28edo
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author TallKite and made on 2016-12-26 04:44:47 UTC.
- The original revision id was 602812686.
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Original Wikitext content:
[[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 ||= Just Interval ||= Just Cents ||= Difference (ET minus Just) ||||||= [[xenharmonic/Ups and Downs Notation|Up/down]] [[xenharmonic/Ups and Downs Notation|Notation]] || ||= 0 ||= 0¢ ||= ||= ||= ||= unison ||= 1 ||= D || ||= 1 ||= 42.86 ||= ||= ||= ||= up-unison ||= ^1 ||= D^ || ||= 2 ||= 85.71 ||= 21:20 ||= 84.47 ||= 1.24 ||= double-up, double-down ||= ^^1, vv2 ||= D^^, Evv || ||= 3 ||= 128.57 ||= 14:13 ||= 128.30 ||= 0.27 ||= down 2nd ||= v2 ||= Ev || ||= 4 ||= 171.43 ||= 11:10 ||= 165.00 ||= 6.43 ||= 2nd ||= 2 ||= E || ||= 5 ||= 214.29 ||= 17:15 ||= 216.69 ||= -2.40 ||= up 2nd ||= ^2 ||= E^ || ||= 6 ||= 257.14 ||= 7:6 ||= 266.87 ||= -9.73 ||= double-up 2nd, double-down 3rd ||= ^^2, vv3 ||= E^^, Fvv || ||= 7 ||= 300 ||= 6:5 ||= 315.64 ||= -15.64 ||= down 3rd ||= v3 ||= Fv || ||= 8 ||= 342.86 ||= 11:9 ||= 347.41 ||= -4.55 ||= 3rd ||= 3 ||= F || ||= 9 ||= 385.71 ||= 5:4 ||= 386.31 ||= -0.60 ||= up 3rd ||= ^3 ||= F^ || ||= 10 ||= 428.57 ||= 9:7 ||= 435.08 ||= -6.51 ||= double-up 3rd, double-down 4th ||= ^^3, vv4 ||= F^^, Gvv || ||= 11 ||= 471.43 ||= 21:16 ||= 470.78 ||= 0.65 ||= down 4th ||= v4 ||= Gv || ||= 12 ||= 514.29 ||= 4:3 ||= 498.04 ||= 16.25 ||= 4th ||= 4 ||= G || ||= 13 ||= 557.14 ||= 11:8 ||= 551.32 ||= 5.82 ||= up 4th ||= ^4 ||= G^ || ||= 14 ||= 600 ||= 7:5 ||= 582.51 ||= 17.49 ||= double-up 4th, double-down 5th ||= ^^4, vv5 ||= G^^, vvA || ||= 15 ||= 642.86 ||= 16:11 ||= 648.68 ||= -5.82 ||= down 5th ||= v5 ||= Av || ||= 16 ||= 685.71 ||= 3:2 ||= 701.96 ||= -16.25 ||= 5th ||= 5 ||= A || ||= 17 ||= 728.57 ||= 32:21 ||= 729.22 ||= -0.65 ||= up 5th ||= ^5 ||= A^ || ||= 18 ||= 771.43 ||= 14:9 ||= 764.92 ||= 6.51 ||= double-up 5th, double-down 6th ||= ^^5, vv6 ||= A^^, Bvv || ||= 19 ||= 814.29 ||= 5:8 ||= 813.68 ||= 0.61 ||= down 6th ||= v6 ||= Bv || ||= 20 ||= 857.14 ||= 18:11 ||= 852.59 ||= 4.55 ||= 6th ||= 6 ||= B || ||= 21 ||= 900 ||= 5:3 ||= 884.36 ||= 15.64 ||= up 6th ||= ^6 ||= B^ || ||= 22 ||= 942.86 ||= 12:7 ||= 933.13 ||= 9.73 ||= double-up 6th, double-down 7th ||= ^^6, vv7 ||= B^^, Cvv || ||= 23 ||= 985.71 ||= 30:17 ||= 983.31 ||= 2.40 ||= down 7th ||= v7 ||= Cv || ||= 24 ||= 1028.57 ||= 20:11 ||= 1035.00 ||= -6.43 ||= 7th ||= 7 ||= C || ||= 25 ||= 1071.42 ||= 13:7 ||= 1071.70 ||= -0.27 ||= up 7th ||= ^7 ||= C^ || ||= 26 ||= 1114.29 ||= 40:21 ||= 1115.53 ||= -1.24 ||= double-up 7th, double-down 8ve ||= ^^7, vv8 ||= C^^, Dvv || ||= 27 ||= 1157.14 ||= ||= ||= ||= down 8ve ||= v8 ||= Dv || ||= 28 ||= 1200 ||= 2:1 ||= 1200 ||= 0 ||= 8ve ||= 8 ||= D || =[[#Chord Names]]Chord Names= Ups and downs can be used to name 28edo chords. Because every interval is perfect, the quality can be omitted, and the words major, minor, augmented and diminished are never used. 0-8-16 = C E G = C = C or C perfect 0-7-16 = C Ev G = C(v3) = C down-three 0-9-16 = C E^ G = C(^3) = C up-three 0-8-15 = C E Gv = C(v5) = C down-five 0-9-17 = C E^ G^ = C(^3,^5) = C up-three up-five 0-8-16-24 = C E G B = C7 = C seven 0-8-16-23 = C E G Bv = C(v7) = C down-seven 0-7-16-24 = C Ev G B = C7(v3) = C seven down-three 0-7-16-23 = C Ev G Bv = C.v7 = C dot down seven For a more complete list, see [[xenharmonic/Ups and Downs Notation#Chord%20names%20in%20other%20EDOs|Ups and Downs Notation - Chord names in other EDOs]]. =<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 < 28 44 65 79 97 104 |.) ||~ Comma ||~ Monzo ||~ 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:16:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --><a href="#Basic properties">Basic properties</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#Subgroups">Subgroups</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | <a href="#Table of intervals">Table of intervals</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --> | <a href="#Chord Names">Chord Names</a><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --> | <a href="#Rank two temperaments">Rank two temperaments</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --> | <a href="#Some scales">Some scales</a><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> | <a href="#Compositions">Compositions</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: -->
<!-- ws:end:WikiTextTocRule:25 --><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 style="text-align: center;">Step #<br />
</td>
<td style="text-align: center;">ET Cents<br />
</td>
<td style="text-align: center;">Just Interval<br />
</td>
<td style="text-align: center;">Just Cents<br />
</td>
<td style="text-align: center;">Difference<br />
(ET minus Just)<br />
</td>
<td colspan="3" style="text-align: center;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation">Up/down</a><br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation">Notation</a><br />
</td>
</tr>
<tr>
<td style="text-align: center;">0<br />
</td>
<td style="text-align: center;">0¢<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">unison<br />
</td>
<td style="text-align: center;">1<br />
</td>
<td style="text-align: center;">D<br />
</td>
</tr>
<tr>
<td style="text-align: center;">1<br />
</td>
<td style="text-align: center;">42.86<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">up-unison<br />
</td>
<td style="text-align: center;">^1<br />
</td>
<td style="text-align: center;">D^<br />
</td>
</tr>
<tr>
<td style="text-align: center;">2<br />
</td>
<td style="text-align: center;">85.71<br />
</td>
<td style="text-align: center;">21:20<br />
</td>
<td style="text-align: center;">84.47<br />
</td>
<td style="text-align: center;">1.24<br />
</td>
<td style="text-align: center;">double-up, double-down<br />
</td>
<td style="text-align: center;">^^1, vv2<br />
</td>
<td style="text-align: center;">D^^, Evv<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3<br />
</td>
<td style="text-align: center;">128.57<br />
</td>
<td style="text-align: center;">14:13<br />
</td>
<td style="text-align: center;">128.30<br />
</td>
<td style="text-align: center;">0.27<br />
</td>
<td style="text-align: center;">down 2nd<br />
</td>
<td style="text-align: center;">v2<br />
</td>
<td style="text-align: center;">Ev<br />
</td>
</tr>
<tr>
<td style="text-align: center;">4<br />
</td>
<td style="text-align: center;">171.43<br />
</td>
<td style="text-align: center;">11:10<br />
</td>
<td style="text-align: center;">165.00<br />
</td>
<td style="text-align: center;">6.43<br />
</td>
<td style="text-align: center;">2nd<br />
</td>
<td style="text-align: center;">2<br />
</td>
<td style="text-align: center;">E<br />
</td>
</tr>
<tr>
<td style="text-align: center;">5<br />
</td>
<td style="text-align: center;">214.29<br />
</td>
<td style="text-align: center;">17:15<br />
</td>
<td style="text-align: center;">216.69<br />
</td>
<td style="text-align: center;">-2.40<br />
</td>
<td style="text-align: center;">up 2nd<br />
</td>
<td style="text-align: center;">^2<br />
</td>
<td style="text-align: center;">E^<br />
</td>
</tr>
<tr>
<td style="text-align: center;">6<br />
</td>
<td style="text-align: center;">257.14<br />
</td>
<td style="text-align: center;">7:6<br />
</td>
<td style="text-align: center;">266.87<br />
</td>
<td style="text-align: center;">-9.73<br />
</td>
<td style="text-align: center;">double-up 2nd, double-down 3rd<br />
</td>
<td style="text-align: center;">^^2, vv3<br />
</td>
<td style="text-align: center;">E^^, Fvv<br />
</td>
</tr>
<tr>
<td style="text-align: center;">7<br />
</td>
<td style="text-align: center;">300<br />
</td>
<td style="text-align: center;">6:5<br />
</td>
<td style="text-align: center;">315.64<br />
</td>
<td style="text-align: center;">-15.64<br />
</td>
<td style="text-align: center;">down 3rd<br />
</td>
<td style="text-align: center;">v3<br />
</td>
<td style="text-align: center;">Fv<br />
</td>
</tr>
<tr>
<td style="text-align: center;">8<br />
</td>
<td style="text-align: center;">342.86<br />
</td>
<td style="text-align: center;">11:9<br />
</td>
<td style="text-align: center;">347.41<br />
</td>
<td style="text-align: center;">-4.55<br />
</td>
<td style="text-align: center;">3rd<br />
</td>
<td style="text-align: center;">3<br />
</td>
<td style="text-align: center;">F<br />
</td>
</tr>
<tr>
<td style="text-align: center;">9<br />
</td>
<td style="text-align: center;">385.71<br />
</td>
<td style="text-align: center;">5:4<br />
</td>
<td style="text-align: center;">386.31<br />
</td>
<td style="text-align: center;">-0.60<br />
</td>
<td style="text-align: center;">up 3rd<br />
</td>
<td style="text-align: center;">^3<br />
</td>
<td style="text-align: center;">F^<br />
</td>
</tr>
<tr>
<td style="text-align: center;">10<br />
</td>
<td style="text-align: center;">428.57<br />
</td>
<td style="text-align: center;">9:7<br />
</td>
<td style="text-align: center;">435.08<br />
</td>
<td style="text-align: center;">-6.51<br />
</td>
<td style="text-align: center;">double-up 3rd, double-down 4th<br />
</td>
<td style="text-align: center;">^^3, vv4<br />
</td>
<td style="text-align: center;">F^^, Gvv<br />
</td>
</tr>
<tr>
<td style="text-align: center;">11<br />
</td>
<td style="text-align: center;">471.43<br />
</td>
<td style="text-align: center;">21:16<br />
</td>
<td style="text-align: center;">470.78<br />
</td>
<td style="text-align: center;">0.65<br />
</td>
<td style="text-align: center;">down 4th<br />
</td>
<td style="text-align: center;">v4<br />
</td>
<td style="text-align: center;">Gv<br />
</td>
</tr>
<tr>
<td style="text-align: center;">12<br />
</td>
<td style="text-align: center;">514.29<br />
</td>
<td style="text-align: center;">4:3<br />
</td>
<td style="text-align: center;">498.04<br />
</td>
<td style="text-align: center;">16.25<br />
</td>
<td style="text-align: center;">4th<br />
</td>
<td style="text-align: center;">4<br />
</td>
<td style="text-align: center;">G<br />
</td>
</tr>
<tr>
<td style="text-align: center;">13<br />
</td>
<td style="text-align: center;">557.14<br />
</td>
<td style="text-align: center;">11:8<br />
</td>
<td style="text-align: center;">551.32<br />
</td>
<td style="text-align: center;">5.82<br />
</td>
<td style="text-align: center;">up 4th<br />
</td>
<td style="text-align: center;">^4<br />
</td>
<td style="text-align: center;">G^<br />
</td>
</tr>
<tr>
<td style="text-align: center;">14<br />
</td>
<td style="text-align: center;">600<br />
</td>
<td style="text-align: center;">7:5<br />
</td>
<td style="text-align: center;">582.51<br />
</td>
<td style="text-align: center;">17.49<br />
</td>
<td style="text-align: center;">double-up 4th, double-down 5th<br />
</td>
<td style="text-align: center;">^^4, vv5<br />
</td>
<td style="text-align: center;">G^^, vvA<br />
</td>
</tr>
<tr>
<td style="text-align: center;">15<br />
</td>
<td style="text-align: center;">642.86<br />
</td>
<td style="text-align: center;">16:11<br />
</td>
<td style="text-align: center;">648.68<br />
</td>
<td style="text-align: center;">-5.82<br />
</td>
<td style="text-align: center;">down 5th<br />
</td>
<td style="text-align: center;">v5<br />
</td>
<td style="text-align: center;">Av<br />
</td>
</tr>
<tr>
<td style="text-align: center;">16<br />
</td>
<td style="text-align: center;">685.71<br />
</td>
<td style="text-align: center;">3:2<br />
</td>
<td style="text-align: center;">701.96<br />
</td>
<td style="text-align: center;">-16.25<br />
</td>
<td style="text-align: center;">5th<br />
</td>
<td style="text-align: center;">5<br />
</td>
<td style="text-align: center;">A<br />
</td>
</tr>
<tr>
<td style="text-align: center;">17<br />
</td>
<td style="text-align: center;">728.57<br />
</td>
<td style="text-align: center;">32:21<br />
</td>
<td style="text-align: center;">729.22<br />
</td>
<td style="text-align: center;">-0.65<br />
</td>
<td style="text-align: center;">up 5th<br />
</td>
<td style="text-align: center;">^5<br />
</td>
<td style="text-align: center;">A^<br />
</td>
</tr>
<tr>
<td style="text-align: center;">18<br />
</td>
<td style="text-align: center;">771.43<br />
</td>
<td style="text-align: center;">14:9<br />
</td>
<td style="text-align: center;">764.92<br />
</td>
<td style="text-align: center;">6.51<br />
</td>
<td style="text-align: center;">double-up 5th, double-down 6th<br />
</td>
<td style="text-align: center;">^^5, vv6<br />
</td>
<td style="text-align: center;">A^^, Bvv<br />
</td>
</tr>
<tr>
<td style="text-align: center;">19<br />
</td>
<td style="text-align: center;">814.29<br />
</td>
<td style="text-align: center;">5:8<br />
</td>
<td style="text-align: center;">813.68<br />
</td>
<td style="text-align: center;">0.61<br />
</td>
<td style="text-align: center;">down 6th<br />
</td>
<td style="text-align: center;">v6<br />
</td>
<td style="text-align: center;">Bv<br />
</td>
</tr>
<tr>
<td style="text-align: center;">20<br />
</td>
<td style="text-align: center;">857.14<br />
</td>
<td style="text-align: center;">18:11<br />
</td>
<td style="text-align: center;">852.59<br />
</td>
<td style="text-align: center;">4.55<br />
</td>
<td style="text-align: center;">6th<br />
</td>
<td style="text-align: center;">6<br />
</td>
<td style="text-align: center;">B<br />
</td>
</tr>
<tr>
<td style="text-align: center;">21<br />
</td>
<td style="text-align: center;">900<br />
</td>
<td style="text-align: center;">5:3<br />
</td>
<td style="text-align: center;">884.36<br />
</td>
<td style="text-align: center;">15.64<br />
</td>
<td style="text-align: center;">up 6th<br />
</td>
<td style="text-align: center;">^6<br />
</td>
<td style="text-align: center;">B^<br />
</td>
</tr>
<tr>
<td style="text-align: center;">22<br />
</td>
<td style="text-align: center;">942.86<br />
</td>
<td style="text-align: center;">12:7<br />
</td>
<td style="text-align: center;">933.13<br />
</td>
<td style="text-align: center;">9.73<br />
</td>
<td style="text-align: center;">double-up 6th, double-down 7th<br />
</td>
<td style="text-align: center;">^^6, vv7<br />
</td>
<td style="text-align: center;">B^^, Cvv<br />
</td>
</tr>
<tr>
<td style="text-align: center;">23<br />
</td>
<td style="text-align: center;">985.71<br />
</td>
<td style="text-align: center;">30:17<br />
</td>
<td style="text-align: center;">983.31<br />
</td>
<td style="text-align: center;">2.40<br />
</td>
<td style="text-align: center;">down 7th<br />
</td>
<td style="text-align: center;">v7<br />
</td>
<td style="text-align: center;">Cv<br />
</td>
</tr>
<tr>
<td style="text-align: center;">24<br />
</td>
<td style="text-align: center;">1028.57<br />
</td>
<td style="text-align: center;">20:11<br />
</td>
<td style="text-align: center;">1035.00<br />
</td>
<td style="text-align: center;">-6.43<br />
</td>
<td style="text-align: center;">7th<br />
</td>
<td style="text-align: center;">7<br />
</td>
<td style="text-align: center;">C<br />
</td>
</tr>
<tr>
<td style="text-align: center;">25<br />
</td>
<td style="text-align: center;">1071.42<br />
</td>
<td style="text-align: center;">13:7<br />
</td>
<td style="text-align: center;">1071.70<br />
</td>
<td style="text-align: center;">-0.27<br />
</td>
<td style="text-align: center;">up 7th<br />
</td>
<td style="text-align: center;">^7<br />
</td>
<td style="text-align: center;">C^<br />
</td>
</tr>
<tr>
<td style="text-align: center;">26<br />
</td>
<td style="text-align: center;">1114.29<br />
</td>
<td style="text-align: center;">40:21<br />
</td>
<td style="text-align: center;">1115.53<br />
</td>
<td style="text-align: center;">-1.24<br />
</td>
<td style="text-align: center;">double-up 7th, double-down 8ve<br />
</td>
<td style="text-align: center;">^^7, vv8<br />
</td>
<td style="text-align: center;">C^^, Dvv<br />
</td>
</tr>
<tr>
<td style="text-align: center;">27<br />
</td>
<td style="text-align: center;">1157.14<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">down 8ve<br />
</td>
<td style="text-align: center;">v8<br />
</td>
<td style="text-align: center;">Dv<br />
</td>
</tr>
<tr>
<td style="text-align: center;">28<br />
</td>
<td style="text-align: center;">1200<br />
</td>
<td style="text-align: center;">2:1<br />
</td>
<td style="text-align: center;">1200<br />
</td>
<td style="text-align: center;">0<br />
</td>
<td style="text-align: center;">8ve<br />
</td>
<td style="text-align: center;">8<br />
</td>
<td style="text-align: center;">D<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="Chord Names"></a><!-- ws:end:WikiTextHeadingRule:6 --><!-- ws:start:WikiTextAnchorRule:26:<img src="/i/anchor.gif" class="WikiAnchor" alt="Anchor" id="wikitext@@anchor@@Chord Names" title="Anchor: Chord Names"/> --><a name="Chord Names"></a><!-- ws:end:WikiTextAnchorRule:26 -->Chord Names</h1>
<br />
Ups and downs can be used to name 28edo chords. Because every interval is perfect, the quality can be omitted, and the words major, minor, augmented and diminished are never used.<br />
<br />
0-8-16 = C E G = C = C or C perfect<br />
0-7-16 = C Ev G = C(v3) = C down-three<br />
0-9-16 = C E^ G = C(^3) = C up-three<br />
0-8-15 = C E Gv = C(v5) = C down-five<br />
0-9-17 = C E^ G^ = C(^3,^5) = C up-three up-five<br />
<br />
0-8-16-24 = C E G B = C7 = C seven<br />
0-8-16-23 = C E G Bv = C(v7) = C down-seven<br />
0-7-16-24 = C Ev G B = C7(v3) = C seven down-three<br />
0-7-16-23 = C Ev G Bv = C.v7 = C dot down seven<br />
<br />
For a more complete list, see <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Chord%20names%20in%20other%20EDOs">Ups and Downs Notation - Chord names in other EDOs</a>.<br />
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:<h1> --><h1 id="toc4"><a name="Rank two temperaments"></a><!-- ws:end:WikiTextHeadingRule:8 --><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:10:<h1> --><h1 id="toc5"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:10 -->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 < 28 44 65 79 97 104 |.)<br />
<br />
<table class="wiki_table">
<tr>
<th>Comma<br />
</th>
<th>Monzo<br />
</th>
<th>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 style="text-align: left;">| -11 7 ><br />
</td>
<td style="text-align: center;">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 style="text-align: left;">| 3 4 -4 ><br />
</td>
<td style="text-align: center;">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 style="text-align: left;">| -14 3 4 ><br />
</td>
<td style="text-align: center;">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 style="text-align: left;">| 17 1 -8 ><br />
</td>
<td style="text-align: center;">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 style="text-align: left;">| 2 2 -1 -1 ><br />
</td>
<td style="text-align: center;">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 style="text-align: left;">| 1 0 2 -2 ><br />
</td>
<td style="text-align: center;">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 style="text-align: left;">| 0 -2 5 -3 ><br />
</td>
<td style="text-align: center;">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 style="text-align: left;">| 1 2 -3 1 ><br />
</td>
<td style="text-align: center;">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 style="text-align: left;">| -16 1 5 1 ><br />
</td>
<td style="text-align: center;">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 style="text-align: left;">| 47 -7 -7 -7 ><br />
</td>
<td style="text-align: center;">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 style="text-align: left;">| 4 0 -2 -1 1 ><br />
</td>
<td style="text-align: center;">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 style="text-align: left;">| -3 2 -1 2 -1 ><br />
</td>
<td style="text-align: center;">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 style="text-align: left;">| 5 -1 3 0 -3 ><br />
</td>
<td style="text-align: center;">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:12:<h1> --><h1 id="toc6"><a name="Some scales"></a><!-- ws:end:WikiTextHeadingRule:12 -->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:14:<h1> --><h1 id="toc7"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:14 -->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>