28edo
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 18:17:03 UTC.
- The original revision id was 597598532.
- The revision comment was:
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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:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- 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:<h1> --><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:<h1> --><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:<h1> --><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"</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"</span><br />
</td>
<td>21:20<br />
</td>
<td>84.47<br />
101.36<br />
<span style="background-color: #ffffff;">25°20'25"</span><br />
</td>
<td>1.24<br />
1.50<br />
22'26"<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>128.57<br />
154.29<br />
38°<span style="background-color: #ffffff;">34'17"</span><br />
</td>
<td>14:13<br />
</td>
<td>128.30<br />
153.96<br />
38°29<span style="background-color: #ffffff;">'22"</span><br />
</td>
<td>0.27<br />
0.33<br />
4'55"<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>171.43<br />
205.71<br />
<span style="background-color: #ffffff;">51°25'43"</span><br />
</td>
<td>11:10<br />
</td>
<td>165.00<br />
198.005<br />
<span style="background-color: #ffffff;">49°30'5"</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"</span><br />
</td>
<td>17:15<br />
</td>
<td>216.69<br />
260.02<br />
65°22"<br />
</td>
<td>-2.40<br />
-2.88<br />
-43'13"<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>257.14<br />
308.57<br />
<span style="background-color: #ffffff;">77°8'34"</span><br />
</td>
<td>7:6<br />
</td>
<td>266.87<br />
320.245<br />
80°3'41"<br />
</td>
<td>-9.73<br />
-11.675<br />
-2°55'7"<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"<br />
</td>
<td>-15.64<br />
-18.77<br />
-4°41'33"<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>342.86<br />
411.43<br />
<span style="background-color: #ffffff;">102°51'26"</span><br />
</td>
<td>11:9<br />
</td>
<td>347.41<br />
416.89<br />
<span style="background-color: #ffffff;">104°13'21"</span><br />
</td>
<td>-4.55<br />
-5.46<br />
-1°21'55"<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>385.71<br />
462.86<br />
115°<span style="background-color: #ffffff;">42'51"</span><br />
</td>
<td>5:4<br />
</td>
<td>386.31<br />
463.58<br />
115°<span style="background-color: #ffffff;">53'39"</span><br />
</td>
<td>-0.60<br />
-0.72<br />
-10'48"<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>428.57<br />
514.29<br />
<span style="background-color: #ffffff;">128°34'17"</span><br />
</td>
<td>9:7<br />
</td>
<td>435.08<br />
522.10<br />
130°31'30"<br />
</td>
<td>-6.51<br />
-7.81<br />
-1°57'13"<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>471.43<br />
565.71<br />
141°<span style="background-color: #ffffff;">25'43"</span><br />
</td>
<td>21:16<br />
</td>
<td>470.78<br />
564.94<br />
141°<span style="background-color: #ffffff;">14'3"</span><br />
</td>
<td>0.65<br />
0.77<br />
11'40"<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>514.29<br />
617.14<br />
<span style="background-color: #ffffff;">154°17'9"</span><br />
</td>
<td>4:3<br />
</td>
<td>498.04<br />
597.65<br />
149°24<span style="background-color: #ffffff;">'49"</span><br />
</td>
<td>16.25<br />
19.49<br />
4°52'20"<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>557.14<br />
668.57<br />
167°<span style="background-color: #ffffff;">8'34"</span><br />
</td>
<td>11:8<br />
</td>
<td>551.32<br />
661.58<br />
165°<span style="background-color: #ffffff;">23'43"</span><br />
</td>
<td>5.82<br />
6.99<br />
1°45'9"<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" <span style="background-color: #ffffff;">185°14'47"</span><br />
</td>
<td>±17.49<br />
±20.985<br />
±<span style="background-color: #ffffff;">5°14'47"</span><br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>642.86<br />
771.43<br />
<span style="background-color: #ffffff;">192°51'26"</span><br />
</td>
<td>16:11<br />
</td>
<td>648.68<br />
778.42<br />
<span style="background-color: #ffffff;">194°36'35"</span><br />
</td>
<td>-5.82<br />
-6.99<br />
-1°45'9"<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>685.71<br />
822.86<br />
<span style="background-color: #ffffff;">205°42'51"</span><br />
</td>
<td>3:2<br />
</td>
<td>701.96<br />
842.35<br />
<span style="background-color: #ffffff;">210°35'11"</span><br />
</td>
<td>-16.25<br />
-19.49<br />
-4°52'20"<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>728.57<br />
874.29<br />
218°<span style="background-color: #ffffff;">34'17"</span><br />
</td>
<td>32:21<br />
</td>
<td>729.22<br />
875,06<br />
218°45'57"<br />
</td>
<td>-0.65<br />
-0.77<br />
-11'40"<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>771.43<br />
925.71<br />
<span style="background-color: #ffffff;">231°25'43"</span><br />
</td>
<td>14:9<br />
</td>
<td>764.92<br />
917.90<br />
229°28'30"<br />
</td>
<td>6.51<br />
7.81<br />
1°57'13"<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>814.29<br />
977.14<br />
244°<span style="background-color: #ffffff;">17'9"</span><br />
</td>
<td>8:5<br />
</td>
<td>813.68<br />
976.42<br />
244°<span style="background-color: #ffffff;">6'21"</span><br />
</td>
<td>0.61<br />
0.72<br />
10'48"<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>857.14<br />
1028.57<br />
<span style="background-color: #ffffff;">257°8'34"</span><br />
</td>
<td>18:11<br />
</td>
<td>852.59<br />
1023.11<br />
<span style="background-color: #ffffff;">258°30'29"</span><br />
</td>
<td>4.55<br />
5.46<br />
1°21'55"<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"<br />
</td>
<td>15.64<br />
18.77<br />
4°41'33"<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>942.86<br />
1131.43<br />
<span style="background-color: #ffffff;">282°51'26"</span><br />
</td>
<td>12:7<br />
</td>
<td>933.13<br />
1119.755<br />
<span style="background-color: #ffffff;">285°46'33"</span><br />
</td>
<td>9.73<br />
11.675<br />
2°55'7"<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>985.71<br />
1185.86<br />
<span style="background-color: #ffffff;">295°42'51"</span><br />
</td>
<td>30:17<br />
</td>
<td>983.31<br />
1182.98<br />
<span style="background-color: #ffffff;">296°26'4"</span><br />
</td>
<td>2.40<br />
2.88<br />
43'13"<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>1028.57<br />
1234.29<br />
<span style="background-color: #ffffff;">308°34'17"</span><br />
</td>
<td>20:11<br />
</td>
<td>1035.00<br />
1241.995<br />
310°29'55"<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"</span><br />
</td>
<td>13:7<br />
</td>
<td>1071.70<br />
1286.04<br />
321°<span style="background-color: #ffffff;">30'38"</span><br />
</td>
<td>-0.27<br />
-0.33<br />
-4'55"<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>1114.29<br />
1336.14<br />
334°17'9"<br />
</td>
<td>40:21<br />
</td>
<td>1115.53<br />
1337.64<br />
334°39'35"<br />
</td>
<td>-1.24<br />
-1.50<br />
-22'26"<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>1157.14<br />
1387.57<br />
347°<span style="background-color: #ffffff;">8'34"</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:<h1> --><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:<h1> --><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 < <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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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:<h1> --><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:<h1> --><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>