10edo: Difference between revisions

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**Imported revision 589279364 - Original comment: **
Wikispaces>PiotrGrochowski
**Imported revision 589879786 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:PiotrGrochowski|PiotrGrochowski]] and made on <tt>2016-08-13 10:12:49 UTC</tt>.<br>
: This revision was by author [[User:PiotrGrochowski|PiotrGrochowski]] and made on <tt>2016-08-21 13:30:42 UTC</tt>.<br>
: The original revision id was <tt>589279364</tt>.<br>
: The original revision id was <tt>589879786</tt>.<br>
: The revision comment was: <tt></tt><br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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=[[media type="custom" key="10886138"]]=  
=[[media type="custom" key="10886138"]]=  
=Intervals=  
=Intervals=  
|| Degree || Cent
|| Degree || Cents
Values || Approximate
DMS || Approximate
Ratios* || Additional Ratios of 3, 5 and 9 || Name ||
Ratios* || Additional Ratios of 3, 5 and 9 || Name ||
|| 0 || 0 || 1/1 ||   || unison ||
|| 0 || 0
|| 1 || 120 || 15/14, 16/15, 13/14 || 10/9, 13/12 || small neutral second/large minor second ||
0° || 1/1 || 256/243, 50/49 || unison ||
|| 2 || 240 || 15/13, 8/7 || 9/8, 7/6 || second/third ||
|| 1 || 120
|| 3 || 360 || 16/13 || 5/4 || large neutral third ||
36° || 15/14, 16/15, 13/14 || 10/9, 13/12, 81/80 || small neutral second/large minor second ||
|| 4 || 480 || 64/49, 169/128 || 4/3, 9/7, 13/10 || smaller fourth ||
|| 2 || 240
|| 5 || 600 || 91/64, 169/120 || 7/5, 10/7, 13/9, 18/13 || tritone ||
72° || 15/13, 8/7 || 9/8, 7/6 || second/third ||
|| 6 || 720 || 49/32, 256/169 || 3/2, 14/9, 20/13 || bigger fifth ||
|| 3 || 360
|| 7 || 840 || 13/8 || 8/5 || neutral sixth ||
108° || 16/13 || 5/4 || large neutral third ||
|| 8 || 960 || 7/4, 26/15, 125/72 || 16/9, 12/7 || sixth/seventh ||
|| 4 || 480
|| 9 || 1080 || 15/8, 28/15, 13/7 || 9/5, 24/13 || small major 7th ||
144° || 64/49, 169/128 || 4/3, 9/7, 13/10 || smaller fourth ||
|| 10 || 1200 || 2/1 ||   || octave ||
|| 5 || 600
180° || 91/64, 169/120 || 7/5, 10/7, 13/9, 18/13 || tritone ||
|| 6 || 720
216° || 49/32, 256/169 || 3/2, 14/9, 20/13 || bigger fifth ||
|| 7 || 840
252° || 13/8 || 8/5 || neutral sixth ||
|| 8 || 960
288° || 7/4, 26/15, 125/72 || 16/9, 12/7 || sixth/seventh ||
|| 9 || 1080
324° || 15/8, 28/15, 13/7 || 9/5, 24/13, 160/81 || small major 7th ||
|| 10 || 1200
360° || 2/1 || 243/128, 49/25 || octave ||
*based on treating 10-EDO as a 2.7.13.15 subgroup temperament.
*based on treating 10-EDO as a 2.7.13.15 subgroup temperament.
adding the ratios of 3, 5 and 9 introduces greater [[error]] while giving several more harmonic identities to the 10-EDO intervals.
adding the ratios of 3, 5 and 9 introduces greater [[error]] while giving several more harmonic identities to the 10-EDO intervals.
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         &lt;td&gt;Degree&lt;br /&gt;
         &lt;td&gt;Degree&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;Cent&lt;br /&gt;
         &lt;td&gt;Cents&lt;br /&gt;
Values&lt;br /&gt;
DMS&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;Approximate&lt;br /&gt;
         &lt;td&gt;Approximate&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;0&lt;br /&gt;
         &lt;td&gt;0&lt;br /&gt;
0°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1/1&lt;br /&gt;
         &lt;td&gt;1/1&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;256/243, 50/49&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;unison&lt;br /&gt;
         &lt;td&gt;unison&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;120&lt;br /&gt;
         &lt;td&gt;120&lt;br /&gt;
36°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;15/14, 16/15, 13/14&lt;br /&gt;
         &lt;td&gt;15/14, 16/15, 13/14&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;10/9, 13/12&lt;br /&gt;
         &lt;td&gt;10/9, 13/12, 81/80&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;small neutral second/large minor second&lt;br /&gt;
         &lt;td&gt;small neutral second/large minor second&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;240&lt;br /&gt;
         &lt;td&gt;240&lt;br /&gt;
72°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;15/13, 8/7&lt;br /&gt;
         &lt;td&gt;15/13, 8/7&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;360&lt;br /&gt;
         &lt;td&gt;360&lt;br /&gt;
108°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;16/13&lt;br /&gt;
         &lt;td&gt;16/13&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;480&lt;br /&gt;
         &lt;td&gt;480&lt;br /&gt;
144°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;64/49, 169/128&lt;br /&gt;
         &lt;td&gt;64/49, 169/128&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;600&lt;br /&gt;
         &lt;td&gt;600&lt;br /&gt;
180°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;91/64, 169/120&lt;br /&gt;
         &lt;td&gt;91/64, 169/120&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;720&lt;br /&gt;
         &lt;td&gt;720&lt;br /&gt;
216°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;49/32, 256/169&lt;br /&gt;
         &lt;td&gt;49/32, 256/169&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;840&lt;br /&gt;
         &lt;td&gt;840&lt;br /&gt;
252°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;13/8&lt;br /&gt;
         &lt;td&gt;13/8&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;960&lt;br /&gt;
         &lt;td&gt;960&lt;br /&gt;
288°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;7/4, 26/15, 125/72&lt;br /&gt;
         &lt;td&gt;7/4, 26/15, 125/72&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1080&lt;br /&gt;
         &lt;td&gt;1080&lt;br /&gt;
324°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;15/8, 28/15, 13/7&lt;br /&gt;
         &lt;td&gt;15/8, 28/15, 13/7&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;9/5, 24/13&lt;br /&gt;
         &lt;td&gt;9/5, 24/13, 160/81&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;small major 7th&lt;br /&gt;
         &lt;td&gt;small major 7th&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1200&lt;br /&gt;
         &lt;td&gt;1200&lt;br /&gt;
360°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;2/1&lt;br /&gt;
         &lt;td&gt;2/1&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;243/128, 49/25&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;octave&lt;br /&gt;
         &lt;td&gt;octave&lt;br /&gt;

Revision as of 13:30, 21 August 2016

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author PiotrGrochowski and made on 2016-08-21 13:30:42 UTC.
The original revision id was 589879786.
The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

<span style="display: block; text-align: right;">[[10平均律|日本語]]
</span>
10edo, or 10-tone equal temperament, is a tuning system which divides the [[octave]] into 10 equal parts of exactly 120 [[cent]]s. It can be thought of as two circles of [[5edo]] separated by 120 cents (or 5 circles of [[2edo]]). It adds to 5edo a small neutral second (or large minor 2nd) and its inversion a large neutral seventh (or small major 7th); an excellent approximation of [[13_8|13/8]] and its inversion [[16_13|16/13]]; and the happy 600-cent tritone that appears in every even-numbered EDO. Taking the the 360 cent large neutral third as a generator produces a heptatonic [[MOSScales|moment of symmetry scale]] of the form 1 2 1 2 1 2 1 ([[3L 4s|3L 4s - mosh]]). While not an integral or gap edo, it is a [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta peak edo]]. One way to interpret it in terms of a temperament of Just intonation is as a 2.7.13.15 subgroup, such that 105/104, 225/224, and 16807/16384 are tempered out. It can also be treated as a full 13-limit temperament, but it is a closer match to the aforementioned subgroup.

[[toc|flat]]
----

=[[media type="custom" key="10886138"]]= 
=Intervals= 
|| Degree || Cents
DMS || Approximate
Ratios* || Additional Ratios of 3, 5 and 9 || Name ||
|| 0 || 0
0° || 1/1 || 256/243, 50/49 || unison ||
|| 1 || 120
36° || 15/14, 16/15, 13/14 || 10/9, 13/12, 81/80 || small neutral second/large minor second ||
|| 2 || 240
72° || 15/13, 8/7 || 9/8, 7/6 || second/third ||
|| 3 || 360
108° || 16/13 || 5/4 || large neutral third ||
|| 4 || 480
144° || 64/49, 169/128 || 4/3, 9/7, 13/10 || smaller fourth ||
|| 5 || 600
180° || 91/64, 169/120 || 7/5, 10/7, 13/9, 18/13 || tritone ||
|| 6 || 720
216° || 49/32, 256/169 || 3/2, 14/9, 20/13 || bigger fifth ||
|| 7 || 840
252° || 13/8 || 8/5 || neutral sixth ||
|| 8 || 960
288° || 7/4, 26/15, 125/72 || 16/9, 12/7 || sixth/seventh ||
|| 9 || 1080
324° || 15/8, 28/15, 13/7 || 9/5, 24/13, 160/81 || small major 7th ||
|| 10 || 1200
360° || 2/1 || 243/128, 49/25 || octave ||
*based on treating 10-EDO as a 2.7.13.15 subgroup temperament.
adding the ratios of 3, 5 and 9 introduces greater [[error]] while giving several more harmonic identities to the 10-EDO intervals.

[[media type="custom" key="24802496"]]

[[file:10ed2-001.svg]]

=Images= 

[[image:10edo wheel.png width="280" height="285"]]

=Linear temperaments= 
||~ Periods
per octave ||~ Generator ||~ Temperament(s) ||
|| 1 || 1\10 || Messed-up [[Negri|negri]] (or [[Miracle|miracle]]) ||
|| 1 || 3\10 || [[Dicot]]/[[Beatles|beatles]]/neutral thirds scale ||
|| 2 || 1\10 || Messed-up [[pajara]] ||
|| 2 || 2\10 || [[Decimal]] / messed-up [[Lemba|lemba]] ||
|| 5 || 1\10 || [[Blackwood]]/[[blacksmith]] ||
=Commas= 
10 EDO tempers out the following commas. (Note: This assumes the val < 10 16 23 28 35 37 |.)

||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
||= 256/243 || | 8 -5 > ||> 90.22 ||= Limma ||= Pythagorean Minor 2nd ||   ||
||= 16875/16384 || | -14 3 4 > ||> 51.12 ||= Negri Comma ||= Double Augmentation Diesis ||   ||
||= 9931568/9752117 || | -25 7 6 > ||> 31.57 ||= Ampersand's Comma ||=   ||   ||
||= 2048/2025 || | 11 -4 -2 > ||> 19.55 ||= Diaschisma ||=   ||   ||
||= 525/512 || | -9 1 2 1 > ||> 43.41 ||= Avicennma ||= Avicennma's Enharmonic Diesis ||   ||
||= 49/48 || | -4 -1 0 2 > ||> 35.70 ||= Slendro Diesis ||=   ||   ||
||= 50/49 || | 1 0 2 -2 > ||> 34.98 ||= Tritonic Diesis ||= Jubilisma ||   ||
||= 686/675 || | 1 -3 -2 3 > ||> 27.99 ||= Senga ||=   ||   ||
||= 64/63 || | 6 -2 0 -1 > ||> 27.26 ||= Septimal Comma ||= Archytas' Comma || Leipziger Komma ||
||= 9859966/9733137 || | -10 7 8 -7 > ||> 22.41 ||= Blackjackisma ||=   ||   ||
||= 1029/1024 || | -10 1 0 3 > ||> 8.43 ||= Gamelisma ||=   ||   ||
||= 225/224 || | -5 2 2 -1 > ||> 7.71 ||= Septimal Kleisma ||= Marvel Comma ||   ||
||= 16875/16807 || | 0 3 4 -5 > ||> 6.99 ||= Mirkwai ||=   ||   ||
||= 6772805/6751042 || | 11 -10 -10 10 > ||> 5.57 ||= Linus ||=   ||   ||
||= 2401/2400 || | -5 -1 -2 4 > ||> 0.72 ||= Breedsma ||=   ||   ||
||= 243/242 || | -1 5 0 0 -2 > ||> 7.14 ||= Rastma ||=   ||   ||
||= 385/384 || | -7 -1 1 1 1 > ||> 4.50 ||= Keenanisma ||=   ||   ||
||= 441/440 || | -3 2 -1 2 -1 > ||> 3.93 ||= Werckisma ||=   ||   ||
||= 540/539 || | 2 3 1 -2 -1 > ||> 3.21 ||= Swetisma ||=   ||   ||
||= 3025/3024 || | -4 -3 2 -1 2 > ||> 0.57 ||= Lehmerisma ||=   ||   ||
||= 91/90 || | -1 -2 -1 1 0 1 > ||> 19.13 ||= Superleap ||=   ||   ||
||= 676/675 || | 2 -3 -2 0 0 2 > ||> 2.56 ||= Parizeksma ||=   ||   ||
=Music= 
[[http://eceserv0.ece.wisc.edu/%7Esethares/xentone.html|Ten Fingers]] <span class="ymp-btn-page-play ymp-media-0b41d890e4b2e2ea729c8a1c199295e9"><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/Sethares/Ten_Fingers.mp3|play]]//</span></span> by [[Bill Sethares]] (synth guitar)
[[http://eceserv0.ece.wisc.edu/%7Esethares/xentone.html|Circle of Thirds]] <span class="ymp-btn-page-play ymp-media-86d97882546354d45034d3c272cbb56c"><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/Sethares/Circle_of_Thirds.mp3|play]]//</span></span> by Bill Sethares (synth ens.)
[[http://www.akjmusic.com/works.html|10_fantasy]] <span class="ymp-btn-page-play ymp-media-9ccb949290bc6c1cc7c1a4be8065871d"><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/AKJ/10_fantasy.mp3|play]]//</span></span> by [[Aaron Krister Johnson]] (synth monody)
<span class="ymp-btn-page-play ymp-media-edd919cb4d239805e1b5cba4375a1e93"><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%2010ET.mp3|Prelude in 10ET]]//</span></span> by [[Aaron Andrew Hunt]]
[[http://www.ziaspace.com/ZIA/mp3s/Future.html|Future]] <span class="ymp-btn-page-play ymp-media-a5c7622ba1020de4aa13d58769a6c357"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://ziaspace.com/ZIA/mp3s/Future.mp3|play]]//</span></span> and [[http://www.ziaspace.com/ZIA/mp3s/Sol.html|Sol]] <span class="ymp-btn-page-play ymp-media-aa7c2b6de113578643d9a38ca7aa70e4"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://ziaspace.com/ZIA/mp3s/Sol.mp3|play]]//</span></span> by ZIA (synths and voice in 10)
<span class="ymp-btn-page-play ymp-media-08eecd4b04b03702c59dba2eb80c1428"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://azuma-asobi.com/Music/RhinoPrelude-2003-02-22.mp3|Prelude]]//</span></span> by [[Rick McGowan]] (Rhino synthesizer)
<span class="ymp-btn-page-play ymp-media-a9a8a238b39d19122886e0c933d01cca"><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/Igs/City%20Of%20The%20Asleep%20-%20Ideas%20on%20the%20Waterfall%20of%20Expression.mp3|Ideas on the Waterfall of Expression]]//</span></span> by Igliashon Jones (synth)
<span class="ymp-btn-page-play ymp-media-1824c99256ed13ed49cba489058a8493"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/10edo/daily20110713_q49_10_viola_duet_and_gongs.mp3|For two violas and gongs]]//</span></span> by [[@http://www.chrisvaisvil.com|Chris Vaisvil (website)]] [[@http://chrisvaisvil.com/?p=1039|more composition information]]
//[[http://www.seraph.it/dep/det/Blues10.mp3|Blues 10]]// by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/dd7ee3a756851e812778e2fb222b5c47-168.html|blog entry]])
//[[http://www.seraph.it/dep/det/Waltz10.mp3|Waltz 10]]// by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/875fbcf1467c4ed837ac1ba4b666d417-169.html|blog entry]])
//[[http://www.seraph.it/dep/det/Smooth10.mp3|Smooth 10]]// by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/65405f5999f3960d5704b83c7318c673-170.html|blog entry]])

[[file:10preview.ogg]] A sample of orchestral possibilities made using ZynAddSubFx under Linux (cenobyte)
[[file:decexperiment.ogg]]3 tracks made in ZynAddSubFx simply mixed in Audacity (cenobyte)
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/10edo/10_earwigs_invasive.mp3|10 Earwigs Invasive]]//</span> by [[@http://chrisvaisvil.com/?p=1397|Chris Vaisvil]]
<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/09%20-%209.%2010%20octave.mp3|Comets Over Flatland 9]]//</span> by [[Randy Winchester]]
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/10edo/daily20110923-10edo_dramatic_squirrel_overture.mp3|The Dramatic Squirrel Overture]]//</span> by [[Chris Vaisvil]] [[@http://chrisvaisvil.com/?p=1368|Details]]
[[@http://andrewheathwaite.bandcamp.com/track/shimmerwing|Shimmerwing]] by [[Andrew Heathwaite]] and [[Chris Vaisvil]]
//[[http://micro.soonlabel.com/gene_ward_smith/Others/Curley/Zach%20Curley%20-%20The%20Csx%20Freight%20at%201-20%20am.mp3|The Csx Freight at 1:20 am]]// by [[Zach Curley]]
[[http://soundcloud.com/martinsj013/sirmdbidnud2|Sirmdbidnud2 by martinsj013 on SoundCloud]]
[[@https://soundcloud.com/clem-fortuna/10tone|10tone demo]] by [[@http://clemfortuna.com|Clem Fortuna]]

=**Instruments**= 

10-EDO lends itself exceptionally well to guitar (and other fretted strings), on account of the fact that five of its flat 4ths (at 480 cents) exactly spans two octaves (480*5=2400), meaning the open strings can be uniformly tuned in 4ths. This allows for greater uniformity in chord and scale fingering patterns than in 12-TET, making it exceptionally easy to learn. For instance, the fingering for an "E" chord would be 0-2-2-1-0-0 (low to high), an "A" chord would be 0-0-2-2-1-0, and a "D" chord would be 1-0-0-2-2-1. This is also the case in all EDOs which are multiples of 5, but in 10-EDO it is particularly simple.

Retuning a convention keyboard to 10edo may be done in many ways, but neglecting or making redundant the Eb and Ab keys preserves the sLsLsLs scale on the white keys. Redundancy may make modulation easier, but another option is tuning the superfluous keys to selections from [[20edo]] which approximates the 11th harmonic with relative accuracy, among other features.

[[image:Decaphonic_Classic_Guitar.png caption="A Decaphonic (10-EDO) Classical Guitar"]][[image:decaphonic-uke.JPG width="526" height="406"]][[media type="custom" key="10021077"]]

Original HTML content:

<html><head><title>10edo</title></head><body><span style="display: block; text-align: right;"><a class="wiki_link" href="/10%E5%B9%B3%E5%9D%87%E5%BE%8B">日本語</a><br />
</span><br />
10edo, or 10-tone equal temperament, is a tuning system which divides the <a class="wiki_link" href="/octave">octave</a> into 10 equal parts of exactly 120 <a class="wiki_link" href="/cent">cent</a>s. It can be thought of as two circles of <a class="wiki_link" href="/5edo">5edo</a> separated by 120 cents (or 5 circles of <a class="wiki_link" href="/2edo">2edo</a>). It adds to 5edo a small neutral second (or large minor 2nd) and its inversion a large neutral seventh (or small major 7th); an excellent approximation of <a class="wiki_link" href="/13_8">13/8</a> and its inversion <a class="wiki_link" href="/16_13">16/13</a>; and the happy 600-cent tritone that appears in every even-numbered EDO. Taking the the 360 cent large neutral third as a generator produces a heptatonic <a class="wiki_link" href="/MOSScales">moment of symmetry scale</a> of the form 1 2 1 2 1 2 1 (<a class="wiki_link" href="/3L%204s">3L 4s - mosh</a>). While not an integral or gap edo, it is a <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta peak edo</a>. One way to interpret it in terms of a temperament of Just intonation is as a 2.7.13.15 subgroup, such that 105/104, 225/224, and 16807/16384 are tempered out. It can also be treated as a full 13-limit temperament, but it is a closer match to the aforementioned subgroup.<br />
<br />
<!-- ws:start:WikiTextTocRule:17:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --><a href="#toc0"></a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --> | <a href="#Images">Images</a><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --> | <a href="#Linear temperaments">Linear temperaments</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> | <a href="#Instruments">Instruments</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: -->
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 <!-- ws:start:WikiTextHeadingRule:5:&lt;h1&gt; --><h1 id="toc1"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:5 -->Intervals</h1>
 

<table class="wiki_table">
    <tr>
        <td>Degree<br />
</td>
        <td>Cents<br />
DMS<br />
</td>
        <td>Approximate<br />
Ratios*<br />
</td>
        <td>Additional Ratios of 3, 5 and 9<br />
</td>
        <td>Name<br />
</td>
    </tr>
    <tr>
        <td>0<br />
</td>
        <td>0<br />
0°<br />
</td>
        <td>1/1<br />
</td>
        <td>256/243, 50/49<br />
</td>
        <td>unison<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>120<br />
36°<br />
</td>
        <td>15/14, 16/15, 13/14<br />
</td>
        <td>10/9, 13/12, 81/80<br />
</td>
        <td>small neutral second/large minor second<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>240<br />
72°<br />
</td>
        <td>15/13, 8/7<br />
</td>
        <td>9/8, 7/6<br />
</td>
        <td>second/third<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>360<br />
108°<br />
</td>
        <td>16/13<br />
</td>
        <td>5/4<br />
</td>
        <td>large neutral third<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>480<br />
144°<br />
</td>
        <td>64/49, 169/128<br />
</td>
        <td>4/3, 9/7, 13/10<br />
</td>
        <td>smaller fourth<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>600<br />
180°<br />
</td>
        <td>91/64, 169/120<br />
</td>
        <td>7/5, 10/7, 13/9, 18/13<br />
</td>
        <td>tritone<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>720<br />
216°<br />
</td>
        <td>49/32, 256/169<br />
</td>
        <td>3/2, 14/9, 20/13<br />
</td>
        <td>bigger fifth<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>840<br />
252°<br />
</td>
        <td>13/8<br />
</td>
        <td>8/5<br />
</td>
        <td>neutral sixth<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>960<br />
288°<br />
</td>
        <td>7/4, 26/15, 125/72<br />
</td>
        <td>16/9, 12/7<br />
</td>
        <td>sixth/seventh<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>1080<br />
324°<br />
</td>
        <td>15/8, 28/15, 13/7<br />
</td>
        <td>9/5, 24/13, 160/81<br />
</td>
        <td>small major 7th<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>1200<br />
360°<br />
</td>
        <td>2/1<br />
</td>
        <td>243/128, 49/25<br />
</td>
        <td>octave<br />
</td>
    </tr>
</table>

*based on treating 10-EDO as a 2.7.13.15 subgroup temperament.<br />
adding the ratios of 3, 5 and 9 introduces greater <a class="wiki_link" href="/error">error</a> while giving several more harmonic identities to the 10-EDO intervals.<br />
<br />
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<!-- ws:start:WikiTextHeadingRule:7:&lt;h1&gt; --><h1 id="toc2"><a name="Images"></a><!-- ws:end:WikiTextHeadingRule:7 -->Images</h1>
 <br />
<!-- ws:start:WikiTextLocalImageRule:547:&lt;img src=&quot;/file/view/10edo%20wheel.png/516974684/280x285/10edo%20wheel.png&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 285px; width: 280px;&quot; /&gt; --><img src="/file/view/10edo%20wheel.png/516974684/280x285/10edo%20wheel.png" alt="10edo wheel.png" title="10edo wheel.png" style="height: 285px; width: 280px;" /><!-- ws:end:WikiTextLocalImageRule:547 --><br />
<br />
<!-- ws:start:WikiTextHeadingRule:9:&lt;h1&gt; --><h1 id="toc3"><a name="Linear temperaments"></a><!-- ws:end:WikiTextHeadingRule:9 -->Linear temperaments</h1>
 

<table class="wiki_table">
    <tr>
        <th>Periods<br />
per octave<br />
</th>
        <th>Generator<br />
</th>
        <th>Temperament(s)<br />
</th>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>1\10<br />
</td>
        <td>Messed-up <a class="wiki_link" href="/Negri">negri</a> (or <a class="wiki_link" href="/Miracle">miracle</a>)<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>3\10<br />
</td>
        <td><a class="wiki_link" href="/Dicot">Dicot</a>/<a class="wiki_link" href="/Beatles">beatles</a>/neutral thirds scale<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>1\10<br />
</td>
        <td>Messed-up <a class="wiki_link" href="/pajara">pajara</a><br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>2\10<br />
</td>
        <td><a class="wiki_link" href="/Decimal">Decimal</a> / messed-up <a class="wiki_link" href="/Lemba">lemba</a><br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>1\10<br />
</td>
        <td><a class="wiki_link" href="/Blackwood">Blackwood</a>/<a class="wiki_link" href="/blacksmith">blacksmith</a><br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:11:&lt;h1&gt; --><h1 id="toc4"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:11 -->Commas</h1>
 10 EDO tempers out the following commas. (Note: This assumes the val &lt; 10 16 23 28 35 37 |.)<br />
<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;">256/243<br />
</td>
        <td>| 8 -5 &gt;<br />
</td>
        <td style="text-align: right;">90.22<br />
</td>
        <td style="text-align: center;">Limma<br />
</td>
        <td style="text-align: center;">Pythagorean Minor 2nd<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">16875/16384<br />
</td>
        <td>| -14 3 4 &gt;<br />
</td>
        <td style="text-align: right;">51.12<br />
</td>
        <td style="text-align: center;">Negri Comma<br />
</td>
        <td style="text-align: center;">Double Augmentation Diesis<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">9931568/9752117<br />
</td>
        <td>| -25 7 6 &gt;<br />
</td>
        <td style="text-align: right;">31.57<br />
</td>
        <td style="text-align: center;">Ampersand's Comma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">2048/2025<br />
</td>
        <td>| 11 -4 -2 &gt;<br />
</td>
        <td style="text-align: right;">19.55<br />
</td>
        <td style="text-align: center;">Diaschisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">525/512<br />
</td>
        <td>| -9 1 2 1 &gt;<br />
</td>
        <td style="text-align: right;">43.41<br />
</td>
        <td style="text-align: center;">Avicennma<br />
</td>
        <td style="text-align: center;">Avicennma's Enharmonic Diesis<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">49/48<br />
</td>
        <td>| -4 -1 0 2 &gt;<br />
</td>
        <td style="text-align: right;">35.70<br />
</td>
        <td style="text-align: center;">Slendro Diesis<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">50/49<br />
</td>
        <td>| 1 0 2 -2 &gt;<br />
</td>
        <td style="text-align: right;">34.98<br />
</td>
        <td style="text-align: center;">Tritonic Diesis<br />
</td>
        <td style="text-align: center;">Jubilisma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">686/675<br />
</td>
        <td>| 1 -3 -2 3 &gt;<br />
</td>
        <td style="text-align: right;">27.99<br />
</td>
        <td style="text-align: center;">Senga<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">64/63<br />
</td>
        <td>| 6 -2 0 -1 &gt;<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>Leipziger Komma<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">9859966/9733137<br />
</td>
        <td>| -10 7 8 -7 &gt;<br />
</td>
        <td style="text-align: right;">22.41<br />
</td>
        <td style="text-align: center;">Blackjackisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1029/1024<br />
</td>
        <td>| -10 1 0 3 &gt;<br />
</td>
        <td style="text-align: right;">8.43<br />
</td>
        <td style="text-align: center;">Gamelisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">225/224<br />
</td>
        <td>| -5 2 2 -1 &gt;<br />
</td>
        <td style="text-align: right;">7.71<br />
</td>
        <td style="text-align: center;">Septimal Kleisma<br />
</td>
        <td style="text-align: center;">Marvel Comma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">16875/16807<br />
</td>
        <td>| 0 3 4 -5 &gt;<br />
</td>
        <td style="text-align: right;">6.99<br />
</td>
        <td style="text-align: center;">Mirkwai<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">6772805/6751042<br />
</td>
        <td>| 11 -10 -10 10 &gt;<br />
</td>
        <td style="text-align: right;">5.57<br />
</td>
        <td style="text-align: center;">Linus<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">2401/2400<br />
</td>
        <td>| -5 -1 -2 4 &gt;<br />
</td>
        <td style="text-align: right;">0.72<br />
</td>
        <td style="text-align: center;">Breedsma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">243/242<br />
</td>
        <td>| -1 5 0 0 -2 &gt;<br />
</td>
        <td style="text-align: right;">7.14<br />
</td>
        <td style="text-align: center;">Rastma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">385/384<br />
</td>
        <td>| -7 -1 1 1 1 &gt;<br />
</td>
        <td style="text-align: right;">4.50<br />
</td>
        <td style="text-align: center;">Keenanisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">441/440<br />
</td>
        <td>| -3 2 -1 2 -1 &gt;<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><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">540/539<br />
</td>
        <td>| 2 3 1 -2 -1 &gt;<br />
</td>
        <td style="text-align: right;">3.21<br />
</td>
        <td style="text-align: center;">Swetisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">3025/3024<br />
</td>
        <td>| -4 -3 2 -1 2 &gt;<br />
</td>
        <td style="text-align: right;">0.57<br />
</td>
        <td style="text-align: center;">Lehmerisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">91/90<br />
</td>
        <td>| -1 -2 -1 1 0 1 &gt;<br />
</td>
        <td style="text-align: right;">19.13<br />
</td>
        <td style="text-align: center;">Superleap<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">676/675<br />
</td>
        <td>| 2 -3 -2 0 0 2 &gt;<br />
</td>
        <td style="text-align: right;">2.56<br />
</td>
        <td style="text-align: center;">Parizeksma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:13:&lt;h1&gt; --><h1 id="toc5"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:13 -->Music</h1>
 <a class="wiki_link_ext" href="http://eceserv0.ece.wisc.edu/%7Esethares/xentone.html" rel="nofollow">Ten Fingers</a> <span class="ymp-btn-page-play ymp-media-0b41d890e4b2e2ea729c8a1c199295e9"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/Ten_Fingers.mp3" rel="nofollow">play</a></em></span></span> by <a class="wiki_link" href="/Bill%20Sethares">Bill Sethares</a> (synth guitar)<br />
<a class="wiki_link_ext" href="http://eceserv0.ece.wisc.edu/%7Esethares/xentone.html" rel="nofollow">Circle of Thirds</a> <span class="ymp-btn-page-play ymp-media-86d97882546354d45034d3c272cbb56c"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/Circle_of_Thirds.mp3" rel="nofollow">play</a></em></span></span> by Bill Sethares (synth ens.)<br />
<a class="wiki_link_ext" href="http://www.akjmusic.com/works.html" rel="nofollow">10_fantasy</a> <span class="ymp-btn-page-play ymp-media-9ccb949290bc6c1cc7c1a4be8065871d"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/AKJ/10_fantasy.mp3" rel="nofollow">play</a></em></span></span> by <a class="wiki_link" href="/Aaron%20Krister%20Johnson">Aaron Krister Johnson</a> (synth monody)<br />
<span class="ymp-btn-page-play ymp-media-edd919cb4d239805e1b5cba4375a1e93"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Hunt/Prelude%20in%2010ET.mp3" rel="nofollow">Prelude in 10ET</a></em></span></span> by <a class="wiki_link" href="/Aaron%20Andrew%20Hunt">Aaron Andrew Hunt</a><br />
<a class="wiki_link_ext" href="http://www.ziaspace.com/ZIA/mp3s/Future.html" rel="nofollow">Future</a> <span class="ymp-btn-page-play ymp-media-a5c7622ba1020de4aa13d58769a6c357"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://ziaspace.com/ZIA/mp3s/Future.mp3" rel="nofollow">play</a></em></span></span> and <a class="wiki_link_ext" href="http://www.ziaspace.com/ZIA/mp3s/Sol.html" rel="nofollow">Sol</a> <span class="ymp-btn-page-play ymp-media-aa7c2b6de113578643d9a38ca7aa70e4"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://ziaspace.com/ZIA/mp3s/Sol.mp3" rel="nofollow">play</a></em></span></span> by ZIA (synths and voice in 10)<br />
<span class="ymp-btn-page-play ymp-media-08eecd4b04b03702c59dba2eb80c1428"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://azuma-asobi.com/Music/RhinoPrelude-2003-02-22.mp3" rel="nofollow">Prelude</a></em></span></span> by <a class="wiki_link" href="/Rick%20McGowan">Rick McGowan</a> (Rhino synthesizer)<br />
<span class="ymp-btn-page-play ymp-media-a9a8a238b39d19122886e0c933d01cca"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%20Ideas%20on%20the%20Waterfall%20of%20Expression.mp3" rel="nofollow">Ideas on the Waterfall of Expression</a></em></span></span> by Igliashon Jones (synth)<br />
<span class="ymp-btn-page-play ymp-media-1824c99256ed13ed49cba489058a8493"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/10edo/daily20110713_q49_10_viola_duet_and_gongs.mp3" rel="nofollow">For two violas and gongs</a></em></span></span> by <a class="wiki_link_ext" href="http://www.chrisvaisvil.com" rel="nofollow" target="_blank">Chris Vaisvil (website)</a> <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=1039" rel="nofollow" target="_blank">more composition information</a><br />
<em><a class="wiki_link_ext" href="http://www.seraph.it/dep/det/Blues10.mp3" rel="nofollow">Blues 10</a></em> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a> (<a class="wiki_link_ext" href="http://www.seraph.it/blog_files/dd7ee3a756851e812778e2fb222b5c47-168.html" rel="nofollow">blog entry</a>)<br />
<em><a class="wiki_link_ext" href="http://www.seraph.it/dep/det/Waltz10.mp3" rel="nofollow">Waltz 10</a></em> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a> (<a class="wiki_link_ext" href="http://www.seraph.it/blog_files/875fbcf1467c4ed837ac1ba4b666d417-169.html" rel="nofollow">blog entry</a>)<br />
<em><a class="wiki_link_ext" href="http://www.seraph.it/dep/det/Smooth10.mp3" rel="nofollow">Smooth 10</a></em> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a> (<a class="wiki_link_ext" href="http://www.seraph.it/blog_files/65405f5999f3960d5704b83c7318c673-170.html" rel="nofollow">blog entry</a>)<br />
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<!-- ws:start:WikiTextFileRule:551:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file/10preview.ogg?h=52&amp;w=320&quot; class=&quot;WikiFile&quot; id=&quot;wikitext@@file@@10preview.ogg&quot; title=&quot;File: 10preview.ogg&quot; width=&quot;320&quot; height=&quot;52&quot; /&gt; --><div class="objectEmbed"><a href="/file/view/10preview.ogg/246873297/10preview.ogg" onclick="ws.common.trackFileLink('/file/view/10preview.ogg/246873297/10preview.ogg');"><img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="10preview.ogg" /></a><div><a href="/file/view/10preview.ogg/246873297/10preview.ogg" onclick="ws.common.trackFileLink('/file/view/10preview.ogg/246873297/10preview.ogg');" class="filename" title="10preview.ogg">10preview.ogg</a><br /><ul><li><a href="/file/detail/10preview.ogg">Details</a></li><li><a href="/file/view/10preview.ogg/246873297/10preview.ogg">Download</a></li><li style="color: #666">3 MB</li></ul></div></div><!-- ws:end:WikiTextFileRule:551 --> A sample of orchestral possibilities made using ZynAddSubFx under Linux (cenobyte)<br />
<!-- ws:start:WikiTextFileRule:552:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file/decexperiment.ogg?h=52&amp;w=320&quot; class=&quot;WikiFile&quot; id=&quot;wikitext@@file@@decexperiment.ogg&quot; title=&quot;File: decexperiment.ogg&quot; width=&quot;320&quot; height=&quot;52&quot; /&gt; --><div class="objectEmbed"><a href="/file/view/decexperiment.ogg/246971619/decexperiment.ogg" onclick="ws.common.trackFileLink('/file/view/decexperiment.ogg/246971619/decexperiment.ogg');"><img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="decexperiment.ogg" /></a><div><a href="/file/view/decexperiment.ogg/246971619/decexperiment.ogg" onclick="ws.common.trackFileLink('/file/view/decexperiment.ogg/246971619/decexperiment.ogg');" class="filename" title="decexperiment.ogg">decexperiment.ogg</a><br /><ul><li><a href="/file/detail/decexperiment.ogg">Details</a></li><li><a href="/file/view/decexperiment.ogg/246971619/decexperiment.ogg">Download</a></li><li style="color: #666">2 MB</li></ul></div></div><!-- ws:end:WikiTextFileRule:552 -->3 tracks made in ZynAddSubFx simply mixed in Audacity (cenobyte)<br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/10edo/10_earwigs_invasive.mp3" rel="nofollow">10 Earwigs Invasive</a></em></span> by <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=1397" rel="nofollow" target="_blank">Chris Vaisvil</a><br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/09%20-%209.%2010%20octave.mp3" rel="nofollow">Comets Over Flatland 9</a></em></span> by <a class="wiki_link" href="/Randy%20Winchester">Randy Winchester</a><br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/10edo/daily20110923-10edo_dramatic_squirrel_overture.mp3" rel="nofollow">The Dramatic Squirrel Overture</a></em></span> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a> <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=1368" rel="nofollow" target="_blank">Details</a><br />
<a class="wiki_link_ext" href="http://andrewheathwaite.bandcamp.com/track/shimmerwing" rel="nofollow" target="_blank">Shimmerwing</a> by <a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a> and <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br />
<em><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Curley/Zach%20Curley%20-%20The%20Csx%20Freight%20at%201-20%20am.mp3" rel="nofollow">The Csx Freight at 1:20 am</a></em> by <a class="wiki_link" href="/Zach%20Curley">Zach Curley</a><br />
<a class="wiki_link_ext" href="http://soundcloud.com/martinsj013/sirmdbidnud2" rel="nofollow">Sirmdbidnud2 by martinsj013 on SoundCloud</a><br />
<a class="wiki_link_ext" href="https://soundcloud.com/clem-fortuna/10tone" rel="nofollow" target="_blank">10tone demo</a> by <a class="wiki_link_ext" href="http://clemfortuna.com" rel="nofollow" target="_blank">Clem Fortuna</a><br />
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<!-- ws:start:WikiTextHeadingRule:15:&lt;h1&gt; --><h1 id="toc6"><a name="Instruments"></a><!-- ws:end:WikiTextHeadingRule:15 --><strong>Instruments</strong></h1>
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10-EDO lends itself exceptionally well to guitar (and other fretted strings), on account of the fact that five of its flat 4ths (at 480 cents) exactly spans two octaves (480*5=2400), meaning the open strings can be uniformly tuned in 4ths. This allows for greater uniformity in chord and scale fingering patterns than in 12-TET, making it exceptionally easy to learn. For instance, the fingering for an &quot;E&quot; chord would be 0-2-2-1-0-0 (low to high), an &quot;A&quot; chord would be 0-0-2-2-1-0, and a &quot;D&quot; chord would be 1-0-0-2-2-1. This is also the case in all EDOs which are multiples of 5, but in 10-EDO it is particularly simple.<br />
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Retuning a convention keyboard to 10edo may be done in many ways, but neglecting or making redundant the Eb and Ab keys preserves the sLsLsLs scale on the white keys. Redundancy may make modulation easier, but another option is tuning the superfluous keys to selections from <a class="wiki_link" href="/20edo">20edo</a> which approximates the 11th harmonic with relative accuracy, among other features.<br />
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<!-- ws:start:WikiTextLocalImageRule:548:&lt;img src=&quot;/file/view/Decaphonic_Classic_Guitar.png/234752078/Decaphonic_Classic_Guitar.png&quot; alt=&quot;A Decaphonic (10-EDO) Classical Guitar&quot; title=&quot;A Decaphonic (10-EDO) Classical Guitar&quot; /&gt; --><table class="captionBox"><tr><td class="captionedImage"><img src="/file/view/Decaphonic_Classic_Guitar.png/234752078/Decaphonic_Classic_Guitar.png" alt="Decaphonic_Classic_Guitar.png" title="Decaphonic_Classic_Guitar.png" /></td></tr><tr><td class="imageCaption">A Decaphonic (10-EDO) Classical Guitar</td></tr></table><!-- ws:end:WikiTextLocalImageRule:548 --><!-- ws:start:WikiTextLocalImageRule:549:&lt;img src=&quot;/file/view/decaphonic-uke.JPG/251070060/526x406/decaphonic-uke.JPG&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 406px; width: 526px;&quot; /&gt; --><img src="/file/view/decaphonic-uke.JPG/251070060/526x406/decaphonic-uke.JPG" alt="decaphonic-uke.JPG" title="decaphonic-uke.JPG" style="height: 406px; width: 526px;" /><!-- ws:end:WikiTextLocalImageRule:549 --><!-- ws:start:WikiTextMediaRule:2:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/10021077?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;10021077&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><script type="text/javascript" src="http://webplayer.yahooapis.com/player.js">
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