30edo: Difference between revisions

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Wikispaces>JosephRuhf
**Imported revision 545667830 - Original comment: **
Wikispaces>JosephRuhf
**Imported revision 597600064 - Original comment: **
Line 1: Line 1:
<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:JosephRuhf|JosephRuhf]] and made on <tt>2015-03-28 20:46:05 UTC</tt>.<br>
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-31 18:46:03 UTC</tt>.<br>
: The original revision id was <tt>545667830</tt>.<br>
: The original revision id was <tt>597600064</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>
Line 15: Line 15:


=Commas=  
=Commas=  
30 EDO tempers out the following commas. (Note: This assumes the val &lt; 30 48 70 84 104 111 | .)
30 EDO tempers out the following commas. (Note: This assumes the val &lt; [[tel:30 48 70 84 104 111|30 48 70 84 104 111]] | .)
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
||= 256/243 ||&lt; | 8 -5 &gt; ||&gt; 90.22 ||= Limma ||= Pythagorean Minor 2nd ||=  ||
||= 256/243 ||&lt; | 8 -5 &gt; ||&gt; 90.22 ||= Limma ||= Pythagorean Minor 2nd ||=  ||
Line 30: Line 30:
||= 1029/1024 ||&lt; | -10 1 0 3 &gt; ||&gt; 8.43 ||= Gamelisma ||=  ||=  ||
||= 1029/1024 ||&lt; | -10 1 0 3 &gt; ||&gt; 8.43 ||= Gamelisma ||=  ||=  ||
||= 6144/6125 ||&lt; | 11 1 -3 -2 &gt; ||&gt; 5.36 ||= Porwell ||=  ||=  ||
||= 6144/6125 ||&lt; | 11 1 -3 -2 &gt; ||&gt; 5.36 ||= Porwell ||=  ||=  ||
||= 250047/250000 ||&lt; | -4 6 -6 3 &gt; ||&gt; 0.33 ||= Landscape Comma ||=  ||=  ||
||= [[tel:250047/250000|250047/250000]] ||&lt; | -4 6 -6 3 &gt; ||&gt; 0.33 ||= Landscape Comma ||=  ||=  ||
||= 100/99 ||&lt; | 2 -2 2 0 -1 &gt; ||&gt; 17.40 ||= Ptolemisma ||=  ||=  ||
||= 100/99 ||&lt; | 2 -2 2 0 -1 &gt; ||&gt; 17.40 ||= Ptolemisma ||=  ||=  ||
||= 121/120 ||&lt; | -3 -1 -1 0 2 &gt; ||&gt; 14.37 ||= Biyatisma ||=  ||=  ||
||= 121/120 ||&lt; | -3 -1 -1 0 2 &gt; ||&gt; 14.37 ||= Biyatisma ||=  ||=  ||
Line 41: Line 41:


==Intervals==  
==Intervals==  
|| **Step** || **Size in Cents**
|| **Step** || **Size in Cents coarse/fine**
**DMS** ||
**DMS** ||
|| 0 || 0 ||
|| 0 || 0 ||
|| 1 || 40  
|| 1 || 40, 48
12° ||
12° ||
|| 2 || 80  
|| 2 || 80, 96
24° ||
24° ||
|| 3 || 120
|| 3 || 120, 144
36° ||
36° ||
|| 4 || 160
|| 4 || 160, 192
48° ||
48° ||
|| 5 || 200
|| 5 || 200, 240
60° ||
60° ||
|| 6 || 240
|| 6 || 240, 288
72° ||
72° ||
|| 7 || 280
|| 7 || 280, 336
84° ||
84° ||
|| 8 || 320
|| 8 || 320, 384
96° ||
96° ||
|| 9 || 360
|| 9 || 360, 432
108° ||
108° ||
|| 10 || 400
|| 10 || 400, 480
120° ||
120° ||
|| 11 || 440
|| 11 || 440, 528
132° ||
132° ||
|| 12 || 480
|| 12 || 480, 576
144° ||
144° ||
|| 13 || 520
|| 13 || 520, 624
156° ||
156° ||
|| 14 || 560
|| 14 || 560, 672
168° ||
168° ||
|| 15 || 600
|| 15 || 600, 720
180° ||
180° ||
|| 16 || 640
|| 16 || 640, 768
192° ||
192° ||
|| 17 || 680
|| 17 || 680, 816
204° ||
204° ||
|| 18 || 720
|| 18 || 720, 864
216° ||
216° ||
|| 19 || 760
|| 19 || 760, 912
228° ||
228° ||
|| 20 || 800
|| 20 || 800, 960
240° ||
240° ||
|| 21 || 840
|| 21 || 840, 1008
252° ||
252° ||
|| 22 || 880
|| 22 || 880, 1056
264° ||
264° ||
|| 23 || 920
|| 23 || 920, 1104
276° ||
276° ||
|| 24 || 960
|| 24 || 960, 1152
288° ||
288° ||
|| 25 || 1000
|| 25 || 1000, 1200
300° ||
300° ||
|| 26 || 1040
|| 26 || 1040, 1248
312° ||
312° ||
|| 27 || 1080
|| 27 || 1080, 1296
324° ||
324° ||
|| 28 || 1120
|| 28 || 1120, 1344
336° ||
336° ||
|| 29 || 1160
|| 29 || 1160, 1392
348° ||
348° ||


Line 116: Line 116:
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Commas&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Commas&lt;/h1&gt;
  30 EDO tempers out the following commas. (Note: This assumes the val &amp;lt; 30 48 70 84 104 111 | .)&lt;br /&gt;
  30 EDO tempers out the following commas. (Note: This assumes the val &amp;lt; &lt;a class="wiki_link" href="http://tel.wikispaces.com/30%2048%2070%2084%20104%20111"&gt;30 48 70 84 104 111&lt;/a&gt; | .)&lt;br /&gt;




Line 317: Line 317:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td style="text-align: center;"&gt;250047/250000&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;[[tel:250047/250000|250047/250000]]&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: left;"&gt;| -4 6 -6 3 &amp;gt;&lt;br /&gt;
         &lt;td style="text-align: left;"&gt;| -4 6 -6 3 &amp;gt;&lt;br /&gt;
Line 452: Line 452:
         &lt;td&gt;&lt;strong&gt;Step&lt;/strong&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;Step&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;strong&gt;Size in Cents&lt;/strong&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;Size in Cents coarse/fine&lt;/strong&gt;&lt;br /&gt;
&lt;strong&gt;DMS&lt;/strong&gt;&lt;br /&gt;
&lt;strong&gt;DMS&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 465: Line 465:
         &lt;td&gt;1&lt;br /&gt;
         &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;40 &lt;br /&gt;
         &lt;td&gt;40, 48&lt;br /&gt;
12°&lt;br /&gt;
12°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 472: Line 472:
         &lt;td&gt;2&lt;br /&gt;
         &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;80 &lt;br /&gt;
         &lt;td&gt;80, 96&lt;br /&gt;
24°&lt;br /&gt;
24°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 479: Line 479:
         &lt;td&gt;3&lt;br /&gt;
         &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;120&lt;br /&gt;
         &lt;td&gt;120, 144&lt;br /&gt;
36°&lt;br /&gt;
36°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 486: Line 486:
         &lt;td&gt;4&lt;br /&gt;
         &lt;td&gt;4&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;160&lt;br /&gt;
         &lt;td&gt;160, 192&lt;br /&gt;
48°&lt;br /&gt;
48°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 493: Line 493:
         &lt;td&gt;5&lt;br /&gt;
         &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;200&lt;br /&gt;
         &lt;td&gt;200, 240&lt;br /&gt;
60°&lt;br /&gt;
60°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 500: Line 500:
         &lt;td&gt;6&lt;br /&gt;
         &lt;td&gt;6&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;240&lt;br /&gt;
         &lt;td&gt;240, 288&lt;br /&gt;
72°&lt;br /&gt;
72°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 507: Line 507:
         &lt;td&gt;7&lt;br /&gt;
         &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;280&lt;br /&gt;
         &lt;td&gt;280, 336&lt;br /&gt;
84°&lt;br /&gt;
84°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 514: Line 514:
         &lt;td&gt;8&lt;br /&gt;
         &lt;td&gt;8&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;320&lt;br /&gt;
         &lt;td&gt;320, 384&lt;br /&gt;
96°&lt;br /&gt;
96°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 521: Line 521:
         &lt;td&gt;9&lt;br /&gt;
         &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;360&lt;br /&gt;
         &lt;td&gt;360, 432&lt;br /&gt;
108°&lt;br /&gt;
108°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 528: Line 528:
         &lt;td&gt;10&lt;br /&gt;
         &lt;td&gt;10&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;400&lt;br /&gt;
         &lt;td&gt;400, 480&lt;br /&gt;
120°&lt;br /&gt;
120°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 535: Line 535:
         &lt;td&gt;11&lt;br /&gt;
         &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;440&lt;br /&gt;
         &lt;td&gt;440, 528&lt;br /&gt;
132°&lt;br /&gt;
132°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 542: Line 542:
         &lt;td&gt;12&lt;br /&gt;
         &lt;td&gt;12&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;480&lt;br /&gt;
         &lt;td&gt;480, 576&lt;br /&gt;
144°&lt;br /&gt;
144°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 549: Line 549:
         &lt;td&gt;13&lt;br /&gt;
         &lt;td&gt;13&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;520&lt;br /&gt;
         &lt;td&gt;520, 624&lt;br /&gt;
156°&lt;br /&gt;
156°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 556: Line 556:
         &lt;td&gt;14&lt;br /&gt;
         &lt;td&gt;14&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;560&lt;br /&gt;
         &lt;td&gt;560, 672&lt;br /&gt;
168°&lt;br /&gt;
168°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 563: Line 563:
         &lt;td&gt;15&lt;br /&gt;
         &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;600&lt;br /&gt;
         &lt;td&gt;600, 720&lt;br /&gt;
180°&lt;br /&gt;
180°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 570: Line 570:
         &lt;td&gt;16&lt;br /&gt;
         &lt;td&gt;16&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;640&lt;br /&gt;
         &lt;td&gt;640, 768&lt;br /&gt;
192°&lt;br /&gt;
192°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 577: Line 577:
         &lt;td&gt;17&lt;br /&gt;
         &lt;td&gt;17&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;680&lt;br /&gt;
         &lt;td&gt;680, 816&lt;br /&gt;
204°&lt;br /&gt;
204°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 584: Line 584:
         &lt;td&gt;18&lt;br /&gt;
         &lt;td&gt;18&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;720&lt;br /&gt;
         &lt;td&gt;720, 864&lt;br /&gt;
216°&lt;br /&gt;
216°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 591: Line 591:
         &lt;td&gt;19&lt;br /&gt;
         &lt;td&gt;19&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;760&lt;br /&gt;
         &lt;td&gt;760, 912&lt;br /&gt;
228°&lt;br /&gt;
228°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 598: Line 598:
         &lt;td&gt;20&lt;br /&gt;
         &lt;td&gt;20&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;800&lt;br /&gt;
         &lt;td&gt;800, 960&lt;br /&gt;
240°&lt;br /&gt;
240°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 605: Line 605:
         &lt;td&gt;21&lt;br /&gt;
         &lt;td&gt;21&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;840&lt;br /&gt;
         &lt;td&gt;840, 1008&lt;br /&gt;
252°&lt;br /&gt;
252°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 612: Line 612:
         &lt;td&gt;22&lt;br /&gt;
         &lt;td&gt;22&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;880&lt;br /&gt;
         &lt;td&gt;880, 1056&lt;br /&gt;
264°&lt;br /&gt;
264°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 619: Line 619:
         &lt;td&gt;23&lt;br /&gt;
         &lt;td&gt;23&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;920&lt;br /&gt;
         &lt;td&gt;920, 1104&lt;br /&gt;
276°&lt;br /&gt;
276°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 626: Line 626:
         &lt;td&gt;24&lt;br /&gt;
         &lt;td&gt;24&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;960&lt;br /&gt;
         &lt;td&gt;960, 1152&lt;br /&gt;
288°&lt;br /&gt;
288°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 633: Line 633:
         &lt;td&gt;25&lt;br /&gt;
         &lt;td&gt;25&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1000&lt;br /&gt;
         &lt;td&gt;1000, 1200&lt;br /&gt;
300°&lt;br /&gt;
300°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 640: Line 640:
         &lt;td&gt;26&lt;br /&gt;
         &lt;td&gt;26&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1040&lt;br /&gt;
         &lt;td&gt;1040, 1248&lt;br /&gt;
312°&lt;br /&gt;
312°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 647: Line 647:
         &lt;td&gt;27&lt;br /&gt;
         &lt;td&gt;27&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1080&lt;br /&gt;
         &lt;td&gt;1080, 1296&lt;br /&gt;
324°&lt;br /&gt;
324°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 654: Line 654:
         &lt;td&gt;28&lt;br /&gt;
         &lt;td&gt;28&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1120&lt;br /&gt;
         &lt;td&gt;1120, 1344&lt;br /&gt;
336°&lt;br /&gt;
336°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 661: Line 661:
         &lt;td&gt;29&lt;br /&gt;
         &lt;td&gt;29&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1160&lt;br /&gt;
         &lt;td&gt;1160, 1392&lt;br /&gt;
348°&lt;br /&gt;
348°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;

Revision as of 18:46, 31 October 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 JosephRuhf and made on 2016-10-31 18:46:03 UTC.
The original revision id was 597600064.
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:

The //30 equal division// divides the octave into 30 equal steps of precisely 40 cents each. Its [[patent val]] is a doubled version of the patent val for [[15edo]] through the 11-limit, so 30 can be viewed as a [[contorted]] version of 15. In the 13-limit it supplies the optimal patent val for [[Trienstonic clan#Quindecic|quindecic temperament]].

However, 5\30 is 200 cents, which is a good (and familiar) approximation for 9/8, and hence 30 can be viewed inconsistently, as having a 9' at 95\30 as well as a 9 at 96\30. Instead of the 18\30 fifth of 720 cents, 30 also makes available a 17\30 fifth of 680 cents. This is an ideal tuning for pelogic (5-limit mavila), which tempers out 135/128. When 30 is used for pelogic, 5\30 can again be used inconsistently as a 9/8.

Below is a plot of the Z function around 30:

[[image:plot30.png]]

=Commas= 
30 EDO tempers out the following commas. (Note: This assumes the val < [[tel:30 48 70 84 104 111|30 48 70 84 104 111]] | .)
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
||= 256/243 ||< | 8 -5 > ||> 90.22 ||= Limma ||= Pythagorean Minor 2nd ||=   ||
||= 250/243 ||< | 1 -5 3 > ||> 49.17 ||= Maximal Diesis ||= Porcupine Comma ||=   ||
||= 128/125 ||< | 7 0 -3 > ||> 41.06 ||= Diesis ||= Augmented Comma ||=   ||
||= 15625/15552 ||< | -6 -5 6 > ||> 8.11 ||= Kleisma ||= Semicomma Majeur ||=   ||
||= 1029/1000 ||< | -3 1 -3 3 > ||> 49.49 ||= Keega ||=   ||=   ||
||= 49/48 ||< | -4 -1 0 2 > ||> 35.70 ||= Slendro Diesis ||=   ||=   ||
||= 64/63 ||< | 6 -2 0 -1 > ||> 27.26 ||= Septimal Comma ||= Archytas' Comma ||= Leipziger Komma ||
||= 64827/64000 ||< | -9 3 -3 4 > ||> 22.23 ||= Squalentine ||=   ||=   ||
||= 875/864 ||< | -5 -3 3 1 > ||> 21.90 ||= Keema ||=   ||=   ||
||= 126/125 ||< | 1 2 -3 1 > ||> 13.79 ||= Septimal Semicomma ||= Starling Comma ||=   ||
||= 4000/3969 ||< | 5 -4 3 -2 > ||> 13.47 ||= Octagar ||=   ||=   ||
||= 1029/1024 ||< | -10 1 0 3 > ||> 8.43 ||= Gamelisma ||=   ||=   ||
||= 6144/6125 ||< | 11 1 -3 -2 > ||> 5.36 ||= Porwell ||=   ||=   ||
||= [[tel:250047/250000|250047/250000]] ||< | -4 6 -6 3 > ||> 0.33 ||= Landscape Comma ||=   ||=   ||
||= 100/99 ||< | 2 -2 2 0 -1 > ||> 17.40 ||= Ptolemisma ||=   ||=   ||
||= 121/120 ||< | -3 -1 -1 0 2 > ||> 14.37 ||= Biyatisma ||=   ||=   ||
||= 176/175 ||< | 4 0 -2 -1 1 > ||> 9.86 ||= Valinorsma ||=   ||=   ||
||= 65536/65219 ||< | 16 0 0 -2 -3 > ||> 8.39 ||= Orgonisma ||=   ||=   ||
||= 385/384 ||< | -7 -1 1 1 1 > ||> 4.50 ||= Keenanisma ||=   ||=   ||
||= 441/440 ||< | -3 2 -1 2 -1 > ||> 3.93 ||= Werckisma ||=   ||=   ||
||= 4000/3993 ||< | 5 -1 3 0 -3 > ||> 3.03 ||= Wizardharry ||=   ||=   ||
||= 3025/3024 ||< | -4 -3 2 -1 2 > ||> 0.57 ||= Lehmerisma ||=   ||=   ||

==Intervals== 
|| **Step** || **Size in Cents coarse/fine**
**DMS** ||
|| 0 || 0 ||
|| 1 || 40, 48
12° ||
|| 2 || 80, 96
24° ||
|| 3 || 120, 144
36° ||
|| 4 || 160, 192
48° ||
|| 5 || 200, 240
60° ||
|| 6 || 240, 288
72° ||
|| 7 || 280, 336
84° ||
|| 8 || 320, 384
96° ||
|| 9 || 360, 432
108° ||
|| 10 || 400, 480
120° ||
|| 11 || 440, 528
132° ||
|| 12 || 480, 576
144° ||
|| 13 || 520, 624
156° ||
|| 14 || 560, 672
168° ||
|| 15 || 600, 720
180° ||
|| 16 || 640, 768
192° ||
|| 17 || 680, 816
204° ||
|| 18 || 720, 864
216° ||
|| 19 || 760, 912
228° ||
|| 20 || 800, 960
240° ||
|| 21 || 840, 1008
252° ||
|| 22 || 880, 1056
264° ||
|| 23 || 920, 1104
276° ||
|| 24 || 960, 1152
288° ||
|| 25 || 1000, 1200
300° ||
|| 26 || 1040, 1248
312° ||
|| 27 || 1080, 1296
324° ||
|| 28 || 1120, 1344
336° ||
|| 29 || 1160, 1392
348° ||

=Music= 

[[@http://spectropolrecords.bandcamp.com/track/todd-harrop-fifteen-short-pieces|Fifteen Short Pieces]] by <span class="wiki_link_ext">Todd Harrop</span>

Original HTML content:

<html><head><title>30edo</title></head><body>The <em>30 equal division</em> divides the octave into 30 equal steps of precisely 40 cents each. Its <a class="wiki_link" href="/patent%20val">patent val</a> is a doubled version of the patent val for <a class="wiki_link" href="/15edo">15edo</a> through the 11-limit, so 30 can be viewed as a <a class="wiki_link" href="/contorted">contorted</a> version of 15. In the 13-limit it supplies the optimal patent val for <a class="wiki_link" href="/Trienstonic%20clan#Quindecic">quindecic temperament</a>.<br />
<br />
However, 5\30 is 200 cents, which is a good (and familiar) approximation for 9/8, and hence 30 can be viewed inconsistently, as having a 9' at 95\30 as well as a 9 at 96\30. Instead of the 18\30 fifth of 720 cents, 30 also makes available a 17\30 fifth of 680 cents. This is an ideal tuning for pelogic (5-limit mavila), which tempers out 135/128. When 30 is used for pelogic, 5\30 can again be used inconsistently as a 9/8.<br />
<br />
Below is a plot of the Z function around 30:<br />
<br />
<!-- ws:start:WikiTextLocalImageRule:518:&lt;img src=&quot;/file/view/plot30.png/220060356/plot30.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/plot30.png/220060356/plot30.png" alt="plot30.png" title="plot30.png" /><!-- ws:end:WikiTextLocalImageRule:518 --><br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:0 -->Commas</h1>
 30 EDO tempers out the following commas. (Note: This assumes the val &lt; <a class="wiki_link" href="http://tel.wikispaces.com/30%2048%2070%2084%20104%20111">30 48 70 84 104 111</a> | .)<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 style="text-align: left;">| 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 style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">250/243<br />
</td>
        <td style="text-align: left;">| 1 -5 3 &gt;<br />
</td>
        <td style="text-align: right;">49.17<br />
</td>
        <td style="text-align: center;">Maximal Diesis<br />
</td>
        <td style="text-align: center;">Porcupine Comma<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">128/125<br />
</td>
        <td style="text-align: left;">| 7 0 -3 &gt;<br />
</td>
        <td style="text-align: right;">41.06<br />
</td>
        <td style="text-align: center;">Diesis<br />
</td>
        <td style="text-align: center;">Augmented Comma<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">15625/15552<br />
</td>
        <td style="text-align: left;">| -6 -5 6 &gt;<br />
</td>
        <td style="text-align: right;">8.11<br />
</td>
        <td style="text-align: center;">Kleisma<br />
</td>
        <td style="text-align: center;">Semicomma Majeur<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1029/1000<br />
</td>
        <td style="text-align: left;">| -3 1 -3 3 &gt;<br />
</td>
        <td style="text-align: right;">49.49<br />
</td>
        <td style="text-align: center;">Keega<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">49/48<br />
</td>
        <td style="text-align: left;">| -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 style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">64/63<br />
</td>
        <td style="text-align: left;">| 6 -2 0 -1 &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 style="text-align: center;">Leipziger Komma<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">64827/64000<br />
</td>
        <td style="text-align: left;">| -9 3 -3 4 &gt;<br />
</td>
        <td style="text-align: right;">22.23<br />
</td>
        <td style="text-align: center;">Squalentine<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">875/864<br />
</td>
        <td style="text-align: left;">| -5 -3 3 1 &gt;<br />
</td>
        <td style="text-align: right;">21.90<br />
</td>
        <td style="text-align: center;">Keema<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">126/125<br />
</td>
        <td style="text-align: left;">| 1 2 -3 1 &gt;<br />
</td>
        <td style="text-align: right;">13.79<br />
</td>
        <td style="text-align: center;">Septimal Semicomma<br />
</td>
        <td style="text-align: center;">Starling Comma<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">4000/3969<br />
</td>
        <td style="text-align: left;">| 5 -4 3 -2 &gt;<br />
</td>
        <td style="text-align: right;">13.47<br />
</td>
        <td style="text-align: center;">Octagar<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1029/1024<br />
</td>
        <td style="text-align: left;">| -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 style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">6144/6125<br />
</td>
        <td style="text-align: left;">| 11 1 -3 -2 &gt;<br />
</td>
        <td style="text-align: right;">5.36<br />
</td>
        <td style="text-align: center;">Porwell<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">[[tel:250047/250000|250047/250000]]<br />
</td>
        <td style="text-align: left;">| -4 6 -6 3 &gt;<br />
</td>
        <td style="text-align: right;">0.33<br />
</td>
        <td style="text-align: center;">Landscape Comma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">100/99<br />
</td>
        <td style="text-align: left;">| 2 -2 2 0 -1 &gt;<br />
</td>
        <td style="text-align: right;">17.40<br />
</td>
        <td style="text-align: center;">Ptolemisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">121/120<br />
</td>
        <td style="text-align: left;">| -3 -1 -1 0 2 &gt;<br />
</td>
        <td style="text-align: right;">14.37<br />
</td>
        <td style="text-align: center;">Biyatisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">176/175<br />
</td>
        <td style="text-align: left;">| 4 0 -2 -1 1 &gt;<br />
</td>
        <td style="text-align: right;">9.86<br />
</td>
        <td style="text-align: center;">Valinorsma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">65536/65219<br />
</td>
        <td style="text-align: left;">| 16 0 0 -2 -3 &gt;<br />
</td>
        <td style="text-align: right;">8.39<br />
</td>
        <td style="text-align: center;">Orgonisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">385/384<br />
</td>
        <td style="text-align: left;">| -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 style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">441/440<br />
</td>
        <td style="text-align: left;">| -3 2 -1 2 -1 &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 style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">4000/3993<br />
</td>
        <td style="text-align: left;">| 5 -1 3 0 -3 &gt;<br />
</td>
        <td style="text-align: right;">3.03<br />
</td>
        <td style="text-align: center;">Wizardharry<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">3025/3024<br />
</td>
        <td style="text-align: left;">| -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 style="text-align: center;"><br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Commas-Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals</h2>
 

<table class="wiki_table">
    <tr>
        <td><strong>Step</strong><br />
</td>
        <td><strong>Size in Cents coarse/fine</strong><br />
<strong>DMS</strong><br />
</td>
    </tr>
    <tr>
        <td>0<br />
</td>
        <td>0<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>40, 48<br />
12°<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>80, 96<br />
24°<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>120, 144<br />
36°<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>160, 192<br />
48°<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>200, 240<br />
60°<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>240, 288<br />
72°<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>280, 336<br />
84°<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>320, 384<br />
96°<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>360, 432<br />
108°<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>400, 480<br />
120°<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>440, 528<br />
132°<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>480, 576<br />
144°<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>520, 624<br />
156°<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>560, 672<br />
168°<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>600, 720<br />
180°<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>640, 768<br />
192°<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>680, 816<br />
204°<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>720, 864<br />
216°<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>760, 912<br />
228°<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>800, 960<br />
240°<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>840, 1008<br />
252°<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>880, 1056<br />
264°<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>920, 1104<br />
276°<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>960, 1152<br />
288°<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>1000, 1200<br />
300°<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>1040, 1248<br />
312°<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>1080, 1296<br />
324°<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>1120, 1344<br />
336°<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>1160, 1392<br />
348°<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:4 -->Music</h1>
 <br />
<a class="wiki_link_ext" href="http://spectropolrecords.bandcamp.com/track/todd-harrop-fifteen-short-pieces" rel="nofollow" target="_blank">Fifteen Short Pieces</a> by <span class="wiki_link_ext">Todd Harrop</span></body></html>