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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
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 (the tuning favored by Mozart and contemporaries), or 0.16 comma, meantone. In the 7-limit the patent val tempers out 1029/1024 and 1728/1715, so that it supports [[Meantone_family|mothra temperament]]. 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 [[Orgonia|orgone temperament]].
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-12-31 02:06:45 UTC</tt>.<br>
: The original revision id was <tt>288887153</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>
<h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">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 (the tuning favored by Mozart and contemporaries), or 0.16 comma, meantone. In the 7-limit the patent val tempers out 1029/1024 and 1728/1715, so that it supports [[Meantone family|mothra temperament]]. 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 [[Orgonia|orgone temperament]].


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 meantone (26 could be called meantone, but it's more of a flattone) 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.
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 meantone (26 could be called meantone, but it's more of a flattone) 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.


67edo is the 19th [[prime numbers|prime]] edo.
67edo is the 19th [[prime_numbers|prime]] edo.


Music:
Music:
[[http://soonlabel.com/xenharmonic/wp-content/uploads/2011/11/67-edo.mp3|Beginning of a piece in 67 tone]], [[Peter Kosmorsky]]
 
[http://soonlabel.com/xenharmonic/wp-content/uploads/2011/11/67-edo.mp3 Beginning of a piece in 67 tone], [[Peter_Kosmorsky|Peter Kosmorsky]]


Cents
Cents


0: 1/1 0.000 unison, perfect prime
0: 1/1 0.000 unison, perfect prime
1: 17.910 cents 17.910
1: 17.910 cents 17.910
2: 35.821 cents 35.821
2: 35.821 cents 35.821
3: 53.731 cents 53.731
3: 53.731 cents 53.731
4: 71.642 cents 71.642
4: 71.642 cents 71.642
5: 89.552 cents 89.552
5: 89.552 cents 89.552
6: 107.463 cents 107.463
6: 107.463 cents 107.463
7: 125.373 cents 125.373
7: 125.373 cents 125.373
8: 143.284 cents 143.284
8: 143.284 cents 143.284
9: 161.194 cents 161.194
9: 161.194 cents 161.194
10: 179.104 cents 179.104
10: 179.104 cents 179.104
11: 197.015 cents 197.015
11: 197.015 cents 197.015
12: 214.925 cents 214.925
12: 214.925 cents 214.925
13: 232.836 cents 232.836
13: 232.836 cents 232.836
14: 250.746 cents 250.746
14: 250.746 cents 250.746
15: 268.657 cents 7/6
15: 268.657 cents 7/6
16: 286.567 cents 286.567
16: 286.567 cents 286.567
17: 304.478 cents 304.478
17: 304.478 cents 304.478
18: 322.388 cents 322.388
18: 322.388 cents 322.388
19: 340.299 cents 340.299
19: 340.299 cents 340.299
20: 358.209 cents 358.209
20: 358.209 cents 358.209
21: 376.119 cents 5/4 -
21: 376.119 cents 5/4 -
22: 394.030 cents 5/4 +
22: 394.030 cents 5/4 +
23: 411.940 cents 411.940
23: 411.940 cents 411.940
24: 429.851 cents 429.851
24: 429.851 cents 429.851
25: 447.761 cents 447.761
25: 447.761 cents 447.761
26: 465.672 cents 21/16
26: 465.672 cents 21/16
27: 483.582 cents 483.582
27: 483.582 cents 483.582
28: 501.493 cents 501.493
28: 501.493 cents 501.493
29: 519.403 cents 519.403
29: 519.403 cents 519.403
30: 537.313 cents 537.313
30: 537.313 cents 537.313
31: 555.224 cents 11/8
31: 555.224 cents 11/8
32: 573.134 cents 573.134
32: 573.134 cents 573.134
33: 591.045 cents 591.045
33: 591.045 cents 591.045
34: 608.955 cents 608.955
34: 608.955 cents 608.955
35: 626.866 cents 626.866
35: 626.866 cents 626.866
36: 644.776 cents 644.776
36: 644.776 cents 644.776
37: 662.687 cents 662.687
37: 662.687 cents 662.687
38: 680.597 cents 680.597
38: 680.597 cents 680.597
39: 698.507 cents 3/2
39: 698.507 cents 3/2
40: 716.418 cents 716.418
40: 716.418 cents 716.418
41: 734.328 cents 734.328
41: 734.328 cents 734.328
42: 752.239 cents 752.239
42: 752.239 cents 752.239
43: 770.149 cents 770.149
43: 770.149 cents 770.149
44: 788.060 cents 788.060
44: 788.060 cents 788.060
45: 805.970 cents 805.970
45: 805.970 cents 805.970
46: 823.881 cents 823.881
46: 823.881 cents 823.881
47: 841.791 cents 841.791
47: 841.791 cents 841.791
48: 859.701 cents 859.701
48: 859.701 cents 859.701
49: 877.612 cents 877.612
49: 877.612 cents 877.612
50: 895.522 cents 895.522
50: 895.522 cents 895.522
51: 913.433 cents 913.433
51: 913.433 cents 913.433
52: 931.343 cents 931.343
52: 931.343 cents 931.343
53: 949.254 cents 949.254
53: 949.254 cents 949.254
54: 967.164 cents 7/4
54: 967.164 cents 7/4
55: 985.075 cents 985.075
55: 985.075 cents 985.075
56: 1002.985 cents 1002.985
56: 1002.985 cents 1002.985
57: 1020.896 cents 1020.896
57: 1020.896 cents 1020.896
58: 1038.806 cents 1038.806
58: 1038.806 cents 1038.806
59: 1056.716 cents 1056.716
59: 1056.716 cents 1056.716
60: 1074.627 cents 1074.627
60: 1074.627 cents 1074.627
61: 1092.537 cents 1092.537
61: 1092.537 cents 1092.537
62: 1110.448 cents 1110.448
62: 1110.448 cents 1110.448
63: 1128.358 cents 1128.358
63: 1128.358 cents 1128.358
64: 1146.269 cents 1146.269
64: 1146.269 cents 1146.269
65: 1164.179 cents 1164.179
65: 1164.179 cents 1164.179
66: 1182.090 cents 1182.090
66: 1182.090 cents 1182.090
67: 2/1 1200.000 octave</pre></div>
 
<h4>Original HTML content:</h4>
67: 2/1 1200.000 octave
<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 (the tuning favored by Mozart and contemporaries), 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;
[[Category:meantone]]
&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 meantone (26 could be called meantone, but it's more of a flattone) 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;
67edo is the 19th &lt;a class="wiki_link" href="/prime%20numbers"&gt;prime&lt;/a&gt; edo.&lt;br /&gt;
&lt;br /&gt;
Music:&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/wp-content/uploads/2011/11/67-edo.mp3" rel="nofollow"&gt;Beginning of a piece in 67 tone&lt;/a&gt;, &lt;a class="wiki_link" href="/Peter%20Kosmorsky"&gt;Peter Kosmorsky&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
Cents&lt;br /&gt;
&lt;br /&gt;
0: 1/1 0.000 unison, perfect prime&lt;br /&gt;
1: 17.910 cents 17.910&lt;br /&gt;
2: 35.821 cents 35.821&lt;br /&gt;
3: 53.731 cents 53.731&lt;br /&gt;
4: 71.642 cents 71.642&lt;br /&gt;
5: 89.552 cents 89.552&lt;br /&gt;
6: 107.463 cents 107.463&lt;br /&gt;
7: 125.373 cents 125.373&lt;br /&gt;
8: 143.284 cents 143.284&lt;br /&gt;
9: 161.194 cents 161.194&lt;br /&gt;
10: 179.104 cents 179.104&lt;br /&gt;
11: 197.015 cents 197.015&lt;br /&gt;
12: 214.925 cents 214.925&lt;br /&gt;
13: 232.836 cents 232.836&lt;br /&gt;
14: 250.746 cents 250.746&lt;br /&gt;
15: 268.657 cents 7/6&lt;br /&gt;
16: 286.567 cents 286.567&lt;br /&gt;
17: 304.478 cents 304.478&lt;br /&gt;
18: 322.388 cents 322.388&lt;br /&gt;
19: 340.299 cents 340.299&lt;br /&gt;
20: 358.209 cents 358.209&lt;br /&gt;
21: 376.119 cents 5/4 -&lt;br /&gt;
22: 394.030 cents 5/4 +&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;
26: 465.672 cents 21/16&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;
31: 555.224 cents 11/8&lt;br /&gt;
32: 573.134 cents 573.134&lt;br /&gt;
33: 591.045 cents 591.045&lt;br /&gt;
34: 608.955 cents 608.955&lt;br /&gt;
35: 626.866 cents 626.866&lt;br /&gt;
36: 644.776 cents 644.776&lt;br /&gt;
37: 662.687 cents 662.687&lt;br /&gt;
38: 680.597 cents 680.597&lt;br /&gt;
39: 698.507 cents 3/2&lt;br /&gt;
40: 716.418 cents 716.418&lt;br /&gt;
41: 734.328 cents 734.328&lt;br /&gt;
42: 752.239 cents 752.239&lt;br /&gt;
43: 770.149 cents 770.149&lt;br /&gt;
44: 788.060 cents 788.060&lt;br /&gt;
45: 805.970 cents 805.970&lt;br /&gt;
46: 823.881 cents 823.881&lt;br /&gt;
47: 841.791 cents 841.791&lt;br /&gt;
48: 859.701 cents 859.701&lt;br /&gt;
49: 877.612 cents 877.612&lt;br /&gt;
50: 895.522 cents 895.522&lt;br /&gt;
51: 913.433 cents 913.433&lt;br /&gt;
52: 931.343 cents 931.343&lt;br /&gt;
53: 949.254 cents 949.254&lt;br /&gt;
54: 967.164 cents 7/4&lt;br /&gt;
55: 985.075 cents 985.075&lt;br /&gt;
56: 1002.985 cents 1002.985&lt;br /&gt;
57: 1020.896 cents 1020.896&lt;br /&gt;
58: 1038.806 cents 1038.806&lt;br /&gt;
59: 1056.716 cents 1056.716&lt;br /&gt;
60: 1074.627 cents 1074.627&lt;br /&gt;
61: 1092.537 cents 1092.537&lt;br /&gt;
62: 1110.448 cents 1110.448&lt;br /&gt;
63: 1128.358 cents 1128.358&lt;br /&gt;
64: 1146.269 cents 1146.269&lt;br /&gt;
65: 1164.179 cents 1164.179&lt;br /&gt;
66: 1182.090 cents 1182.090&lt;br /&gt;
67: 2/1 1200.000 octave&lt;/body&gt;&lt;/html&gt;</pre></div>
Retrieved from "https://en.xen.wiki/w/67edo"