20edo: Difference between revisions
Wikispaces>TallKite **Imported revision 602738788 - Original comment: ** |
Wikispaces>TallKite **Imported revision 602811208 - 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:TallKite|TallKite]] and made on <tt>2016-12- | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-26 01:59:23 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>602811208</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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=Properties= | =Properties= | ||
==Intervals== | ==Intervals== | ||
||= **Degree** ||= **Cents** ||||||= [[Ups and Downs Notation|up/down notation]] || | ||= **Degree** ||= **Cents** ||= **Approximate** | ||
**Ratios** ||||||= [[Ups and Downs Notation|up/down notation]] |||| even distribution* ||= **Nearest** | |||
**Harmonic** || | **Harmonic** || | ||
||= 0 ||= 0 ||= unison ||= P1 ||= D ||= | ||= 0 ||= 0 ||= 1/1 ||= unison ||= P1 ||= D ||= P1 ||= D ||= 1 || | ||
||= 1 ||= 60 ||= upminor 2nd ||= ^m2 ||= D^ ||= | ||= 1 ||= 60 ||= 29/28 ||= upminor 2nd ||= ^m2 ||= D^ ||= A1 ||= D# ||= 33 || | ||
||= 2 ||= 120 ||= mid 2nd ||= ~2 ||= D^^, Evv ||= | ||= 2 ||= 120 ||= 14/13, 15/14 ||= mid 2nd ||= ~2 ||= D^^, Evv ||= d2 ||= Eb ||= 69 || | ||
||= 3 ||= 180 ||= downmajor 2nd ||= vM2 ||= Ev ||= | ||= 3 ||= 180 ||= 10/9 ||= downmajor 2nd ||= vM2 ||= Ev ||= P2 ||= E ||= 71 || | ||
||= 4 ||= 240 ||= major 2nd, minor 3rd ||= M2, m3 ||= E, F ||= | ||= 4 ||= 240 ||= 8/7, 15/13 ||= major 2nd, minor 3rd ||= M2, m3 ||= E, F ||= A2, d3 ||= E#, Fbb ||= 37 || | ||
||= 5 ||= 300 ||= upminor 3rd ||= ^m3 ||= F^ ||= | ||= 5 ||= 300 ||= 13/11, 19/16 ||= upminor 3rd ||= ^m3 ||= F^ ||= m3 ||= Fb ||= 19 || | ||
||= 6 ||= 360 ||= mid 3rd ||= ~3 ||= F^^ ||= | ||= 6 ||= 360 ||= 16/13, 5/4 ||= mid 3rd ||= ~3 ||= F^^ ||= M3 ||= F ||= 79 || | ||
||= 7 ||= 420 | ||= 7 ||= 420 ||= [[xenharmonic/14_11|14/11]], [[xenharmonic/51_40|51/40]] ||= downmajor 3rd ||= vM3 ||= F#v ||= A3, d4 ||= F#, Gbb ||= 41 || | ||
||= 8 ||= 480 ||= major 3rd, perfect fourth ||= M3, P4 ||= F#, G ||= | ||= 8 ||= 480 ||= 25/19, 4/3 ||= major 3rd, perfect fourth ||= M3, P4 ||= F#, G ||= m4 ||= Gb ||= 21 || | ||
||= 9 ||= 540 ||= up-fourth ||= ^4 ||= G^ ||= | ||= 9 ||= 540 ||= 15/11, 11/8 ||= up-fourth ||= ^4 ||= G^ ||= M4 ||= G ||= 11 || | ||
||= 10 ||= 600 ||= double-up fourth, | ||= 10 ||= 600 ||= 7/5 ||= double-up fourth, | ||
double-down fifth ||= ^^4, vv5 ||= G^^, Avv ||= | double-down fifth ||= ^^4, vv5 ||= G^^, Avv ||= A4, d5 ||= G#, Ab ||= 91 || | ||
||= 11 ||= 660 ||= down-fifth ||= v5 ||= Av ||= | ||= 11 ||= 660 ||= 22/15, 16/11 ||= down-fifth ||= v5 ||= Av ||= m5 ||= A ||= 47 || | ||
||= 12 ||= 720 ||= fifth ||= P5, m6 ||= A ||= | ||= 12 ||= 720 ||= 38/25, 3/2 ||= fifth ||= P5, m6 ||= A ||= M5 ||= A# ||= 97 || | ||
||= 13 ||= 780 ||= upminor 6th ||= ^m6 ||= A^ ||= | ||= 13 ||= 780 ||= 11/7, 25/16 ||= upminor 6th ||= ^m6 ||= A^ ||= A5. d6 ||= Ax, Bb ||= 25 || | ||
||= 14 ||= 840 ||= mid 6th ||= ~6 ||= A^^, Bvv ||= | ||= 14 ||= 840 ||= 13/8, 8/5 ||= mid 6th ||= ~6 ||= A^^, Bvv ||= m6 ||= B ||= 13 || | ||
||= 15 ||= 900 ||= downmajor 6th ||= vM6 ||= Bv ||= | ||= 15 ||= 900 ||= 22/13, 32/19 ||= downmajor 6th ||= vM6 ||= Bv ||= M6 ||= B# ||= 27 || | ||
||= 16 ||= 960 ||= major 6th, minor 7th ||= M6, m7 ||= B, C ||= | ||= 16 ||= 960 ||= 7/4, 26/15 ||= major 6th, minor 7th ||= M6, m7 ||= B, C ||= A6, d7 ||= Bx, Cb ||= 7 || | ||
||= 17 ||= 1020 ||= upminor 7th ||= ^m7 ||= C^ ||= | ||= 17 ||= 1020 ||= 9/5 ||= upminor 7th ||= ^m7 ||= C^ ||= P7 ||= C ||= 115 || | ||
||= 18 ||= 1080 ||= mid 7th ||= ~7 ||= C^^, Dvv ||= | ||= 18 ||= 1080 ||= 15/8, 13/7 ||= mid 7th ||= ~7 ||= C^^, Dvv ||= A7 ||= C# ||= 15 || | ||
||= 19 ||= 1140 ||= downmajor 7th ||= vM7 ||= Dv ||= | ||= 19 ||= 1140 ||= 56/29 ||= downmajor 7th ||= vM7 ||= Dv ||= d8 ||= Db ||= 31 || | ||
||= 20 ||= 1200 ||= octave ||= P8 ||= D ||= | ||= 20 ||= 1200 ||= 2/1 ||= octave ||= P8 ||= D ||= P8 ||= D ||= 2 || | ||
* Evenly distributing the 7 naturals around the keyboard suggests a temperament generated by a 3\20 2nd. There are no such 7-limit temperaments, but this notation would be ideal for the yellow-deep-amberish-minus-white rank-2 temperament, which tempers out 125/121. | |||
== == | |||
==Modes== | ==Modes== | ||
20 tone equal modes: | 20 tone equal modes: | ||
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<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>20edo</title></head><body>20-tone equal temperament, or 20edo, divides the octave into exactly 20 equal steps of 60 <a class="wiki_link" href="/cent">cent</a>s each. It contains smaller <a class="wiki_link" href="/edo">edo</a>s <a class="wiki_link" href="/2edo">2</a>, <a class="wiki_link" href="/4edo">4</a>, <a class="wiki_link" href="/5edo">5</a>, and <a class="wiki_link" href="/10edo">10</a> and is part of the 5n Family of equal divisions of the octave. 20 edo fairly approximates the harmonics 7 (from 5 edo), 11, 13 &amp; 15 (from 10 edo), 19 &amp; 27 (from 4 edo), 29 and 31; as well as the other harmonics more loosely (though to some people, still functionally) approximated. Thus, 20-EDO does a reasonably convincing approximation of harmonics 4:7:11:13:15.<br /> | <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>20edo</title></head><body>20-tone equal temperament, or 20edo, divides the octave into exactly 20 equal steps of 60 <a class="wiki_link" href="/cent">cent</a>s each. It contains smaller <a class="wiki_link" href="/edo">edo</a>s <a class="wiki_link" href="/2edo">2</a>, <a class="wiki_link" href="/4edo">4</a>, <a class="wiki_link" href="/5edo">5</a>, and <a class="wiki_link" href="/10edo">10</a> and is part of the 5n Family of equal divisions of the octave. 20 edo fairly approximates the harmonics 7 (from 5 edo), 11, 13 &amp; 15 (from 10 edo), 19 &amp; 27 (from 4 edo), 29 and 31; as well as the other harmonics more loosely (though to some people, still functionally) approximated. Thus, 20-EDO does a reasonably convincing approximation of harmonics 4:7:11:13:15.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextTocRule: | <!-- ws:start:WikiTextTocRule:16:&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:16 --><!-- ws:start:WikiTextTocRule:17: --><a href="#Compositions">Compositions</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | <a href="#Properties">Properties</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:25 --><hr /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:0 -->Compositions</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:0 -->Compositions</h1> | ||
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</td> | </td> | ||
<td style="text-align: center;"><strong>Cents</strong><br /> | <td style="text-align: center;"><strong>Cents</strong><br /> | ||
</td> | |||
<td style="text-align: center;"><strong>Approximate</strong><br /> | |||
<strong>Ratios</strong><br /> | |||
</td> | </td> | ||
<td colspan="3" style="text-align: center;"><a class="wiki_link" href="/Ups%20and%20Downs%20Notation">up/down notation</a><br /> | <td colspan="3" style="text-align: center;"><a class="wiki_link" href="/Ups%20and%20Downs%20Notation">up/down notation</a><br /> | ||
</td> | </td> | ||
<td | <td colspan="2">even distribution*<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><strong>Nearest</strong><br /> | <td style="text-align: center;"><strong>Nearest</strong><br /> | ||
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</td> | </td> | ||
<td style="text-align: center;">0<br /> | <td style="text-align: center;">0<br /> | ||
</td> | |||
<td style="text-align: center;">1/1<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">unison<br /> | <td style="text-align: center;">unison<br /> | ||
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<td style="text-align: center;">D<br /> | <td style="text-align: center;">D<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">P1<br /> | ||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">1<br /> | <td style="text-align: center;">1<br /> | ||
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</td> | </td> | ||
<td style="text-align: center;">60<br /> | <td style="text-align: center;">60<br /> | ||
</td> | |||
<td style="text-align: center;">29/28<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">upminor 2nd<br /> | <td style="text-align: center;">upminor 2nd<br /> | ||
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<td style="text-align: center;">D^<br /> | <td style="text-align: center;">D^<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">A1<br /> | ||
</td> | |||
<td style="text-align: center;">D#<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">33<br /> | <td style="text-align: center;">33<br /> | ||
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</td> | </td> | ||
<td style="text-align: center;">120<br /> | <td style="text-align: center;">120<br /> | ||
</td> | |||
<td style="text-align: center;">14/13, 15/14<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">mid 2nd<br /> | <td style="text-align: center;">mid 2nd<br /> | ||
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<td style="text-align: center;">D^^, Evv<br /> | <td style="text-align: center;">D^^, Evv<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">d2<br /> | ||
</td> | |||
<td style="text-align: center;">Eb<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">69<br /> | <td style="text-align: center;">69<br /> | ||
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</td> | </td> | ||
<td style="text-align: center;">180<br /> | <td style="text-align: center;">180<br /> | ||
</td> | |||
<td style="text-align: center;">10/9<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">downmajor 2nd<br /> | <td style="text-align: center;">downmajor 2nd<br /> | ||
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<td style="text-align: center;">Ev<br /> | <td style="text-align: center;">Ev<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">P2<br /> | ||
</td> | |||
<td style="text-align: center;">E<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">71<br /> | <td style="text-align: center;">71<br /> | ||
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</td> | </td> | ||
<td style="text-align: center;">240<br /> | <td style="text-align: center;">240<br /> | ||
</td> | |||
<td style="text-align: center;">8/7, 15/13<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">major 2nd, minor 3rd<br /> | <td style="text-align: center;">major 2nd, minor 3rd<br /> | ||
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<td style="text-align: center;">E, F<br /> | <td style="text-align: center;">E, F<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">A2, d3<br /> | ||
</td> | |||
<td style="text-align: center;">E#, Fbb<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">37<br /> | <td style="text-align: center;">37<br /> | ||
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</td> | </td> | ||
<td style="text-align: center;">300<br /> | <td style="text-align: center;">300<br /> | ||
</td> | |||
<td style="text-align: center;">13/11, 19/16<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">upminor 3rd<br /> | <td style="text-align: center;">upminor 3rd<br /> | ||
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<td style="text-align: center;">F^<br /> | <td style="text-align: center;">F^<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">m3<br /> | ||
</td> | |||
<td style="text-align: center;">Fb<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">19<br /> | <td style="text-align: center;">19<br /> | ||
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</td> | </td> | ||
<td style="text-align: center;">360<br /> | <td style="text-align: center;">360<br /> | ||
</td> | |||
<td style="text-align: center;">16/13, 5/4<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">mid 3rd<br /> | <td style="text-align: center;">mid 3rd<br /> | ||
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<td style="text-align: center;">F^^<br /> | <td style="text-align: center;">F^^<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">M3<br /> | ||
</td> | |||
<td style="text-align: center;">F<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">79<br /> | <td style="text-align: center;">79<br /> | ||
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</td> | </td> | ||
<td style="text-align: center;">420<br /> | <td style="text-align: center;">420<br /> | ||
</td> | |||
<td style="text-align: center;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/14_11">14/11</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/51_40">51/40</a><br /> | |||
</td> | </td> | ||
<td style="text-align: center;">downmajor 3rd<br /> | <td style="text-align: center;">downmajor 3rd<br /> | ||
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<td style="text-align: center;">F#v<br /> | <td style="text-align: center;">F#v<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">< | <td style="text-align: center;">A3, d4<br /> | ||
</td> | |||
<td style="text-align: center;">F#, Gbb<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">41<br /> | <td style="text-align: center;">41<br /> | ||
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</td> | </td> | ||
<td style="text-align: center;">480<br /> | <td style="text-align: center;">480<br /> | ||
</td> | |||
<td style="text-align: center;">25/19, 4/3<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">major 3rd, perfect fourth<br /> | <td style="text-align: center;">major 3rd, perfect fourth<br /> | ||
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<td style="text-align: center;">F#, G<br /> | <td style="text-align: center;">F#, G<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">m4<br /> | ||
</td> | |||
<td style="text-align: center;">Gb<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">21<br /> | <td style="text-align: center;">21<br /> | ||
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</td> | </td> | ||
<td style="text-align: center;">540<br /> | <td style="text-align: center;">540<br /> | ||
</td> | |||
<td style="text-align: center;">15/11, 11/8<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">up-fourth<br /> | <td style="text-align: center;">up-fourth<br /> | ||
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<td style="text-align: center;">G^<br /> | <td style="text-align: center;">G^<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">M4<br /> | ||
</td> | |||
<td style="text-align: center;">G<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">11<br /> | <td style="text-align: center;">11<br /> | ||
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</td> | </td> | ||
<td style="text-align: center;">600<br /> | <td style="text-align: center;">600<br /> | ||
</td> | |||
<td style="text-align: center;">7/5<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">double-up fourth,<br /> | <td style="text-align: center;">double-up fourth,<br /> | ||
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<td style="text-align: center;">G^^, Avv<br /> | <td style="text-align: center;">G^^, Avv<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">A4, d5<br /> | ||
</td> | |||
<td style="text-align: center;">G#, Ab<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">91<br /> | <td style="text-align: center;">91<br /> | ||
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</td> | </td> | ||
<td style="text-align: center;">660<br /> | <td style="text-align: center;">660<br /> | ||
</td> | |||
<td style="text-align: center;">22/15, 16/11<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">down-fifth<br /> | <td style="text-align: center;">down-fifth<br /> | ||
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<td style="text-align: center;">Av<br /> | <td style="text-align: center;">Av<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">m5<br /> | ||
</td> | |||
<td style="text-align: center;">A<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">47<br /> | <td style="text-align: center;">47<br /> | ||
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</td> | </td> | ||
<td style="text-align: center;">720<br /> | <td style="text-align: center;">720<br /> | ||
</td> | |||
<td style="text-align: center;">38/25, 3/2<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">fifth<br /> | <td style="text-align: center;">fifth<br /> | ||
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<td style="text-align: center;">A<br /> | <td style="text-align: center;">A<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">M5<br /> | ||
</td> | |||
<td style="text-align: center;">A#<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">97<br /> | <td style="text-align: center;">97<br /> | ||
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</td> | </td> | ||
<td style="text-align: center;">780<br /> | <td style="text-align: center;">780<br /> | ||
</td> | |||
<td style="text-align: center;">11/7, 25/16<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">upminor 6th<br /> | <td style="text-align: center;">upminor 6th<br /> | ||
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<td style="text-align: center;">A^<br /> | <td style="text-align: center;">A^<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">A5. d6<br /> | ||
</td> | |||
<td style="text-align: center;">Ax, Bb<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">25<br /> | <td style="text-align: center;">25<br /> | ||
| Line 353: | Line 413: | ||
</td> | </td> | ||
<td style="text-align: center;">840<br /> | <td style="text-align: center;">840<br /> | ||
</td> | |||
<td style="text-align: center;">13/8, 8/5<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">mid 6th<br /> | <td style="text-align: center;">mid 6th<br /> | ||
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<td style="text-align: center;">A^^, Bvv<br /> | <td style="text-align: center;">A^^, Bvv<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">m6<br /> | ||
</td> | |||
<td style="text-align: center;">B<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">13<br /> | <td style="text-align: center;">13<br /> | ||
| Line 369: | Line 433: | ||
</td> | </td> | ||
<td style="text-align: center;">900<br /> | <td style="text-align: center;">900<br /> | ||
</td> | |||
<td style="text-align: center;">22/13, 32/19<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">downmajor 6th<br /> | <td style="text-align: center;">downmajor 6th<br /> | ||
| Line 376: | Line 442: | ||
<td style="text-align: center;">Bv<br /> | <td style="text-align: center;">Bv<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">M6<br /> | ||
</td> | |||
<td style="text-align: center;">B#<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">27<br /> | <td style="text-align: center;">27<br /> | ||
| Line 385: | Line 453: | ||
</td> | </td> | ||
<td style="text-align: center;">960<br /> | <td style="text-align: center;">960<br /> | ||
</td> | |||
<td style="text-align: center;">7/4, 26/15<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">major 6th, minor 7th<br /> | <td style="text-align: center;">major 6th, minor 7th<br /> | ||
| Line 392: | Line 462: | ||
<td style="text-align: center;">B, C<br /> | <td style="text-align: center;">B, C<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">A6, d7<br /> | ||
</td> | |||
<td style="text-align: center;">Bx, Cb<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">7<br /> | <td style="text-align: center;">7<br /> | ||
| Line 401: | Line 473: | ||
</td> | </td> | ||
<td style="text-align: center;">1020<br /> | <td style="text-align: center;">1020<br /> | ||
</td> | |||
<td style="text-align: center;">9/5<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">upminor 7th<br /> | <td style="text-align: center;">upminor 7th<br /> | ||
| Line 408: | Line 482: | ||
<td style="text-align: center;">C^<br /> | <td style="text-align: center;">C^<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">P7<br /> | ||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">115<br /> | <td style="text-align: center;">115<br /> | ||
| Line 417: | Line 493: | ||
</td> | </td> | ||
<td style="text-align: center;">1080<br /> | <td style="text-align: center;">1080<br /> | ||
</td> | |||
<td style="text-align: center;">15/8, 13/7<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">mid 7th<br /> | <td style="text-align: center;">mid 7th<br /> | ||
| Line 424: | Line 502: | ||
<td style="text-align: center;">C^^, Dvv<br /> | <td style="text-align: center;">C^^, Dvv<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">A7<br /> | ||
</td> | |||
<td style="text-align: center;">C#<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">15<br /> | <td style="text-align: center;">15<br /> | ||
| Line 433: | Line 513: | ||
</td> | </td> | ||
<td style="text-align: center;">1140<br /> | <td style="text-align: center;">1140<br /> | ||
</td> | |||
<td style="text-align: center;">56/29<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">downmajor 7th<br /> | <td style="text-align: center;">downmajor 7th<br /> | ||
| Line 440: | Line 522: | ||
<td style="text-align: center;">Dv<br /> | <td style="text-align: center;">Dv<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">d8<br /> | ||
</td> | |||
<td style="text-align: center;">Db<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">31<br /> | <td style="text-align: center;">31<br /> | ||
| Line 449: | Line 533: | ||
</td> | </td> | ||
<td style="text-align: center;">1200<br /> | <td style="text-align: center;">1200<br /> | ||
</td> | |||
<td style="text-align: center;">2/1<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">octave<br /> | <td style="text-align: center;">octave<br /> | ||
| Line 456: | Line 542: | ||
<td style="text-align: center;">D<br /> | <td style="text-align: center;">D<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">P8<br /> | ||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">2<br /> | <td style="text-align: center;">2<br /> | ||
| Line 463: | Line 551: | ||
</table> | </table> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Properties-Modes"></a><!-- ws:end:WikiTextHeadingRule: | <ul><li>Evenly distributing the 7 naturals around the keyboard suggests a temperament generated by a 3\20 2nd. There are no such 7-limit temperaments, but this notation would be ideal for the yellow-deep-amberish-minus-white rank-2 temperament, which tempers out 125/121.</li></ul><!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><!-- ws:end:WikiTextHeadingRule:8 --> </h2> | ||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Properties-Modes"></a><!-- ws:end:WikiTextHeadingRule:10 -->Modes</h2> | |||
20 tone equal modes:<br /> | 20 tone equal modes:<br /> | ||
| Line 585: | Line 674: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Properties-Commas"></a><!-- ws:end:WikiTextHeadingRule:12 -->Commas</h2> | ||
20 EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes the <a class="wiki_link" href="/val">val</a> &lt; <a class="wiki_link" href="http://tel.wikispaces.com/20%2032%2046%2056%2069%2074">20 32 46 56 69 74</a>/1 |.)<br /> | 20 EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes the <a class="wiki_link" href="/val">val</a> &lt; <a class="wiki_link" href="http://tel.wikispaces.com/20%2032%2046%2056%2069%2074">20 32 46 56 69 74</a>/1 |.)<br /> | ||
| Line 859: | Line 948: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Properties-Books"></a><!-- ws:end:WikiTextHeadingRule:14 --><strong>Books</strong></h2> | ||
<!-- ws:start:WikiTextRemoteImageRule: | <!-- ws:start:WikiTextRemoteImageRule:872:&lt;a href=&quot;http://www.ronsword.com/&quot; target=&quot;_blank&quot; rel=&quot;nofollow&quot;&gt;&lt;img src=&quot;http://ronsword.com/images/20_tet_Coversm.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 114px; width: 82px;&quot; /&gt;&lt;/a&gt; --><a href="http://www.ronsword.com/" target="_blank" rel="nofollow"><img src="http://ronsword.com/images/20_tet_Coversm.jpg" alt="external image 20_tet_Coversm.jpg" title="external image 20_tet_Coversm.jpg" style="height: 114px; width: 82px;" /></a><!-- ws:end:WikiTextRemoteImageRule:872 --><br /> | ||
<a class="wiki_link_ext" href="http://www.ronsword.com/" rel="nofollow" target="_blank">&quot;Icosaphonic Scales for Guitar&quot; - Theory / Scale book with above modes and more</a> by <a class="wiki_link" href="/Ron%20Sword">Ron Sword</a></body></html></pre></div> | <a class="wiki_link_ext" href="http://www.ronsword.com/" rel="nofollow" target="_blank">&quot;Icosaphonic Scales for Guitar&quot; - Theory / Scale book with above modes and more</a> by <a class="wiki_link" href="/Ron%20Sword">Ron Sword</a></body></html></pre></div> | ||