29edo: Difference between revisions

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[[@http://www.microtonalismo.com/|Guitar 29EDO]][[toc|flat]]

----

=<span style="color: #ff4700; font-family: 'Times New Roman',Times,serif; font-size: 113%;">29 tone equal temperament</span>= 

29edo divides the 2:1 [[xenharmonic/octave|octave]] into 29 equal steps of approximately 41.37931 [[cent|cents]]. It is the 10th [[prime numbers|prime]] edo, following [[23edo]] and coming before [[31edo]].

29 is the lowest edo which approximates the [[xenharmonic/3_2|3:2]] just fifth more accurately than [[xenharmonic/12edo|12edo]]: 3/2 = 701.955... cents; 17 degrees of 29edo = 703.448... cents. Since the fifth is slightly sharp, 29edo is a [[xenharmonic/positive temperament|positive temperament]] -- a Superpythagorean instead of a Meantone system.

The 3 is the only harmonic, of the intelligibly low ones anyway, that 29edo approximates very closely, and it does so quite well. Nonetheless, and rather surprisingly, 29 is the smallest equal division which [[xenharmonic/consistent|consistent]]ly represents the 15 odd limit. It is able to do this since it has an accurate 3, and the 5, 7, 11 and 13, while not very accurate, are all tuned flatly. Hence it tempers out a succession of fairly large commas: 250/243 in the [[xenharmonic/5-limit|5-limit]], 49/48 in the [[xenharmonic/7-limit|7-limit]], 55/54 in the [[xenharmonic/11-limit|11-limit]], and 65/64 in the [[xenharmonic/13-limit|13-limit]]. If using these approximations is desired, 29edo actually shines, and it can be used for such things as an alternative to [[xenharmonic/19edo|19edo]] for [[xenharmonic/Marvel temperaments|negri]], as well as an alternative to [[xenharmonic/22edo|22edo]] or [[xenharmonic/15edo|15edo]] for porcupine. For those who enjoy the bizarre character of Father temperament, 29edo can also be used to support that temperament, if one imagines 11\29 is approximating both 5/4 and 4/3 (ignoring the better approximations at 10\29 and 12\29, respectively).

Another possible use for 29edo is as an equally tempered para-pythagorean scale. Using its fifth as a generator leads to a variant of [[xenharmonic/Schismatic family|garibaldi temperament]] which is not very accurate but which has relatively low 13-limit complexity.

Moreover, it represents the 2.3.11/5.13/5 subgroup to very high accuracy, and 2.3.7/5.11/5.13/5 to a lesser but still good accuracy, and so can be used with this subgroup, which is liberally supplied with chords such as the 1-11/7-13/7 (7:11:13) chord, the [[xenharmonic/The Archipelago|barbados triad]] 1-13/10-3/2 (10:13:15), the minor barbados triad 1-15/13-3/2, the 1-14/11-3/2 (22:28:33) triad, the 1-13/11-3/2 triad (22:26:33), and the [[xenharmonic/petrmic triad|petrmic triad]], a 13-limit [[xenharmonic/Dyadic chord|essentially tempered dyadic chord]]. 29 tempers out 352/351, 676/675 and 4000/3993 from the 2.3.11/5.13/5 subgroup, and in addition 196/195 and 364/363 from the 2.3.7/5.11/5.13/5 subgroup, so we have various relationships from the tempering, such as the fact that the 1-13/11-3/2 chord and the 1-14/11-3/2 chord are inverses of each other, a major-minor pairing. A larger subgroup containing both of these subgroups is the [[xenharmonic/k*N subgroups|3*29 subgroup]] 2.3.125.175.275.325; on this subgroup 29 tunes the same as 87, and the commas of 29 on this subgroup are the same as the 13-limit commas of 87. Still another subgroup of interest is the [[xenharmonic/k*N subgroups|2*29 subgroup]] 2.3.25.35.55.65.85; on this subgroup 29 tunes the same as 58 and has the same 17-limit commas.

=Intervals and linear temperaments= 
[[List of 29et rank two temperaments by badness]]

||~ Degrees of 29-EDO ||~ Cents value ||~ Approx. ratios of the [[15-limit]] ||~ Generator for temperaments ||
|| 0 || 0 || 1/1 ||   ||
|| 1 || 41.379 ||   ||   ||
|| 2 || 82.759 ||   || [[xenharmonic/Nautilus|Nautilus]] ||
|| 3 || 124.138 || 16/15, 15/14, 14/13, 13/12 || [[xenharmonic/Negri|Negri]]/[[xenharmonic/Negril|Negril]] ||
|| 4 || 165.517 || 12/11, 11/10 || [[xenharmonic/Porcupine|Porcupine]]/[[xenharmonic/Porky|Porky]]/[[xenharmonic/Coendou|Coendou]] ||
|| 5 || 206.897 || 9/8 ||   ||
|| 6 || 248.276 || 8/7, 7/6, 15/13 || [[xenharmonic/Chromatic pairs#Bridgetown|Bridgetown]]/[[xenharmonic/Immunity|Immunity]] ||
|| 7· || 289.655 || 13/11 ||   ||
|| 8 || 331.034 || 6/5, 11/9 ||   ||
|| 9 || 372.414 || 5/4, 16/13 ||   ||
|| 10 || 413.793 || 14/11 || [[xenharmonic/Roman|Roman]] ||
|| 11 || 455.172 || 9/7, 13/10 || [[xenharmonic/Ammonite|Ammonite]] ||
|| 12· || 496.552 || 4/3 || [[xenharmonic/Helmholtz|Helmholtz]]/[[xenharmonic/Garibaldi|Garibaldi]]/[[xenharmonic/Cassandra|Cassandra]]/[[xenharmonic/Leapday|Leapday]] ||
|| 13 || 537.931 || 11/8, 15/11 ||   ||
|| 14 || 579.310 || 7/5, 18/13 || [[xenharmonic/Tritonic|Tritonic]] ||
|| 15 || 620.690 || 10/7, 13/9 ||   ||
|| 16 || 662.069 || 16/11, 22/15 ||   ||
|| 17· || 703.448 || 3/2 ||   ||
|| 18 || 744.828 || 14/9, 20/13 ||   ||
|| 19 || 786.207 || 11/7 ||   ||
|| 20 || 827.586 || 8/5, 13/8 ||   ||
|| 21 || 868.966 || 5/3, 18/11 ||   ||
|| 22· || 910.345 || 22/13 ||   ||
|| 23 || 951.724 || 7/4, 12/7, 26/15 ||   ||
|| 24 || 993.103 || 16/9 ||   ||
|| 25 || 1034.483 || 11/6, 20/11 ||   ||
|| 26 || 1075.862 || 15/8, 28/15, 13/7, 24/13 ||   ||
|| 27 || 1117.241 ||   ||   ||
|| 28 || 1158.621 ||   ||   ||
See also: [[29edo solfege]]
[[image:29edothumb.png caption="this example in Sagittal notation shows 29-edo as a fifth-tone system."]]

=Commas= 
29 EDO tempers out the following commas. (Note: This assumes the val < 29 46 67 81 100 107 |, cent values rounded to 5 digits.)
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||
||= 16875/16384 || | -14 3 4 > ||> 51.120 ||= Negri Comma ||= Double Augmentation Diesis ||
||= 250/243 || | 1 -5 3 > ||> 49.166 ||= Maximal Diesis ||= Porcupine Comma ||
||= 32805/32768 || | -15 8 1 > ||> 1.9537 ||= Schisma ||=   ||
||= 525/512 || | -9 1 2 1 > ||> 43.408 ||= Avicennma ||= Avicenna's Enharmonic Diesis ||
||= 49/48 || | -4 -1 0 2 > ||> 35.697 ||= Slendro Diesis ||=   ||
||= 686/675 || | 1 -3 -2 3 > ||> 27.985 ||= Senga ||=   ||
||= 64827/64000 || | -9 3 -3 4 > ||> 22.227 ||= Squalentine ||=   ||
||= 3125/3087 || | 0 -2 5 -3 > ||> 21.181 ||= Gariboh ||=   ||
||= 50421/50000 || | -4 1 -5 5 > ||> 14.516 ||= Trimyna ||=   ||
||= 4000/3969 || | 5 -4 3 -2 > ||> 13.469 ||= Octagar ||=   ||
||= 225/224 || | -5 2 2 -1 > ||> 7.7115 ||= Septimal Kleisma ||= Marvel Comma ||
||= 5120/5103 || | 10 -6 1 -1 > ||> 5.7578 ||= Hemifamity ||=   ||
||= 4994735/4983772 || | 25 -14 0 -1 > ||> 3.8041 ||= Garischisma ||=   ||
||= 100/99 || | 2 -2 2 0 -1 > ||> 17.399 ||= Ptolemisma ||=   ||
||= 121/120 || | -3 -1 -1 0 2 > ||> 14.367 ||= Biyatisma ||=   ||
||= 896/891 || | 7 -4 0 1 -1 > ||> 9.6880 ||= Pentacircle ||=   ||
||= 441/440 || | -3 2 -1 2 -1 > ||> 3.9302 ||= Werckisma ||=   ||
||= 4000/3993 || | 5 -1 3 0 -3 > ||> 3.0323 ||= Wizardharry ||=   ||
||= 9801/9800 || | -3 4 -2 -2 2 > ||> 0.17665 ||= Kalisma ||= Gauss' Comma ||
||= 91/90 || | -1 -2 -1 1 0 1 > ||> 19.130 ||= Superleap ||=   ||

=Scales= 
[[xenharmonic/bridgetown9|bridgetown9]]
[[xenharmonic/bridgetown14|bridgetown14]]

=Music= 
[[http://www.microtonalismo.com/el-teclado-29-edo|Mp3 29EDO - Escala tonal de 17 notas]]by [[http://musicool.us/musicool/armonia.htm|Charles Loli A.]]
[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/Paint%20in%20the%20Water%2029.mp3|Paint in the Water 29]] by [[xenharmonic/IgliashonJones|Igliashon Jones]]
[[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/NautilusReverie.mp3|Nautilus Reverie]] by [[IgliashonJones|Igliashon Calvin Jones-Coolidge]]
[[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Howling%20of%20the%20Holy.mp3|Howling of the Holy]] by [[xenharmonic/IgliashonJones|Igliashon Jones]]
[[http://micro.soonlabel.com/tuning-survey/daily20111026-bridgetown-14.mp3|Route 14 in Bridgetown]] by [[xenharmonic/Chris Vaisvil|Chris Vaisvil]]
[[http://www.angelfire.com/mo/oljare/images/crowning.mid|The Crowning Song]] by Mats Öljare
[[http://www.angelfire.com/mo/oljare/images/ninedays.mid|Nine Days Later]] by Mats Öljare
[[http://www.angelfire.com/mo/oljare/images/stranded.mid|Stranded at Sea]] by Mats Öljare

==Instruments== 
* ====**[[http://www.microtonalismo.com/proyecto-xvii|Guitar 29EDO from Peruvian - Charles Loli and Antonio Huamani]]**==== 
> ====[[image:http://a3.sphotos.ak.fbcdn.net/hphotos-ak-ash4/390283_319667331383904_100000219181856_1552582_422186605_n.jpg]]==== 
>

Original HTML content:

<html><head><title>29edo</title></head><body><a class="wiki_link_ext" href="http://www.microtonalismo.com/" rel="nofollow" target="_blank">Guitar 29EDO</a><!-- ws:start:WikiTextTocRule:16:&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:16 --><!-- ws:start:WikiTextTocRule:17: --><a href="#x29 tone equal temperament">29 tone equal temperament</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#Intervals and linear temperaments">Intervals and linear temperaments</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --> | <a href="#Scales">Scales</a><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: -->
<!-- ws:end:WikiTextTocRule:25 --><br />
<br />
<hr />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x29 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #ff4700; font-family: 'Times New Roman',Times,serif; font-size: 113%;">29 tone equal temperament</span></h1>
 <br />
29edo divides the 2:1 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/octave">octave</a> into 29 equal steps of approximately 41.37931 <a class="wiki_link" href="/cent">cents</a>. It is the 10th <a class="wiki_link" href="/prime%20numbers">prime</a> edo, following <a class="wiki_link" href="/23edo">23edo</a> and coming before <a class="wiki_link" href="/31edo">31edo</a>.<br />
<br />
29 is the lowest edo which approximates the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/3_2">3:2</a> just fifth more accurately than <a class="wiki_link" href="http://xenharmonic.wikispaces.com/12edo">12edo</a>: 3/2 = 701.955... cents; 17 degrees of 29edo = 703.448... cents. Since the fifth is slightly sharp, 29edo is a <a class="wiki_link" href="http://xenharmonic.wikispaces.com/positive%20temperament">positive temperament</a> -- a Superpythagorean instead of a Meantone system.<br />
<br />
The 3 is the only harmonic, of the intelligibly low ones anyway, that 29edo approximates very closely, and it does so quite well. Nonetheless, and rather surprisingly, 29 is the smallest equal division which <a class="wiki_link" href="http://xenharmonic.wikispaces.com/consistent">consistent</a>ly represents the 15 odd limit. It is able to do this since it has an accurate 3, and the 5, 7, 11 and 13, while not very accurate, are all tuned flatly. Hence it tempers out a succession of fairly large commas: 250/243 in the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/5-limit">5-limit</a>, 49/48 in the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/7-limit">7-limit</a>, 55/54 in the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/11-limit">11-limit</a>, and 65/64 in the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/13-limit">13-limit</a>. If using these approximations is desired, 29edo actually shines, and it can be used for such things as an alternative to <a class="wiki_link" href="http://xenharmonic.wikispaces.com/19edo">19edo</a> for <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Marvel%20temperaments">negri</a>, as well as an alternative to <a class="wiki_link" href="http://xenharmonic.wikispaces.com/22edo">22edo</a> or <a class="wiki_link" href="http://xenharmonic.wikispaces.com/15edo">15edo</a> for porcupine. For those who enjoy the bizarre character of Father temperament, 29edo can also be used to support that temperament, if one imagines 11\29 is approximating both 5/4 and 4/3 (ignoring the better approximations at 10\29 and 12\29, respectively).<br />
<br />
Another possible use for 29edo is as an equally tempered para-pythagorean scale. Using its fifth as a generator leads to a variant of <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Schismatic%20family">garibaldi temperament</a> which is not very accurate but which has relatively low 13-limit complexity.<br />
<br />
Moreover, it represents the 2.3.11/5.13/5 subgroup to very high accuracy, and 2.3.7/5.11/5.13/5 to a lesser but still good accuracy, and so can be used with this subgroup, which is liberally supplied with chords such as the 1-11/7-13/7 (7:11:13) chord, the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/The%20Archipelago">barbados triad</a> 1-13/10-3/2 (10:13:15), the minor barbados triad 1-15/13-3/2, the 1-14/11-3/2 (22:28:33) triad, the 1-13/11-3/2 triad (22:26:33), and the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/petrmic%20triad">petrmic triad</a>, a 13-limit <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Dyadic%20chord">essentially tempered dyadic chord</a>. 29 tempers out 352/351, 676/675 and 4000/3993 from the 2.3.11/5.13/5 subgroup, and in addition 196/195 and 364/363 from the 2.3.7/5.11/5.13/5 subgroup, so we have various relationships from the tempering, such as the fact that the 1-13/11-3/2 chord and the 1-14/11-3/2 chord are inverses of each other, a major-minor pairing. A larger subgroup containing both of these subgroups is the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/k%2AN%20subgroups">3*29 subgroup</a> 2.3.125.175.275.325; on this subgroup 29 tunes the same as 87, and the commas of 29 on this subgroup are the same as the 13-limit commas of 87. Still another subgroup of interest is the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/k%2AN%20subgroups">2*29 subgroup</a> 2.3.25.35.55.65.85; on this subgroup 29 tunes the same as 58 and has the same 17-limit commas.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Intervals and linear temperaments"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals and linear temperaments</h1>
 <a class="wiki_link" href="/List%20of%2029et%20rank%20two%20temperaments%20by%20badness">List of 29et rank two temperaments by badness</a><br />
<br />


<table class="wiki_table">
    <tr>
        <th>Degrees of 29-EDO<br />
</th>
        <th>Cents value<br />
</th>
        <th>Approx. ratios of the <a class="wiki_link" href="/15-limit">15-limit</a><br />
</th>
        <th>Generator for temperaments<br />
</th>
    </tr>
    <tr>
        <td>0<br />
</td>
        <td>0<br />
</td>
        <td>1/1<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>41.379<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>82.759<br />
</td>
        <td><br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Nautilus">Nautilus</a><br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>124.138<br />
</td>
        <td>16/15, 15/14, 14/13, 13/12<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Negri">Negri</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Negril">Negril</a><br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>165.517<br />
</td>
        <td>12/11, 11/10<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Porcupine">Porcupine</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Porky">Porky</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Coendou">Coendou</a><br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>206.897<br />
</td>
        <td>9/8<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>248.276<br />
</td>
        <td>8/7, 7/6, 15/13<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Chromatic%20pairs#Bridgetown">Bridgetown</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Immunity">Immunity</a><br />
</td>
    </tr>
    <tr>
        <td>7·<br />
</td>
        <td>289.655<br />
</td>
        <td>13/11<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>331.034<br />
</td>
        <td>6/5, 11/9<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>372.414<br />
</td>
        <td>5/4, 16/13<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>413.793<br />
</td>
        <td>14/11<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Roman">Roman</a><br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>455.172<br />
</td>
        <td>9/7, 13/10<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ammonite">Ammonite</a><br />
</td>
    </tr>
    <tr>
        <td>12·<br />
</td>
        <td>496.552<br />
</td>
        <td>4/3<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Helmholtz">Helmholtz</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Garibaldi">Garibaldi</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Cassandra">Cassandra</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Leapday">Leapday</a><br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>537.931<br />
</td>
        <td>11/8, 15/11<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>579.310<br />
</td>
        <td>7/5, 18/13<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Tritonic">Tritonic</a><br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>620.690<br />
</td>
        <td>10/7, 13/9<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>662.069<br />
</td>
        <td>16/11, 22/15<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>17·<br />
</td>
        <td>703.448<br />
</td>
        <td>3/2<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>744.828<br />
</td>
        <td>14/9, 20/13<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>786.207<br />
</td>
        <td>11/7<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>827.586<br />
</td>
        <td>8/5, 13/8<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>868.966<br />
</td>
        <td>5/3, 18/11<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>22·<br />
</td>
        <td>910.345<br />
</td>
        <td>22/13<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>951.724<br />
</td>
        <td>7/4, 12/7, 26/15<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>993.103<br />
</td>
        <td>16/9<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>1034.483<br />
</td>
        <td>11/6, 20/11<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>1075.862<br />
</td>
        <td>15/8, 28/15, 13/7, 24/13<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>1117.241<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>1158.621<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
</table>

See also: <a class="wiki_link" href="/29edo%20solfege">29edo solfege</a><br />
<!-- ws:start:WikiTextLocalImageRule:590:&lt;img src=&quot;/file/view/29edothumb.png/277524658/29edothumb.png&quot; alt=&quot;this example in Sagittal notation shows 29-edo as a fifth-tone system.&quot; title=&quot;this example in Sagittal notation shows 29-edo as a fifth-tone system.&quot; /&gt; --><table class="captionBox"><tr><td class="captionedImage"><img src="/file/view/29edothumb.png/277524658/29edothumb.png" alt="29edothumb.png" title="29edothumb.png" /></td></tr><tr><td class="imageCaption">this example in Sagittal notation shows 29-edo as a fifth-tone system.</td></tr></table><!-- ws:end:WikiTextLocalImageRule:590 --><br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:4 -->Commas</h1>
 29 EDO tempers out the following commas. (Note: This assumes the val &lt; 29 46 67 81 100 107 |, cent values rounded to 5 digits.)<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>
    </tr>
    <tr>
        <td style="text-align: center;">16875/16384<br />
</td>
        <td>| -14 3 4 &gt;<br />
</td>
        <td style="text-align: right;">51.120<br />
</td>
        <td style="text-align: center;">Negri Comma<br />
</td>
        <td style="text-align: center;">Double Augmentation Diesis<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">250/243<br />
</td>
        <td>| 1 -5 3 &gt;<br />
</td>
        <td style="text-align: right;">49.166<br />
</td>
        <td style="text-align: center;">Maximal Diesis<br />
</td>
        <td style="text-align: center;">Porcupine Comma<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">32805/32768<br />
</td>
        <td>| -15 8 1 &gt;<br />
</td>
        <td style="text-align: right;">1.9537<br />
</td>
        <td style="text-align: center;">Schisma<br />
</td>
        <td style="text-align: center;"><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;">43.408<br />
</td>
        <td style="text-align: center;">Avicennma<br />
</td>
        <td style="text-align: center;">Avicenna's Enharmonic Diesis<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;">35.697<br />
</td>
        <td style="text-align: center;">Slendro Diesis<br />
</td>
        <td style="text-align: center;"><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;">27.985<br />
</td>
        <td style="text-align: center;">Senga<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">64827/64000<br />
</td>
        <td>| -9 3 -3 4 &gt;<br />
</td>
        <td style="text-align: right;">22.227<br />
</td>
        <td style="text-align: center;">Squalentine<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">3125/3087<br />
</td>
        <td>| 0 -2 5 -3 &gt;<br />
</td>
        <td style="text-align: right;">21.181<br />
</td>
        <td style="text-align: center;">Gariboh<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">50421/50000<br />
</td>
        <td>| -4 1 -5 5 &gt;<br />
</td>
        <td style="text-align: right;">14.516<br />
</td>
        <td style="text-align: center;">Trimyna<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">4000/3969<br />
</td>
        <td>| 5 -4 3 -2 &gt;<br />
</td>
        <td style="text-align: right;">13.469<br />
</td>
        <td style="text-align: center;">Octagar<br />
</td>
        <td style="text-align: center;"><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;">7.7115<br />
</td>
        <td style="text-align: center;">Septimal Kleisma<br />
</td>
        <td style="text-align: center;">Marvel Comma<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">5120/5103<br />
</td>
        <td>| 10 -6 1 -1 &gt;<br />
</td>
        <td style="text-align: right;">5.7578<br />
</td>
        <td style="text-align: center;">Hemifamity<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">4994735/4983772<br />
</td>
        <td>| 25 -14 0 -1 &gt;<br />
</td>
        <td style="text-align: right;">3.8041<br />
</td>
        <td style="text-align: center;">Garischisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">100/99<br />
</td>
        <td>| 2 -2 2 0 -1 &gt;<br />
</td>
        <td style="text-align: right;">17.399<br />
</td>
        <td style="text-align: center;">Ptolemisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">121/120<br />
</td>
        <td>| -3 -1 -1 0 2 &gt;<br />
</td>
        <td style="text-align: right;">14.367<br />
</td>
        <td style="text-align: center;">Biyatisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">896/891<br />
</td>
        <td>| 7 -4 0 1 -1 &gt;<br />
</td>
        <td style="text-align: right;">9.6880<br />
</td>
        <td style="text-align: center;">Pentacircle<br />
</td>
        <td style="text-align: center;"><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;">3.9302<br />
</td>
        <td style="text-align: center;">Werckisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">4000/3993<br />
</td>
        <td>| 5 -1 3 0 -3 &gt;<br />
</td>
        <td style="text-align: right;">3.0323<br />
</td>
        <td style="text-align: center;">Wizardharry<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">9801/9800<br />
</td>
        <td>| -3 4 -2 -2 2 &gt;<br />
</td>
        <td style="text-align: right;">0.17665<br />
</td>
        <td style="text-align: center;">Kalisma<br />
</td>
        <td style="text-align: center;">Gauss' Comma<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;">19.130<br />
</td>
        <td style="text-align: center;">Superleap<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Scales"></a><!-- ws:end:WikiTextHeadingRule:6 -->Scales</h1>
 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/bridgetown9">bridgetown9</a><br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/bridgetown14">bridgetown14</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:8 -->Music</h1>
 <a class="wiki_link_ext" href="http://www.microtonalismo.com/el-teclado-29-edo" rel="nofollow">Mp3 29EDO - Escala tonal de 17 notas</a>by <a class="wiki_link_ext" href="http://musicool.us/musicool/armonia.htm" rel="nofollow">Charles Loli A.</a><br />
<a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/Paint%20in%20the%20Water%2029.mp3" rel="nofollow">Paint in the Water 29</a> by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/IgliashonJones">Igliashon Jones</a><br />
<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Igs/NautilusReverie.mp3" rel="nofollow">Nautilus Reverie</a> by <a class="wiki_link" href="/IgliashonJones">Igliashon Calvin Jones-Coolidge</a><br />
<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Howling%20of%20the%20Holy.mp3" rel="nofollow">Howling of the Holy</a> by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/IgliashonJones">Igliashon Jones</a><br />
<a class="wiki_link_ext" href="http://micro.soonlabel.com/tuning-survey/daily20111026-bridgetown-14.mp3" rel="nofollow">Route 14 in Bridgetown</a> by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Chris%20Vaisvil">Chris Vaisvil</a><br />
<a class="wiki_link_ext" href="http://www.angelfire.com/mo/oljare/images/crowning.mid" rel="nofollow">The Crowning Song</a> by Mats Öljare<br />
<a class="wiki_link_ext" href="http://www.angelfire.com/mo/oljare/images/ninedays.mid" rel="nofollow">Nine Days Later</a> by Mats Öljare<br />
<a class="wiki_link_ext" href="http://www.angelfire.com/mo/oljare/images/stranded.mid" rel="nofollow">Stranded at Sea</a> by Mats Öljare<br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Music-Instruments"></a><!-- ws:end:WikiTextHeadingRule:10 -->Instruments</h2>
 <ul><li><!-- ws:start:WikiTextHeadingRule:12:&lt;h4&gt; --><h4 id="toc6"><a name="Music-Instruments--Guitar 29EDO from Peruvian - Charles Loli and Antonio Huamani"></a><!-- ws:end:WikiTextHeadingRule:12 --><strong><a class="wiki_link_ext" href="http://www.microtonalismo.com/proyecto-xvii" rel="nofollow">Guitar 29EDO from Peruvian - Charles Loli and Antonio Huamani</a></strong></h4>
<br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h4&gt; --><h4 id="toc7"><!-- ws:end:WikiTextHeadingRule:14 --><!-- ws:start:WikiTextRemoteImageRule:591:&lt;img src=&quot;http://a3.sphotos.ak.fbcdn.net/hphotos-ak-ash4/390283_319667331383904_100000219181856_1552582_422186605_n.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://a3.sphotos.ak.fbcdn.net/hphotos-ak-ash4/390283_319667331383904_100000219181856_1552582_422186605_n.jpg" alt="external image 390283_319667331383904_100000219181856_1552582_422186605_n.jpg" title="external image 390283_319667331383904_100000219181856_1552582_422186605_n.jpg" /><!-- ws:end:WikiTextRemoteImageRule:591 --></h4>
<br />
<br />
</li></ul></body></html>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-04-09 18:23:18 UTC</tt>.<br>
+: This revision was by author [[User:phylingual|phylingual]] and made on <tt>2012-06-10 16:04:44 UTC</tt>.<br>
-: The original revision id was <tt>318885978</tt>.<br>
+: The original revision id was <tt>344233142</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>
@@ Line 55: / Line 55: @@
 || 27 || 1117.241 ||   ||   ||
 || 28 || 1158.621 ||   ||   ||
+See also: [[29edo solfege]]
 [[image:29edothumb.png caption="this example in Sagittal notation shows 29-edo as a fifth-tone system."]]
@@ Line 425: / Line 426: @@
 &lt;/table&gt;
+See also: &lt;a class="wiki_link" href="/29edo%20solfege"&gt;29edo solfege&lt;/a&gt;&lt;br /&gt;
 &lt;!-- ws:start:WikiTextLocalImageRule:590:&amp;lt;img src=&amp;quot;/file/view/29edothumb.png/277524658/29edothumb.png&amp;quot; alt=&amp;quot;this example in Sagittal notation shows 29-edo as a fifth-tone system.&amp;quot; title=&amp;quot;this example in Sagittal notation shows 29-edo as a fifth-tone system.&amp;quot; /&amp;gt; --&gt;&lt;table class="captionBox"&gt;&lt;tr&gt;&lt;td class="captionedImage"&gt;&lt;img src="/file/view/29edothumb.png/277524658/29edothumb.png" alt="29edothumb.png" title="29edothumb.png" /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="imageCaption"&gt;this example in Sagittal notation shows 29-edo as a fifth-tone system.&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;!-- ws:end:WikiTextLocalImageRule:590 --&gt;&lt;br /&gt;
 &lt;br /&gt;

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