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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 instrument tuning with a limit of seven</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Harmonic_seventh_on_C.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Harmonic_seventh_on_C.png/220px-Harmonic_seventh_on_C.png" decoding="async" width="220" height="103" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Harmonic_seventh_on_C.png/330px-Harmonic_seventh_on_C.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Harmonic_seventh_on_C.png/440px-Harmonic_seventh_on_C.png 2x" data-file-width="539" data-file-height="252" /></a><figcaption>Harmonic seventh, septimal seventh<span class="mw-default-size" typeof="mw:File"><span><audio id="mwe_player_0" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-mwtitle="Harmonic_seventh_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/d/dd/Harmonic_seventh_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/d/dd/Harmonic_seventh_on_C.mid/Harmonic_seventh_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/d/dd/Harmonic_seventh_on_C.mid/Harmonic_seventh_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span></figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Septimal_chromatic_semitone_on_C.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/27/Septimal_chromatic_semitone_on_C.png/220px-Septimal_chromatic_semitone_on_C.png" decoding="async" width="220" height="103" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/27/Septimal_chromatic_semitone_on_C.png/330px-Septimal_chromatic_semitone_on_C.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/27/Septimal_chromatic_semitone_on_C.png/440px-Septimal_chromatic_semitone_on_C.png 2x" data-file-width="539" data-file-height="252" /></a><figcaption>Septimal chromatic semitone on C<span class="mw-default-size" typeof="mw:File"><span><audio id="mwe_player_1" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-mwtitle="Septimal_chromatic_semitone_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/b/ba/Septimal_chromatic_semitone_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/ba/Septimal_chromatic_semitone_on_C.mid/Septimal_chromatic_semitone_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/ba/Septimal_chromatic_semitone_on_C.mid/Septimal_chromatic_semitone_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span></figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Septimal_major_third_on_C.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Septimal_major_third_on_C.png/220px-Septimal_major_third_on_C.png" decoding="async" width="220" height="103" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Septimal_major_third_on_C.png/330px-Septimal_major_third_on_C.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Septimal_major_third_on_C.png/440px-Septimal_major_third_on_C.png 2x" data-file-width="539" data-file-height="252" /></a><figcaption><a href="/wiki/Septimal_major_third" title="Septimal major third">9/7 major third</a> from C to E<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="mw-default-size skin-invert" typeof="mw:File"><a href="/wiki/File:7_upside_down.png" class="mw-file-description" title="7 upside-down"><img alt="7 upside-down" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/7_upside_down.png/8px-7_upside_down.png" decoding="async" width="8" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/7_upside_down.png/13px-7_upside_down.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4b/7_upside_down.png/17px-7_upside_down.png 2x" data-file-width="84" data-file-height="158" /></a></span></span>.<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> This, "extremely large third", may resemble a <a href="/wiki/Neutral_third" title="Neutral third">neutral third</a> or <a href="/wiki/Blue_note" title="Blue note">blue note</a>.<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><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-mwtitle="Septimal_major_third_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/5/55/Septimal_major_third_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/55/Septimal_major_third_on_C.mid/Septimal_major_third_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/55/Septimal_major_third_on_C.mid/Septimal_major_third_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span></figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Septimal_minor_third_on_C.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6e/Septimal_minor_third_on_C.png/220px-Septimal_minor_third_on_C.png" decoding="async" width="220" height="103" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6e/Septimal_minor_third_on_C.png/330px-Septimal_minor_third_on_C.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6e/Septimal_minor_third_on_C.png/440px-Septimal_minor_third_on_C.png 2x" data-file-width="539" data-file-height="252" /></a><figcaption><a href="/wiki/Septimal_minor_third" title="Septimal minor third">Septimal minor third</a> on C<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="Septimal_minor_third_on_C.mid" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/7/73/Septimal_minor_third_on_C.mid" type="audio/midi" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/7/73/Septimal_minor_third_on_C.mid/Septimal_minor_third_on_C.mid.ogg" type="audio/ogg; codecs="vorbis"" data-transcodekey="ogg" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/7/73/Septimal_minor_third_on_C.mid/Septimal_minor_third_on_C.mid.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span></span></figcaption></figure> <p><b>7-limit</b> or <b>septimal</b> <a href="/wiki/Musical_tuning#Tuning_systems" title="Musical tuning">tunings</a> and <a href="/wiki/Interval_(music)" title="Interval (music)">intervals</a> are musical instrument tunings that have a <a href="/wiki/Limit_(music)" title="Limit (music)">limit</a> of seven: the largest <a href="/wiki/Prime_number" title="Prime number">prime</a> factor contained in the <a href="/wiki/Interval_ratio" title="Interval ratio">interval ratios</a> between <a href="/wiki/Pitch_(music)" title="Pitch (music)">pitches</a> is seven. Thus, for example, 50:49 is a 7-limit interval, but 14:11 is not. </p><p>For example, the greater just <a href="/wiki/Minor_seventh" title="Minor seventh">minor seventh</a>, 9:5 (<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\/e\/e2\/Greater_just_minor_seventh_on_C.mid\/Greater_just_minor_seventh_on_C.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"Play"},"data":{"ipa":"","text":"","lang":"en","wikibase":"","file":"Greater just minor seventh on C.mid"},"classes":["ext-phonos-PhonosButton","noexcerpt"]}"><a role="button" tabindex="0" href="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e2/Greater_just_minor_seventh_on_C.mid/Greater_just_minor_seventh_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:Greater_just_minor_seventh_on_C.mid" title="File:Greater just minor seventh on C.mid">ⓘ</a></sup></span></span>) is a <a href="/wiki/5-limit_tuning" class="mw-redirect" title="5-limit tuning">5-limit</a> ratio, the <a href="/wiki/Harmonic_seventh" title="Harmonic seventh">harmonic seventh</a> has the ratio 7:4 and is thus a septimal interval. Similarly, the <a href="/wiki/Septimal_chromatic_semitone" title="Septimal chromatic semitone">septimal chromatic semitone</a>, 21:20, is a septimal interval as 21÷7=3. The harmonic seventh is used in the <a href="/wiki/Barbershop_seventh_chord" class="mw-redirect" title="Barbershop seventh chord">barbershop seventh chord</a> and <a href="/wiki/Barbershop_music" title="Barbershop music">music</a>. (<span class="noprint"><span class="ext-phonos"><span data-nosnippet="" id="ooui-php-2" class="ext-phonos-PhonosButton noexcerpt oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-ooui="{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/1\/1b\/Barbershop_secondary_dominant.mid\/Barbershop_secondary_dominant.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"Play"},"data":{"ipa":"","text":"","lang":"en","wikibase":"","file":"Barbershop secondary dominant.mid"},"classes":["ext-phonos-PhonosButton","noexcerpt"]}"><a role="button" tabindex="0" href="//upload.wikimedia.org/wikipedia/commons/transcoded/1/1b/Barbershop_secondary_dominant.mid/Barbershop_secondary_dominant.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:Barbershop_secondary_dominant.mid" title="File:Barbershop secondary dominant.mid">ⓘ</a></sup></span></span>) Compositions with septimal tunings include <a href="/wiki/La_Monte_Young" title="La Monte Young">La Monte Young</a>'s <i><a href="/wiki/The_Well-Tuned_Piano" title="The Well-Tuned Piano">The Well-Tuned Piano</a></i>, <a href="/wiki/Ben_Johnston_(composer)" title="Ben Johnston (composer)">Ben Johnston</a>'s String Quartet No. 4, <a href="/wiki/Lou_Harrison" title="Lou Harrison">Lou Harrison</a>'s <i>Incidental Music for Corneille's Cinna</i>, and <a href="/wiki/Michael_Harrison_(musician)" title="Michael Harrison (musician)">Michael Harrison</a>'s <i>Revelation: Music in Pure Intonation</i>. </p><p>The <a href="/wiki/Great_Highland_bagpipe" title="Great Highland bagpipe">Great Highland bagpipe</a> is tuned to a ten-note seven-limit <a href="/wiki/Scale_(music)" title="Scale (music)">scale</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> <a href="/wiki/Unison" title="Unison">1:1</a>, <a href="/wiki/Major_tone" class="mw-redirect" title="Major tone">9:8</a>, <a href="/wiki/Major_third" title="Major third">5:4</a>, <a href="/wiki/Perfect_fourth" title="Perfect fourth">4:3</a>, <a href="/wiki/Wolf_interval" title="Wolf interval">27:20</a>, <a href="/wiki/Perfect_fifth" title="Perfect fifth">3:2</a>, <a href="/wiki/Major_sixth" title="Major sixth">5:3</a>, <b><a href="/wiki/Harmonic_seventh" title="Harmonic seventh">7:4</a></b>, <a href="/wiki/Pythagorean_minor_seventh" class="mw-redirect" title="Pythagorean minor seventh">16:9</a>, <a href="/wiki/Greater_just_minor_seventh" class="mw-redirect" title="Greater just minor seventh">9:5</a>. </p><p>In the 2nd century <a href="/wiki/Ptolemy" title="Ptolemy">Ptolemy</a> described the septimal intervals: 21/20, 7/4, 8/7, 7/6, 9/7, 12/7, 7/5, and 10/7.<sup id="cite_ref-Partch_4-0" class="reference"><a href="#cite_note-Partch-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Archytas" title="Archytas">Archytas</a> of <a href="/wiki/Taranto" title="Taranto">Tarantum</a> is the oldest recorded musicologist to calculate 7-limit tuning systems. Those considering 7 to be <a href="/wiki/Consonance_and_dissonance" title="Consonance and dissonance">consonant</a> include <a href="/wiki/Marin_Mersenne" title="Marin Mersenne">Marin Mersenne</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> <a href="/wiki/Giuseppe_Tartini" title="Giuseppe Tartini">Giuseppe Tartini</a>, <a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Leonhard Euler</a>, <a href="/wiki/Fran%C3%A7ois-Joseph_F%C3%A9tis" title="François-Joseph Fétis">François-Joseph Fétis</a>, J. A. Serre, <a href="/wiki/Moritz_Hauptmann" title="Moritz Hauptmann">Moritz Hauptmann</a>, <a href="/wiki/Alexander_John_Ellis" title="Alexander John Ellis">Alexander John Ellis</a>, Wilfred Perrett, <a href="/wiki/Max_Friedrich_Meyer" title="Max Friedrich Meyer">Max Friedrich Meyer</a>.<sup id="cite_ref-Partch_4-1" class="reference"><a href="#cite_note-Partch-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Those considering 7 to be dissonant include <a href="/wiki/Gioseffo_Zarlino" title="Gioseffo Zarlino">Gioseffo Zarlino</a>, <a href="/wiki/Ren%C3%A9_Descartes" title="René Descartes">René Descartes</a>, <a href="/wiki/Jean-Philippe_Rameau" title="Jean-Philippe Rameau">Jean-Philippe Rameau</a>, <a href="/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz">Hermann von Helmholtz</a>, <a href="/wiki/Arthur_von_Oettingen" title="Arthur von Oettingen">Arthur von Oettingen</a>, <a href="/wiki/Hugo_Riemann" title="Hugo Riemann">Hugo Riemann</a>, Colin Brown, and <a href="/wiki/Paul_Hindemith" title="Paul Hindemith">Paul Hindemith</a> ("chaos"<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>).<sup id="cite_ref-Partch_4-2" class="reference"><a href="#cite_note-Partch-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Lattice_and_tonality_diamond">Lattice and tonality diamond</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=7-limit_tuning&action=edit&section=1" title="Edit section: Lattice and tonality diamond"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Tonality_diamond#7-limit" title="Tonality diamond">7-limit tonality diamond</a>: </p> <table border="0" cellspacing="0" frame="void" rules="none"> <tbody><tr> <td></td> <td></td> <td></td> <td><a href="/wiki/Harmonic_seventh" title="Harmonic seventh">7/4</a></td> <td></td> <td></td> <td> </td></tr> <tr> <td></td> <td></td> <td><a href="/wiki/Perfect_fifth" title="Perfect fifth">3/2</a></td> <td></td> <td><a href="/wiki/Septimal_tritone" title="Septimal tritone">7/5</a></td> <td></td> <td> </td></tr> <tr> <td></td> <td><a href="/wiki/Major_third" title="Major third">5/4</a></td> <td></td> <td><a href="/wiki/Just_minor_third" class="mw-redirect" title="Just minor third">6/5</a></td> <td></td> <td><a href="/wiki/Septimal_minor_third" title="Septimal minor third">7/6</a></td> <td> </td></tr> <tr> <td><a href="/wiki/Unison" title="Unison">1/1</a></td> <td></td> <td>1/1</td> <td></td> <td>1/1</td> <td></td> <td>1/1 </td></tr> <tr> <td></td> <td><a href="/wiki/Just_minor_sixth" class="mw-redirect" title="Just minor sixth">8/5</a></td> <td></td> <td><a href="/wiki/Major_sixth" title="Major sixth">5/3</a></td> <td></td> <td><a href="/wiki/Septimal_major_sixth" class="mw-redirect" title="Septimal major sixth">12/7</a></td> <td> </td></tr> <tr> <td></td> <td></td> <td><a href="/wiki/Perfect_fourth" title="Perfect fourth">4/3</a></td> <td></td> <td><a href="/wiki/Septimal_tritone" title="Septimal tritone">10/7</a></td> <td></td> <td> </td></tr> <tr> <td></td> <td></td> <td></td> <td><a href="/wiki/Septimal_major_second" class="mw-redirect" title="Septimal major second">8/7</a></td> <td></td> <td></td> <td> </td></tr></tbody></table> <p>This diamond contains four <a href="/wiki/Limit_(music)#Identity" title="Limit (music)">identities</a> (1, 3, 5, 7 [P8, P5, M3, H7]). Similarly, the 2,3,5,7 <a href="/wiki/Pitch_lattice" class="mw-redirect" title="Pitch lattice">pitch lattice</a> contains four identities and thus 3-4 axes, but a potentially infinite number of pitches. LaMonte Young created a lattice containing only identities 3 and 7, thus requiring only two axes, for <i>The Well-Tuned Piano</i>. </p> <div class="mw-heading mw-heading3"><h3 id="Approximation_using_equal_temperament">Approximation using equal temperament</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=7-limit_tuning&action=edit&section=2" title="Edit section: Approximation using equal temperament"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>It is possible to approximate 7-limit music using equal temperament, for example <a href="/wiki/31_equal_temperament" title="31 equal temperament">31-ET</a>. </p> <table class="wikitable"> <tbody><tr> <th>Fraction</th> <th>Cents</th> <th>Degree (31-ET)</th> <th>Name (31-ET) </th></tr> <tr> <td>1/1</td> <td>0</td> <td>0.0</td> <td>C </td></tr> <tr> <td>8/7</td> <td>231</td> <td>6.0</td> <td>D<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="mw-default-size skin-invert" typeof="mw:File"><a href="/wiki/File:Arabic_music_notation_half_sharp.svg" class="mw-file-description" title="half sharp"><img alt="half sharp" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Arabic_music_notation_half_sharp.svg/6px-Arabic_music_notation_half_sharp.svg.png" decoding="async" width="6" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Arabic_music_notation_half_sharp.svg/9px-Arabic_music_notation_half_sharp.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Arabic_music_notation_half_sharp.svg/12px-Arabic_music_notation_half_sharp.svg.png 2x" data-file-width="106" data-file-height="200" /></a></span></span> or E<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="mw-default-size skin-invert" typeof="mw:File"><a href="/wiki/File:Doubleflat.svg" class="mw-file-description" title="double flat"><img alt="double flat" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/Doubleflat.svg/8px-Doubleflat.svg.png" decoding="async" width="8" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/Doubleflat.svg/12px-Doubleflat.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/23/Doubleflat.svg/16px-Doubleflat.svg.png 2x" data-file-width="133" data-file-height="200" /></a></span></span> </td></tr> <tr> <td>7/6</td> <td>267</td> <td>6.9</td> <td>D<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span> </td></tr> <tr> <td>6/5</td> <td>316</td> <td>8.2</td> <td>E<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span> </td></tr> <tr> <td>5/4</td> <td>386</td> <td>10.0</td> <td>E </td></tr> <tr> <td>4/3</td> <td>498</td> <td>12.9</td> <td>F </td></tr> <tr> <td>7/5</td> <td>583</td> <td>15.0</td> <td>F<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span> </td></tr> <tr> <td>10/7</td> <td>617</td> <td>16.0</td> <td>G<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span> </td></tr> <tr> <td>3/2</td> <td>702</td> <td>18.1</td> <td>G </td></tr> <tr> <td>8/5</td> <td>814</td> <td>21.0</td> <td>A<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span> </td></tr> <tr> <td>5/3</td> <td>884</td> <td>22.8</td> <td>A </td></tr> <tr> <td>12/7</td> <td>933</td> <td>24.1</td> <td>A<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="mw-default-size skin-invert" typeof="mw:File"><a href="/wiki/File:Arabic_music_notation_half_sharp.svg" class="mw-file-description" title="half sharp"><img alt="half sharp" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Arabic_music_notation_half_sharp.svg/6px-Arabic_music_notation_half_sharp.svg.png" decoding="async" width="6" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Arabic_music_notation_half_sharp.svg/9px-Arabic_music_notation_half_sharp.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Arabic_music_notation_half_sharp.svg/12px-Arabic_music_notation_half_sharp.svg.png 2x" data-file-width="106" data-file-height="200" /></a></span></span> or B<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="mw-default-size skin-invert" typeof="mw:File"><a href="/wiki/File:Doubleflat.svg" class="mw-file-description" title="double flat"><img alt="double flat" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/Doubleflat.svg/8px-Doubleflat.svg.png" decoding="async" width="8" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/Doubleflat.svg/12px-Doubleflat.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/23/Doubleflat.svg/16px-Doubleflat.svg.png 2x" data-file-width="133" data-file-height="200" /></a></span></span> </td></tr> <tr> <td>7/4</td> <td>969</td> <td>25.0</td> <td>A<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span> </td></tr> <tr> <td>2/1</td> <td>1200</td> <td>31.0</td> <td>C </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Ptolemy's_Harmonikon"><span id="Ptolemy.27s_Harmonikon"></span>Ptolemy's <i>Harmonikon</i></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=7-limit_tuning&action=edit&section=3" title="Edit section: Ptolemy's Harmonikon"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Ptolemy" title="Ptolemy">Claudius Ptolemy</a> of Alexandria described several 7-limit tuning systems for the <a href="/wiki/Diatonic_scale" title="Diatonic scale">diatonic</a> and <a href="/wiki/Chromatic" class="mw-redirect" title="Chromatic">chromatic</a> genera. He describes several "soft" (<a href="https://en.wiktionary.org/wiki/%CE%BC%CE%B1%CE%BB%CE%B1%CE%BA%CF%8C%CF%82" class="extiw" title="wiktionary:μαλακός">μαλακός</a>) diatonic tunings which all use 7-limit intervals.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> One, called by Ptolemy the "<a rel="nofollow" class="external text" href="https://sevish.com/scaleworkshop/?n=Tonic%20Diatonic&l=sFr_wFr_4F3_3F2_eF9_gF9_2F1&version=2.1.0">tonic diatonic</a>," is ascribed to the <a href="/wiki/Pythagoreanism" title="Pythagoreanism">Pythagorean</a> philosopher and statesman <a href="/wiki/Archytas" title="Archytas">Archytas of Tarentum</a>. It used the following <a href="/wiki/Tetrachord" title="Tetrachord">tetrachord:</a> 28:27, 8:7, 9:8. Ptolemy also shares the "<a rel="nofollow" class="external text" href="https://sevish.com/scaleworkshop/?n=Aristoxenus%20soft%20diatonic&l=kFj_8F7_4F3_3F2_uFj_cF7_2F1__&version=2.1.0">soft diatonic</a>" according to <a href="/wiki/Peripatetic_school" title="Peripatetic school">peripatetic philosopher</a> <a href="/wiki/Aristoxenus" title="Aristoxenus">Aristoxenus</a> of Tarentum: 20:19, 38:35, 7:6. Ptolemy offers his own "<a rel="nofollow" class="external text" href="https://sevish.com/scaleworkshop/?n=soft%20diatonic&l=lFk_7F6_4F3_3F2_1rF14_7F4_2F1&version=2.1.0">soft diatonic</a>" as the best alternative to Archytas and Aristoxenus, with a tetrachord of: 21:20, 10:9, 8:7. </p><p>Ptolemy also describes a "tense chromatic" tuning that utilizes the following tetrachord: 22:21, 12:11, 7:6. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=7-limit_tuning&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/%C4%90%C3%A0n_b%E1%BA%A7u" title="Đàn bầu">Đàn bầu</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=7-limit_tuning&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-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><a href="/wiki/John_Fonville" title="John Fonville">Fonville, John</a>. "<a href="/wiki/Ben_Johnston_(composer)" title="Ben Johnston (composer)">Ben Johnston</a>'s Extended Just Intonation – A Guide for Interpreters", p. 112, <i><a href="/wiki/Perspectives_of_New_Music" title="Perspectives of New Music">Perspectives of New Music</a></i>, vol. 29, no. 2 (Summer 1991), pp. 106–137.</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">Fonville (1991), p. 128.</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">Benson, Dave (2007). <i>Music: A Mathematical Offering</i>, p. 212. <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/9780521853873" title="Special:BookSources/9780521853873">9780521853873</a>.</span> </li> <li id="cite_note-Partch-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-Partch_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Partch_4-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Partch_4-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><a href="/wiki/Harry_Partch" title="Harry Partch">Partch, Harry</a> (2009). <i><a href="/wiki/Genesis_of_a_Music" title="Genesis of a Music">Genesis of a Music</a>: An Account of a Creative Work, Its Roots, and Its Fulfillments</i>, pp. 90–91. <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/9780786751006" title="Special:BookSources/9780786751006">9780786751006</a>.</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">Shirlaw, Matthew (1900). <i>Theory of Harmony</i>, p. 32. <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/978-1-4510-1534-8" title="Special:BookSources/978-1-4510-1534-8">978-1-4510-1534-8</a>.</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><a href="/wiki/Paul_Hindemith" title="Paul Hindemith">Hindemith, Paul</a> (1942). <i>Craft of Musical Composition</i>, vol. 1, p. 38. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0901938300" title="Special:BookSources/0901938300">0901938300</a>.</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBarker1989" class="citation book cs1">Barker, Andrew (1989). <i>Greek Musical Writings: II Harmonic and Acoustic Theory</i>. Cambridge: Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0521616972" title="Special:BookSources/0521616972"><bdi>0521616972</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Greek+Musical+Writings%3A+II+Harmonic+and+Acoustic+Theory&rft.place=Cambridge&rft.pub=Cambridge+University+Press&rft.date=1989&rft.isbn=0521616972&rft.aulast=Barker&rft.aufirst=Andrew&rfr_id=info%3Asid%2Fen.wikipedia.org%3A7-limit+tuning" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=7-limit_tuning&action=edit&section=6" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://anaphoria.com/centaur.html">Centaur a 7 limit tuning</a> shows Centaur tuning plus other related 7 tone tunings by others</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .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 dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt 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style="font-size:114%;margin:0 4em"><a href="/wiki/Musical_tuning" title="Musical tuning">Musical tunings</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Measurement</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Pitch_(music)" title="Pitch (music)">Pitch</a></li> <li><a href="/wiki/Cent_(music)" title="Cent (music)">Cent</a></li> <li><a href="/wiki/Millioctave" title="Millioctave">Millioctave</a></li> <li><a href="/wiki/Savart" title="Savart">Savart</a></li> <li><a href="/wiki/Interval_(music)" title="Interval (music)">Interval</a></li> <li><a href="/wiki/Interval_ratio" title="Interval ratio">Interval ratio</a></li> <li><a href="/wiki/Pitch_class" title="Pitch class">Pitch class</a></li> <li><a href="/wiki/Consonance_and_dissonance" title="Consonance and dissonance">Consonance and dissonance</a></li> <li><a href="/wiki/List_of_pitch_intervals" title="List of pitch intervals">List of musical intervals</a></li> <li><a href="/wiki/List_of_intervals_in_5-limit_just_intonation" title="List of intervals in 5-limit just intonation">List of intervals in 5-limit just intonation</a></li> <li><a href="/wiki/List_of_meantone_intervals" title="List of meantone intervals">List of meantone intervals</a></li> <li><a href="/wiki/Microtonal_music" class="mw-redirect" title="Microtonal music">Microtone</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Just_intonation" title="Just intonation">Just intonation</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Euler%E2%80%93Fokker_genus" title="Euler–Fokker genus">Euler–Fokker genus</a></li> <li><a href="/wiki/Harmonic_scale" title="Harmonic scale">Harmonic scale</a></li> <li><a href="/wiki/Harry_Partch%27s_43-tone_scale" title="Harry Partch's 43-tone scale">Harry Partch's 43-tone scale</a></li> <li><a href="/wiki/Hexany" title="Hexany">Hexany</a></li> <li><a href="/wiki/Limit_(music)" title="Limit (music)">Limit</a> <ul><li><a href="/wiki/Five-limit_tuning" title="Five-limit tuning">5-limit</a></li> <li><a class="mw-selflink selflink">7-limit</a></li></ul></li> <li><a href="/wiki/List_of_compositions_in_just_intonation" title="List of compositions in just intonation">List of compositions</a></li> <li><a href="/wiki/Otonality_and_Utonality" class="mw-redirect" title="Otonality and Utonality">Otonality</a></li> <li><a href="/wiki/Ptolemy%27s_intense_diatonic_scale" title="Ptolemy's intense diatonic scale">Ptolemy's intense diatonic scale</a></li> <li><a href="/wiki/Pythagorean_tuning" title="Pythagorean tuning">Pythagorean tuning</a></li> <li><a href="/wiki/Scale_of_harmonics" title="Scale of harmonics">Scale of harmonics</a></li> <li><a href="/wiki/Tonality_diamond" title="Tonality diamond">Tonality diamond</a></li> <li><a href="/wiki/Tonality_flux" title="Tonality flux">Tonality flux</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Musical_temperament" title="Musical temperament">Temperaments</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Equal_temperament" title="Equal temperament">Equal</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Whole-tone_scale" title="Whole-tone scale">6-tone</a></li> <li><a href="/wiki/12_equal_temperament" title="12 equal temperament">12-tone</a></li> <li><a href="/wiki/15_equal_temperament" title="15 equal temperament">15-tone</a></li> <li><a href="/wiki/17_equal_temperament" title="17 equal temperament">17-tone</a></li> <li><a href="/wiki/19_equal_temperament" title="19 equal temperament">19-tone</a></li> <li><a href="/wiki/22_equal_temperament" title="22 equal temperament">22-tone</a></li> <li><a href="/wiki/23_equal_temperament" title="23 equal temperament">23-tone</a></li> <li><a href="/wiki/Quarter_tone" title="Quarter tone">24-tone</a> (<a href="/wiki/List_of_quarter_tone_pieces" title="List of quarter tone pieces">pieces</a>)</li> <li><a href="/wiki/31_equal_temperament" title="31 equal temperament">31-tone</a></li> <li><a href="/wiki/34_equal_temperament" title="34 equal temperament">34-tone</a></li> <li><a href="/wiki/41_equal_temperament" title="41 equal temperament">41-tone</a></li> <li><a href="/wiki/53_equal_temperament" title="53 equal temperament">53-tone</a></li> <li><a href="/wiki/58_equal_temperament" title="58 equal temperament">58-tone</a></li> <li><a href="/wiki/72_equal_temperament" title="72 equal temperament">72-tone</a></li> <li><a href="/wiki/96_equal_temperament" title="96 equal temperament">96-tone</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Regular_temperament" title="Regular temperament">Linear</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Meantone_temperament" title="Meantone temperament">Meantone</a> (<a href="/wiki/Quarter-comma_meantone" title="Quarter-comma meantone">quarter-comma</a>, <a href="/wiki/Septimal_meantone_temperament" title="Septimal meantone temperament">septimal</a>)</li> <li><a href="/wiki/Schismatic_temperament" title="Schismatic temperament">Schismatic</a></li> <li><a href="/wiki/Miracle_temperament" class="mw-redirect" title="Miracle temperament">Miracle</a></li> <li><a href="/wiki/Magic_temperament" title="Magic temperament">Magic</a></li> <li><a href="/wiki/Regular_diatonic_tuning" title="Regular diatonic tuning">Regular diatonic</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Irregular</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><a href="/wiki/Well_temperament" title="Well temperament">Well temperament</a>/<a href="/wiki/Temperament_ordinaire" title="Temperament ordinaire">Temperament ordinaire</a> (<a href="/wiki/Kirnberger_temperament" title="Kirnberger temperament">Kirnberger</a>, <a href="/wiki/Vallotti_temperament" title="Vallotti temperament">Vallotti</a>, <a href="/wiki/Werckmeister_temperament" title="Werckmeister temperament">Werckmeister</a>, <a href="/wiki/Young_temperament" title="Young temperament">Young</a>)</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Traditional<br /> non-Western</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chinese_musicology" title="Chinese musicology">Chinese musicology</a></li> <li><a href="/wiki/Sh%C3%AD-%C3%A8r-l%C7%9C" class="mw-redirect" title="Shí-èr-lǜ">Shí-èr-lǜ</a></li> <li><a href="/wiki/Dastgah" class="mw-redirect" title="Dastgah">Dastgah</a></li> <li>Maqam <ul><li><a href="/wiki/Arabic_maqam" title="Arabic maqam">Arabic maqam</a></li> <li><a href="/wiki/Turkish_makam" title="Turkish makam">Turkish makam</a></li> <li><a href="/wiki/Mugham" title="Mugham">Mugham</a></li> <li><a href="/wiki/Muqam" title="Muqam">Muqam</a></li></ul></li> <li><a href="/wiki/Octoechos" title="Octoechos">Octoechos</a></li> <li><a href="/wiki/Pelog" title="Pelog">Pelog</a></li> <li><a href="/wiki/Raga" title="Raga">Raga</a> (<a href="/wiki/Carnatic_raga" title="Carnatic raga">Carnatic raga</a>)</li> <li><a href="/wiki/Slendro" title="Slendro">Slendro</a></li> <li><a href="/wiki/Tetrachord" title="Tetrachord">Tetrachord</a></li></ul> </div></td></tr><tr><th scope="row" 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