13edo
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[[toc|flat]] [[media type="custom" key="12670900"]] ---- =13 tone equal temperament / 13edo= 13edo refers to a tuning system which divides the octave (frequency ratio 2:1) into 13 equal parts. It is the sixth [[prime numbers|prime]] edo, following [[11edo]] and coming before [[17edo]]. The steps are of similar size to those of 12edo (albeit squashed), while the intervals between a minor third & major sixth are xenharmonic (not similar to anything available in 12edo). [[file:13edo-chromatic-scale.mid|13 edo chromatic ascending and descending scale on C]] || Degree || Cents ||= Approximate Ratios* || 6L1s Names || 5L3s Names || [[26edo]] names || || 0 || 0 ||= 1/1 || C || C || C || || 1 || 92.3077 ||= 22/21, 55/52, 117/110, 26/25 || C#/Db || C#/Db || Cx/Dbb || || 2 || 184.6154 ||= 10/9, 9/8, 11/10 || D || D || D || || 3 || 276.9231 ||= 13/11, 7/6 || D#/Eb || D#/Eb || Dx/Ebb || || 4 || 369.2308 ||= 5/4, 16/13, 11/9, 26/21 || E || E || E || || 5 || 461.5385 ||= 13/10, 21/16 || E#/Fb || F || Ex/Fb || || 6 || 553.84 ||= 11/8, 18/13 || F || F#/Gb || F# || || 7 || 646.15 ||= 16/11, 13/9 || F#/Gb || G || Gb || || 8 || 738.46 ||= 20/13, 32/21 || G || G#/Hb || G# || || 9 || 830.77 ||= 8/5, 13/8, 18/11, 21/13 || G#/Ab || H || Ab || || 10 || 923.08 ||= 22/13, 12/7 || A || A || A# || || 11 || 1015.38 ||= 9/5, 16/9, 20/11 || A#/Bb || A#/Bb || Bb || || 12 || 1107.69 ||= 21/11, 25/13, 104/55 || B/Cb || B || B#/Cbb || || 13 || 1200 ||= 2/1 || C/B# || C || C || *based on treating 13-EDO as a 2.5.9.11.13.21 subgroup temperament; other approaches are possible. =Harmony in 13edo= Contrary to popular belief, consonant harmony is possible in 13-EDO, but it requires a radically different approach than that used in 12-EDO (or other Pythagorean or Meantone-based tunings). Trying to approximate the usual major and minor triads of 12-EDO within 13-EDO is usually a disappointment if consonance is the goal; 0-3-7, 0-4-7, 0-3-8, and 0-4-8 are all rather rough in 13-EDO. Typically, the most consonant harmonies do not use a "stack of 3rds" the way they do in 12-TET, since the strongest dissonances in 13-EDO are near the middle of the octave (degrees 6, 7, and 8). Instead, a stack of whole-tones, or a mixture of whole-tones and minor 3rds, often yields good results. For example, one way to view 13-EDO is as a subgroup temperament of harmonics 2.5.9.11.13. It actually performs quite admirably in this regard, and a chord of 0-4-15-19-22 (approximating 4:5:9:11:13) sounds very convincing. An even larger subgroup is the [[k*N subgroups|2*13 subgroup]] 2.9.5.21.11.13, on which 13 has the same tuning and commas as 26et. The 2.9.5.11.13 subgroup has commas 45/44, 65/64 and 81/80, leading to a linear temperament with POTE generator 185.728 cents, quite close to 2\13. Use this as a generator, and at 7 notes (6L1s) two full pentads are available (as well as two more 4:5:9:11 tetrad, and one 4:5:9:13 tetrad). =Scales in 13edo= Due to the prime character of the number 13, 13edo can form several xenharmonic [[MOSScales|moment of symmetry scales]]. The diagram below shows five "families" of MOS scales: those generated by making a chain of 2\13 (two degrees of 13edo), 3\13, 4\13, 5\13, & 6\13, respectively. [[image:13edo_horograms.jpg]] [[file:13edo horograms.pdf]] ~diagram by Andrew Heathwaite, based on horograms pioneered by Erv Wilson Another neat facet of 13-EDO is the fact that any 12-EDO scale can be "turned into" a 13-EDO scale by either adding an extra semitone, or turning an existent semitone into a whole-tone. Because of this, melody in 13-EDO can be quite mind-bending and uncanny, and phrases that begin in a familiar way quickly lead to something totally unexpected. == == =Animism= The animist comma, 105/104, appears whenever 3*5*7=13... 26 edo approximates 3, 5, and 7 individually, however 13 edo has 21/16 (=3*7) and is also an animist temperament. In 13 edo, the 5th harmonic is tuned so flatly that 5/4 = 16/13, leading to some interesting identities. So two scales stand out through this construction 0 4 5 8 9 13 pentatonic and 0 1 3 4 5 8 9 10 12 13 nonatonic =**Compositions**= <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">////[[http://www.microtonalmusic.net/audio/slowdance13edo.mp3|Slow Dance]]////</span> by [[http://danielthompson.blogspot.com/|Daniel Thompson]] <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">////[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Hunt/Prelude%20in%2013ET.mp3|Prelude in 13ET]]////</span> by [[Aaron Andrew Hunt]] <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">////[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Hunt/13ET.mp3|Two-Part Invention in 13ET]]////</span> by [[Aaron Andrew Hunt]] <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">////[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/triskaidekaphobia.mp3|Triskaidekaphobia]]////</span> by [[http://www.io.com/%7Ehmiller/music/|Herman Miller]] [[http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&songID=835265|Spikey Hair in 13tET]] <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">////[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+improvisationin13tet.mp3|play]]////</span> by [[Andrew Heathwaite]] [[@http://cityoftheasleep.bandcamp.com/track/broken-dream-jar|Broken Dream Jar]] by [[IgliashonJones|City of the Asleep]] [[@http://www.last.fm/music/City+of+the+Asleep/Map+of+an+Internal+Landscape/Blinding+White+Darkness|Blinding White Darkness]] by [[IgliashonJones|City of the Asleep]] [[http://soundcloud.com/cityoftheasleep/fuzz-reef|Fuzz Reef]] by City of the Asleep [[http://soundcloud.com/cityoftheasleep/lunar-approach|Lunar Approach]] by City of the Asleep [[http://soundcloud.com/cityoftheasleep/farthur|Farthur]] by City of the Asleep [[@http://www.elvenminstrel.com/music/tuning/equal/13equal/13tet.htm|Upsidedown and Backwards: Explorations in 13-tone Equal Temperament]] by [[http://www.elvenminstrel.com/|David J. Finnamore]] <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">////[[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/11%20-%2011.%2013%20octave.mp3|Comets Over Flatland 11]]////</span> by [[Randy Winchester]] <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">////[[http://micro.soonlabel.com/13edo/20120225-midiaxe-prelude-for-synthesizer-in-13-equal.mp3|Prelude for Synthesizer in 13 Equal]]////</span> by [[Chris Vaisvil]] <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">////[[http://micro.soonlabel.com/13edo/muon_catalyzed_fusion_13_edo.mp3|Muon Catalyzed Fusion]]////</span> by [[Chris Vaisvil]] <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">////[[http://www.seraph.it/dep/det/13Miles.mp3|13 Miles]]////</span> by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/ca5de720a48c401bcab8fc82c3b81ddc-152.html|blog entry]]) <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">////[[http://www.seraph.it/dep/det/FastAndFurious13.mp3|Fast And Furious 13]]////</span> by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/d2849db485fe3de42e769dad4db3a6ac-153.html|blog entry]]) <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">////[[http://www.seraph.it/dep/det/SazDul13.mp3|SazDul 13]]////</span> by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/bb5f0dcff57ba4fc56fcf50f54f10e4b-154.html|blog entry]]) <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">////[[http://www.seraph.it/dep/det/Thirteenstan.mp3|Thirteenstan]]////</span> by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/2cd2657e7fc17cdbe44dcd5fc255a951-155.html|blog entry]]) <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">////[[http://www.seraph.it/dep/det/Concertina13.mp3|Concertina 13]]////</span> by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/3e06afae9b0565b3bc0f39581683cfa7-156.html|blog entry]]) [[@http://soundcloud.com/xenvotta/sets/votta-liber-stellarum-for/|Liber Stellarum]] by [[@http://www.alvotta.net|Alfredo Votta]]Mapping to Standard Keyboards =Commas= 13 EDO [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes the val < 13 21 30 36 45 48 |.) ||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 || ||= 2109375/2097152 ||< | -21 3 7 > ||> 10.06 ||= Semicomma ||= Fokker Comma ||= || ||= 1029/1000 ||< | -3 1 -3 3 > ||> 49.49 ||= Keega ||= ||= || ||= 525/512 ||< | -9 1 2 1 > ||> 43.41 ||= Avicennma ||= Avicenna's Enharmonic Diesis ||= || ||= 64/63 ||< | 6 -2 0 -1 > ||> 27.26 ||= Septimal Comma ||= Archytas' Comma ||= Leipziger Komma || ||= 64827/64000 ||< | -9 3 -3 4 > ||> 22.23 ||= Squalentine ||= ||= || ||= 3125/3087 ||< | 0 -2 5 -3 > ||> 21.18 ||= Gariboh ||= ||= || ||= 3136/3125 ||< | 6 0 -5 2 > ||> 6.08 ||= Hemimean ||= ||= || ||= 121/120 ||< | -3 -1 -1 0 2 > ||> 14.37 ||= Biyatisma ||= ||= || ||= 441/440 ||< | -3 2 -1 2 -1 > ||> 3.93 ||= Werckisma ||= ||= ||
Original HTML content:
<html><head><title>13edo</title></head><body><!-- ws:start:WikiTextTocRule:15:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --><a href="#x13 tone equal temperament / 13edo">13 tone equal temperament / 13edo</a><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --> | <a href="#Harmony in 13edo">Harmony in 13edo</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#Scales in 13edo">Scales in 13edo</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --> | <a href="#Animism">Animism</a><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --> | <a href="#Compositions">Compositions</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: -->
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<!-- ws:start:WikiTextHeadingRule:1:<h1> --><h1 id="toc0"><a name="x13 tone equal temperament / 13edo"></a><!-- ws:end:WikiTextHeadingRule:1 -->13 tone equal temperament / 13edo</h1>
13edo refers to a tuning system which divides the octave (frequency ratio 2:1) into 13 equal parts. It is the sixth <a class="wiki_link" href="/prime%20numbers">prime</a> edo, following <a class="wiki_link" href="/11edo">11edo</a> and coming before <a class="wiki_link" href="/17edo">17edo</a>. The steps are of similar size to those of 12edo (albeit squashed), while the intervals between a minor third & major sixth are xenharmonic (not similar to anything available in 12edo).<br />
<a href="/file/view/13edo-chromatic-scale.mid/389281456/13edo-chromatic-scale.mid" onclick="ws.common.trackFileLink('/file/view/13edo-chromatic-scale.mid/389281456/13edo-chromatic-scale.mid');">13 edo chromatic ascending and descending scale on C</a><br />
<table class="wiki_table">
<tr>
<td>Degree<br />
</td>
<td>Cents<br />
</td>
<td style="text-align: center;">Approximate Ratios*<br />
</td>
<td>6L1s Names<br />
</td>
<td>5L3s Names<br />
</td>
<td><a class="wiki_link" href="/26edo">26edo</a> names<br />
</td>
</tr>
<tr>
<td>0<br />
</td>
<td>0<br />
</td>
<td style="text-align: center;">1/1<br />
</td>
<td>C<br />
</td>
<td>C<br />
</td>
<td>C<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>92.3077<br />
</td>
<td style="text-align: center;">22/21, 55/52, 117/110, 26/25<br />
</td>
<td>C#/Db<br />
</td>
<td>C#/Db<br />
</td>
<td>Cx/Dbb<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>184.6154<br />
</td>
<td style="text-align: center;">10/9, 9/8, 11/10<br />
</td>
<td>D<br />
</td>
<td>D<br />
</td>
<td>D<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>276.9231<br />
</td>
<td style="text-align: center;">13/11, 7/6<br />
</td>
<td>D#/Eb<br />
</td>
<td>D#/Eb<br />
</td>
<td>Dx/Ebb<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>369.2308<br />
</td>
<td style="text-align: center;">5/4, 16/13, 11/9, 26/21<br />
</td>
<td>E<br />
</td>
<td>E<br />
</td>
<td>E<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>461.5385<br />
</td>
<td style="text-align: center;">13/10, 21/16<br />
</td>
<td>E#/Fb<br />
</td>
<td>F<br />
</td>
<td>Ex/Fb<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>553.84<br />
</td>
<td style="text-align: center;">11/8, 18/13<br />
</td>
<td>F<br />
</td>
<td>F#/Gb<br />
</td>
<td>F#<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>646.15<br />
</td>
<td style="text-align: center;">16/11, 13/9<br />
</td>
<td>F#/Gb<br />
</td>
<td>G<br />
</td>
<td>Gb<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>738.46<br />
</td>
<td style="text-align: center;">20/13, 32/21<br />
</td>
<td>G<br />
</td>
<td>G#/Hb<br />
</td>
<td>G#<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>830.77<br />
</td>
<td style="text-align: center;">8/5, 13/8, 18/11, 21/13<br />
</td>
<td>G#/Ab<br />
</td>
<td>H<br />
</td>
<td>Ab<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>923.08<br />
</td>
<td style="text-align: center;">22/13, 12/7<br />
</td>
<td>A<br />
</td>
<td>A<br />
</td>
<td>A#<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>1015.38<br />
</td>
<td style="text-align: center;">9/5, 16/9, 20/11<br />
</td>
<td>A#/Bb<br />
</td>
<td>A#/Bb<br />
</td>
<td>Bb<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>1107.69<br />
</td>
<td style="text-align: center;">21/11, 25/13, 104/55<br />
</td>
<td>B/Cb<br />
</td>
<td>B<br />
</td>
<td>B#/Cbb<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>1200<br />
</td>
<td style="text-align: center;">2/1<br />
</td>
<td>C/B#<br />
</td>
<td>C<br />
</td>
<td>C<br />
</td>
</tr>
</table>
*based on treating 13-EDO as a 2.5.9.11.13.21 subgroup temperament; other approaches are possible.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:3:<h1> --><h1 id="toc1"><a name="Harmony in 13edo"></a><!-- ws:end:WikiTextHeadingRule:3 -->Harmony in 13edo</h1>
Contrary to popular belief, consonant harmony is possible in 13-EDO, but it requires a radically different approach than that used in 12-EDO (or other Pythagorean or Meantone-based tunings). Trying to approximate the usual major and minor triads of 12-EDO within 13-EDO is usually a disappointment if consonance is the goal; 0-3-7, 0-4-7, 0-3-8, and 0-4-8 are all rather rough in 13-EDO. Typically, the most consonant harmonies do not use a "stack of 3rds" the way they do in 12-TET, since the strongest dissonances in 13-EDO are near the middle of the octave (degrees 6, 7, and 8). Instead, a stack of whole-tones, or a mixture of whole-tones and minor 3rds, often yields good results. For example, one way to view 13-EDO is as a subgroup temperament of harmonics 2.5.9.11.13. It actually performs quite admirably in this regard, and a chord of 0-4-15-19-22 (approximating 4:5:9:11:13) sounds very convincing. An even larger subgroup is the <a class="wiki_link" href="/k%2AN%20subgroups">2*13 subgroup</a> 2.9.5.21.11.13, on which 13 has the same tuning and commas as 26et.<br />
<br />
The 2.9.5.11.13 subgroup has commas 45/44, 65/64 and 81/80, leading to a linear temperament with POTE generator 185.728 cents, quite close to 2\13. Use this as a generator, and at 7 notes (6L1s) two full pentads are available (as well as two more 4:5:9:11 tetrad, and one 4:5:9:13 tetrad).<br />
<br />
<!-- ws:start:WikiTextHeadingRule:5:<h1> --><h1 id="toc2"><a name="Scales in 13edo"></a><!-- ws:end:WikiTextHeadingRule:5 -->Scales in 13edo</h1>
Due to the prime character of the number 13, 13edo can form several xenharmonic <a class="wiki_link" href="/MOSScales">moment of symmetry scales</a>. The diagram below shows five "families" of MOS scales: those generated by making a chain of 2\13 (two degrees of 13edo), 3\13, 4\13, 5\13, & 6\13, respectively.<br />
<br />
<!-- ws:start:WikiTextLocalImageRule:379:<img src="/file/view/13edo_horograms.jpg/104015789/13edo_horograms.jpg" alt="" title="" /> --><img src="/file/view/13edo_horograms.jpg/104015789/13edo_horograms.jpg" alt="13edo_horograms.jpg" title="13edo_horograms.jpg" /><!-- ws:end:WikiTextLocalImageRule:379 --><br />
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~diagram by Andrew Heathwaite, based on horograms pioneered by Erv Wilson<br />
<br />
Another neat facet of 13-EDO is the fact that any 12-EDO scale can be "turned into" a 13-EDO scale by either adding an extra semitone, or turning an existent semitone into a whole-tone. Because of this, melody in 13-EDO can be quite mind-bending and uncanny, and phrases that begin in a familiar way quickly lead to something totally unexpected.<br />
<!-- ws:start:WikiTextHeadingRule:7:<h2> --><h2 id="toc3"><!-- ws:end:WikiTextHeadingRule:7 --> </h2>
<!-- ws:start:WikiTextHeadingRule:9:<h1> --><h1 id="toc4"><a name="Animism"></a><!-- ws:end:WikiTextHeadingRule:9 -->Animism</h1>
<br />
The animist comma, 105/104, appears whenever 3*5*7=13... 26 edo approximates 3, 5, and 7 individually, however 13 edo has 21/16 (=3*7) and is also an animist temperament. In 13 edo, the 5th harmonic is tuned so flatly that 5/4 = 16/13, leading to some interesting identities. So two scales stand out through this construction<br />
<br />
0 4 5 8 9 13 pentatonic<br />
and<br />
0 1 3 4 5 8 9 10 12 13 nonatonic<br />
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:11:<h1> --><h1 id="toc5"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:11 --><strong>Compositions</strong></h1>
<br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://www.microtonalmusic.net/audio/slowdance13edo.mp3" rel="nofollow">Slow Dance</a></span> by <a class="wiki_link_ext" href="http://danielthompson.blogspot.com/" rel="nofollow">Daniel Thompson</a><br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Hunt/Prelude%20in%2013ET.mp3" rel="nofollow">Prelude in 13ET</a></span> by <a class="wiki_link" href="/Aaron%20Andrew%20Hunt">Aaron Andrew Hunt</a><br />
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<br />
<!-- ws:start:WikiTextHeadingRule:13:<h1> --><h1 id="toc6"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:13 -->Commas</h1>
13 EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes the val < 13 21 30 36 45 48 |.)<br />
<table class="wiki_table">
<tr>
<th>Comma<br />
</th>
<th>Monzo<br />
</th>
<th>Value (Cents)<br />
</th>
<th>Name 1<br />
</th>
<th>Name 2<br />
</th>
<th>Name 3<br />
</th>
</tr>
<tr>
<td style="text-align: center;">2109375/2097152<br />
</td>
<td style="text-align: left;">| -21 3 7 ><br />
</td>
<td style="text-align: right;">10.06<br />
</td>
<td style="text-align: center;">Semicomma<br />
</td>
<td style="text-align: center;">Fokker Comma<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">1029/1000<br />
</td>
<td style="text-align: left;">| -3 1 -3 3 ><br />
</td>
<td style="text-align: right;">49.49<br />
</td>
<td style="text-align: center;">Keega<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">525/512<br />
</td>
<td style="text-align: left;">| -9 1 2 1 ><br />
</td>
<td style="text-align: right;">43.41<br />
</td>
<td style="text-align: center;">Avicennma<br />
</td>
<td style="text-align: center;">Avicenna's Enharmonic Diesis<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">64/63<br />
</td>
<td style="text-align: left;">| 6 -2 0 -1 ><br />
</td>
<td style="text-align: right;">27.26<br />
</td>
<td style="text-align: center;">Septimal Comma<br />
</td>
<td style="text-align: center;">Archytas' Comma<br />
</td>
<td style="text-align: center;">Leipziger Komma<br />
</td>
</tr>
<tr>
<td style="text-align: center;">64827/64000<br />
</td>
<td style="text-align: left;">| -9 3 -3 4 ><br />
</td>
<td style="text-align: right;">22.23<br />
</td>
<td style="text-align: center;">Squalentine<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">3125/3087<br />
</td>
<td style="text-align: left;">| 0 -2 5 -3 ><br />
</td>
<td style="text-align: right;">21.18<br />
</td>
<td style="text-align: center;">Gariboh<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">3136/3125<br />
</td>
<td style="text-align: left;">| 6 0 -5 2 ><br />
</td>
<td style="text-align: right;">6.08<br />
</td>
<td style="text-align: center;">Hemimean<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">121/120<br />
</td>
<td style="text-align: left;">| -3 -1 -1 0 2 ><br />
</td>
<td style="text-align: right;">14.37<br />
</td>
<td style="text-align: center;">Biyatisma<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">441/440<br />
</td>
<td style="text-align: left;">| -3 2 -1 2 -1 ><br />
</td>
<td style="text-align: right;">3.93<br />
</td>
<td style="text-align: center;">Werckisma<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
</table>
</body></html>