28edo: Difference between revisions
Wikispaces>JosephRuhf **Imported revision 601449620 - Original comment: ** |
Wikispaces>TallKite **Imported revision 602812588 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : 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> | : The original revision id was <tt>602812588</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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The following table compares it to potentially useful nearby [[xenharmonic/just intervals|just intervals]]. | The following table compares it to potentially useful nearby [[xenharmonic/just intervals|just intervals]]. | ||
|| Step # || ET Cents | |||
||= Step # ||= ET Cents ||= Just Interval ||= Just Cents ||= Difference | |||
(ET minus Just) ||||||= [[xenharmonic/Ups and Downs Notation|Up/down]] | |||
|| 1 || 42.86 | [[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 | ||= 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 || | |||
|| 3 || 128.57 | ||= 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 || | |||
|| 4 || 171.43 | ||= 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 || | |||
|| 5 || 214.29 | ||= 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 || | |||
|| 6 || 257.14 | =[[#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 | ||
|| 7 || 300 | 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 | |||
|| 8 || 342.86 | |||
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]]. | |||
|| 9 || 385.71 | |||
|| 10 || 428.57 | |||
- | |||
- | |||
|| 11 || 471.43 | |||
|| 12 || 514.29 | |||
|| 13 || 557.14 | |||
|| 14 || 600 | |||
|| 15 || 642.86 | |||
|| 16 || 685.71 | |||
|| 17 || 728.57 | |||
|| 18 || 771.43 | |||
|| 19 || 814.29 | |||
|| 20 || 857.14 | |||
|| 21 || 900 | |||
|| 22 || 942.86 | |||
|| 23 || 985.71 | |||
|| 24 || 1028.57 | |||
|| 25 || 1071.42 | |||
|| 26 || 1114.29 | |||
- | |||
- | |||
|| 27 || 1157.14 | |||
|| 28 || 1200 | |||
=<span style="background-color: #ffffff;">Rank two temperaments</span>= | =<span style="background-color: #ffffff;">Rank two temperaments</span>= | ||
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=Commas= | =Commas= | ||
28 EDO tempers out the following [[xenharmonic/comma|comma]]s. (Note: This assumes the val < [[tel/28 44 65 79 97 104/1 |.) | 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]] | ||
||~ 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 || | |||
||= | |||
||= 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 ||= | |||
||= | |||
||= 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/machine6|machine6]] | ||
[[xenharmonic/machine11|machine11]] | [[xenharmonic/machine11|machine11]] | ||
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[[http://www.youtube.com/watch?v=26UpCbrb3mE|28 tone Prelude]] by Kosmorksy</pre></div> | [[http://www.youtube.com/watch?v=26UpCbrb3mE|28 tone Prelude]] by Kosmorksy</pre></div> | ||
<h4>Original HTML content:</h4> | <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"><html><head><title>28edo</title></head><body><!-- ws:start:WikiTextTocRule: | <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"><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: | <!-- ws:end:WikiTextTocRule:22 --><hr /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Basic properties"></a><!-- ws:end:WikiTextHeadingRule:0 -->Basic properties</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Basic properties"></a><!-- ws:end:WikiTextHeadingRule:0 -->Basic properties</h1> | ||
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<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Table of intervals"></a><!-- ws:end:WikiTextHeadingRule:4 -->Table of intervals</h1> | <!-- 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 /> | 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 /> | <br /> | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<td>Step #<br /> | <td style="text-align: center;">Step #<br /> | ||
</td> | |||
<td style="text-align: center;">ET Cents<br /> | |||
</td> | </td> | ||
<td | <td style="text-align: center;">Just Interval<br /> | ||
</td> | </td> | ||
<td>Just | <td style="text-align: center;">Just Cents<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">Difference <br /> | ||
(ET minus Just)<br /> | |||
</td> | </td> | ||
<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> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>1<br /> | <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> | ||
<td | <td style="text-align: center;">0¢<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">unison<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">1<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">D<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <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> | ||
<td | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">up-unison<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">^1<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">D^<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">2<br /> | ||
</td> | |||
<td style="text-align: center;">85.71<br /> | |||
</td> | </td> | ||
<td | <td style="text-align: center;">21:20<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">84.47<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">1.24<br /> | ||
</td> | </td> | ||
<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> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <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> | ||
<td | <td style="text-align: center;">0.27<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">down 2nd<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">v2<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">Ev<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <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> | ||
<td | <td style="text-align: center;">6.43<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">2nd<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">2<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">E<br /> | ||
- | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <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> | ||
<td | <td style="text-align: center;">-2.40<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">up 2nd<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">^2<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">E^<br /> | ||
- | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>7<br /> | <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> | ||
<td | <td style="text-align: center;">-9.73<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">double-up 2nd, double-down 3rd<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">^^2, vv3<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">E^^, Fvv<br /> | ||
- | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <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> | ||
<td | <td style="text-align: center;">-15.64<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">down 3rd<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">v3<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">Fv<br /> | ||
- | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>9<br /> | <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> | ||
<td | <td style="text-align: center;">-4.55<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">3rd<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">3<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">F<br /> | ||
- | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">9<br /> | ||
</td> | |||
<td style="text-align: center;">385.71<br /> | |||
</td> | </td> | ||
<td | <td style="text-align: center;">5:4<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">386.31<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">-0.60<br /> | ||
</td> | </td> | ||
<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> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <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> | ||
<td | <td style="text-align: center;">-6.51<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">double-up 3rd, double-down 4th<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">^^3, vv4<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">F^^, Gvv<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <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> | ||
<td | <td style="text-align: center;">0.65<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">down 4th<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">v4<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">Gv<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">12<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">514.29<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">4:3<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">498.04<br /> | ||
</td> | </td> | ||
<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> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>14<br /> | <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> | ||
<td | <td style="text-align: center;">17.49<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">double-up 4th, double-down 5th<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">^^4, vv5<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">G^^, vvA<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>15<br /> | <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> | ||
<td | <td style="text-align: center;">-5.82<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">down 5th<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">v5<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">Av<br /> | ||
- | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>16<br /> | <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> | ||
<td | <td style="text-align: center;">-16.25<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">5th<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">5<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">A<br /> | ||
- | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>17<br /> | <td style="text-align: center;">17<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">728.57<br /> | ||
</td> | </td> | ||
<td>32:21<br /> | <td style="text-align: center;">32:21<br /> | ||
</td> | </td> | ||
<td>729.22 | <td style="text-align: center;">729.22<br /> | ||
</td> | </td> | ||
<td>-0.65<br /> | <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> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>18<br /> | <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> | ||
<td | <td style="text-align: center;">6.51<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">double-up 5th, double-down 6th<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">^^5, vv6<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">A^^, Bvv<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>19<br /> | <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> | ||
<td | <td style="text-align: center;">813.68<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">0.61<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">down 6th<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">v6<br /> | ||
</td> | |||
<td style="text-align: center;">Bv<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>20<br /> | <td style="text-align: center;">20<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">857.14<br /> | ||
</td> | </td> | ||
<td>18:11<br /> | <td style="text-align: center;">18:11<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">852.59<br /> | ||
</td> | </td> | ||
<td>4.55<br /> | <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> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>21<br /> | <td style="text-align: center;">21<br /> | ||
</td> | </td> | ||
<td>900 | <td style="text-align: center;">900<br /> | ||
</td> | </td> | ||
<td>5:3<br /> | <td style="text-align: center;">5:3<br /> | ||
</td> | </td> | ||
<td>884.36 | <td style="text-align: center;">884.36<br /> | ||
</td> | </td> | ||
<td>15.64<br /> | <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> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>22<br /> | <td style="text-align: center;">22<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">942.86<br /> | ||
</td> | </td> | ||
<td>12:7<br /> | <td style="text-align: center;">12:7<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">933.13<br /> | ||
</td> | </td> | ||
<td>9.73<br /> | <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> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>23<br /> | <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> | ||
<td | <td style="text-align: center;">2.40<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">down 7th<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">v7<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">Cv<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>24<br /> | <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> | ||
<td | <td style="text-align: center;">1035.00<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">-6.43<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">7th<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">7<br /> | ||
</td> | |||
- | <td style="text-align: center;">C<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>25<br /> | <td style="text-align: center;">25<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">1071.42<br /> | ||
</td> | </td> | ||
<td>13:7<br /> | <td style="text-align: center;">13:7<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">1071.70<br /> | ||
</td> | </td> | ||
<td>-0.27<br /> | <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> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>26<br /> | <td style="text-align: center;">26<br /> | ||
</td> | </td> | ||
<td>1114.29 | <td style="text-align: center;">1114.29<br /> | ||
</td> | </td> | ||
<td>40:21<br /> | <td style="text-align: center;">40:21<br /> | ||
</td> | </td> | ||
<td>1115.53 | <td style="text-align: center;">1115.53<br /> | ||
</td> | </td> | ||
<td>-1.24<br /> | <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> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>27<br /> | <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> | ||
<td | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">down 8ve<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">v8<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">Dv<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>28<br /> | <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> | ||
<td | <td style="text-align: center;">1200<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">0<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">8ve<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">8<br /> | ||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
</table> | </table> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Rank two temperaments"></a><!-- ws:end:WikiTextHeadingRule: | <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 /> | <br /> | ||
Line 903: | Line 805: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- 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 ||= | 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/machine6">machine6</a><br /> | ||
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/machine11">machine11</a><br /> | <a class="wiki_link" href="http://xenharmonic.wikispaces.com/machine11">machine11</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- 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></pre></div> | <a class="wiki_link_ext" href="http://www.youtube.com/watch?v=26UpCbrb3mE" rel="nofollow">28 tone Prelude</a> by Kosmorksy</body></html></pre></div> |