28edo: Difference between revisions

Revision as of 04:36, 26 December 2016

IMPORTED REVISION FROM WIKISPACES

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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 ||= Just Interval ||= Just Cents ||= Difference 
(ET minus Just) ||||||= [[xenharmonic/Ups and Downs Notation|Up/down]]
[[xenharmonic/Ups and Downs Notation|Notation]] ||
||= 0 ||= 0¢ ||= 1/1 ||= 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 < [[tel/28 44 65 79 97 104/1 |.)||~ 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="#Chord Names">Chord Names</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | <a href="#Rank two temperaments">Rank two temperaments</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --> | <a href="#Commas">Commas</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 />
<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;">1/1<br />
</td>
        <td style="text-align: center;">0¢<br />
</td>
        <td style="text-align: center;">0¢<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:&lt;h1&gt; --><h1 id="toc3"><a name="Chord Names"></a><!-- ws:end:WikiTextHeadingRule:6 --><!-- ws:start:WikiTextAnchorRule:23:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Chord Names&quot; title=&quot;Anchor: Chord Names&quot;/&gt; --><a name="Chord Names"></a><!-- ws:end:WikiTextAnchorRule:23 -->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:&lt;h1&gt; --><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:&lt;h1&gt; --><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 &lt; <a class="wiki_link" href="http://tel.wikispaces.com/-/28%2044%2065%2079%2097%20104/1%20%7C.%29%7C%7C~%20Comma%20%7C%7C~%20Monzo%20%7C%7C~%20Value%20%28Cents%29%20%7C%7C~%20Name%201%20%7C%7C~%20Name%202%20%7C%7C%7C%7C%3D%202187/2048">| | -11 7 &gt; ||&gt; 113.69 ||= Apotome ||= ||||= 648/625 || | 3 4 -4 &gt; ||&gt; 62.57 ||= Major Diesis ||= Diminished Comma ||||= 16875/16384 || | -14 3 4 &gt; ||&gt; 51.12 ||= Negri Comma ||= Double Augmentation Diesis ||||= || | 17 1 -8 &gt; ||&gt; 11.45 ||= Wuerschmidt Comma ||= ||||= 36/35 || | 2 2 -1 -1 &gt; ||&gt; 48.77 ||= Septimal Quarter Tone ||= ||||= 50/49 || | 1 0 2 -2 &gt; ||&gt; 34.98 ||= Tritonic Diesis ||= Jubilisma ||||= 3125/3087 || | 0 -2 5 -3 &gt; ||&gt; 21.18 ||= Gariboh ||= ||||= 126/125 || | 1 2 -3 1 &gt; ||&gt; 13.79 ||= Septimal Semicomma ||= Starling Comma ||||= 65625/65536 || | -16 1 5 1 &gt; ||&gt; 2.35 ||= Horwell ||= ||||= || | 47 -7 -7 -7 &gt; ||&gt; 0.34 ||= Akjaysma ||= 5\7 Octave Comma ||||= 176/175 || | 4 0 -2 -1 1 &gt; ||&gt; 9.86 ||= Valinorsma ||= ||||= 441/440 || | -3 2 -1 2 -1 &gt; ||&gt; 3.93 ||= Werckisma ||= ||||= 4000/3993 || | 5 -1 3 0 -3 &gt; ||&gt; 3.03 ||= Wizardharry ||= ||=Some scales= [[xenharmonic/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>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-05 15:14:37 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-26 04:36:49 UTC</tt>.<br>
-: The original revision id was <tt>601449620</tt>.<br>
+: The original revision id was <tt>602812588</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
@@ Line 20: / Line 20: @@
 The following table compares it to potentially useful nearby [[xenharmonic/just intervals|just intervals]].
-|| Step # || ET Cents coarse/fine
-DMS || Just Interval || Just Cents
+||= Step # ||= ET Cents ||= Just Interval ||= Just Cents ||= Difference
-DMS || Difference (ET minus Just) ||
+(ET minus Just) ||||||= [[xenharmonic/Ups and Downs Notation|Up/down]]
-|| 1 || 42.86
+[[xenharmonic/Ups and Downs Notation|Notation]] ||
-.43
+||= 0 ||= 0¢ ||= 1/1 ||= 0¢ ||= 0¢ ||= unison ||= 1 ||= D ||
-°&lt;span style="background-color: #ffffff;"&gt;51'26"&lt;/span&gt; ||   ||   ||   ||
+||= 1 ||= 42.86 ||=   ||=   ||=   ||= up-unison ||= ^1 ||= D^ ||
-|| 2 || 85.71
+||= 2 ||= 85.71 ||= 21:20 ||= 84.47 ||= 1.24 ||= double-up, double-down ||= ^^1, vv2 ||= D^^, Evv ||
-.86
+||= 3 ||= 128.57 ||= 14:13 ||= 128.30 ||= 0.27 ||= down 2nd ||= v2 ||= Ev ||
-&lt;span style="background-color: #ffffff;"&gt;25°42'51"&lt;/span&gt; || 21:20 || 84.47
+||= 4 ||= 171.43 ||= 11:10 ||= 165.00 ||= 6.43 ||= 2nd ||= 2 ||= E ||
-.36
+||= 5 ||= 214.29 ||= 17:15 ||= 216.69 ||= -2.40 ||= up 2nd ||= ^2 ||= E^ ||
-&lt;span style="background-color: #ffffff;"&gt;25°20'25"&lt;/span&gt; || 1.24
+||= 6 ||= 257.14 ||= 7:6 ||= 266.87 ||= -9.73 ||= double-up 2nd, double-down 3rd ||= ^^2, vv3 ||= E^^, Fvv ||
-.50
+||= 7 ||= 300 ||= 6:5 ||= 315.64 ||= -15.64 ||= down 3rd ||= v3 ||= Fv ||
-'26" ||
+||= 8 ||= 342.86 ||= 11:9 ||= 347.41 ||= -4.55 ||= 3rd ||= 3 ||= F ||
-|| 3 || 128.57
+||= 9 ||= 385.71 ||= 5:4 ||= 386.31 ||= -0.60 ||= up 3rd ||= ^3 ||= F^ ||
-.29
+||= 10 ||= 428.57 ||= 9:7 ||= 435.08 ||= -6.51 ||= double-up 3rd, double-down 4th ||= ^^3, vv4 ||= F^^, Gvv ||
-°&lt;span style="background-color: #ffffff;"&gt;34'17"&lt;/span&gt; || 14:13 || 128.30
+||= 11 ||= 471.43 ||= 21:16 ||= 470.78 ||= 0.65 ||= down 4th ||= v4 ||= Gv ||
-.96
+||= 12 ||= 514.29 ||= 4:3 ||= 498.04 ||= 16.25 ||= 4th ||= 4 ||= G ||
-°29&lt;span style="background-color: #ffffff;"&gt;'22"&lt;/span&gt; || 0.27
+||= 13 ||= 557.14 ||= 11:8 ||= 551.32 ||= 5.82 ||= up 4th ||= ^4 ||= G^ ||
-.33
+||= 14 ||= 600 ||= 7:5 ||= 582.51 ||= 17.49 ||= double-up 4th, double-down 5th ||= ^^4, vv5 ||= G^^, vvA ||
-'55" ||
+||= 15 ||= 642.86 ||= 16:11 ||= 648.68 ||= -5.82 ||= down 5th ||= v5 ||= Av ||
-|| 4 || 171.43
+||= 16 ||= 685.71 ||= 3:2 ||= 701.96 ||= -16.25 ||= 5th ||= 5 ||= A ||
-.71
+||= 17 ||= 728.57 ||= 32:21 ||= 729.22 ||= -0.65 ||= up 5th ||= ^5 ||= A^ ||
-&lt;span style="background-color: #ffffff;"&gt;51°25'43"&lt;/span&gt; || 11:10 || 165.00
+||= 18 ||= 771.43 ||= 14:9 ||= 764.92 ||= 6.51 ||= double-up 5th, double-down 6th ||= ^^5, vv6 ||= A^^, Bvv ||
-.005
+||= 19 ||= 814.29 ||= 5:8 ||= 813.68 ||= 0.61 ||= down 6th ||= v6 ||= Bv ||
-&lt;span style="background-color: #ffffff;"&gt;49°30'5"&lt;/span&gt; || 6.43
+||= 20 ||= 857.14 ||= 18:11 ||= 852.59 ||= 4.55 ||= 6th ||= 6 ||= B ||
-.705
+||= 21 ||= 900 ||= 5:3 ||= 884.36 ||= 15.64 ||= up 6th ||= ^6 ||= B^ ||
-°55'38° ||
+||= 22 ||= 942.86 ||= 12:7 ||= 933.13 ||= 9.73 ||= double-up 6th, double-down 7th ||= ^^6, vv7 ||= B^^, Cvv ||
-|| 5 || 214.29
+||= 23 ||= 985.71 ||= 30:17 ||= 983.31 ||= 2.40 ||= down 7th ||= v7 ||= Cv ||
-.14
+||= 24 ||= 1028.57 ||= 20:11 ||= 1035.00 ||= -6.43 ||= 7th ||= 7 ||= C ||
-°&lt;span style="background-color: #ffffff;"&gt;17'9"&lt;/span&gt; || 17:15 || 216.69
+||= 25 ||= 1071.42 ||= 13:7 ||= 1071.70 ||= -0.27 ||= up 7th ||= ^7 ||= C^ ||
-.02
+||= 26 ||= 1114.29 ||= 40:21 ||= 1115.53 ||= -1.24 ||= double-up 7th, double-down 8ve ||= ^^7, vv8 ||= C^^, Dvv ||
-°22" || -2.40
+||= 27 ||= 1157.14 ||=   ||=   ||=   ||= down 8ve ||= v8 ||= Dv ||
--2.88
+||= 28 ||= 1200 ||= 2:1 ||= 1200 ||= 0 ||= 8ve ||= 8 ||= D ||
--43'13" ||
-|| 6 || 257.14
+=[[#Chord Names]]Chord Names=
-.57
-&lt;span style="background-color: #ffffff;"&gt;77°8'34"&lt;/span&gt; || 7:6 || 266.87
+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.
-.245
-°3'41" || -9.73
+-8-16 = C E G = C = C or C perfect
--11.675
+-7-16 = C Ev G = C(v3) = C down-three
--2°55'7" ||
+-9-16 = C E^ G = C(^3) = C up-three
-|| 7 || 300
+-8-15 = C E Gv = C(v5) = C down-five
+-9-17 = C E^ G^ = C(^3,^5) = C up-three up-five
-° || 6:5 || 315.64
-.77
+-8-16-24 = C E G B = C7 = C seven
-°41'33" || -15.64
+-8-16-23 = C E G Bv = C(v7) = C down-seven
--18.77
+-7-16-24 = C Ev G B = C7(v3) = C seven down-three
--4°41'33" ||
+-7-16-23 = C Ev G Bv = C.v7 = C dot down seven
-|| 8 || 342.86
-.43
+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]].
-&lt;span style="background-color: #ffffff;"&gt;102°51'26"&lt;/span&gt; || 11:9 || 347.41
-.89
-&lt;span style="background-color: #ffffff;"&gt;104°13'21"&lt;/span&gt; || -4.55
--5.46
--1°21'55" ||
-|| 9 || 385.71
-.86
-°&lt;span style="background-color: #ffffff;"&gt;42'51"&lt;/span&gt; || 5:4 || 386.31
-.58
-°&lt;span style="background-color: #ffffff;"&gt;53'39"&lt;/span&gt; || -0.60
--0.72
--10'48" ||
-|| 10 || 428.57
-.29
-&lt;span style="background-color: #ffffff;"&gt;128°34'17"&lt;/span&gt; || 9:7 || 435.08
-.10
-°31'30" || -6.51
--7.81
--1°57'13" ||
-|| 11 || 471.43
-.71
-°&lt;span style="background-color: #ffffff;"&gt;25'43"&lt;/span&gt; || 21:16 || 470.78
-.94
-°&lt;span style="background-color: #ffffff;"&gt;14'3"&lt;/span&gt; || 0.65
-.77
-'40" ||
-|| 12 || 514.29
-.14
-&lt;span style="background-color: #ffffff;"&gt;154°17'9"&lt;/span&gt; || 4:3 || 498.04
-.65
-°24&lt;span style="background-color: #ffffff;"&gt;'49"&lt;/span&gt; || 16.25
-.49
-°52'20" ||
-|| 13 || 557.14
-.57
-°&lt;span style="background-color: #ffffff;"&gt;8'34"&lt;/span&gt; || 11:8 || 551.32
-.58
-°&lt;span style="background-color: #ffffff;"&gt;23'43"&lt;/span&gt; || 5.82
-.99
-°45'9" ||
-|| 14 || 600
-&lt;span style="background-color: #ffffff;"&gt;180°&lt;/span&gt; || 7:5 10:7 || 582.51 617.49
-.015 740.985
-°45'13" &lt;span style="background-color: #ffffff;"&gt;185°14'47"&lt;/span&gt; || ±17.49
-±20.985
-±&lt;span style="background-color: #ffffff;"&gt;5°14'47"&lt;/span&gt; ||
-|| 15 || 642.86
-.43
-&lt;span style="background-color: #ffffff;"&gt;192°51'26"&lt;/span&gt; || 16:11 || 648.68
-.42
-&lt;span style="background-color: #ffffff;"&gt;194°36'35"&lt;/span&gt; || -5.82
--6.99
--1°45'9" ||
-|| 16 || 685.71
-.86
-&lt;span style="background-color: #ffffff;"&gt;205°42'51"&lt;/span&gt; || 3:2 || 701.96
-.35
-&lt;span style="background-color: #ffffff;"&gt;210°35'11"&lt;/span&gt; || -16.25
--19.49
--4°52'20" ||
-|| 17 || 728.57
-.29
-°&lt;span style="background-color: #ffffff;"&gt;34'17"&lt;/span&gt; || 32:21 || 729.22
-,06
-°45'57" || -0.65
--0.77
--11'40" ||
-|| 18 || 771.43
-.71
-&lt;span style="background-color: #ffffff;"&gt;231°25'43"&lt;/span&gt; || 14:9 || 764.92
-.90
-°28'30" || 6.51
-.81
-°57'13" ||
-|| 19 || 814.29
-.14
-°&lt;span style="background-color: #ffffff;"&gt;17'9"&lt;/span&gt; || 8:5 || 813.68
-.42
-°&lt;span style="background-color: #ffffff;"&gt;6'21"&lt;/span&gt; || 0.61
-.72
-'48" ||
-|| 20 || 857.14
-.57
-&lt;span style="background-color: #ffffff;"&gt;257°8'34"&lt;/span&gt; || 18:11 || 852.59
-.11
-&lt;span style="background-color: #ffffff;"&gt;258°30'29"&lt;/span&gt; || 4.55
-.46
-°21'55" ||
-|| 21 || 900
-° || 5:3 || 884.36
-.23
-°18'27" || 15.64
-.77
-°41'33" ||
-|| 22 || 942.86
-.43
-&lt;span style="background-color: #ffffff;"&gt;282°51'26"&lt;/span&gt; || 12:7 || 933.13
-.755
-&lt;span style="background-color: #ffffff;"&gt;285°46'33"&lt;/span&gt; || 9.73
-.675
-°55'7" ||
-|| 23 || 985.71
-.86
-&lt;span style="background-color: #ffffff;"&gt;295°42'51"&lt;/span&gt; || 30:17 || 983.31
-.98
-&lt;span style="background-color: #ffffff;"&gt;296°26'4"&lt;/span&gt; || 2.40
-.88
-'13" ||
-|| 24 || 1028.57
-.29
-&lt;span style="background-color: #ffffff;"&gt;308°34'17"&lt;/span&gt; || 20:11 || 1035.00
-.995
-°29'55" || -6.43
--7.705
--1°55'38° ||
-|| 25 || 1071.42
-.71
-°&lt;span style="background-color: #ffffff;"&gt;25'43"&lt;/span&gt; || 13:7 || 1071.70
-.04
-°&lt;span style="background-color: #ffffff;"&gt;30'38"&lt;/span&gt; || -0.27
--0.33
--4'55" ||
-|| 26 || 1114.29
-.14
-°17'9" || 40:21 || 1115.53
-.64
-°39'35" || -1.24
--1.50
--22'26" ||
-|| 27 || 1157.14
-.57
-°&lt;span style="background-color: #ffffff;"&gt;8'34"&lt;/span&gt; ||   ||   ||   ||
-|| 28 || 1200, 1440
-&lt;span style="background-color: #ffffff;"&gt;360°&lt;/span&gt; || 2:1 || 1200, 1440 || 0 ||
 =&lt;span style="background-color: #ffffff;"&gt;Rank two temperaments&lt;/span&gt;=
@@ Line 226: / Line 92: @@
 =Commas=
-EDO tempers out the following [[xenharmonic/comma|comma]]s. (Note: This assumes the val &lt; [[tel/28 44 65 79 97 104/1 |.)
+EDO tempers out the following [[xenharmonic/comma|comma]]s. (Note: This assumes the val &lt; [[tel/28 44 65 79 97 104/1 |.)||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||||= 2187/2048|| | -11 7 &gt; ||&gt; 113.69 ||= Apotome ||= ||||= 648/625 || | 3 4 -4 &gt; ||&gt; 62.57 ||= Major Diesis ||= Diminished Comma ||||= 16875/16384 || | -14 3 4 &gt; ||&gt; 51.12 ||= Negri Comma ||= Double Augmentation Diesis ||||= || | 17 1 -8 &gt; ||&gt; 11.45 ||= Wuerschmidt Comma ||= ||||= 36/35 || | 2 2 -1 -1 &gt; ||&gt; 48.77 ||= Septimal Quarter Tone ||= ||||= 50/49 || | 1 0 2 -2 &gt; ||&gt; 34.98 ||= Tritonic Diesis ||= Jubilisma ||||= 3125/3087 || | 0 -2 5 -3 &gt; ||&gt; 21.18 ||= Gariboh ||= ||||= 126/125 || | 1 2 -3 1 &gt; ||&gt; 13.79 ||= Septimal Semicomma ||= Starling Comma ||||= 65625/65536 || | -16 1 5 1 &gt; ||&gt; 2.35 ||= Horwell ||= ||||= || | 47 -7 -7 -7 &gt; ||&gt; 0.34 ||= Akjaysma ||= 5\7 Octave Comma ||||= 176/175 || | 4 0 -2 -1 1 &gt; ||&gt; 9.86 ||= Valinorsma ||= ||||= 441/440 || | -3 2 -1 2 -1 &gt; ||&gt; 3.93 ||= Werckisma ||= ||||= 4000/3993 || | 5 -1 3 0 -3 &gt; ||&gt; 3.03 ||= Wizardharry ||= ||=Some scales= [[xenharmonic/machine5|machine5]]
-||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||
-||= 2187/2048 || | -11 7 &gt; ||&gt; 113.69 ||= Apotome ||=   ||
-||= 648/625 || | 3 4 -4 &gt; ||&gt; 62.57 ||= Major Diesis ||= Diminished Comma ||
-||= 16875/16384 || | -14 3 4 &gt; ||&gt; 51.12 ||= Negri Comma ||= Double Augmentation Diesis ||
-||=   || | 17 1 -8 &gt; ||&gt; 11.45 ||= Wuerschmidt Comma ||=   ||
-||= 36/35 || | 2 2 -1 -1 &gt; ||&gt; 48.77 ||= Septimal Quarter Tone ||=   ||
-||= 50/49 || | 1 0 2 -2 &gt; ||&gt; 34.98 ||= Tritonic Diesis ||= Jubilisma ||
-||= 3125/3087 || | 0 -2 5 -3 &gt; ||&gt; 21.18 ||= Gariboh ||=   ||
-||= 126/125 || | 1 2 -3 1 &gt; ||&gt; 13.79 ||= Septimal Semicomma ||= Starling Comma ||
-||= 65625/65536 || | -16 1 5 1 &gt; ||&gt; 2.35 ||= Horwell ||=   ||
-||=   || | 47 -7 -7 -7 &gt; ||&gt; 0.34 ||= Akjaysma ||= 5\7 Octave Comma ||
-||= 176/175 || | 4 0 -2 -1 1 &gt; ||&gt; 9.86 ||= Valinorsma ||=   ||
-||= 441/440 || | -3 2 -1 2 -1 &gt; ||&gt; 3.93 ||= Werckisma ||=   ||
-||= 4000/3993 || | 5 -1 3 0 -3 &gt; ||&gt; 3.03 ||= Wizardharry ||=   ||
-=Some scales=
-[[xenharmonic/machine5|machine5]]
 [[xenharmonic/machine6|machine6]]
 [[xenharmonic/machine11|machine11]]
@@ Line 250: / Line 99: @@
 [[http://www.youtube.com/watch?v=26UpCbrb3mE|28 tone Prelude]] by Kosmorksy</pre></div>
 <h4>Original HTML content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;28edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:12:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt;&lt;a href="#Basic properties"&gt;Basic properties&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;!-- ws:start:WikiTextTocRule:14: --&gt; | &lt;a href="#Subgroups"&gt;Subgroups&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt; | &lt;a href="#Table of intervals"&gt;Table of intervals&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt; | &lt;a href="#Rank two temperaments"&gt;Rank two temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt; | &lt;a href="#Commas"&gt;Commas&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt; | &lt;a href="#Compositions"&gt;Compositions&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;
+<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;28edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:14:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt;&lt;a href="#Basic properties"&gt;Basic properties&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt; | &lt;a href="#Subgroups"&gt;Subgroups&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt; | &lt;a href="#Table of intervals"&gt;Table of intervals&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt; | &lt;a href="#Chord Names"&gt;Chord Names&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt; | &lt;a href="#Rank two temperaments"&gt;Rank two temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextTocRule:20: --&gt; | &lt;a href="#Commas"&gt;Commas&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt; | &lt;a href="#Compositions"&gt;Compositions&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt;
-&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;hr /&gt;
+&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;hr /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Basic properties"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Basic properties&lt;/h1&gt;
@@ Line 263: / Line 112: @@
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Table of intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Table of intervals&lt;/h1&gt;
   The following table compares it to potentially useful nearby &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/just%20intervals"&gt;just intervals&lt;/a&gt;.&lt;br /&gt;
+&lt;br /&gt;
 &lt;br /&gt;
@@ Line 268: / Line 118: @@
 &lt;table class="wiki_table"&gt;
      &lt;tr&gt;
-         &lt;td&gt;Step #&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Step #&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;ET Cents&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;ET Cents coarse/fine&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Just Interval&lt;br /&gt;
-DMS&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Just Interval&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Just Cents&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Just Cents&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Difference &lt;br /&gt;
-DMS&lt;br /&gt;
+(ET minus Just)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Difference (ET minus Just)&lt;br /&gt;
+         &lt;td colspan="3" style="text-align: center;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation"&gt;Up/down&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation"&gt;Notation&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;0&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;0¢&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;1/1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;0¢&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;42.86&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;0¢&lt;br /&gt;
-.43&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;51'26&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;unison&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;D&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;42.86&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;85.71&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
-.86&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;25°42'51&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;21:20&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;up-unison&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;84.47&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^1&lt;br /&gt;
-.36&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;25°20'25&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1.24&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;D^&lt;br /&gt;
-.50&lt;br /&gt;
-'26&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;3&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;85.71&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;128.57&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;21:20&lt;br /&gt;
-.29&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;34'17&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;14:13&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;84.47&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;128.30&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1.24&lt;br /&gt;
-.96&lt;br /&gt;
-°29&lt;span style="background-color: #ffffff;"&gt;'22&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;0.27&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;double-up, double-down&lt;br /&gt;
-.33&lt;br /&gt;
+&lt;/td&gt;
-'55&amp;quot;&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;^^1, vv2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;D^^, Evv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;4&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;128.57&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;14:13&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;128.30&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;171.43&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;0.27&lt;br /&gt;
-.71&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;51°25'43&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;11:10&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;down 2nd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;165.00&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;v2&lt;br /&gt;
-.005&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;49°30'5&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;6.43&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Ev&lt;br /&gt;
-.705&lt;br /&gt;
-°55'38°&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;5&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;171.43&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;11:10&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;165.00&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;214.29&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;6.43&lt;br /&gt;
-.14&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;17'9&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;17:15&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;2nd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;216.69&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;2&lt;br /&gt;
-.02&lt;br /&gt;
-°22&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;-2.40&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;E&lt;br /&gt;
--2.88&lt;br /&gt;
--43'13&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;6&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;214.29&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;17:15&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;216.69&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;257.14&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;-2.40&lt;br /&gt;
-.57&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;77°8'34&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;7:6&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;up 2nd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;266.87&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^2&lt;br /&gt;
-.245&lt;br /&gt;
-°3'41&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;-9.73&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;E^&lt;br /&gt;
--11.675&lt;br /&gt;
--2°55'7&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;7&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;257.14&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;7:6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;266.87&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;300&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;-9.73&lt;br /&gt;
-&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;6:5&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;double-up 2nd, double-down 3rd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;315.64&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^^2, vv3&lt;br /&gt;
-.77&lt;br /&gt;
-°41'33&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;-15.64&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;E^^, Fvv&lt;br /&gt;
--18.77&lt;br /&gt;
--4°41'33&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;8&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;300&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;6:5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;315.64&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;342.86&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;-15.64&lt;br /&gt;
-.43&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;102°51'26&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;11:9&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;down 3rd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;347.41&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;v3&lt;br /&gt;
-.89&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;104°13'21&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;-4.55&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Fv&lt;br /&gt;
--5.46&lt;br /&gt;
--1°21'55&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;9&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;342.86&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;11:9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;347.41&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;385.71&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;-4.55&lt;br /&gt;
-.86&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;42'51&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;5:4&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;3rd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;386.31&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;3&lt;br /&gt;
-.58&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;53'39&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;-0.60&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;F&lt;br /&gt;
--0.72&lt;br /&gt;
--10'48&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;10&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;385.71&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;428.57&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;5:4&lt;br /&gt;
-.29&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;128°34'17&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;9:7&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;386.31&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;435.08&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;-0.60&lt;br /&gt;
-.10&lt;br /&gt;
-°31'30&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;-6.51&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;up 3rd&lt;br /&gt;
--7.81&lt;br /&gt;
+&lt;/td&gt;
--1°57'13&amp;quot;&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;^3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;F^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;11&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;10&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;428.57&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;9:7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;435.08&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;471.43&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;-6.51&lt;br /&gt;
-.71&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;25'43&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;21:16&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;double-up 3rd, double-down 4th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;470.78&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^^3, vv4&lt;br /&gt;
-.94&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;14'3&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;0.65&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;F^^, Gvv&lt;br /&gt;
-.77&lt;br /&gt;
-'40&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;12&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;471.43&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;21:16&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;470.78&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;514.29&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;0.65&lt;br /&gt;
-.14&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;154°17'9&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;4:3&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;down 4th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;498.04&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;v4&lt;br /&gt;
-.65&lt;br /&gt;
-°24&lt;span style="background-color: #ffffff;"&gt;'49&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;16.25&lt;br /&gt;
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-.49&lt;br /&gt;
-°52'20&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;13&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;12&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;557.14&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;514.29&lt;br /&gt;
-.57&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;8'34&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;11:8&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;4:3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;551.32&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;498.04&lt;br /&gt;
-.58&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;23'43&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;5.82&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;16.25&lt;br /&gt;
-.99&lt;br /&gt;
+&lt;/td&gt;
-°45'9&amp;quot;&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;4th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;G&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;14&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;13&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;557.14&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;11:8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;551.32&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;5.82&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;up 4th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;^4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;G^&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;14&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;600&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;7:5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;582.51&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;600&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;17.49&lt;br /&gt;
-&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;180°&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;7:5 10:7&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;double-up 4th, double-down 5th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;582.51 617.49&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^^4, vv5&lt;br /&gt;
-.015 740.985&lt;br /&gt;
-°45'13&amp;quot; &lt;span style="background-color: #ffffff;"&gt;185°14'47&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;±17.49&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;G^^, vvA&lt;br /&gt;
-±20.985&lt;br /&gt;
-±&lt;span style="background-color: #ffffff;"&gt;5°14'47&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;15&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;15&lt;br /&gt;
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+        &lt;td style="text-align: center;"&gt;642.86&lt;br /&gt;
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+        &lt;td style="text-align: center;"&gt;16:11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;648.68&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;642.86&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;-5.82&lt;br /&gt;
-.43&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;192°51'26&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;16:11&lt;br /&gt;
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 &lt;/td&gt;
-         &lt;td&gt;648.68&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;v5&lt;br /&gt;
-.42&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;194°36'35&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;-5.82&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Av&lt;br /&gt;
--6.99&lt;br /&gt;
--1°45'9&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;16&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;16&lt;br /&gt;
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+        &lt;td style="text-align: center;"&gt;685.71&lt;br /&gt;
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+        &lt;td style="text-align: center;"&gt;3:2&lt;br /&gt;
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+        &lt;td style="text-align: center;"&gt;701.96&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;685.71&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;-16.25&lt;br /&gt;
-.86&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;205°42'51&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;3:2&lt;br /&gt;
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 &lt;/td&gt;
-         &lt;td&gt;701.96&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;5&lt;br /&gt;
-.35&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;210°35'11&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;-16.25&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;A&lt;br /&gt;
--19.49&lt;br /&gt;
--4°52'20&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;17&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;17&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;728.57&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;728.57&lt;br /&gt;
-.29&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;34'17&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;32:21&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;32:21&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;729.22&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;729.22&lt;br /&gt;
-,06&lt;br /&gt;
-°45'57&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;-0.65&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;-0.65&lt;br /&gt;
--0.77&lt;br /&gt;
+&lt;/td&gt;
--11'40&amp;quot;&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;up 5th&lt;br /&gt;
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+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;A^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;18&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;18&lt;br /&gt;
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+        &lt;td style="text-align: center;"&gt;771.43&lt;br /&gt;
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+        &lt;td style="text-align: center;"&gt;14:9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;764.92&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;771.43&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;6.51&lt;br /&gt;
-.71&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;231°25'43&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;14:9&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;double-up 5th, double-down 6th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;764.92&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^^5, vv6&lt;br /&gt;
-.90&lt;br /&gt;
-°28'30&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;6.51&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;A^^, Bvv&lt;br /&gt;
-.81&lt;br /&gt;
-°57'13&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;19&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;19&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;814.29&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;5:8&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;814.29&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;813.68&lt;br /&gt;
-.14&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;17'9&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;8:5&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;0.61&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;813.68&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;down 6th&lt;br /&gt;
-.42&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;6'21&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;0.61&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;v6&lt;br /&gt;
-.72&lt;br /&gt;
+&lt;/td&gt;
-'48&amp;quot;&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;Bv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;20&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;20&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;857.14&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;857.14&lt;br /&gt;
-.57&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;257°8'34&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;18:11&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;18:11&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;852.59&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;852.59&lt;br /&gt;
-.11&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;258°30'29&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;4.55&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;4.55&lt;br /&gt;
-.46&lt;br /&gt;
+&lt;/td&gt;
-°21'55&amp;quot;&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;6th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;B&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;21&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;21&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;900&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;900&lt;br /&gt;
-&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;5:3&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;5:3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;884.36&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;884.36&lt;br /&gt;
-.23&lt;br /&gt;
-°18'27&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;15.64&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;15.64&lt;br /&gt;
-.77&lt;br /&gt;
+&lt;/td&gt;
-°41'33&amp;quot;&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;up 6th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;^6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;B^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;22&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;22&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;942.86&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;942.86&lt;br /&gt;
-.43&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;282°51'26&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;12:7&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;12:7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;933.13&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;933.13&lt;br /&gt;
-.755&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;285°46'33&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;9.73&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;9.73&lt;br /&gt;
-.675&lt;br /&gt;
+&lt;/td&gt;
-°55'7&amp;quot;&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;double-up 6th, double-down 7th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;^^6, vv7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;B^^, Cvv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;23&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;23&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;985.71&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;30:17&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;983.31&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;985.71&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;2.40&lt;br /&gt;
-.86&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;295°42'51&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;30:17&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;down 7th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;983.31&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;v7&lt;br /&gt;
-.98&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;296°26'4&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;2.40&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Cv&lt;br /&gt;
-.88&lt;br /&gt;
-'13&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;24&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;24&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;1028.57&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;20:11&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1028.57&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1035.00&lt;br /&gt;
-.29&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;308°34'17&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;20:11&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;-6.43&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1035.00&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;7th&lt;br /&gt;
-.995&lt;br /&gt;
-°29'55&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;-6.43&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;7&lt;br /&gt;
--7.705&lt;br /&gt;
+&lt;/td&gt;
--1°55'38°&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;C&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;25&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;25&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1071.42&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1071.42&lt;br /&gt;
-.71&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;25'43&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;13:7&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;13:7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1071.70&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1071.70&lt;br /&gt;
-.04&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;30'38&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;-0.27&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;-0.27&lt;br /&gt;
--0.33&lt;br /&gt;
+&lt;/td&gt;
--4'55&amp;quot;&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;up 7th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;^7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;C^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;26&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;26&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1114.29&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1114.29&lt;br /&gt;
-.14&lt;br /&gt;
-°17'9&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;40:21&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;40:21&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1115.53&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1115.53&lt;br /&gt;
-.64&lt;br /&gt;
-°39'35&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;-1.24&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;-1.24&lt;br /&gt;
--1.50&lt;br /&gt;
+&lt;/td&gt;
--22'26&amp;quot;&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;double-up 7th, double-down 8ve&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;^^7, vv8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;C^^, Dvv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;27&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;27&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;1157.14&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1157.14&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
-.57&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;8'34&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;down 8ve&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;v8&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Dv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;28&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;28&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;1200&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;2:1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1200, 1440&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1200&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;360°&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;2:1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1200, 1440&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;8ve&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;0&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;D&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
 &lt;/table&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Rank two temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;&lt;span style="background-color: #ffffff;"&gt;Rank two temperaments&lt;/span&gt;&lt;/h1&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Chord Names"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:23:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Chord Names&amp;quot; title=&amp;quot;Anchor: Chord Names&amp;quot;/&amp;gt; --&gt;&lt;a name="Chord Names"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:23 --&gt;Chord Names&lt;/h1&gt;
+ &lt;br /&gt;
+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.&lt;br /&gt;
+&lt;br /&gt;
+-8-16 = C E G = C = C or C perfect&lt;br /&gt;
+-7-16 = C Ev G = C(v3) = C down-three&lt;br /&gt;
+-9-16 = C E^ G = C(^3) = C up-three&lt;br /&gt;
+-8-15 = C E Gv = C(v5) = C down-five&lt;br /&gt;
+-9-17 = C E^ G^ = C(^3,^5) = C up-three up-five&lt;br /&gt;
+&lt;br /&gt;
+-8-16-24 = C E G B = C7 = C seven&lt;br /&gt;
+-8-16-23 = C E G Bv = C(v7) = C down-seven&lt;br /&gt;
+-7-16-24 = C Ev G B = C7(v3) = C seven down-three&lt;br /&gt;
+-7-16-23 = C Ev G Bv = C.v7 = C dot down seven&lt;br /&gt;
+&lt;br /&gt;
+For a more complete list, see &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Chord%20names%20in%20other%20EDOs"&gt;Ups and Downs Notation - Chord names in other EDOs&lt;/a&gt;.&lt;br /&gt;
+&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Rank two temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;&lt;span style="background-color: #ffffff;"&gt;Rank two temperaments&lt;/span&gt;&lt;/h1&gt;
   &lt;br /&gt;
@@ Line 903: / Line 805: @@
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Commas&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Commas&lt;/h1&gt;
-EDO tempers out the following &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/comma"&gt;comma&lt;/a&gt;s. (Note: This assumes the val &amp;lt; &lt;a class="wiki_link" href="http://tel.wikispaces.com/-/28%2044%2065%2079%2097%20104/1%20%7C.%29%7C%7C~%20Comma%20%7C%7C~%20Monzo%20%7C%7C~%20Value%20%28Cents%29%20%7C%7C~%20Name%201%20%7C%7C~%20Name%202%20%7C%7C%7C%7C%3D%202187/2048"&gt;| | -11 7 &amp;gt; ||&amp;gt; 113.69 ||= Apotome ||=   ||||= 648/625 || | 3 4 -4 &amp;gt; ||&amp;gt; 62.57 ||= Major Diesis ||= Diminished Comma ||||= 16875/16384 || | -14 3 4 &amp;gt; ||&amp;gt; 51.12 ||= Negri Comma ||= Double Augmentation Diesis ||||=   || | 17 1 -8 &amp;gt; ||&amp;gt; 11.45 ||= Wuerschmidt Comma ||=   ||||= 36/35 || | 2 2 -1 -1 &amp;gt; ||&amp;gt; 48.77 ||= Septimal Quarter Tone ||=   ||||= 50/49 || | 1 0 2 -2 &amp;gt; ||&amp;gt; 34.98 ||= Tritonic Diesis ||= Jubilisma ||||= 3125/3087 || | 0 -2 5 -3 &amp;gt; ||&amp;gt; 21.18 ||= Gariboh ||=   ||||= 126/125 || | 1 2 -3 1 &amp;gt; ||&amp;gt; 13.79 ||= Septimal Semicomma ||= Starling Comma ||||= 65625/65536 || | -16 1 5 1 &amp;gt; ||&amp;gt; 2.35 ||= Horwell ||=   ||||=   || | 47 -7 -7 -7 &amp;gt; ||&amp;gt; 0.34 ||= Akjaysma ||= 5\7 Octave Comma ||||= 176/175 || | 4 0 -2 -1 1 &amp;gt; ||&amp;gt; 9.86 ||= Valinorsma ||=   ||||= 441/440 || | -3 2 -1 2 -1 &amp;gt; ||&amp;gt; 3.93 ||= Werckisma ||=   ||||= 4000/3993 || | 5 -1 3 0 -3 &amp;gt; ||&amp;gt; 3.03 ||= Wizardharry ||=   ||=Some scales= [[xenharmonic/machine5|machine5&lt;/a&gt;&lt;br /&gt;
+EDO tempers out the following &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/comma"&gt;comma&lt;/a&gt;s. (Note: This assumes the val &amp;lt; &lt;a class="wiki_link" href="http://tel.wikispaces.com/-/28%2044%2065%2079%2097%20104/1%20%7C.%29%7C%7C~%20Comma%20%7C%7C~%20Monzo%20%7C%7C~%20Value%20%28Cents%29%20%7C%7C~%20Name%201%20%7C%7C~%20Name%202%20%7C%7C%7C%7C%3D%202187/2048"&gt;| | -11 7 &amp;gt; ||&amp;gt; 113.69 ||= Apotome ||= ||||= 648/625 || | 3 4 -4 &amp;gt; ||&amp;gt; 62.57 ||= Major Diesis ||= Diminished Comma ||||= 16875/16384 || | -14 3 4 &amp;gt; ||&amp;gt; 51.12 ||= Negri Comma ||= Double Augmentation Diesis ||||= || | 17 1 -8 &amp;gt; ||&amp;gt; 11.45 ||= Wuerschmidt Comma ||= ||||= 36/35 || | 2 2 -1 -1 &amp;gt; ||&amp;gt; 48.77 ||= Septimal Quarter Tone ||= ||||= 50/49 || | 1 0 2 -2 &amp;gt; ||&amp;gt; 34.98 ||= Tritonic Diesis ||= Jubilisma ||||= 3125/3087 || | 0 -2 5 -3 &amp;gt; ||&amp;gt; 21.18 ||= Gariboh ||= ||||= 126/125 || | 1 2 -3 1 &amp;gt; ||&amp;gt; 13.79 ||= Septimal Semicomma ||= Starling Comma ||||= 65625/65536 || | -16 1 5 1 &amp;gt; ||&amp;gt; 2.35 ||= Horwell ||= ||||= || | 47 -7 -7 -7 &amp;gt; ||&amp;gt; 0.34 ||= Akjaysma ||= 5\7 Octave Comma ||||= 176/175 || | 4 0 -2 -1 1 &amp;gt; ||&amp;gt; 9.86 ||= Valinorsma ||= ||||= 441/440 || | -3 2 -1 2 -1 &amp;gt; ||&amp;gt; 3.93 ||= Werckisma ||= ||||= 4000/3993 || | 5 -1 3 0 -3 &amp;gt; ||&amp;gt; 3.03 ||= Wizardharry ||= ||=Some scales= [[xenharmonic/machine5|machine5&lt;/a&gt;&lt;br /&gt;
 &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/machine6"&gt;machine6&lt;/a&gt;&lt;br /&gt;
 &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/machine11"&gt;machine11&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Compositions&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Compositions&lt;/h1&gt;
   &lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=26UpCbrb3mE" rel="nofollow"&gt;28 tone Prelude&lt;/a&gt; by Kosmorksy&lt;/body&gt;&lt;/html&gt;</pre></div>

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