Xenharmonic Wiki

80edo: Difference between revisions

← Older editNewer edit →
VisualWikitext
Wikispaces>xenwolf
**Imported revision 239564411 - Original comment: **
Wikispaces>phylingual
**Imported revision 353014670 - Original comment: **
Line 1: Line 1:
<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:xenwolf|xenwolf]] and made on <tt>2011-06-30 18:04:18 UTC</tt>.<br>
: This revision was by author [[User:phylingual|phylingual]] and made on <tt>2012-07-13 14:04:47 UTC</tt>.<br>
: The original revision id was <tt>239564411</tt>.<br>
: The original revision id was <tt>353014670</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 [[cent]]s. 80et is the first equal temperament to represent the [[19-limit]] [[tonality diamond]] [[consistent]]ly, 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 [[cent]]s. 80et is the first equal temperament that represent the [[19-limit]] [[tonality diamond]] [[consistent]]ly (it barely manages to do so), and in fact represents the 21 odd limit tonality diamond consistently also.


80 et [[tempering out|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 [[tempering out|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&amp;80 &lt;&lt;7 26 25 -3 -24 -33 20 ... ||
41&amp;80 &lt;&lt;7 26 25 -3 -24 -33 20 ... ||


In each case, the numbers joined by an ampersand represent 19-limit [[Patent val|patent vals]] (meaning obtained by rounding to the nearest integer) and the first and most important part of the wedgie is given.</pre></div>
In each case, the numbers joined by an ampersand represent 19-limit [[Patent val|patent vals]] (meaning obtained by rounding to the nearest integer) and the first and most important part of the wedgie is given.
 
=Intervals of 80edo=
||~ degrees ||~ cents ||~ 19 prime limit ratios ||
|| 0 || 0 || 1/1 ||
|| 1 || 15 || 64/63 ||
|| 2 || 30 || 81/80 ||
|| 3 || 45 || 34/33, 36/35 ||
|| 4 || 60 || 26/25, 28/27, 33/32, 35/34 ||
|| 5 || 75 || 22/21, 25/24, 27/26 ||
|| 6 || 90 || 19/18, 20/19, 21/20 ||
|| 7 || 105 || 16/15, 17/16, 18/17 ||
|| 8 || 120 || 14/13, 15/14 ||
|| 9 || 135 || 13/12 ||
|| 10 || 150 || 12/11 ||
|| 11 || 165 || 11/10 ||
|| 12 || 180 || 10/9, 21/19 ||
|| 13 || 195 || 19/17 ||
|| 14 || 210 || 9/8, 17/15 ||
|| 15 || 225 || 8/7 ||
|| 16 || 240 ||  ||
|| 17 || 255 || 15/13, 22/19 ||
|| 18 || 270 || 7/6 ||
|| 19 || 285 || 13/11, 20/17 ||
|| 20 || 300 || 19/16, 25/21 ||
|| 21 || 315 || 6/5 ||
|| 22 || 330 || 17/14 ||
|| 23 || 345 || 11/9 ||
|| 24 || 360 || 16/13, 21/17 ||
|| 25 || 375 ||  ||
|| 26 || 390 || 5/4 ||
|| 27 || 405 || 19/15, 24/19 ||
|| 28 || 420 || 14/11 ||
|| 29 || 435 || 9/7 ||
|| 30 || 450 || 13/10, 22/17 ||
|| 31 || 465 || 17/13 ||
|| 32 || 480 || 21/16, 25/19 ||
|| 33 || 495 || 4/3 ||
|| 34 || 510 ||  ||
|| 35 || 525 || 19/14 ||
|| 36 || 540 || 26/19 ||
|| 37 || 555 || 11/8 ||
|| 38 || 570 || 18/13 ||
|| 39 || 585 || 7/5 ||
|| 40 || 600 || 17/12, 24/17 ||</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">&lt;html&gt;&lt;head&gt;&lt;title&gt;80edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;80 equal temperament&lt;/em&gt;, 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 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s. 80et is the first equal temperament to represent the &lt;a class="wiki_link" href="/19-limit"&gt;19-limit&lt;/a&gt; &lt;a class="wiki_link" href="/tonality%20diamond"&gt;tonality diamond&lt;/a&gt; &lt;a class="wiki_link" href="/consistent"&gt;consistent&lt;/a&gt;ly, and in fact represents the 21 odd limit tonality diamond consistently also.&lt;br /&gt;
<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;80edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;80 equal temperament&lt;/em&gt;, 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 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s. 80et is the first equal temperament that represent the &lt;a class="wiki_link" href="/19-limit"&gt;19-limit&lt;/a&gt; &lt;a class="wiki_link" href="/tonality%20diamond"&gt;tonality diamond&lt;/a&gt; &lt;a class="wiki_link" href="/consistent"&gt;consistent&lt;/a&gt;ly (it barely manages to do so), and in fact represents the 21 odd limit tonality diamond consistently also.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
80 et &lt;a class="wiki_link" href="/tempering%20out"&gt;tempers out&lt;/a&gt; 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.&lt;br /&gt;
80 et &lt;a class="wiki_link" href="/tempering%20out"&gt;tempers out&lt;/a&gt; 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.&lt;br /&gt;
Line 40: Line 84:
41&amp;amp;80 &amp;lt;&amp;lt;7 26 25 -3 -24 -33 20 ... ||&lt;br /&gt;
41&amp;amp;80 &amp;lt;&amp;lt;7 26 25 -3 -24 -33 20 ... ||&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In each case, the numbers joined by an ampersand represent 19-limit &lt;a class="wiki_link" href="/Patent%20val"&gt;patent vals&lt;/a&gt; (meaning obtained by rounding to the nearest integer) and the first and most important part of the wedgie is given.&lt;/body&gt;&lt;/html&gt;</pre></div>
In each case, the numbers joined by an ampersand represent 19-limit &lt;a class="wiki_link" href="/Patent%20val"&gt;patent vals&lt;/a&gt; (meaning obtained by rounding to the nearest integer) and the first and most important part of the wedgie is given.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Intervals of 80edo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Intervals of 80edo&lt;/h1&gt;
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;th&gt;degrees&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;cents&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;19 prime limit ratios&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;64/63&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;81/80&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;45&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;34/33, 36/35&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;60&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;26/25, 28/27, 33/32, 35/34&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;75&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;22/21, 25/24, 27/26&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;90&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;19/18, 20/19, 21/20&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;105&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/15, 17/16, 18/17&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;120&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14/13, 15/14&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;135&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/12&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;150&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12/11&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;165&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/10&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;180&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10/9, 21/19&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;195&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;19/17&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;210&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/8, 17/15&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;225&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8/7&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;240&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;255&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15/13, 22/19&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;270&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/6&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;285&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/11, 20/17&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;20&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;300&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;19/16, 25/21&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;315&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6/5&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;22&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;330&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;17/14&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;345&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/9&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;24&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;360&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/13, 21/17&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;375&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;26&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;390&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/4&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;405&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;19/15, 24/19&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;420&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14/11&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;29&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;435&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/7&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;450&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/10, 22/17&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;465&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;17/13&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;480&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;21/16, 25/19&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;33&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;495&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4/3&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;34&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;510&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;35&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;525&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;19/14&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;36&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;540&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;26/19&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;37&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;555&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/8&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;38&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;570&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;18/13&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;39&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;585&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/5&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;40&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;600&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;17/12, 24/17&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/body&gt;&lt;/html&gt;</pre></div>
Retrieved from "https://en.xen.wiki/w/80edo"