67edo: Difference between revisions

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:<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>

A promising tuning which has, as many relatively large equal temperaments do, a variety of tonal resources: it is the first edo to have both a light meantone and an orgone temperament. It has relatively good approximations of the 3rd, 7th, 11th, 13th, 15th, 17th harmonics, although the 5th, 9th, and 19th as well as certain higher ones are workable as well. 33+34 can be used to construct this temperament explaining some of its properties.

0: 1/1 0.000 unison, perfect prime

13: 232.836 cents 232.836

14: 250.746 cents 250.746

16: 286.567 cents 286.567

17: 304.478 cents 304.478

19: 340.299 cents 340.299

20: 358.209 cents 358.209

23: 411.940 cents 411.940

24: 429.851 cents 429.851

25: 447.761 cents 447.761

27: 483.582 cents 483.582

28: 501.493 cents 501.493

29: 519.403 cents 519.403

30: 537.313 cents 537.313

32: 573.134 cents 573.134

33: 591.045 cents 591.045

37: 662.687 cents 662.687

38: 680.597 cents 680.597

40: 716.418 cents 716.418

41: 734.328 cents 734.328

52: 931.343 cents 931.343

53: 949.254 cents 949.254

55: 985.075 cents 985.075

56: 1002.985 cents 1002.985

65: 1164.179 cents 1164.179

66: 1182.090 cents 1182.090

<h4>Original HTML content:</h4>

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;67edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;67 equal divisions of the octave divides the octave into 67 equal parts of 17.910 cents each. It tempers out 81/80, supporting meantone temperament, with a tuning which is approximately 1/6 comma, or 0.16 comma, meantone. In the 7-limit the patent val tempers out 1029/1024 and 1728/1715, so that it supports &lt;a class="wiki_link" href="/Meantone%20family"&gt;mothra temperament&lt;/a&gt;. In the 11-limit it tempers out 176/175 and 540/539, supporting mosura, an alternative 11-limit mothra. In the 13-limit it tempers out 144/143 and 196/195, supporting 13-limit mosura. It tempers out the orgonisma, and on the 2.7.11 subgroup it supports &lt;a class="wiki_link" href="/Orgonia"&gt;orgone temperament&lt;/a&gt;.&lt;br /&gt;

&lt;br /&gt;

A promising tuning which has, as many relatively large equal temperaments do, a variety of tonal resources: it is the first edo to have both a light meantone and an orgone temperament. It has relatively good approximations of the 3rd, 7th, 11th, 13th, 15th, 17th harmonics, although the 5th, 9th, and 19th as well as certain higher ones are workable as well. 33+34 can be used to construct this temperament explaining some of its properties.&lt;br /&gt;

&lt;br /&gt;

0: 1/1 0.000 unison, perfect prime&lt;br /&gt;

13: 232.836 cents 232.836&lt;br /&gt;

14: 250.746 cents 250.746&lt;br /&gt;

16: 286.567 cents 286.567&lt;br /&gt;

17: 304.478 cents 304.478&lt;br /&gt;

19: 340.299 cents 340.299&lt;br /&gt;

20: 358.209 cents 358.209&lt;br /&gt;

23: 411.940 cents 411.940&lt;br /&gt;

24: 429.851 cents 429.851&lt;br /&gt;

25: 447.761 cents 447.761&lt;br /&gt;

27: 483.582 cents 483.582&lt;br /&gt;

28: 501.493 cents 501.493&lt;br /&gt;

29: 519.403 cents 519.403&lt;br /&gt;

30: 537.313 cents 537.313&lt;br /&gt;

32: 573.134 cents 573.134&lt;br /&gt;

33: 591.045 cents 591.045&lt;br /&gt;

37: 662.687 cents 662.687&lt;br /&gt;

38: 680.597 cents 680.597&lt;br /&gt;

40: 716.418 cents 716.418&lt;br /&gt;

41: 734.328 cents 734.328&lt;br /&gt;

52: 931.343 cents 931.343&lt;br /&gt;

53: 949.254 cents 949.254&lt;br /&gt;

55: 985.075 cents 985.075&lt;br /&gt;

56: 1002.985 cents 1002.985&lt;br /&gt;