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<span style="display: block; text-align: right;">[[xenharmonie/29edo|Deutsch]]
</span>
[[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. However, it gives the POL2 generator for [[Chromatic pairs#Edson|edson temperaament]] with essentially perfect accuracy, only 0.034 cents sharp of it.

Edson is a 2.3.7/5.11/5.13/5 subgroup temperament, and 29 it represents the 2.3.11/5.13/5 subgroup to very high accuracy, and the 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 coarse/fine
DMS value ||~ Approx. ratios of the [[15-limit]] ||~ Generator for temperaments ||
|| 0 || 0
0° || 1/1 ||   ||
|| 1 || 41.379, 49.655
12°24'50" || 25/24~33/32~56/55~81/80 ||   ||
|| 2 || 82.759, 99.310
24°49'39" || 21/20 || [[xenharmonic/Nautilus|Nautilus]] ||
|| 3 || 124.138, [[tel/148.9655|148.9655]]
37°14'29" || 16/15, 15/14, 14/13, 13/12 || [[xenharmonic/Negri|Negri]]/[[xenharmonic/Negril|Negril]] ||
|| 4 || 165.517, 198.621
49°39'19" || 12/11, 11/10 || [[xenharmonic/Porcupine|Porcupine]]/[[xenharmonic/Porky|Porky]]/[[xenharmonic/Coendou|Coendou]] ||
|| 5 || 206.897, 248.276
62°4'8" || 9/8 ||   ||
|| 6 || 248.276, 297.391
74°28'58" || 8/7, 7/6, 15/13 || [[xenharmonic/Chromatic pairs#Bridgetown|Bridgetown]]/[[xenharmonic/Immunity|Immunity]] ||
|| 7· || 289.655, 347.586
86°53'48" || 13/11 ||   ||
|| 8 || [[tel/331.0345|331.0345]], 397.241
99°18'37" || 6/5, 11/9 ||   ||
|| 9 || 372.414, 446.896
111°43'27" || 5/4, 16/13 ||   ||
|| 10 || 413.793, 496.552
124°8'17" || 14/11 || [[xenharmonic/Roman|Roman]] ||
|| 11 || 455.172, 546.207
136°33'6" || 9/7, 13/10 || [[xenharmonic/Ammonite|Ammonite]] ||
|| 12· || 496.552, 595.862
148°57'56" || 4/3 || [[xenharmonic/Cassandra|Cassandra]] [[Chromatic pairs#Edson|Edson]] [[Chromatic pairs#Pepperoni|Pepperoni]] ||
|| 13 || 537.931, 645.517
161°21'46" || 11/8, 15/11 || [[Wilsec]] ||
|| 14 || 579.310, 695.172
173°46'35" || 7/5, 18/13 || [[xenharmonic/Tritonic|Tritonic]] ||
|| 15 || 620.690, 744.828
186°13'25" || 10/7, 13/9 ||   ||
|| 16 || 662.069, 794.483
198°38'14" || 16/11, 22/15 ||   ||
|| 17· || 703.448, 844.138
211°2'4" || 3/2 ||   ||
|| 18 || 744.828, 893.793
223°26'54" || 14/9, 20/13 ||   ||
|| 19 || 786.207, 943.448
235°51'43" || 11/7 ||   ||
|| 20 || 827.586, 993.103
248°16'33* || 8/5, 13/8 ||   ||
|| 21 || [[tel/868.9655|868.9655]], 1042.759
262°41'23" || 5/3, 18/11 ||   ||
|| 22· || 910.345, 1092.414
273°6'12" || 22/13 ||   ||
|| 23 || 951.724, 1142.069
285°31'2" || 7/4, 12/7, 26/15 ||   ||
|| 24 || 993.103, 1191.724
297°55'52" || 16/9 ||   ||
|| 25 || 1034.483, 1241.379
310°20'41" || 11/6, 20/11 ||   ||
|| 26 || 1075.862, 1291.0345
322°45'31" || 15/8, 28/15, 13/7, 24/13 ||   ||
|| 27 || 1117.241, 1340.690
335°10'21" || 40/21 ||   ||
|| 28 || 1158.621, 1390.345
347°35'10" || 48/25~64/33~55/28 ~160/81 ||   ||
See also: [[29edo solfege]]
[[image:29edothumb.png caption="this example in Sagittal notation shows 29-edo as a fifth-tone system."]]

==Selected just intervals by error== 
The following table shows how [[Just-24|some prominent just intervals]] are represented in 29edo (ordered by absolute error).
|| **Interval, complement** || **Error (abs., in [[cent|cents]])** ||
||= [[13_11|13/11]], [[22_13|22/13]] ||= 0.445 ||
||= [[11_10|11/10]], [[20_11|20/11]] ||= 0.513 ||
||= [[15_13|15/13]], [[26_15|26/15]] ||= 0.535 ||
||= [[13_10|13/10]], [[20_13|20/13]] ||= 0.958 ||
||= [[15_11|15/11]], [[22_15|22/15]] ||= 0.980 ||
||= [[4_3|4/3]], [[3_2|3/2]] ||= 1.493 ||
||= [[9_8|9/8]], [[16_9|16/9]] ||= 2.987 ||
||= [[7_5|7/5]], [[10_7|10/7]] ||= 3.202 ||
||= [[14_11|14/11]], [[11_7|11/7]] ||= 3.715 ||
||= [[14_13|14/13]], [[13_7|13/7]] ||= 4.160 ||
||= [[15_14|15/14]], [[28_15|28/15]] ||= 4.695 ||
||= [[16_15|16/15]], [[15_8|15/8]] ||= 12.407 ||
||= [[16_13|16/13]], [[13_8|13/8]] ||= 12.941 ||
||= [[11_8|11/8]], [[16_11|16/11]] ||= 13.387 ||
||= [[5_4|5/4]], [[8_5|8/5]] ||= 13.900 ||
||= [[13_12|13/12]], [[24_13|24/13]] ||= 14.435 ||
||= [[12_11|12/11]], [[11_6|11/6]] ||= 14.880 ||
||= [[6_5|6/5]], [[5_3|5/3]] ||= 15.393 ||
||= [[18_13|18/13]], [[13_9|13/9]] ||= 15.928 ||
||= [[11_9|11/9]], [[18_11|18/11]] ||= 16.373 ||
||= [[10_9|10/9]], [[9_5|9/5]] ||= 16.886 ||
||= [[8_7|8/7]], [[7_4|7/4]] ||= 17.102 ||
||= [[7_6|7/6]], [[12_7|12/7]] ||= 18.595 ||
||= [[9_7|9/7]], [[14_9|14/9]] ||= 20.088 ||

=Commas= 
29 EDO tempers out the following commas. (Note: This assumes the val < 29 46 67 81 100 107/1 |, 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 ||=   ||
||=   || | 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 ||=   ||

==The Tetradecatonic System== 

A variant of porcupine supported in 29edo is [[xenharmonic/nautilus|nautilus]], which splits the porcupine generator in half (tempering out 50:49 in the process), thus resulting in a different mapping for 7 than standard porcupine. Nautilus also extends to the 13-limit much more easily than does standard porcupine.

The MOS nautilus[14] contains both "even" tetrads (approximating 4:5:6:7 or its inverse) as well as "odd" tetrads (approximating the "Bohlen-Pierce-like" chord 9:11:13:15, or its inverse). Both types are recognizable and consonant, if somewhat heavily tempered. Moreover, one of the four types of tetrads may be built on **each** scale degree of nautilus[14], thus there are as many chords as there are notes, so nautilus[14] has a "circulating" quality to it with as much freedom of modulation as possible. To be exact, there are 4 "major-even", 4 "minor-even", 3 "major-odd", and 3 "minor-odd" chords.

Fourteen-note MOSes are worth looking at because taking every other note of them gives a heptatonic, and in many cases diatonic-like, scale. Nautilus[14] is no exception; although the resulting porcupine "diatonic" scale sounds somewhat different from diatonic scales generated from fifths, it can still provide some degree of familiarity. Furthermore, every diatonic chord progression will have at least one loose analogue in nautilus[14], although the chord types might change (for instance, it is possible to have a I-IV-V chord progression where the I is major-odd, and the IV and V are both major-even; the V in this case being on a narrow or "odd" fifth rather than a perfect or "even" fifth).

The fact that the generator size is also a step size means that nautilus makes a good candidate for a [[https://en.wikipedia.org/wiki/Generalized_keyboard|generalized keyboard]]; the fingering of nautilus[14] becomes very simple as a result, perhaps even simpler than with traditional keyboards, despite there being more notes.

If one can tolerate the tuning error (which is roughly equal to that of 12edo, albeit in the opposite direction for the 5- and 7-limits), this tetradecatonic scale is worth exploring. 29edo is often neglected since it falls so close to the much more popular and well-studied 31edo, but 29 does have its own advantages, and this is one of them.

=Scales= 
[[xenharmonic/bridgetown9|bridgetown9]]
[[xenharmonic/bridgetown14|bridgetown14]]
[[http://www.youtube.com/watch?v=uP2Z4Gy8lds|Escala Tonal de 17 tonos - Charles Loli]]
=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/|Guitar 29EDO]]
* ====**[[http://www.microtonalismo.com/proyecto-xvii|Guitar 29EDO from Peruvian - Charles Loli and Antonio Huamani]]**==== 
> [[image:http://content.pimp-my-profile.com/i116/2/10/29/f_735065b21747.jpg width="321" height="891"]]

[[@http://www.microtonalismo.com/|Bass 29EDO]]
* ====**[[http://www.microtonalismo.com/proyecto-xvii|Bass 29EDO from Peruvian - Charles Loli and Antonio Huamani]]**==== 
> [[image:https://fbcdn-sphotos-c-a.akamaihd.net/hphotos-ak-prn1/r90/550502_538613626155939_2005925977_n.jpg width="305" height="936"]]

Original HTML content:

<html><head><title>29edo</title></head><body><span style="display: block; text-align: right;"><a class="wiki_link" href="http://xenharmonie.wikispaces.com/29edo">Deutsch</a><br />
</span><br />
<!-- ws:start:WikiTextTocRule:20:&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:20 --><!-- ws:start:WikiTextTocRule:21: --><a href="#x29 tone equal temperament">29 tone equal temperament</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | <a href="#Intervals and linear temperaments">Intervals and linear temperaments</a><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --> | <a href="#Scales">Scales</a><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: -->
<!-- ws:end:WikiTextTocRule:31 --><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. However, it gives the POL2 generator for <a class="wiki_link" href="/Chromatic%20pairs#Edson">edson temperaament</a> with essentially perfect accuracy, only 0.034 cents sharp of it.<br />
<br />
Edson is a 2.3.7/5.11/5.13/5 subgroup temperament, and 29 it represents the 2.3.11/5.13/5 subgroup to very high accuracy, and the 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 coarse/fine<br />
DMS 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 />
0°<br />
</td>
        <td>1/1<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>41.379, 49.655<br />
12°24'50&quot;<br />
</td>
        <td>25/24~33/32~56/55~81/80<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>82.759, 99.310<br />
24°49'39&quot;<br />
</td>
        <td>21/20<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, <a class="wiki_link" href="http://tel.wikispaces.com/148.9655">148.9655</a><br />
37°14'29&quot;<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, 198.621<br />
49°39'19&quot;<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, 248.276<br />
62°4'8&quot;<br />
</td>
        <td>9/8<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>248.276, 297.391<br />
74°28'58&quot;<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, 347.586<br />
86°53'48&quot;<br />
</td>
        <td>13/11<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/331.0345">331.0345</a>, 397.241<br />
99°18'37&quot;<br />
</td>
        <td>6/5, 11/9<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>372.414, 446.896<br />
111°43'27&quot;<br />
</td>
        <td>5/4, 16/13<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>413.793, 496.552<br />
124°8'17&quot;<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, 546.207<br />
136°33'6&quot;<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, 595.862<br />
148°57'56&quot;<br />
</td>
        <td>4/3<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Cassandra">Cassandra</a> <a class="wiki_link" href="/Chromatic%20pairs#Edson">Edson</a> <a class="wiki_link" href="/Chromatic%20pairs#Pepperoni">Pepperoni</a><br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>537.931, 645.517<br />
161°21'46&quot;<br />
</td>
        <td>11/8, 15/11<br />
</td>
        <td><a class="wiki_link" href="/Wilsec">Wilsec</a><br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>579.310, 695.172<br />
173°46'35&quot;<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, 744.828<br />
186°13'25&quot;<br />
</td>
        <td>10/7, 13/9<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>662.069, 794.483<br />
198°38'14&quot;<br />
</td>
        <td>16/11, 22/15<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>17·<br />
</td>
        <td>703.448, 844.138<br />
211°2'4&quot;<br />
</td>
        <td>3/2<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>744.828, 893.793<br />
223°26'54&quot;<br />
</td>
        <td>14/9, 20/13<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>786.207, 943.448<br />
235°51'43&quot;<br />
</td>
        <td>11/7<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>827.586, 993.103<br />
248°16'33*<br />
</td>
        <td>8/5, 13/8<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/868.9655">868.9655</a>, 1042.759<br />
262°41'23&quot;<br />
</td>
        <td>5/3, 18/11<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>22·<br />
</td>
        <td>910.345, 1092.414<br />
273°6'12&quot;<br />
</td>
        <td>22/13<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>951.724, 1142.069<br />
285°31'2&quot;<br />
</td>
        <td>7/4, 12/7, 26/15<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>993.103, 1191.724<br />
297°55'52&quot;<br />
</td>
        <td>16/9<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>1034.483, 1241.379<br />
310°20'41&quot;<br />
</td>
        <td>11/6, 20/11<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>1075.862, 1291.0345<br />
322°45'31&quot;<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, 1340.690<br />
335°10'21&quot;<br />
</td>
        <td>40/21<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>1158.621, 1390.345<br />
347°35'10&quot;<br />
</td>
        <td>48/25~64/33~55/28 ~160/81<br />
</td>
        <td><br />
</td>
    </tr>
</table>

See also: <a class="wiki_link" href="/29edo%20solfege">29edo solfege</a><br />
<!-- ws:start:WikiTextLocalImageRule:751:&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:751 --><br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Intervals and linear temperaments-Selected just intervals by error"></a><!-- ws:end:WikiTextHeadingRule:4 -->Selected just intervals by error</h2>
 The following table shows how <a class="wiki_link" href="/Just-24">some prominent just intervals</a> are represented in 29edo (ordered by absolute error).<br />


<table class="wiki_table">
    <tr>
        <td><strong>Interval, complement</strong><br />
</td>
        <td><strong>Error (abs., in <a class="wiki_link" href="/cent">cents</a>)</strong><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><a class="wiki_link" href="/13_11">13/11</a>, <a class="wiki_link" href="/22_13">22/13</a><br />
</td>
        <td style="text-align: center;">0.445<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><a class="wiki_link" href="/11_10">11/10</a>, <a class="wiki_link" href="/20_11">20/11</a><br />
</td>
        <td style="text-align: center;">0.513<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><a class="wiki_link" href="/15_13">15/13</a>, <a class="wiki_link" href="/26_15">26/15</a><br />
</td>
        <td style="text-align: center;">0.535<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><a class="wiki_link" href="/13_10">13/10</a>, <a class="wiki_link" href="/20_13">20/13</a><br />
</td>
        <td style="text-align: center;">0.958<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><a class="wiki_link" href="/15_11">15/11</a>, <a class="wiki_link" href="/22_15">22/15</a><br />
</td>
        <td style="text-align: center;">0.980<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><a class="wiki_link" href="/4_3">4/3</a>, <a class="wiki_link" href="/3_2">3/2</a><br />
</td>
        <td style="text-align: center;">1.493<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><a class="wiki_link" href="/9_8">9/8</a>, <a class="wiki_link" href="/16_9">16/9</a><br />
</td>
        <td style="text-align: center;">2.987<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><a class="wiki_link" href="/7_5">7/5</a>, <a class="wiki_link" href="/10_7">10/7</a><br />
</td>
        <td style="text-align: center;">3.202<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><a class="wiki_link" href="/14_11">14/11</a>, <a class="wiki_link" href="/11_7">11/7</a><br />
</td>
        <td style="text-align: center;">3.715<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><a class="wiki_link" href="/14_13">14/13</a>, <a class="wiki_link" href="/13_7">13/7</a><br />
</td>
        <td style="text-align: center;">4.160<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><a class="wiki_link" href="/15_14">15/14</a>, <a class="wiki_link" href="/28_15">28/15</a><br />
</td>
        <td style="text-align: center;">4.695<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><a class="wiki_link" href="/16_15">16/15</a>, <a class="wiki_link" href="/15_8">15/8</a><br />
</td>
        <td style="text-align: center;">12.407<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><a class="wiki_link" href="/16_13">16/13</a>, <a class="wiki_link" href="/13_8">13/8</a><br />
</td>
        <td style="text-align: center;">12.941<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><a class="wiki_link" href="/11_8">11/8</a>, <a class="wiki_link" href="/16_11">16/11</a><br />
</td>
        <td style="text-align: center;">13.387<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><a class="wiki_link" href="/5_4">5/4</a>, <a class="wiki_link" href="/8_5">8/5</a><br />
</td>
        <td style="text-align: center;">13.900<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><a class="wiki_link" href="/13_12">13/12</a>, <a class="wiki_link" href="/24_13">24/13</a><br />
</td>
        <td style="text-align: center;">14.435<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><a class="wiki_link" href="/12_11">12/11</a>, <a class="wiki_link" href="/11_6">11/6</a><br />
</td>
        <td style="text-align: center;">14.880<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><a class="wiki_link" href="/6_5">6/5</a>, <a class="wiki_link" href="/5_3">5/3</a><br />
</td>
        <td style="text-align: center;">15.393<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><a class="wiki_link" href="/18_13">18/13</a>, <a class="wiki_link" href="/13_9">13/9</a><br />
</td>
        <td style="text-align: center;">15.928<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><a class="wiki_link" href="/11_9">11/9</a>, <a class="wiki_link" href="/18_11">18/11</a><br />
</td>
        <td style="text-align: center;">16.373<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><a class="wiki_link" href="/10_9">10/9</a>, <a class="wiki_link" href="/9_5">9/5</a><br />
</td>
        <td style="text-align: center;">16.886<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><a class="wiki_link" href="/8_7">8/7</a>, <a class="wiki_link" href="/7_4">7/4</a><br />
</td>
        <td style="text-align: center;">17.102<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><a class="wiki_link" href="/7_6">7/6</a>, <a class="wiki_link" href="/12_7">12/7</a><br />
</td>
        <td style="text-align: center;">18.595<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><a class="wiki_link" href="/9_7">9/7</a>, <a class="wiki_link" href="/14_9">14/9</a><br />
</td>
        <td style="text-align: center;">20.088<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:6 -->Commas</h1>
 29 EDO tempers out the following commas. (Note: This assumes the val &lt; 29 46 67 81 100 107/1 |, 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;"><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:8:&lt;h2&gt; --><h2 id="toc4"><a name="Commas-The Tetradecatonic System"></a><!-- ws:end:WikiTextHeadingRule:8 -->The Tetradecatonic System</h2>
 <br />
A variant of porcupine supported in 29edo is <a class="wiki_link" href="http://xenharmonic.wikispaces.com/nautilus">nautilus</a>, which splits the porcupine generator in half (tempering out 50:49 in the process), thus resulting in a different mapping for 7 than standard porcupine. Nautilus also extends to the 13-limit much more easily than does standard porcupine.<br />
<br />
The MOS nautilus[14] contains both &quot;even&quot; tetrads (approximating 4:5:6:7 or its inverse) as well as &quot;odd&quot; tetrads (approximating the &quot;Bohlen-Pierce-like&quot; chord 9:11:13:15, or its inverse). Both types are recognizable and consonant, if somewhat heavily tempered. Moreover, one of the four types of tetrads may be built on <strong>each</strong> scale degree of nautilus[14], thus there are as many chords as there are notes, so nautilus[14] has a &quot;circulating&quot; quality to it with as much freedom of modulation as possible. To be exact, there are 4 &quot;major-even&quot;, 4 &quot;minor-even&quot;, 3 &quot;major-odd&quot;, and 3 &quot;minor-odd&quot; chords.<br />
<br />
Fourteen-note MOSes are worth looking at because taking every other note of them gives a heptatonic, and in many cases diatonic-like, scale. Nautilus[14] is no exception; although the resulting porcupine &quot;diatonic&quot; scale sounds somewhat different from diatonic scales generated from fifths, it can still provide some degree of familiarity. Furthermore, every diatonic chord progression will have at least one loose analogue in nautilus[14], although the chord types might change (for instance, it is possible to have a I-IV-V chord progression where the I is major-odd, and the IV and V are both major-even; the V in this case being on a narrow or &quot;odd&quot; fifth rather than a perfect or &quot;even&quot; fifth).<br />
<br />
The fact that the generator size is also a step size means that nautilus makes a good candidate for a <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Generalized_keyboard" rel="nofollow">generalized keyboard</a>; the fingering of nautilus[14] becomes very simple as a result, perhaps even simpler than with traditional keyboards, despite there being more notes.<br />
<br />
If one can tolerate the tuning error (which is roughly equal to that of 12edo, albeit in the opposite direction for the 5- and 7-limits), this tetradecatonic scale is worth exploring. 29edo is often neglected since it falls so close to the much more popular and well-studied 31edo, but 29 does have its own advantages, and this is one of them.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Scales"></a><!-- ws:end:WikiTextHeadingRule:10 -->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 />
<a class="wiki_link_ext" href="http://www.youtube.com/watch?v=uP2Z4Gy8lds" rel="nofollow">Escala Tonal de 17 tonos - Charles Loli</a><br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:12 -->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:14:&lt;h2&gt; --><h2 id="toc7"><a name="Music-Instruments"></a><!-- ws:end:WikiTextHeadingRule:14 -->Instruments</h2>
 <a class="wiki_link_ext" href="http://www.microtonalismo.com/" rel="nofollow" target="_blank">Guitar 29EDO</a><br />
<ul><li><!-- ws:start:WikiTextHeadingRule:16:&lt;h4&gt; --><h4 id="toc8"><a name="Music-Instruments--Guitar 29EDO from Peruvian - Charles Loli and Antonio Huamani"></a><!-- ws:end:WikiTextHeadingRule:16 --><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:WikiTextRemoteImageRule:752:&lt;img src=&quot;http://content.pimp-my-profile.com/i116/2/10/29/f_735065b21747.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 891px; width: 321px;&quot; /&gt; --><img src="http://content.pimp-my-profile.com/i116/2/10/29/f_735065b21747.jpg" alt="external image f_735065b21747.jpg" title="external image f_735065b21747.jpg" style="height: 891px; width: 321px;" /><!-- ws:end:WikiTextRemoteImageRule:752 --></li></ul><br />
<a class="wiki_link_ext" href="http://www.microtonalismo.com/" rel="nofollow" target="_blank">Bass 29EDO</a><br />
<ul><li><!-- ws:start:WikiTextHeadingRule:18:&lt;h4&gt; --><h4 id="toc9"><a name="Music-Instruments--Bass 29EDO from Peruvian - Charles Loli and Antonio Huamani"></a><!-- ws:end:WikiTextHeadingRule:18 --><strong><a class="wiki_link_ext" href="http://www.microtonalismo.com/proyecto-xvii" rel="nofollow">Bass 29EDO from Peruvian - Charles Loli and Antonio Huamani</a></strong></h4>
<br />
<!-- ws:start:WikiTextRemoteImageRule:753:&lt;img src=&quot;https://fbcdn-sphotos-c-a.akamaihd.net/hphotos-ak-prn1/r90/550502_538613626155939_2005925977_n.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 936px; width: 305px;&quot; /&gt; --><img src="https://fbcdn-sphotos-c-a.akamaihd.net/hphotos-ak-prn1/r90/550502_538613626155939_2005925977_n.jpg" alt="external image 550502_538613626155939_2005925977_n.jpg" title="external image 550502_538613626155939_2005925977_n.jpg" style="height: 936px; width: 305px;" /><!-- ws:end:WikiTextRemoteImageRule:753 --></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:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-05 15:17:09 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-05 15:18:39 UTC</tt>.<br>
-: The original revision id was <tt>601449880</tt>.<br>
+: The original revision id was <tt>601450028</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 34: / Line 34: @@
 || 2 || 82.759, 99.310
 °49'39" || 21/20 || [[xenharmonic/Nautilus|Nautilus]] ||
-|| 3 || 124.138, [[tel:148.9655|148.9655]]
+|| 3 || 124.138, [[tel/148.9655|148.9655]]
 °14'29" || 16/15, 15/14, 14/13, 13/12 || [[xenharmonic/Negri|Negri]]/[[xenharmonic/Negril|Negril]] ||
 || 4 || 165.517, 198.621
@@ Line 44: / Line 44: @@
 || 7· || 289.655, 347.586
 °53'48" || 13/11 ||   ||
-|| 8 || [[tel:331.0345|331.0345]], 397.241
+|| 8 || [[tel/331.0345|331.0345]], 397.241
 °18'37" || 6/5, 11/9 ||   ||
 || 9 || 372.414, 446.896
@@ Line 70: / Line 70: @@
 || 20 || 827.586, 993.103
 °16'33* || 8/5, 13/8 ||   ||
-|| 21 || [[tel:868.9655|868.9655]], 1042.759
+|| 21 || [[tel/868.9655|868.9655]], 1042.759
 °41'23" || 5/3, 18/11 ||   ||
 || 22· || 910.345, 1092.414
@@ Line 118: / Line 118: @@
 =Commas=
-EDO tempers out the following commas. (Note: This assumes the val &lt; [[tel:29 46 67 81 100 107|29 46 67 81 100 107]] |, cent values rounded to 5 digits.)
+EDO tempers out the following commas. (Note: This assumes the val &lt; 29 46 67 81 100 107/1 |, cent values rounded to 5 digits.)
 ||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||
 ||= 16875/16384 || | -14 3 4 &gt; ||&gt; 51.120 ||= Negri Comma ||= Double Augmentation Diesis ||
@@ Line 693: / Line 693: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Commas&lt;/h1&gt;
-EDO tempers out the following commas. (Note: This assumes the val &amp;lt; &lt;a class="wiki_link" href="http://tel.wikispaces.com/29%2046%2067%2081%20100%20107"&gt;29 46 67 81 100 107&lt;/a&gt; |, cent values rounded to 5 digits.)&lt;br /&gt;
+EDO tempers out the following commas. (Note: This assumes the val &amp;lt; 29 46 67 81 100 107/1 |, cent values rounded to 5 digits.)&lt;br /&gt;

29edo: Difference between revisions

Revision as of 15:18, 5 December 2016

IMPORTED REVISION FROM WIKISPACES

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