72edo: Difference between revisions
Wikispaces>hstraub **Imported revision 527592214 - Original comment: ** |
Wikispaces>TallKite **Imported revision 602866126 - 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>2016-12-28 04:58:46 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>602866126</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> | ||
| Line 33: | Line 33: | ||
=Intervals= | =Intervals= | ||
|| degrees || cents value || approximate ratios (11-limit) || | || degrees || cents value || approximate ratios (11-limit) ||||= [[xenharmonic/Ups and Downs Notation|ups and downs ]][[xenharmonic/Ups and Downs Notation|notation]] || | ||
|| 0 || 0 || 1/1 || | || 0 || 0 || 1/1 ||= P1 ||= D || | ||
|| 1 || 16.667 || 81/80 || | || 1 || 16.667 || 81/80 ||= ^1 ||= D^ || | ||
|| 2 || 33.333 || 45/44 || | || 2 || 33.333 || 45/44 ||= ^^1 ||= D^^ || | ||
|| 3 || 50 || 33/32 || | || 3 || 50 || 33/32 ||= ^<span style="font-size: 90%; vertical-align: super;">3</span>1, v<span style="font-size: 90%; vertical-align: super;">3</span>m2 || D^<span style="font-size: 90%; vertical-align: super;">3</span>, Ebv<span style="font-size: 90%; vertical-align: super;">3</span> || | ||
|| 4 || 66.667 || 25/24 || | || 4 || 66.667 || 25/24 ||= vvm2 ||= Ebvv || | ||
|| 5 || 83.333 || 21/20 || | || 5 || 83.333 || 21/20 ||= vm2 ||= Ebv || | ||
|| 6 || 100 || 35/33 || | || 6 || 100 || 35/33 ||= m2 ||= Eb || | ||
|| 7 || 116.667 || 15/14 || | || 7 || 116.667 || 15/14 ||= ^m2 ||= Eb^ || | ||
|| 8 || 133.333 || 27/25 || | || 8 || 133.333 || 27/25 ||= v~2 ||= Eb^^ || | ||
|| 9 || 150 || 12/11 || | || 9 || 150 || 12/11 ||= ~2 ||= Ev<span style="font-size: 90%; vertical-align: super;">3</span> || | ||
|| 10 || 166.667 || 11/10 || | || 10 || 166.667 || 11/10 ||= ^~2 ||= Evv || | ||
|| 11 || 183.333 || 10/9 || | || 11 || 183.333 || 10/9 ||= vM2 ||= Ev || | ||
|| 12 || 200 || 9/8 || | || 12 || 200 || 9/8 ||= M2 ||= E || | ||
|| 13 || 216.667 || 25/22 || | || 13 || 216.667 || 25/22 ||= ^M2 ||= E^ || | ||
|| 14 || 233.333 || 8/7 || | || 14 || 233.333 || 8/7 ||= ^^M2 ||= E^^ || | ||
|| 15 || 250 || 81/70 || | || 15 || 250 || 81/70 ||= ^<span style="font-size: 90%; vertical-align: super;">3</span>M2, v<span style="font-size: 90%; vertical-align: super;">3</span>m3 ||= E^<span style="font-size: 90%; vertical-align: super;">3</span>, Fv<span style="font-size: 90%; vertical-align: super;">3</span> || | ||
|| 16 || 266.667 || 7/6 || | || 16 || 266.667 || 7/6 ||= vvm3 ||= Fvv || | ||
|| 17 || 283.333 || 33/28 || | || 17 || 283.333 || 33/28 ||= vm3 ||= Fv || | ||
|| 18 || 300 || 25/21 || | || 18 || 300 || 25/21 ||= m3 ||= F || | ||
|| 19 || 316.667 || 6/5 || | || 19 || 316.667 || 6/5 ||= ^m3 ||= F^ || | ||
|| 20 || 333.333 || 40/33 || | || 20 || 333.333 || 40/33 ||= v~3 ||= F^^ || | ||
|| 21 || 350 || 11/9 || | || 21 || 350 || 11/9 ||= ~3 ||= F^<span style="font-size: 90%; vertical-align: super;">3</span> || | ||
|| 22 || 366.667 || 99/80 || | || 22 || 366.667 || 99/80 ||= ^~3 ||= F#vv || | ||
|| 23 || 383.333 || 5/4 || | || 23 || 383.333 || 5/4 ||= vM3 ||= F#v || | ||
|| 24 || 400 || 44/35 || | || 24 || 400 || 44/35 ||= M3 ||= F# || | ||
|| 25 || 416.667 || 14/11 || | || 25 || 416.667 || 14/11 ||= ^M3 ||= F#^ || | ||
|| 26 || 433.333 || 9/7 || | || 26 || 433.333 || 9/7 ||= ^^M3 ||= F#^^ || | ||
|| 27 || 450 || 35/27 || | || 27 || 450 || 35/27 ||= ^<span style="font-size: 90%; vertical-align: super;">3</span>M3, v<span style="font-size: 90%; vertical-align: super;">3</span>4 ||= F#^<span style="font-size: 90%; vertical-align: super;">3</span>, Gv<span style="font-size: 90%; vertical-align: super;">3</span> || | ||
|| 28 || 466.667 || 21/16 || | || 28 || 466.667 || 21/16 ||= vv4 ||= Gvv || | ||
|| 29 || 483.333 || 33/25 || | || 29 || 483.333 || 33/25 ||= v4 ||= Gv || | ||
|| 30 || 500 || 4/3 || | || 30 || 500 || 4/3 ||= P4 ||= G || | ||
|| 31 || 516.667 || 27/20 || | || 31 || 516.667 || 27/20 ||= ^4 ||= G^ || | ||
|| 32 || 533.333 || 15/11 || | || 32 || 533.333 || 15/11 ||= ^^4 ||= G^^ || | ||
|| 33 || 550 || 11/8 || | || 33 || 550 || 11/8 ||= ^<span style="font-size: 90%; vertical-align: super;">3</span>4<span style="font-size: 90%; vertical-align: super;"> </span> ||= G^<span style="font-size: 90%; vertical-align: super;">3</span> || | ||
|| 34 || 566.667 || 25/18 || | || 34 || 566.667 || 25/18 ||= vvA4 ||= G#vv || | ||
|| 35 || 583.333 || 7/5 || | || 35 || 583.333 || 7/5 ||= vA4, vd5 ||= G#v, Abv || | ||
|| 36 || 600 || 99/70 || | || 36 || 600 || 99/70 ||= A4, d5 ||= G#, Ab || | ||
|| 37 || 616.667 || 10/7 || | || 37 || 616.667 || 10/7 ||= ^A4, ^d5 ||= G#^, Ab^ || | ||
|| 38 || 633.333 || 36/25 || | || 38 || 633.333 || 36/25 ||= ^^d5 ||= Ab^^ || | ||
|| 39 || 650 || 16/11 || | || 39 || 650 || 16/11 ||= <span style="font-size: 90%; vertical-align: super;"> </span>v<span style="font-size: 90%; vertical-align: super;">3</span>5 ||= Av<span style="font-size: 90%; vertical-align: super;">3</span> || | ||
|| 40 || 666.667 || 22/15 || | || 40 || 666.667 || 22/15 ||= vv5 ||= Avv || | ||
|| 41 || 683.333 || 40/27 || | || 41 || 683.333 || 40/27 ||= v5 ||= Av || | ||
|| 42 || 700 || 3/2 || | || 42 || 700 || 3/2 ||= P5 ||= A || | ||
|| 43 || 716.667 || 50/33 || | || 43 || 716.667 || 50/33 ||= ^5 ||= A^ || | ||
|| 44 || 733.333 || 32/21 || | || 44 || 733.333 || 32/21 ||= ^^5 ||= A^^ || | ||
|| 45 || 750 || 54/35 || | || 45 || 750 || 54/35 ||= ^<span style="font-size: 90%; vertical-align: super;">3</span>5, v<span style="font-size: 90%; vertical-align: super;">3</span>m6 ||= A^<span style="font-size: 90%; vertical-align: super;">3</span>, Bbv<span style="font-size: 90%; vertical-align: super;">3</span> || | ||
|| 46 || 766.667 || 14/9 || | || 46 || 766.667 || 14/9 ||= vvm6 ||= Bbvv || | ||
|| 47 || 783.333 || 11/7 || | || 47 || 783.333 || 11/7 ||= vm6 ||= Bbv || | ||
|| 48 || 800 || 35/22 || | || 48 || 800 || 35/22 ||= m6 ||= Bb || | ||
|| 49 || 816.667 || 8/5 || | || 49 || 816.667 || 8/5 ||= ^m6 ||= Bb^ || | ||
|| 50 || 833.333 || 81/50 || | || 50 || 833.333 || 81/50 ||= v~6 ||= Bb^^ || | ||
|| 51 || 850 || 18/11 || | || 51 || 850 || 18/11 ||= ~6 ||= Bv<span style="font-size: 90%; vertical-align: super;">3</span> || | ||
|| 52 || 866.667 || 33/20 || | || 52 || 866.667 || 33/20 ||= ^~6 ||= Bvv || | ||
|| 53 || 883.333 || 5/3 || | || 53 || 883.333 || 5/3 ||= vM6 ||= Bv || | ||
|| 54 || 900 || 27/16 || | || 54 || 900 || 27/16 ||= M6 ||= B || | ||
|| 55 || 916.667 || 56/33 || | || 55 || 916.667 || 56/33 ||= ^M6 ||= B^ || | ||
|| 56 || 933.333 || 12/7 || | || 56 || 933.333 || 12/7 ||= ^^M6 ||= B^^ || | ||
|| 57 || 950 || 121/70 || | || 57 || 950 || 121/70 ||= ^<span style="font-size: 90%; vertical-align: super;">3</span>M6, v<span style="font-size: 90%; vertical-align: super;">3</span>m7 ||= B^<span style="font-size: 90%; vertical-align: super;">3</span>, Cv<span style="font-size: 90%; vertical-align: super;">3</span> || | ||
|| 58 || 966.667 || 7/4 || | || 58 || 966.667 || 7/4 ||= vvm7 ||= Cvv || | ||
|| 59 || 983.333 || 44/25 || | || 59 || 983.333 || 44/25 ||= vm7 ||= Cv || | ||
|| 60 || 1000 || 16/9 || | || 60 || 1000 || 16/9 ||= m7 ||= C || | ||
|| 61 || 1016.667 || 9/5 || | || 61 || 1016.667 || 9/5 ||= ^m7 ||= C^ || | ||
|| 62 || 1033.333 || 20/11 || | || 62 || 1033.333 || 20/11 ||= v~7 ||= C^^ || | ||
|| 63 || 1050 || 11/6 || | || 63 || 1050 || 11/6 ||= ~7 ||= C^<span style="font-size: 90%; vertical-align: super;">3</span> || | ||
|| 64 || 1066.667 || 50/27 || | || 64 || 1066.667 || 50/27 ||= ^~7 ||= C#vv || | ||
|| 65 || 1083.333 || 15/8 || | || 65 || 1083.333 || 15/8 ||= vM7 ||= C#v || | ||
|| 66 || 1100 || 66/35 || | || 66 || 1100 || 66/35 ||= M7 ||= C# || | ||
|| 67 || 1116.667 || 21/11 || | || 67 || 1116.667 || 21/11 ||= ^M7 ||= C#^ || | ||
|| 68 || 1133.333 || 27/14 || | || 68 || 1133.333 || 27/14 ||= ^^M7 ||= C#^^ || | ||
|| 69 || 1150 || 35/18 || | || 69 || 1150 || 35/18 ||= ^<span style="font-size: 90%; vertical-align: super;">3</span>M7, v<span style="font-size: 90%; vertical-align: super;">3</span>8 ||= C#^<span style="font-size: 90%; vertical-align: super;">3</span>, Dv<span style="font-size: 90%; vertical-align: super;">3</span> || | ||
|| 70 || 1166.667 || 49/25 || | || 70 || 1166.667 || 49/25 ||= vv8 ||= Dvv || | ||
|| 71 || 1183.333 || 99/50 || | || 71 || 1183.333 || 99/50 ||= v8 ||= Dv || | ||
|| 72 || 1200 || 2/1 || | || 72 || 1200 || 2/1 ||= P8 ||= D || | ||
= = | Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[xenharmonic/Ups and Downs Notation#Chord%20names%20in%20other%20EDOs|Ups and Downs Notation - Chord names in other EDOs]]. | ||
=Linear temperaments= | =Linear temperaments= | ||
||~ Periods per octave ||~ Generator ||~ Names || | ||~ Periods per octave ||~ Generator ||~ Names || | ||
| Line 173: | Line 174: | ||
* [[@http://www.myspace.com/dawier|Danny Wier, composer and musician who specializes in 72-edo]]</pre></div> | * [[@http://www.myspace.com/dawier|Danny Wier, composer and musician who specializes in 72-edo]]</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>72edo</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>72edo</title></head><body><!-- 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="#Commas and Temperaments">Commas and Temperaments</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#Harmonic Scale">Harmonic Scale</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --> | <a href="#Linear temperaments">Linear temperaments</a><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --> | <a href="#Z function">Z function</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --> | <a href="#Scales">Scales</a><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> | <a href="#External links">External links</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:25 --><hr /> | ||
72-tone equal temperament (or 72-edo) divides the octave into 72 steps or <em>moria</em>. This produces a twelfth-tone tuning, with the whole tone measuring 200 cents, the same as in 12-tone equal temperament. 72-tone is also a superset of <a class="wiki_link" href="http://xenharmonic.wikispaces.com/24edo">24-tone equal temperament</a>, a common and standard tuning of <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Arabic%2C%20Turkish%2C%20Persian">Arabic</a> music, and has itself been used to tune Turkish music.<br /> | 72-tone equal temperament (or 72-edo) divides the octave into 72 steps or <em>moria</em>. This produces a twelfth-tone tuning, with the whole tone measuring 200 cents, the same as in 12-tone equal temperament. 72-tone is also a superset of <a class="wiki_link" href="http://xenharmonic.wikispaces.com/24edo">24-tone equal temperament</a>, a common and standard tuning of <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Arabic%2C%20Turkish%2C%20Persian">Arabic</a> music, and has itself been used to tune Turkish music.<br /> | ||
<br /> | <br /> | ||
| Line 547: | Line 548: | ||
</td> | </td> | ||
<td>approximate ratios (11-limit)<br /> | <td>approximate ratios (11-limit)<br /> | ||
</td> | |||
<td colspan="2" style="text-align: center;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation">ups and downs </a><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation">notation</a><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 555: | Line 558: | ||
</td> | </td> | ||
<td>1/1<br /> | <td>1/1<br /> | ||
</td> | |||
<td style="text-align: center;">P1<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 563: | Line 570: | ||
</td> | </td> | ||
<td>81/80<br /> | <td>81/80<br /> | ||
</td> | |||
<td style="text-align: center;">^1<br /> | |||
</td> | |||
<td style="text-align: center;">D^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 571: | Line 582: | ||
</td> | </td> | ||
<td>45/44<br /> | <td>45/44<br /> | ||
</td> | |||
<td style="text-align: center;">^^1<br /> | |||
</td> | |||
<td style="text-align: center;">D^^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 579: | Line 594: | ||
</td> | </td> | ||
<td>33/32<br /> | <td>33/32<br /> | ||
</td> | |||
<td style="text-align: center;">^<span style="font-size: 90%; vertical-align: super;">3</span>1, v<span style="font-size: 90%; vertical-align: super;">3</span>m2<br /> | |||
</td> | |||
<td>D^<span style="font-size: 90%; vertical-align: super;">3</span>, Ebv<span style="font-size: 90%; vertical-align: super;">3</span><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 587: | Line 606: | ||
</td> | </td> | ||
<td>25/24<br /> | <td>25/24<br /> | ||
</td> | |||
<td style="text-align: center;">vvm2<br /> | |||
</td> | |||
<td style="text-align: center;">Ebvv<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 595: | Line 618: | ||
</td> | </td> | ||
<td>21/20<br /> | <td>21/20<br /> | ||
</td> | |||
<td style="text-align: center;">vm2<br /> | |||
</td> | |||
<td style="text-align: center;">Ebv<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 603: | Line 630: | ||
</td> | </td> | ||
<td>35/33<br /> | <td>35/33<br /> | ||
</td> | |||
<td style="text-align: center;">m2<br /> | |||
</td> | |||
<td style="text-align: center;">Eb<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 611: | Line 642: | ||
</td> | </td> | ||
<td>15/14<br /> | <td>15/14<br /> | ||
</td> | |||
<td style="text-align: center;">^m2<br /> | |||
</td> | |||
<td style="text-align: center;">Eb^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 619: | Line 654: | ||
</td> | </td> | ||
<td>27/25<br /> | <td>27/25<br /> | ||
</td> | |||
<td style="text-align: center;">v~2<br /> | |||
</td> | |||
<td style="text-align: center;">Eb^^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 627: | Line 666: | ||
</td> | </td> | ||
<td>12/11<br /> | <td>12/11<br /> | ||
</td> | |||
<td style="text-align: center;">~2<br /> | |||
</td> | |||
<td style="text-align: center;">Ev<span style="font-size: 90%; vertical-align: super;">3</span><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 635: | Line 678: | ||
</td> | </td> | ||
<td>11/10<br /> | <td>11/10<br /> | ||
</td> | |||
<td style="text-align: center;">^~2<br /> | |||
</td> | |||
<td style="text-align: center;">Evv<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 643: | Line 690: | ||
</td> | </td> | ||
<td>10/9<br /> | <td>10/9<br /> | ||
</td> | |||
<td style="text-align: center;">vM2<br /> | |||
</td> | |||
<td style="text-align: center;">Ev<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 651: | Line 702: | ||
</td> | </td> | ||
<td>9/8<br /> | <td>9/8<br /> | ||
</td> | |||
<td style="text-align: center;">M2<br /> | |||
</td> | |||
<td style="text-align: center;">E<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 659: | Line 714: | ||
</td> | </td> | ||
<td>25/22<br /> | <td>25/22<br /> | ||
</td> | |||
<td style="text-align: center;">^M2<br /> | |||
</td> | |||
<td style="text-align: center;">E^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 667: | Line 726: | ||
</td> | </td> | ||
<td>8/7<br /> | <td>8/7<br /> | ||
</td> | |||
<td style="text-align: center;">^^M2<br /> | |||
</td> | |||
<td style="text-align: center;">E^^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 675: | Line 738: | ||
</td> | </td> | ||
<td>81/70<br /> | <td>81/70<br /> | ||
</td> | |||
<td style="text-align: center;">^<span style="font-size: 90%; vertical-align: super;">3</span>M2, v<span style="font-size: 90%; vertical-align: super;">3</span>m3<br /> | |||
</td> | |||
<td style="text-align: center;">E^<span style="font-size: 90%; vertical-align: super;">3</span>, Fv<span style="font-size: 90%; vertical-align: super;">3</span><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 683: | Line 750: | ||
</td> | </td> | ||
<td>7/6<br /> | <td>7/6<br /> | ||
</td> | |||
<td style="text-align: center;">vvm3<br /> | |||
</td> | |||
<td style="text-align: center;">Fvv<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 691: | Line 762: | ||
</td> | </td> | ||
<td>33/28<br /> | <td>33/28<br /> | ||
</td> | |||
<td style="text-align: center;">vm3<br /> | |||
</td> | |||
<td style="text-align: center;">Fv<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 699: | Line 774: | ||
</td> | </td> | ||
<td>25/21<br /> | <td>25/21<br /> | ||
</td> | |||
<td style="text-align: center;">m3<br /> | |||
</td> | |||
<td style="text-align: center;">F<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 707: | Line 786: | ||
</td> | </td> | ||
<td>6/5<br /> | <td>6/5<br /> | ||
</td> | |||
<td style="text-align: center;">^m3<br /> | |||
</td> | |||
<td style="text-align: center;">F^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 715: | Line 798: | ||
</td> | </td> | ||
<td>40/33<br /> | <td>40/33<br /> | ||
</td> | |||
<td style="text-align: center;">v~3<br /> | |||
</td> | |||
<td style="text-align: center;">F^^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 723: | Line 810: | ||
</td> | </td> | ||
<td>11/9<br /> | <td>11/9<br /> | ||
</td> | |||
<td style="text-align: center;">~3<br /> | |||
</td> | |||
<td style="text-align: center;">F^<span style="font-size: 90%; vertical-align: super;">3</span><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 731: | Line 822: | ||
</td> | </td> | ||
<td>99/80<br /> | <td>99/80<br /> | ||
</td> | |||
<td style="text-align: center;">^~3<br /> | |||
</td> | |||
<td style="text-align: center;">F#vv<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 739: | Line 834: | ||
</td> | </td> | ||
<td>5/4<br /> | <td>5/4<br /> | ||
</td> | |||
<td style="text-align: center;">vM3<br /> | |||
</td> | |||
<td style="text-align: center;">F#v<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 747: | Line 846: | ||
</td> | </td> | ||
<td>44/35<br /> | <td>44/35<br /> | ||
</td> | |||
<td style="text-align: center;">M3<br /> | |||
</td> | |||
<td style="text-align: center;">F#<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 755: | Line 858: | ||
</td> | </td> | ||
<td>14/11<br /> | <td>14/11<br /> | ||
</td> | |||
<td style="text-align: center;">^M3<br /> | |||
</td> | |||
<td style="text-align: center;">F#^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 763: | Line 870: | ||
</td> | </td> | ||
<td>9/7<br /> | <td>9/7<br /> | ||
</td> | |||
<td style="text-align: center;">^^M3<br /> | |||
</td> | |||
<td style="text-align: center;">F#^^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 771: | Line 882: | ||
</td> | </td> | ||
<td>35/27<br /> | <td>35/27<br /> | ||
</td> | |||
<td style="text-align: center;">^<span style="font-size: 90%; vertical-align: super;">3</span>M3, v<span style="font-size: 90%; vertical-align: super;">3</span>4<br /> | |||
</td> | |||
<td style="text-align: center;">F#^<span style="font-size: 90%; vertical-align: super;">3</span>, Gv<span style="font-size: 90%; vertical-align: super;">3</span><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 779: | Line 894: | ||
</td> | </td> | ||
<td>21/16<br /> | <td>21/16<br /> | ||
</td> | |||
<td style="text-align: center;">vv4<br /> | |||
</td> | |||
<td style="text-align: center;">Gvv<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 787: | Line 906: | ||
</td> | </td> | ||
<td>33/25<br /> | <td>33/25<br /> | ||
</td> | |||
<td style="text-align: center;">v4<br /> | |||
</td> | |||
<td style="text-align: center;">Gv<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 795: | Line 918: | ||
</td> | </td> | ||
<td>4/3<br /> | <td>4/3<br /> | ||
</td> | |||
<td style="text-align: center;">P4<br /> | |||
</td> | |||
<td style="text-align: center;">G<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 803: | Line 930: | ||
</td> | </td> | ||
<td>27/20<br /> | <td>27/20<br /> | ||
</td> | |||
<td style="text-align: center;">^4<br /> | |||
</td> | |||
<td style="text-align: center;">G^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 811: | Line 942: | ||
</td> | </td> | ||
<td>15/11<br /> | <td>15/11<br /> | ||
</td> | |||
<td style="text-align: center;">^^4<br /> | |||
</td> | |||
<td style="text-align: center;">G^^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 819: | Line 954: | ||
</td> | </td> | ||
<td>11/8<br /> | <td>11/8<br /> | ||
</td> | |||
<td style="text-align: center;">^<span style="font-size: 90%; vertical-align: super;">3</span>4<span style="font-size: 90%; vertical-align: super;"> </span><br /> | |||
</td> | |||
<td style="text-align: center;">G^<span style="font-size: 90%; vertical-align: super;">3</span><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 827: | Line 966: | ||
</td> | </td> | ||
<td>25/18<br /> | <td>25/18<br /> | ||
</td> | |||
<td style="text-align: center;">vvA4<br /> | |||
</td> | |||
<td style="text-align: center;">G#vv<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 835: | Line 978: | ||
</td> | </td> | ||
<td>7/5<br /> | <td>7/5<br /> | ||
</td> | |||
<td style="text-align: center;">vA4, vd5<br /> | |||
</td> | |||
<td style="text-align: center;">G#v, Abv<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 843: | Line 990: | ||
</td> | </td> | ||
<td>99/70<br /> | <td>99/70<br /> | ||
</td> | |||
<td style="text-align: center;">A4, d5<br /> | |||
</td> | |||
<td style="text-align: center;">G#, Ab<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 851: | Line 1,002: | ||
</td> | </td> | ||
<td>10/7<br /> | <td>10/7<br /> | ||
</td> | |||
<td style="text-align: center;">^A4, ^d5<br /> | |||
</td> | |||
<td style="text-align: center;">G#^, Ab^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 859: | Line 1,014: | ||
</td> | </td> | ||
<td>36/25<br /> | <td>36/25<br /> | ||
</td> | |||
<td style="text-align: center;">^^d5<br /> | |||
</td> | |||
<td style="text-align: center;">Ab^^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 867: | Line 1,026: | ||
</td> | </td> | ||
<td>16/11<br /> | <td>16/11<br /> | ||
</td> | |||
<td style="text-align: center;"><span style="font-size: 90%; vertical-align: super;"> </span>v<span style="font-size: 90%; vertical-align: super;">3</span>5<br /> | |||
</td> | |||
<td style="text-align: center;">Av<span style="font-size: 90%; vertical-align: super;">3</span><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 875: | Line 1,038: | ||
</td> | </td> | ||
<td>22/15<br /> | <td>22/15<br /> | ||
</td> | |||
<td style="text-align: center;">vv5<br /> | |||
</td> | |||
<td style="text-align: center;">Avv<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 883: | Line 1,050: | ||
</td> | </td> | ||
<td>40/27<br /> | <td>40/27<br /> | ||
</td> | |||
<td style="text-align: center;">v5<br /> | |||
</td> | |||
<td style="text-align: center;">Av<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 891: | Line 1,062: | ||
</td> | </td> | ||
<td>3/2<br /> | <td>3/2<br /> | ||
</td> | |||
<td style="text-align: center;">P5<br /> | |||
</td> | |||
<td style="text-align: center;">A<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 899: | Line 1,074: | ||
</td> | </td> | ||
<td>50/33<br /> | <td>50/33<br /> | ||
</td> | |||
<td style="text-align: center;">^5<br /> | |||
</td> | |||
<td style="text-align: center;">A^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 907: | Line 1,086: | ||
</td> | </td> | ||
<td>32/21<br /> | <td>32/21<br /> | ||
</td> | |||
<td style="text-align: center;">^^5<br /> | |||
</td> | |||
<td style="text-align: center;">A^^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 915: | Line 1,098: | ||
</td> | </td> | ||
<td>54/35<br /> | <td>54/35<br /> | ||
</td> | |||
<td style="text-align: center;">^<span style="font-size: 90%; vertical-align: super;">3</span>5, v<span style="font-size: 90%; vertical-align: super;">3</span>m6<br /> | |||
</td> | |||
<td style="text-align: center;">A^<span style="font-size: 90%; vertical-align: super;">3</span>, Bbv<span style="font-size: 90%; vertical-align: super;">3</span><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 923: | Line 1,110: | ||
</td> | </td> | ||
<td>14/9<br /> | <td>14/9<br /> | ||
</td> | |||
<td style="text-align: center;">vvm6<br /> | |||
</td> | |||
<td style="text-align: center;">Bbvv<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 931: | Line 1,122: | ||
</td> | </td> | ||
<td>11/7<br /> | <td>11/7<br /> | ||
</td> | |||
<td style="text-align: center;">vm6<br /> | |||
</td> | |||
<td style="text-align: center;">Bbv<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 939: | Line 1,134: | ||
</td> | </td> | ||
<td>35/22<br /> | <td>35/22<br /> | ||
</td> | |||
<td style="text-align: center;">m6<br /> | |||
</td> | |||
<td style="text-align: center;">Bb<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 947: | Line 1,146: | ||
</td> | </td> | ||
<td>8/5<br /> | <td>8/5<br /> | ||
</td> | |||
<td style="text-align: center;">^m6<br /> | |||
</td> | |||
<td style="text-align: center;">Bb^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 955: | Line 1,158: | ||
</td> | </td> | ||
<td>81/50<br /> | <td>81/50<br /> | ||
</td> | |||
<td style="text-align: center;">v~6<br /> | |||
</td> | |||
<td style="text-align: center;">Bb^^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 963: | Line 1,170: | ||
</td> | </td> | ||
<td>18/11<br /> | <td>18/11<br /> | ||
</td> | |||
<td style="text-align: center;">~6<br /> | |||
</td> | |||
<td style="text-align: center;">Bv<span style="font-size: 90%; vertical-align: super;">3</span><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 971: | Line 1,182: | ||
</td> | </td> | ||
<td>33/20<br /> | <td>33/20<br /> | ||
</td> | |||
<td style="text-align: center;">^~6<br /> | |||
</td> | |||
<td style="text-align: center;">Bvv<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 979: | Line 1,194: | ||
</td> | </td> | ||
<td>5/3<br /> | <td>5/3<br /> | ||
</td> | |||
<td style="text-align: center;">vM6<br /> | |||
</td> | |||
<td style="text-align: center;">Bv<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 987: | Line 1,206: | ||
</td> | </td> | ||
<td>27/16<br /> | <td>27/16<br /> | ||
</td> | |||
<td style="text-align: center;">M6<br /> | |||
</td> | |||
<td style="text-align: center;">B<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 995: | Line 1,218: | ||
</td> | </td> | ||
<td>56/33<br /> | <td>56/33<br /> | ||
</td> | |||
<td style="text-align: center;">^M6<br /> | |||
</td> | |||
<td style="text-align: center;">B^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,003: | Line 1,230: | ||
</td> | </td> | ||
<td>12/7<br /> | <td>12/7<br /> | ||
</td> | |||
<td style="text-align: center;">^^M6<br /> | |||
</td> | |||
<td style="text-align: center;">B^^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,011: | Line 1,242: | ||
</td> | </td> | ||
<td>121/70<br /> | <td>121/70<br /> | ||
</td> | |||
<td style="text-align: center;">^<span style="font-size: 90%; vertical-align: super;">3</span>M6, v<span style="font-size: 90%; vertical-align: super;">3</span>m7<br /> | |||
</td> | |||
<td style="text-align: center;">B^<span style="font-size: 90%; vertical-align: super;">3</span>, Cv<span style="font-size: 90%; vertical-align: super;">3</span><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,019: | Line 1,254: | ||
</td> | </td> | ||
<td>7/4<br /> | <td>7/4<br /> | ||
</td> | |||
<td style="text-align: center;">vvm7<br /> | |||
</td> | |||
<td style="text-align: center;">Cvv<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,027: | Line 1,266: | ||
</td> | </td> | ||
<td>44/25<br /> | <td>44/25<br /> | ||
</td> | |||
<td style="text-align: center;">vm7<br /> | |||
</td> | |||
<td style="text-align: center;">Cv<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,035: | Line 1,278: | ||
</td> | </td> | ||
<td>16/9<br /> | <td>16/9<br /> | ||
</td> | |||
<td style="text-align: center;">m7<br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,043: | Line 1,290: | ||
</td> | </td> | ||
<td>9/5<br /> | <td>9/5<br /> | ||
</td> | |||
<td style="text-align: center;">^m7<br /> | |||
</td> | |||
<td style="text-align: center;">C^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,051: | Line 1,302: | ||
</td> | </td> | ||
<td>20/11<br /> | <td>20/11<br /> | ||
</td> | |||
<td style="text-align: center;">v~7<br /> | |||
</td> | |||
<td style="text-align: center;">C^^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,059: | Line 1,314: | ||
</td> | </td> | ||
<td>11/6<br /> | <td>11/6<br /> | ||
</td> | |||
<td style="text-align: center;">~7<br /> | |||
</td> | |||
<td style="text-align: center;">C^<span style="font-size: 90%; vertical-align: super;">3</span><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,067: | Line 1,326: | ||
</td> | </td> | ||
<td>50/27<br /> | <td>50/27<br /> | ||
</td> | |||
<td style="text-align: center;">^~7<br /> | |||
</td> | |||
<td style="text-align: center;">C#vv<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,075: | Line 1,338: | ||
</td> | </td> | ||
<td>15/8<br /> | <td>15/8<br /> | ||
</td> | |||
<td style="text-align: center;">vM7<br /> | |||
</td> | |||
<td style="text-align: center;">C#v<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,083: | Line 1,350: | ||
</td> | </td> | ||
<td>66/35<br /> | <td>66/35<br /> | ||
</td> | |||
<td style="text-align: center;">M7<br /> | |||
</td> | |||
<td style="text-align: center;">C#<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,091: | Line 1,362: | ||
</td> | </td> | ||
<td>21/11<br /> | <td>21/11<br /> | ||
</td> | |||
<td style="text-align: center;">^M7<br /> | |||
</td> | |||
<td style="text-align: center;">C#^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,099: | Line 1,374: | ||
</td> | </td> | ||
<td>27/14<br /> | <td>27/14<br /> | ||
</td> | |||
<td style="text-align: center;">^^M7<br /> | |||
</td> | |||
<td style="text-align: center;">C#^^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,107: | Line 1,386: | ||
</td> | </td> | ||
<td>35/18<br /> | <td>35/18<br /> | ||
</td> | |||
<td style="text-align: center;">^<span style="font-size: 90%; vertical-align: super;">3</span>M7, v<span style="font-size: 90%; vertical-align: super;">3</span>8<br /> | |||
</td> | |||
<td style="text-align: center;">C#^<span style="font-size: 90%; vertical-align: super;">3</span>, Dv<span style="font-size: 90%; vertical-align: super;">3</span><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,115: | Line 1,398: | ||
</td> | </td> | ||
<td>49/25<br /> | <td>49/25<br /> | ||
</td> | |||
<td style="text-align: center;">vv8<br /> | |||
</td> | |||
<td style="text-align: center;">Dvv<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,123: | Line 1,410: | ||
</td> | </td> | ||
<td>99/50<br /> | <td>99/50<br /> | ||
</td> | |||
<td style="text-align: center;">v8<br /> | |||
</td> | |||
<td style="text-align: center;">Dv<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,131: | Line 1,422: | ||
</td> | </td> | ||
<td>2/1<br /> | <td>2/1<br /> | ||
</td> | |||
<td style="text-align: center;">P8<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
</table> | </table> | ||
< | Chords can be named using ups and downs as C upminor, D downmajor seven, etc. 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 /> | |||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Linear temperaments"></a><!-- ws:end:WikiTextHeadingRule:6 -->Linear temperaments</h1> | |||
| Line 1,439: | Line 1,735: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Z function"></a><!-- ws:end:WikiTextHeadingRule:8 -->Z function</h1> | ||
72edo is the ninth <a class="wiki_link" href="http://xenharmonic.wikispaces.com/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta integral edo</a>, as well as being a peak and gap edo, and the maximum value of the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/The%20Riemann%20Zeta%20Function%20and%20Tuning#The%20Z%20function">Z function</a> in the region near 72 occurs at 71.9506, giving an octave of 1200.824 cents, the stretched octaves of the zeta tuning. Below is a plot of Z in the region around 72.<br /> | 72edo is the ninth <a class="wiki_link" href="http://xenharmonic.wikispaces.com/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta integral edo</a>, as well as being a peak and gap edo, and the maximum value of the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/The%20Riemann%20Zeta%20Function%20and%20Tuning#The%20Z%20function">Z function</a> in the region near 72 occurs at 71.9506, giving an octave of 1200.824 cents, the stretched octaves of the zeta tuning. Below is a plot of Z in the region around 72.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:1571:&lt;img src=&quot;http://xenharmonic.wikispaces.com/file/view/plot72.png/219772696/plot72.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://xenharmonic.wikispaces.com/file/view/plot72.png/219772696/plot72.png" alt="plot72.png" title="plot72.png" /><!-- ws:end:WikiTextLocalImageRule:1571 --><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:10 -->Music</h1> | ||
<a class="wiki_link_ext" href="http://www.archive.org/details/Kotekant" rel="nofollow">Kotekant</a> <em><a class="wiki_link_ext" href="http://www.archive.org/download/Kotekant/kotekant.mp3" rel="nofollow">play</a></em> by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Gene%20Ward%20Smith">Gene Ward Smith</a><br /> | <a class="wiki_link_ext" href="http://www.archive.org/details/Kotekant" rel="nofollow">Kotekant</a> <em><a class="wiki_link_ext" href="http://www.archive.org/download/Kotekant/kotekant.mp3" rel="nofollow">play</a></em> by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Gene%20Ward%20Smith">Gene Ward Smith</a><br /> | ||
<em><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-72-edo.mp3" rel="nofollow">Twinkle canon – 72 edo</a></em> by <a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/archives/573" rel="nofollow">Claudi Meneghin</a><br /> | <em><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-72-edo.mp3" rel="nofollow">Twinkle canon – 72 edo</a></em> by <a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/archives/573" rel="nofollow">Claudi Meneghin</a><br /> | ||
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<em><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Rodgers/drum12a-c-t9.mp3" rel="nofollow">June Gloom #9</a></em> by Prent Rodgers<br /> | <em><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Rodgers/drum12a-c-t9.mp3" rel="nofollow">June Gloom #9</a></em> by Prent Rodgers<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Scales"></a><!-- ws:end:WikiTextHeadingRule:12 -->Scales</h1> | ||
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/smithgw72a">smithgw72a</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/smithgw72b">smithgw72b</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/smithgw72c">smithgw72c</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/smithgw72d">smithgw72d</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/smithgw72e">smithgw72e</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/smithgw72f">smithgw72f</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/smithgw72g">smithgw72g</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/smithgw72h">smithgw72h</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/smithgw72i">smithgw72i</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/smithgw72j">smithgw72j</a><br /> | <a class="wiki_link" href="http://xenharmonic.wikispaces.com/smithgw72a">smithgw72a</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/smithgw72b">smithgw72b</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/smithgw72c">smithgw72c</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/smithgw72d">smithgw72d</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/smithgw72e">smithgw72e</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/smithgw72f">smithgw72f</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/smithgw72g">smithgw72g</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/smithgw72h">smithgw72h</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/smithgw72i">smithgw72i</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/smithgw72j">smithgw72j</a><br /> | ||
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/blackjack">blackjack</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/miracle_8">miracle_8</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/miracle_10">miracle_10</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/miracle_12">miracle_12</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/miracle_12a">miracle_12a</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/miracle_24hi">miracle_24hi</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/miracle_24lo">miracle_24lo</a><br /> | <a class="wiki_link" href="http://xenharmonic.wikispaces.com/blackjack">blackjack</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/miracle_8">miracle_8</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/miracle_10">miracle_10</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/miracle_12">miracle_12</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/miracle_12a">miracle_12a</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/miracle_24hi">miracle_24hi</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/miracle_24lo">miracle_24lo</a><br /> | ||
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<a class="wiki_link" href="/JuneGloom">JuneGloom</a><br /> | <a class="wiki_link" href="/JuneGloom">JuneGloom</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="External links"></a><!-- ws:end:WikiTextHeadingRule:14 -->External links</h1> | ||
<ul><li><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/72_tone_equal_temperament" rel="nofollow">Wikipedia article on 72edo</a></li><li><a class="wiki_link_ext" href="http://orthodoxwiki.org/Byzantine_Chant" rel="nofollow">OrthodoxWiki Article on Byzantine chant, which uses 72edo</a></li><li><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Joe_Maneri" rel="nofollow">Wikipedia article on Joe Maneri (1927-2009)</a></li><li><a class="wiki_link_ext" href="http://www.ekmelic-music.org/en/" rel="nofollow">Ekmelic Music Society/Gesellschaft für Ekmelische Musik</a>, a group of composers and researchers dedicated to 72edo music</li><li><a class="wiki_link_ext" href="http://72note.com/site/original.html" rel="nofollow">Rick Tagawa's 72edo site</a>, including theory and composers' list</li><li><a class="wiki_link_ext" href="http://www.myspace.com/dawier" rel="nofollow" target="_blank">Danny Wier, composer and musician who specializes in 72-edo</a></li></ul></body></html></pre></div> | <ul><li><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/72_tone_equal_temperament" rel="nofollow">Wikipedia article on 72edo</a></li><li><a class="wiki_link_ext" href="http://orthodoxwiki.org/Byzantine_Chant" rel="nofollow">OrthodoxWiki Article on Byzantine chant, which uses 72edo</a></li><li><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Joe_Maneri" rel="nofollow">Wikipedia article on Joe Maneri (1927-2009)</a></li><li><a class="wiki_link_ext" href="http://www.ekmelic-music.org/en/" rel="nofollow">Ekmelic Music Society/Gesellschaft für Ekmelische Musik</a>, a group of composers and researchers dedicated to 72edo music</li><li><a class="wiki_link_ext" href="http://72note.com/site/original.html" rel="nofollow">Rick Tagawa's 72edo site</a>, including theory and composers' list</li><li><a class="wiki_link_ext" href="http://www.myspace.com/dawier" rel="nofollow" target="_blank">Danny Wier, composer and musician who specializes in 72-edo</a></li></ul></body></html></pre></div> | ||