80edo: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 149406481 - Original comment: ** |
Wikispaces>xenwolf **Imported revision 149491519 - 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:xenwolf|xenwolf]] and made on <tt>2010-06-18 07:30:09 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>149491519</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> | ||
<h4>Original Wikitext content:</h4> | <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">The //80 equal temperament//, often abbreviated 80-tET, 80-EDO, or 80-ET, is the scale derived by dividing the octave into 80 equally-sized steps. Each step represents a frequency ratio of exactly 15 cents. 80et is the first equal temperament to represent the 19-limit tonality diamond consistently, and in fact represents the 21 odd limit tonality diamond consistently also. | <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">The //80 equal temperament//, often abbreviated 80-tET, 80-EDO, or 80-ET, is the scale derived by dividing the octave into 80 equally-sized steps. Each step represents a frequency ratio of exactly 15 cents. 80et is the first equal temperament to represent the 19-limit [[tonality diamond]] consistently, and in fact represents the 21 odd limit tonality diamond consistently also. | ||
80 et tempers out 136/135, 169/168, 176/175, 190/189, 221/220, 256/255, 286/285, 289/288, 325/324, 351/350, 352/351, 361/360, 364/363, 400/399, 456/455, 476/475, 540/539, 561/560, 595/594, 715/714, 936/935, 969/968, 1001/1000, 1275/1274, 1331/1330, 1445/1444, 1521/1520, 1540/1539 and 1729/1728, not to mention such important non-superparticular commas as 2048/2025, 4000/3969, 1728/1715 and 3136/3125. | 80 et tempers out 136/135, 169/168, 176/175, 190/189, 221/220, 256/255, 286/285, 289/288, 325/324, 351/350, 352/351, 361/360, 364/363, 400/399, 456/455, 476/475, 540/539, 561/560, 595/594, 715/714, 936/935, 969/968, 1001/1000, 1275/1274, 1331/1330, 1445/1444, 1521/1520, 1540/1539 and 1729/1728, not to mention such important non-superparticular commas as 2048/2025, 4000/3969, 1728/1715 and 3136/3125. | ||
| Line 22: | Line 22: | ||
41&80 <<7 26 25 -3 -24 -33 20 ... || | 41&80 <<7 26 25 -3 -24 -33 20 ... || | ||
In each case, the numbers joined by an ampersand represent 19-limit patent vals (meaning | In each case, the numbers joined by an ampersand represent 19-limit patent vals (meaning obtained by rounding to the nearest integer) and the first and most important part of the wedgie is given. | ||
</pre></div> | </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>80edo</title></head><body>The <em>80 equal temperament</em>, often abbreviated 80-tET, 80-EDO, or 80-ET, is the scale derived by dividing the octave into 80 equally-sized steps. Each step represents a frequency ratio of exactly 15 cents. 80et is the first equal temperament to represent the 19-limit tonality diamond consistently, and in fact represents the 21 odd limit tonality diamond consistently also.<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>80edo</title></head><body>The <em>80 equal temperament</em>, often abbreviated 80-tET, 80-EDO, or 80-ET, is the scale derived by dividing the octave into 80 equally-sized steps. Each step represents a frequency ratio of exactly 15 cents. 80et is the first equal temperament to represent the 19-limit <a class="wiki_link" href="/tonality%20diamond">tonality diamond</a> consistently, and in fact represents the 21 odd limit tonality diamond consistently also.<br /> | ||
<br /> | <br /> | ||
80 et tempers out 136/135, 169/168, 176/175, 190/189, 221/220, 256/255, 286/285, 289/288, 325/324, 351/350, 352/351, 361/360, 364/363, 400/399, 456/455, 476/475, 540/539, 561/560, 595/594, 715/714, 936/935, 969/968, 1001/1000, 1275/1274, 1331/1330, 1445/1444, 1521/1520, 1540/1539 and 1729/1728, not to mention such important non-superparticular commas as 2048/2025, 4000/3969, 1728/1715 and 3136/3125.<br /> | 80 et tempers out 136/135, 169/168, 176/175, 190/189, 221/220, 256/255, 286/285, 289/288, 325/324, 351/350, 352/351, 361/360, 364/363, 400/399, 456/455, 476/475, 540/539, 561/560, 595/594, 715/714, 936/935, 969/968, 1001/1000, 1275/1274, 1331/1330, 1445/1444, 1521/1520, 1540/1539 and 1729/1728, not to mention such important non-superparticular commas as 2048/2025, 4000/3969, 1728/1715 and 3136/3125.<br /> | ||
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41&amp;80 &lt;&lt;7 26 25 -3 -24 -33 20 ... ||<br /> | 41&amp;80 &lt;&lt;7 26 25 -3 -24 -33 20 ... ||<br /> | ||
<br /> | <br /> | ||
In each case, the numbers joined by an ampersand represent 19-limit patent vals (meaning | In each case, the numbers joined by an ampersand represent 19-limit patent vals (meaning obtained by rounding to the nearest integer) and the first and most important part of the wedgie is given.</body></html></pre></div> | ||
Revision as of 07:30, 18 June 2010
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author xenwolf and made on 2010-06-18 07:30:09 UTC.
- The original revision id was 149491519.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
The //80 equal temperament//, often abbreviated 80-tET, 80-EDO, or 80-ET, is the scale derived by dividing the octave into 80 equally-sized steps. Each step represents a frequency ratio of exactly 15 cents. 80et is the first equal temperament to represent the 19-limit [[tonality diamond]] consistently, and in fact represents the 21 odd limit tonality diamond consistently also. 80 et tempers out 136/135, 169/168, 176/175, 190/189, 221/220, 256/255, 286/285, 289/288, 325/324, 351/350, 352/351, 361/360, 364/363, 400/399, 456/455, 476/475, 540/539, 561/560, 595/594, 715/714, 936/935, 969/968, 1001/1000, 1275/1274, 1331/1330, 1445/1444, 1521/1520, 1540/1539 and 1729/1728, not to mention such important non-superparticular commas as 2048/2025, 4000/3969, 1728/1715 and 3136/3125. 80 supports a profusion of 19-limit (and lower) rank two temperaments which have mostly not been explored. We might mention: 31&80 <<7 6 15 27 -24 -23 -20 ... || 72&80 <<24 30 40 24 32 24 0 ... || 34&80 <<2 -4 -50 22 16 2 -40 ... || 46&80 <<2 -4 30 22 16 2 40 ... || 29&80 <<3 34 45 33 24 -37 20 ... || 12&80 <<4 -8 -20 -36 32 4 0 ... || 22&80 <<6 -10 12 -14 -32 6 -40 ... || 58&80 <<6 -10 12 -14 -32 6 40 ... || 41&80 <<7 26 25 -3 -24 -33 20 ... || In each case, the numbers joined by an ampersand represent 19-limit patent vals (meaning obtained by rounding to the nearest integer) and the first and most important part of the wedgie is given.
Original HTML content:
<html><head><title>80edo</title></head><body>The <em>80 equal temperament</em>, often abbreviated 80-tET, 80-EDO, or 80-ET, is the scale derived by dividing the octave into 80 equally-sized steps. Each step represents a frequency ratio of exactly 15 cents. 80et is the first equal temperament to represent the 19-limit <a class="wiki_link" href="/tonality%20diamond">tonality diamond</a> consistently, and in fact represents the 21 odd limit tonality diamond consistently also.<br /> <br /> 80 et tempers out 136/135, 169/168, 176/175, 190/189, 221/220, 256/255, 286/285, 289/288, 325/324, 351/350, 352/351, 361/360, 364/363, 400/399, 456/455, 476/475, 540/539, 561/560, 595/594, 715/714, 936/935, 969/968, 1001/1000, 1275/1274, 1331/1330, 1445/1444, 1521/1520, 1540/1539 and 1729/1728, not to mention such important non-superparticular commas as 2048/2025, 4000/3969, 1728/1715 and 3136/3125.<br /> <br /> 80 supports a profusion of 19-limit (and lower) rank two temperaments which have mostly not been explored. We might mention:<br /> <br /> 31&80 <<7 6 15 27 -24 -23 -20 ... ||<br /> 72&80 <<24 30 40 24 32 24 0 ... ||<br /> 34&80 <<2 -4 -50 22 16 2 -40 ... ||<br /> 46&80 <<2 -4 30 22 16 2 40 ... ||<br /> 29&80 <<3 34 45 33 24 -37 20 ... ||<br /> 12&80 <<4 -8 -20 -36 32 4 0 ... ||<br /> 22&80 <<6 -10 12 -14 -32 6 -40 ... ||<br /> 58&80 <<6 -10 12 -14 -32 6 40 ... ||<br /> 41&80 <<7 26 25 -3 -24 -33 20 ... ||<br /> <br /> In each case, the numbers joined by an ampersand represent 19-limit patent vals (meaning obtained by rounding to the nearest integer) and the first and most important part of the wedgie is given.</body></html>