28edo: Difference between revisions

Revision as of 18:17, 31 October 2016

IMPORTED REVISION FROM WIKISPACES

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This revision was by author JosephRuhf and made on 2016-10-31 18:17:03 UTC.

The original revision id was 597598532.

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[[toc|flat]]
----

=Basic properties= 
28edo, a multiple of both [[xenharmonic/7edo|7edo]] and [[xenharmonic/14edo|14edo]] (and of course [[xenharmonic/2edo|2edo]] and [[xenharmonic/4edo|4edo]]), has a step size of 42.857 [[xenharmonic/cent|cent]]s. It shares three intervals with [[xenharmonic/12edo|12edo]]: the 300 cent minor third, the 600 cent tritone, and the 900 cent major sixth. Thus it [[xenharmonic/tempering out|tempers out]] the [[xenharmonic/greater diesis|greater diesis]] [[xenharmonic/648_625|648:625]]. It does not however temper out the [[xenharmonic/128_125|128:125]] [[xenharmonic/lesser diesis|lesser diesis]], as its major third is less than 1 cent flat (and its inversion the minor sixth less than 1 cent sharp). It has the same perfect fourth and fifth as 7edo. It also has decent approximations of several septimal intervals, of which [[xenharmonic/9_7|9/7]] and its inversion [[xenharmonic/14_9|14/9]] are also found in 14edo.

=Subgroups= 
28edo can approximate the [[xenharmonic/7-limit|7-limit]] subgroup 2.27.5.21 quite well, and on this subgroup it has the same commas and tunings as 84edo. The temperament corresponding to [[xenharmonic/Semicomma family|orwell temperament]] now has a major third as generator, though as before 225/224, 1728/1715 and 6144/6125 are tempered out. The 225/224-tempered version of the [[xenharmonic/augmented triad|augmented triad]] has a very low complexity, so many of them appear in the [[xenharmonic/MOS scales|MOS scales]] for this temperament, which have sizes 7, 10, 13, 16, 19, 22, 25.

Another subgroup for which 28edo works quite well is 2.5.11.19.21.27.29.39.

=Table of intervals= 
The following table compares it to potentially useful nearby [[xenharmonic/just intervals|just intervals]].

|| Step # || ET Cents coarse/fine
DMS || Just Interval || Just Cents
DMS || Difference (ET minus Just) ||
|| 1 || 42.86
51.43
12°<span style="background-color: #ffffff;">51'26"</span> ||   ||   ||   ||
|| 2 || 85.71
102.86
<span style="background-color: #ffffff;">25°42'51"</span> || 21:20 || 84.47
101.36
<span style="background-color: #ffffff;">25°20'25"</span> || 1.24
1.50
22'26" ||
|| 3 || 128.57
154.29
38°<span style="background-color: #ffffff;">34'17"</span> || 14:13 || 128.30
153.96
38°29<span style="background-color: #ffffff;">'22"</span> || 0.27
0.33
4'55" ||
|| 4 || 171.43
205.71
<span style="background-color: #ffffff;">51°25'43"</span> || 11:10 || 165.00
198.005
<span style="background-color: #ffffff;">49°30'5"</span> || 6.43
7.705
1°55'38° ||
|| 5 || 214.29
257.14
64°<span style="background-color: #ffffff;">17'9"</span> || 17:15 || 216.69
260.02
65°22" || -2.40
-2.88
-43'13" ||
|| 6 || 257.14
308.57
<span style="background-color: #ffffff;">77°8'34"</span> || 7:6 || 266.87
320.245
80°3'41" || -9.73
-11.675
-2°55'7" ||
|| 7 || 300
360
90° || 6:5 || 315.64
378.77
94°41'33" || -15.64
-18.77
-4°41'33" ||
|| 8 || 342.86
411.43
<span style="background-color: #ffffff;">102°51'26"</span> || 11:9 || 347.41
416.89
<span style="background-color: #ffffff;">104°13'21"</span> || -4.55
-5.46
-1°21'55" ||
|| 9 || 385.71
462.86
115°<span style="background-color: #ffffff;">42'51"</span> || 5:4 || 386.31
463.58
115°<span style="background-color: #ffffff;">53'39"</span> || -0.60
-0.72
-10'48" ||
|| 10 || 428.57
514.29
<span style="background-color: #ffffff;">128°34'17"</span> || 9:7 || 435.08
522.10
130°31'30" || -6.51
-7.81
-1°57'13" ||
|| 11 || 471.43
565.71
141°<span style="background-color: #ffffff;">25'43"</span> || 21:16 || 470.78
564.94
141°<span style="background-color: #ffffff;">14'3"</span> || 0.65
0.77
11'40" ||
|| 12 || 514.29
617.14
<span style="background-color: #ffffff;">154°17'9"</span> || 4:3 || 498.04
597.65
149°24<span style="background-color: #ffffff;">'49"</span> || 16.25
19.49
4°52'20" ||
|| 13 || 557.14
668.57
167°<span style="background-color: #ffffff;">8'34"</span> || 11:8 || 551.32
661.58
165°<span style="background-color: #ffffff;">23'43"</span> || 5.82
6.99
1°45'9" ||
|| 14 || 600
720
<span style="background-color: #ffffff;">180°</span> || 7:5 10:7 || 582.51 617.49
699.015 740.985
174°45'13" <span style="background-color: #ffffff;">185°14'47"</span> || ±17.49
±20.985
±<span style="background-color: #ffffff;">5°14'47"</span> ||
|| 15 || 642.86
771.43
<span style="background-color: #ffffff;">192°51'26"</span> || 16:11 || 648.68
778.42
<span style="background-color: #ffffff;">194°36'35"</span> || -5.82
-6.99
-1°45'9" ||
|| 16 || 685.71
822.86
<span style="background-color: #ffffff;">205°42'51"</span> || 3:2 || 701.96
842.35
<span style="background-color: #ffffff;">210°35'11"</span> || -16.25
-19.49
-4°52'20" ||
|| 17 || 728.57
874.29
218°<span style="background-color: #ffffff;">34'17"</span> || 32:21 || 729.22
875,06
218°45'57" || -0.65
-0.77
-11'40" ||
|| 18 || 771.43
925.71
<span style="background-color: #ffffff;">231°25'43"</span> || 14:9 || 764.92
917.90
229°28'30" || 6.51
7.81
1°57'13" ||
|| 19 || 814.29
977.14
244°<span style="background-color: #ffffff;">17'9"</span> || 8:5 || 813.68
976.42
244°<span style="background-color: #ffffff;">6'21"</span> || 0.61
0.72
10'48" ||
|| 20 || 857.14
1028.57
<span style="background-color: #ffffff;">257°8'34"</span> || 18:11 || 852.59
1023.11
<span style="background-color: #ffffff;">258°30'29"</span> || 4.55
5.46
1°21'55" ||
|| 21 || 900
1080
270° || 5:3 || 884.36
1061.23
265°18'27" || 15.64
18.77
4°41'33" ||
|| 22 || 942.86
1131.43
<span style="background-color: #ffffff;">282°51'26"</span> || 12:7 || 933.13
1119.755
<span style="background-color: #ffffff;">285°46'33"</span> || 9.73
11.675
2°55'7" ||
|| 23 || 985.71
1185.86
<span style="background-color: #ffffff;">295°42'51"</span> || 30:17 || 983.31
1182.98
<span style="background-color: #ffffff;">296°26'4"</span> || 2.40
2.88
43'13" ||
|| 24 || 1028.57
1234.29
<span style="background-color: #ffffff;">308°34'17"</span> || 20:11 || 1035.00
1241.995
310°29'55" || -6.43
-7.705
-1°55'38° ||
|| 25 || 1071.42
1285.71
321°<span style="background-color: #ffffff;">25'43"</span> || 13:7 || 1071.70
1286.04
321°<span style="background-color: #ffffff;">30'38"</span> || -0.27
-0.33
-4'55" ||
|| 26 || 1114.29
1336.14
334°17'9" || 40:21 || 1115.53
1337.64
334°39'35" || -1.24
-1.50
-22'26" ||
|| 27 || 1157.14
1387.57
347°<span style="background-color: #ffffff;">8'34"</span> ||   ||   ||   ||
|| 28 || 1200, 1440
<span style="background-color: #ffffff;">360°</span> || 2:1 || 1200, 1440 || 0 ||
=<span style="background-color: #ffffff;">Rank two temperaments</span>= 

||~ Periods
per octave ||~ Generator ||~ Temperaments ||
|| 1 || 1\28 ||   ||
|| 1 || 3\28 || [[xenharmonic/Negri|Negri]] ||
|| 1 || 5\28 || [[xenharmonic/Machine|Machine]] ||
|| 1 || 9\28 || [[xenharmonic/Würschmidt family#Worschmidt|Worschmidt]] ||
|| 1 || 11\28 ||   ||
|| 1 || 13\28 || <span style="background-color: #ffffff;">[[xenharmonic/Thuja|Thuja]]</span> ||
|| 2 || 1\28 ||   ||
|| 2 || 3\28 ||   ||
|| 2 || 5\28 || [[antikythera|Antikythera]] ||
|| 4 || 1\28 ||   ||
|| 4 || 2\28 || [[xenharmonic/Diminished#Demolished|Demolished]] ||
|| 4 || 3\28 ||   ||
|| 7 || 1\28 || [[xenharmonic/Apotome family|Whitewood]] ||
|| 14 || 1\28 ||   ||

=Commas= 
28 EDO tempers out the following [[xenharmonic/comma|comma]]s. (Note: This assumes the val < [[tel/28 44 65 79 97 104|28 44 65 79 97 104]] |.)
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||
||= 2187/2048 || | -11 7 > ||> 113.69 ||= Apotome ||=   ||
||= 648/625 || | 3 4 -4 > ||> 62.57 ||= Major Diesis ||= Diminished Comma ||
||= 16875/16384 || | -14 3 4 > ||> 51.12 ||= Negri Comma ||= Double Augmentation Diesis ||
||=   || | 17 1 -8 > ||> 11.45 ||= Wuerschmidt Comma ||=   ||
||= 36/35 || | 2 2 -1 -1 > ||> 48.77 ||= Septimal Quarter Tone ||=   ||
||= 50/49 || | 1 0 2 -2 > ||> 34.98 ||= Tritonic Diesis ||= Jubilisma ||
||= 3125/3087 || | 0 -2 5 -3 > ||> 21.18 ||= Gariboh ||=   ||
||= 126/125 || | 1 2 -3 1 > ||> 13.79 ||= Septimal Semicomma ||= Starling Comma ||
||= 65625/65536 || | -16 1 5 1 > ||> 2.35 ||= Horwell ||=   ||
||=   || | 47 -7 -7 -7 > ||> 0.34 ||= Akjaysma ||= 5\7 Octave Comma ||
||= 176/175 || | 4 0 -2 -1 1 > ||> 9.86 ||= Valinorsma ||=   ||
||= 441/440 || | -3 2 -1 2 -1 > ||> 3.93 ||= Werckisma ||=   ||
||= 4000/3993 || | 5 -1 3 0 -3 > ||> 3.03 ||= Wizardharry ||=   ||

=Some scales= 
[[xenharmonic/machine5|machine5]]
[[xenharmonic/machine6|machine6]]
[[xenharmonic/machine11|machine11]]

=Compositions= 
[[http://www.youtube.com/watch?v=26UpCbrb3mE|28 tone Prelude]] by Kosmorksy

Original HTML content:

<html><head><title>28edo</title></head><body><!-- ws:start:WikiTextTocRule:14:&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:14 --><!-- ws:start:WikiTextTocRule:15: --><a href="#Basic properties">Basic properties</a><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --> | <a href="#Subgroups">Subgroups</a><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --> | <a href="#Table of intervals">Table of intervals</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#Rank two temperaments">Rank two 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="#Some scales">Some scales</a><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --> | <a href="#Compositions">Compositions</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: -->
<!-- ws:end:WikiTextTocRule:22 --><hr />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Basic properties"></a><!-- ws:end:WikiTextHeadingRule:0 -->Basic properties</h1>
 28edo, a multiple of both <a class="wiki_link" href="http://xenharmonic.wikispaces.com/7edo">7edo</a> and <a class="wiki_link" href="http://xenharmonic.wikispaces.com/14edo">14edo</a> (and of course <a class="wiki_link" href="http://xenharmonic.wikispaces.com/2edo">2edo</a> and <a class="wiki_link" href="http://xenharmonic.wikispaces.com/4edo">4edo</a>), has a step size of 42.857 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/cent">cent</a>s. It shares three intervals with <a class="wiki_link" href="http://xenharmonic.wikispaces.com/12edo">12edo</a>: the 300 cent minor third, the 600 cent tritone, and the 900 cent major sixth. Thus it <a class="wiki_link" href="http://xenharmonic.wikispaces.com/tempering%20out">tempers out</a> the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/greater%20diesis">greater diesis</a> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/648_625">648:625</a>. It does not however temper out the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/128_125">128:125</a> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/lesser%20diesis">lesser diesis</a>, as its major third is less than 1 cent flat (and its inversion the minor sixth less than 1 cent sharp). It has the same perfect fourth and fifth as 7edo. It also has decent approximations of several septimal intervals, of which <a class="wiki_link" href="http://xenharmonic.wikispaces.com/9_7">9/7</a> and its inversion <a class="wiki_link" href="http://xenharmonic.wikispaces.com/14_9">14/9</a> are also found in 14edo.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Subgroups"></a><!-- ws:end:WikiTextHeadingRule:2 -->Subgroups</h1>
 28edo can approximate the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/7-limit">7-limit</a> subgroup 2.27.5.21 quite well, and on this subgroup it has the same commas and tunings as 84edo. The temperament corresponding to <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Semicomma%20family">orwell temperament</a> now has a major third as generator, though as before 225/224, 1728/1715 and 6144/6125 are tempered out. The 225/224-tempered version of the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/augmented%20triad">augmented triad</a> has a very low complexity, so many of them appear in the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOS%20scales">MOS scales</a> for this temperament, which have sizes 7, 10, 13, 16, 19, 22, 25.<br />
<br />
Another subgroup for which 28edo works quite well is 2.5.11.19.21.27.29.39.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Table of intervals"></a><!-- ws:end:WikiTextHeadingRule:4 -->Table of intervals</h1>
 The following table compares it to potentially useful nearby <a class="wiki_link" href="http://xenharmonic.wikispaces.com/just%20intervals">just intervals</a>.<br />
<br />


<table class="wiki_table">
    <tr>
        <td>Step #<br />
</td>
        <td>ET Cents coarse/fine<br />
DMS<br />
</td>
        <td>Just Interval<br />
</td>
        <td>Just Cents<br />
DMS<br />
</td>
        <td>Difference (ET minus Just)<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>42.86<br />
51.43<br />
12°<span style="background-color: #ffffff;">51'26&quot;</span><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>85.71<br />
102.86<br />
<span style="background-color: #ffffff;">25°42'51&quot;</span><br />
</td>
        <td>21:20<br />
</td>
        <td>84.47<br />
101.36<br />
<span style="background-color: #ffffff;">25°20'25&quot;</span><br />
</td>
        <td>1.24<br />
1.50<br />
22'26&quot;<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>128.57<br />
154.29<br />
38°<span style="background-color: #ffffff;">34'17&quot;</span><br />
</td>
        <td>14:13<br />
</td>
        <td>128.30<br />
153.96<br />
38°29<span style="background-color: #ffffff;">'22&quot;</span><br />
</td>
        <td>0.27<br />
0.33<br />
4'55&quot;<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>171.43<br />
205.71<br />
<span style="background-color: #ffffff;">51°25'43&quot;</span><br />
</td>
        <td>11:10<br />
</td>
        <td>165.00<br />
198.005<br />
<span style="background-color: #ffffff;">49°30'5&quot;</span><br />
</td>
        <td>6.43<br />
7.705<br />
1°55'38°<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>214.29<br />
257.14<br />
64°<span style="background-color: #ffffff;">17'9&quot;</span><br />
</td>
        <td>17:15<br />
</td>
        <td>216.69<br />
260.02<br />
65°22&quot;<br />
</td>
        <td>-2.40<br />
-2.88<br />
-43'13&quot;<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>257.14<br />
308.57<br />
<span style="background-color: #ffffff;">77°8'34&quot;</span><br />
</td>
        <td>7:6<br />
</td>
        <td>266.87<br />
320.245<br />
80°3'41&quot;<br />
</td>
        <td>-9.73<br />
-11.675<br />
-2°55'7&quot;<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>300<br />
360<br />
90°<br />
</td>
        <td>6:5<br />
</td>
        <td>315.64<br />
378.77<br />
94°41'33&quot;<br />
</td>
        <td>-15.64<br />
-18.77<br />
-4°41'33&quot;<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>342.86<br />
411.43<br />
<span style="background-color: #ffffff;">102°51'26&quot;</span><br />
</td>
        <td>11:9<br />
</td>
        <td>347.41<br />
416.89<br />
<span style="background-color: #ffffff;">104°13'21&quot;</span><br />
</td>
        <td>-4.55<br />
-5.46<br />
-1°21'55&quot;<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>385.71<br />
462.86<br />
115°<span style="background-color: #ffffff;">42'51&quot;</span><br />
</td>
        <td>5:4<br />
</td>
        <td>386.31<br />
463.58<br />
115°<span style="background-color: #ffffff;">53'39&quot;</span><br />
</td>
        <td>-0.60<br />
-0.72<br />
-10'48&quot;<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>428.57<br />
514.29<br />
<span style="background-color: #ffffff;">128°34'17&quot;</span><br />
</td>
        <td>9:7<br />
</td>
        <td>435.08<br />
522.10<br />
130°31'30&quot;<br />
</td>
        <td>-6.51<br />
-7.81<br />
-1°57'13&quot;<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>471.43<br />
565.71<br />
141°<span style="background-color: #ffffff;">25'43&quot;</span><br />
</td>
        <td>21:16<br />
</td>
        <td>470.78<br />
564.94<br />
141°<span style="background-color: #ffffff;">14'3&quot;</span><br />
</td>
        <td>0.65<br />
0.77<br />
11'40&quot;<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>514.29<br />
617.14<br />
<span style="background-color: #ffffff;">154°17'9&quot;</span><br />
</td>
        <td>4:3<br />
</td>
        <td>498.04<br />
597.65<br />
149°24<span style="background-color: #ffffff;">'49&quot;</span><br />
</td>
        <td>16.25<br />
19.49<br />
4°52'20&quot;<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>557.14<br />
668.57<br />
167°<span style="background-color: #ffffff;">8'34&quot;</span><br />
</td>
        <td>11:8<br />
</td>
        <td>551.32<br />
661.58<br />
165°<span style="background-color: #ffffff;">23'43&quot;</span><br />
</td>
        <td>5.82<br />
6.99<br />
1°45'9&quot;<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>600<br />
720<br />
<span style="background-color: #ffffff;">180°</span><br />
</td>
        <td>7:5 10:7<br />
</td>
        <td>582.51 617.49<br />
699.015 740.985<br />
174°45'13&quot; <span style="background-color: #ffffff;">185°14'47&quot;</span><br />
</td>
        <td>±17.49<br />
±20.985<br />
±<span style="background-color: #ffffff;">5°14'47&quot;</span><br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>642.86<br />
771.43<br />
<span style="background-color: #ffffff;">192°51'26&quot;</span><br />
</td>
        <td>16:11<br />
</td>
        <td>648.68<br />
778.42<br />
<span style="background-color: #ffffff;">194°36'35&quot;</span><br />
</td>
        <td>-5.82<br />
-6.99<br />
-1°45'9&quot;<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>685.71<br />
822.86<br />
<span style="background-color: #ffffff;">205°42'51&quot;</span><br />
</td>
        <td>3:2<br />
</td>
        <td>701.96<br />
842.35<br />
<span style="background-color: #ffffff;">210°35'11&quot;</span><br />
</td>
        <td>-16.25<br />
-19.49<br />
-4°52'20&quot;<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>728.57<br />
874.29<br />
218°<span style="background-color: #ffffff;">34'17&quot;</span><br />
</td>
        <td>32:21<br />
</td>
        <td>729.22<br />
875,06<br />
218°45'57&quot;<br />
</td>
        <td>-0.65<br />
-0.77<br />
-11'40&quot;<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>771.43<br />
925.71<br />
<span style="background-color: #ffffff;">231°25'43&quot;</span><br />
</td>
        <td>14:9<br />
</td>
        <td>764.92<br />
917.90<br />
229°28'30&quot;<br />
</td>
        <td>6.51<br />
7.81<br />
1°57'13&quot;<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>814.29<br />
977.14<br />
244°<span style="background-color: #ffffff;">17'9&quot;</span><br />
</td>
        <td>8:5<br />
</td>
        <td>813.68<br />
976.42<br />
244°<span style="background-color: #ffffff;">6'21&quot;</span><br />
</td>
        <td>0.61<br />
0.72<br />
10'48&quot;<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>857.14<br />
1028.57<br />
<span style="background-color: #ffffff;">257°8'34&quot;</span><br />
</td>
        <td>18:11<br />
</td>
        <td>852.59<br />
1023.11<br />
<span style="background-color: #ffffff;">258°30'29&quot;</span><br />
</td>
        <td>4.55<br />
5.46<br />
1°21'55&quot;<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>900<br />
1080<br />
270°<br />
</td>
        <td>5:3<br />
</td>
        <td>884.36<br />
1061.23<br />
265°18'27&quot;<br />
</td>
        <td>15.64<br />
18.77<br />
4°41'33&quot;<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>942.86<br />
1131.43<br />
<span style="background-color: #ffffff;">282°51'26&quot;</span><br />
</td>
        <td>12:7<br />
</td>
        <td>933.13<br />
1119.755<br />
<span style="background-color: #ffffff;">285°46'33&quot;</span><br />
</td>
        <td>9.73<br />
11.675<br />
2°55'7&quot;<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>985.71<br />
1185.86<br />
<span style="background-color: #ffffff;">295°42'51&quot;</span><br />
</td>
        <td>30:17<br />
</td>
        <td>983.31<br />
1182.98<br />
<span style="background-color: #ffffff;">296°26'4&quot;</span><br />
</td>
        <td>2.40<br />
2.88<br />
43'13&quot;<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>1028.57<br />
1234.29<br />
<span style="background-color: #ffffff;">308°34'17&quot;</span><br />
</td>
        <td>20:11<br />
</td>
        <td>1035.00<br />
1241.995<br />
310°29'55&quot;<br />
</td>
        <td>-6.43<br />
-7.705<br />
-1°55'38°<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>1071.42<br />
1285.71<br />
321°<span style="background-color: #ffffff;">25'43&quot;</span><br />
</td>
        <td>13:7<br />
</td>
        <td>1071.70<br />
1286.04<br />
321°<span style="background-color: #ffffff;">30'38&quot;</span><br />
</td>
        <td>-0.27<br />
-0.33<br />
-4'55&quot;<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>1114.29<br />
1336.14<br />
334°17'9&quot;<br />
</td>
        <td>40:21<br />
</td>
        <td>1115.53<br />
1337.64<br />
334°39'35&quot;<br />
</td>
        <td>-1.24<br />
-1.50<br />
-22'26&quot;<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>1157.14<br />
1387.57<br />
347°<span style="background-color: #ffffff;">8'34&quot;</span><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>1200, 1440<br />
<span style="background-color: #ffffff;">360°</span><br />
</td>
        <td>2:1<br />
</td>
        <td>1200, 1440<br />
</td>
        <td>0<br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Rank two temperaments"></a><!-- ws:end:WikiTextHeadingRule:6 --><span style="background-color: #ffffff;">Rank two temperaments</span></h1>
 <br />


<table class="wiki_table">
    <tr>
        <th>Periods<br />
per octave<br />
</th>
        <th>Generator<br />
</th>
        <th>Temperaments<br />
</th>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>1\28<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>3\28<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Negri">Negri</a><br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>5\28<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Machine">Machine</a><br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>9\28<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/W%C3%BCrschmidt%20family#Worschmidt">Worschmidt</a><br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>11\28<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>13\28<br />
</td>
        <td><span style="background-color: #ffffff;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Thuja">Thuja</a></span><br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>1\28<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>3\28<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>5\28<br />
</td>
        <td><a class="wiki_link" href="/antikythera">Antikythera</a><br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>1\28<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>2\28<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Diminished#Demolished">Demolished</a><br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>3\28<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>1\28<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Apotome%20family">Whitewood</a><br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>1\28<br />
</td>
        <td><br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:8 -->Commas</h1>
 28 EDO tempers out the following <a class="wiki_link" href="http://xenharmonic.wikispaces.com/comma">comma</a>s. (Note: This assumes the val &lt; <a class="wiki_link" href="http://tel.wikispaces.com/28%2044%2065%2079%2097%20104">28 44 65 79 97 104</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>
    </tr>
    <tr>
        <td style="text-align: center;">2187/2048<br />
</td>
        <td>| -11 7 &gt;<br />
</td>
        <td style="text-align: right;">113.69<br />
</td>
        <td style="text-align: center;">Apotome<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">648/625<br />
</td>
        <td>| 3 4 -4 &gt;<br />
</td>
        <td style="text-align: right;">62.57<br />
</td>
        <td style="text-align: center;">Major Diesis<br />
</td>
        <td style="text-align: center;">Diminished Comma<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">16875/16384<br />
</td>
        <td>| -14 3 4 &gt;<br />
</td>
        <td style="text-align: right;">51.12<br />
</td>
        <td style="text-align: center;">Negri Comma<br />
</td>
        <td style="text-align: center;">Double Augmentation Diesis<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td>| 17 1 -8 &gt;<br />
</td>
        <td style="text-align: right;">11.45<br />
</td>
        <td style="text-align: center;">Wuerschmidt Comma<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">36/35<br />
</td>
        <td>| 2 2 -1 -1 &gt;<br />
</td>
        <td style="text-align: right;">48.77<br />
</td>
        <td style="text-align: center;">Septimal Quarter Tone<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">50/49<br />
</td>
        <td>| 1 0 2 -2 &gt;<br />
</td>
        <td style="text-align: right;">34.98<br />
</td>
        <td style="text-align: center;">Tritonic Diesis<br />
</td>
        <td style="text-align: center;">Jubilisma<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">3125/3087<br />
</td>
        <td>| 0 -2 5 -3 &gt;<br />
</td>
        <td style="text-align: right;">21.18<br />
</td>
        <td style="text-align: center;">Gariboh<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">126/125<br />
</td>
        <td>| 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>
    </tr>
    <tr>
        <td style="text-align: center;">65625/65536<br />
</td>
        <td>| -16 1 5 1 &gt;<br />
</td>
        <td style="text-align: right;">2.35<br />
</td>
        <td style="text-align: center;">Horwell<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td>| 47 -7 -7 -7 &gt;<br />
</td>
        <td style="text-align: right;">0.34<br />
</td>
        <td style="text-align: center;">Akjaysma<br />
</td>
        <td style="text-align: center;">5\7 Octave Comma<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">176/175<br />
</td>
        <td>| 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>
    </tr>
    <tr>
        <td style="text-align: center;">441/440<br />
</td>
        <td>| -3 2 -1 2 -1 &gt;<br />
</td>
        <td style="text-align: right;">3.93<br />
</td>
        <td style="text-align: center;">Werckisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </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;">3.03<br />
</td>
        <td style="text-align: center;">Wizardharry<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Some scales"></a><!-- ws:end:WikiTextHeadingRule:10 -->Some scales</h1>
 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/machine5">machine5</a><br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/machine6">machine6</a><br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/machine11">machine11</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:12 -->Compositions</h1>
 <a class="wiki_link_ext" href="http://www.youtube.com/watch?v=26UpCbrb3mE" rel="nofollow">28 tone Prelude</a> by Kosmorksy</body></html>

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