky</i>, p.25. ProQuest. <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780542998478" title="Special:BookSources/9780542998478">9780542998478</a>.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBenson2007" class="citation book cs1">Benson, Dave (2007-01-01). <i>Music: A Mathematical Offering</i>. Cambridge University Press. p. 370. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780521853873" title="Special:BookSources/9780521853873"><bdi>9780521853873</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Music%3A+A+Mathematical+Offering&rft.pages=370&rft.pub=Cambridge+University+Press&rft.date=2007-01-01&rft.isbn=9780521853873&rft.aulast=Benson&rft.aufirst=Dave&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMajor+fourth+and+minor+fifth" class="Z3988"></span></span> </li> <li id="cite_note-Bacon-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-Bacon_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Bacon_3-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Bacon_3-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Bacon_3-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-Bacon_3-4"><sup><i><b>e</b></i></sup></a></span> <span class="reference-text"><a href="/wiki/Richard_Bacon_(writer)" class="mw-redirect" title="Richard Bacon (writer)">Richard Mackenzie Bacon</a> (1821). "Manuscript Work of Francesco Bianchl", <i>The Quarterly Musical Magazine and Review</i>, Volume 3, p.56.</span> </li> <li id="cite_note-Edinburgh-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-Edinburgh_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Edinburgh_4-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Edinburgh_4-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text">(1832). <i><a rel="nofollow" class="external text" href="https://books.google.com/books?id=ZuNEAQAAMAAJ">The Edinburgh Encyclopaedia</a></i>, Volume 9, p.249. Joseph Parker. [ISBN unspecified]</span> </li> </ol></div></div> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist 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.navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Intervals" style="padding:3px"><table class="nowraplinks hlist mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style 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 ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Intervals" title="Template:Intervals"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Intervals" title="Template talk:Intervals"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Intervals" title="Special:EditPage/Template:Intervals"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Intervals" style="font-size:114%;margin:0 4em"><a href="/wiki/Interval_(music)" title="Interval (music)">Intervals</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Equal_temperament" title="Equal temperament">Twelve-<br />semitone</a><br />(post-Bach<br />Western)</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="(Numbers_in_bracketsare_the_number_ofsemitones_in_theinterval.)" scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><i>(Numbers in brackets<br />are the number of<br /><a href="/wiki/Semitone" title="Semitone">semitones</a> in the<br />interval.)</i></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:6em;font-weight:normal;">Perfect</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Unison" title="Unison">unison</a> (0)</li> <li><a href="/wiki/Perfect_fourth" title="Perfect fourth">fourth</a> (5)</li> <li><a href="/wiki/Perfect_fifth" title="Perfect fifth">fifth</a> (7)</li> <li><a href="/wiki/Octave" title="Octave">octave</a> (12)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;font-weight:normal;"><a href="/wiki/Major_and_minor#Intervals_and_chords" title="Major and minor">Major</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Major_second" title="Major second">second</a> (2)</li> <li><a href="/wiki/Major_third" title="Major third">third</a> (4)</li> <li><a href="/wiki/Major_sixth" title="Major sixth">sixth</a> (9)</li> <li><a href="/wiki/Major_seventh" title="Major seventh">seventh</a> (11)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;font-weight:normal;"><a href="/wiki/Major_and_minor#Intervals_and_chords" title="Major and minor">Minor</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Minor_second" class="mw-redirect" title="Minor second">second</a> (1)</li> <li><a href="/wiki/Minor_third" title="Minor third">third</a> (3)</li> <li><a href="/wiki/Minor_sixth" title="Minor sixth">sixth</a> (8)</li> <li><a href="/wiki/Minor_seventh" title="Minor seventh">seventh</a> (10)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;font-weight:normal;"><a href="/wiki/Augmentation_(music)#Augmentation_of_intervals" title="Augmentation (music)">Augmented</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Augmented_unison" title="Augmented unison">unison</a> (1)</li> <li><a href="/wiki/Augmented_second" title="Augmented second">second</a> (3)</li> <li><a href="/wiki/Augmented_third" title="Augmented third">third</a> (5)</li> <li><a href="/wiki/Tritone" title="Tritone">fourth</a> (6)</li> <li><a href="/wiki/Augmented_fifth" title="Augmented fifth">fifth</a> (8)</li> <li><a href="/wiki/Augmented_sixth" title="Augmented sixth">sixth</a> (10)</li> <li><a href="/wiki/Augmented_seventh" title="Augmented seventh">seventh</a> (12)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;font-weight:normal;"><a href="/wiki/Diminution#Diminution_of_intervals" title="Diminution">Diminished</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Diminished_second" title="Diminished second">second</a> (0)</li> <li><a href="/wiki/Diminished_third" title="Diminished third">third</a> (2)</li> <li><a href="/wiki/Diminished_fourth" title="Diminished fourth">fourth</a> (4)</li> <li><a href="/wiki/Tritone" title="Tritone">fifth</a> (6)</li> <li><a href="/wiki/Diminished_sixth" title="Diminished sixth">sixth</a> (7)</li> <li><a href="/wiki/Diminished_seventh" title="Diminished seventh">seventh</a> (9)</li> <li><a href="/wiki/Diminished_octave" title="Diminished octave">octave</a> (11)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;font-weight:normal;"><a href="/wiki/Interval_(music)#Simple_and_compound" title="Interval (music)">Compound</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ninth" title="Ninth">ninth</a> (13 or 14)</li> <li><a href="/wiki/Third_(chord)" title="Third (chord)">tenth</a> (15 or 16)</li> <li><a href="/wiki/Eleventh" title="Eleventh">eleventh</a> (17 or 18)</li> <li><a href="/wiki/Fifth_(chord)" title="Fifth (chord)">twelfth</a> (18 or 19)</li> <li><a href="/wiki/Thirteenth" title="Thirteenth">thirteenth</a> (20 or 21)</li> <li><a href="/wiki/Seventh_(chord)" title="Seventh (chord)">fourteenth</a> (22 or 23)</li> <li><a href="/wiki/Fifteenth" title="Fifteenth">fifteenth</a> (24)</li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other<br />tuning<br />systems</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><b><a href="/wiki/24-tone_equal_temperament" class="mw-redirect" title="24-tone equal temperament">24-tone equal temperament</a></b><br /><i>(Numbers in brackets refer<br />to fractional semitones.)</i></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Neutral" scope="row" class="navbox-group" style="width:5em;font-weight:normal;"><div><br /><a href="/wiki/Neutral_interval" title="Neutral interval">Neutral</a><br /><br /></div></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a 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 class="mw-selflink selflink">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 class="mw-selflink selflink">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 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