94edo: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 300231154 - Original comment: ** |
Wikispaces>keenanpepper **Imported revision 309325440 - 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:keenanpepper|keenanpepper]] and made on <tt>2012-03-09 03:55:32 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>309325440</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> | ||
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46&94 <<8 30 -18 -4 -28 8 -24 2 ... || | 46&94 <<8 30 -18 -4 -28 8 -24 2 ... || | ||
68&94 <<20 28 2 -10 24 20 34 52 ... || | 68&94 <<20 28 2 -10 24 20 34 52 ... || | ||
53&94 <<1 -8 -14 23 20 -46 -3 -35 ... || | 53&94 <<1 -8 -14 23 20 -46 -3 -35 ... || (one garibaldi) | ||
41&94 <<1 -8 -14 23 20 48 -3 -35 ... || | 41&94 <<1 -8 -14 23 20 48 -3 -35 ... || (another garibaldi, only differing in the mappings of 17 and 23) | ||
135&94 <<1 -8 -14 23 20 48 -3 59 ... || | 135&94 <<1 -8 -14 23 20 48 -3 59 ... || (another garibaldi) | ||
130&94 <<6 -48 10 -50 26 6 -18 -22 ... || | 130&94 <<6 -48 10 -50 26 6 -18 -22 ... || (a pogo extension) | ||
58&94 <<6 46 10 44 26 6 -18 -22 ... || | 58&94 <<6 46 10 44 26 6 -18 -22 ... || (a supers extension) | ||
50&94 <<24 -4 40 -12 10 24 22 6 ... || | 50&94 <<24 -4 40 -12 10 24 22 6 ... || | ||
72&94 <<12 -2 20 -6 52 12 -36 -44 ... || | 72&94 <<12 -2 20 -6 52 12 -36 -44 ... || (a gizzard extension) | ||
94 solo <<12 -2 20 -6 -42 12 -36 -44 ... || | 94 solo <<12 -2 20 -6 -42 12 -36 -44 ... || | ||
80&94 <<18 44 30 38 -16 18 40 28 ... || | 80&94 <<18 44 30 38 -16 18 40 28 ... || | ||
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46&amp;94 &lt;&lt;8 30 -18 -4 -28 8 -24 2 ... ||<br /> | 46&amp;94 &lt;&lt;8 30 -18 -4 -28 8 -24 2 ... ||<br /> | ||
68&amp;94 &lt;&lt;20 28 2 -10 24 20 34 52 ... ||<br /> | 68&amp;94 &lt;&lt;20 28 2 -10 24 20 34 52 ... ||<br /> | ||
53&amp;94 &lt;&lt;1 -8 -14 23 20 -46 -3 -35 ... ||<br /> | 53&amp;94 &lt;&lt;1 -8 -14 23 20 -46 -3 -35 ... || (one garibaldi)<br /> | ||
41&amp;94 &lt;&lt;1 -8 -14 23 20 48 -3 -35 ... ||<br /> | 41&amp;94 &lt;&lt;1 -8 -14 23 20 48 -3 -35 ... || (another garibaldi, only differing in the mappings of 17 and 23)<br /> | ||
135&amp;94 &lt;&lt;1 -8 -14 23 20 48 -3 59 ... ||<br /> | 135&amp;94 &lt;&lt;1 -8 -14 23 20 48 -3 59 ... || (another garibaldi)<br /> | ||
130&amp;94 &lt;&lt;6 -48 10 -50 26 6 -18 -22 ... ||<br /> | 130&amp;94 &lt;&lt;6 -48 10 -50 26 6 -18 -22 ... || (a pogo extension)<br /> | ||
58&amp;94 &lt;&lt;6 46 10 44 26 6 -18 -22 ... ||<br /> | 58&amp;94 &lt;&lt;6 46 10 44 26 6 -18 -22 ... || (a supers extension)<br /> | ||
50&amp;94 &lt;&lt;24 -4 40 -12 10 24 22 6 ... ||<br /> | 50&amp;94 &lt;&lt;24 -4 40 -12 10 24 22 6 ... ||<br /> | ||
72&amp;94 &lt;&lt;12 -2 20 -6 52 12 -36 -44 ... ||<br /> | 72&amp;94 &lt;&lt;12 -2 20 -6 52 12 -36 -44 ... || (a gizzard extension)<br /> | ||
94 solo &lt;&lt;12 -2 20 -6 -42 12 -36 -44 ... ||<br /> | 94 solo &lt;&lt;12 -2 20 -6 -42 12 -36 -44 ... ||<br /> | ||
80&amp;94 &lt;&lt;18 44 30 38 -16 18 40 28 ... ||<br /> | 80&amp;94 &lt;&lt;18 44 30 38 -16 18 40 28 ... ||<br /> | ||
Revision as of 03:55, 9 March 2012
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author keenanpepper and made on 2012-03-09 03:55:32 UTC.
- The original revision id was 309325440.
- 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 94 equal temperament, often abbreviated 94-tET, 94-[[EDO]], or 94-ET, is the scale derived by dividing the [[octave]] into 94 equally-sized steps, where each step represents a frequency ratio of 12.766 [[cent]]s. It is a remarkable all-around utility temperament, good from low prime limit to very high prime limit situations. It is the first equal temperament to be[[consistent| consistent]] though the [[23-limit]], and no other equal temperament is so consistent until 282 and 311 make their appearance. The list of 23-limit commas it tempers out is huge, but it's worth noting that it tempers out 32805/32768 and is thus a schismatic system, that it tempers out 225/224 and 385/384 and so is a marvel system, and that it also tempers out 3125/3087, 4000/3969, 5120/5103 and 540/539. It provides the optimal patent val for the rank five temperament tempering out 275/273, and for a number of other temperaments, such as [[Marvel family#Isis|isis]]. Below are some 23-limit temperaments supported by 94et. It might be noted that 94, a very good tuning for [[garibaldi temperament]], shows us how to extend it to the 23-limit. 46&94 <<8 30 -18 -4 -28 8 -24 2 ... || 68&94 <<20 28 2 -10 24 20 34 52 ... || 53&94 <<1 -8 -14 23 20 -46 -3 -35 ... || (one garibaldi) 41&94 <<1 -8 -14 23 20 48 -3 -35 ... || (another garibaldi, only differing in the mappings of 17 and 23) 135&94 <<1 -8 -14 23 20 48 -3 59 ... || (another garibaldi) 130&94 <<6 -48 10 -50 26 6 -18 -22 ... || (a pogo extension) 58&94 <<6 46 10 44 26 6 -18 -22 ... || (a supers extension) 50&94 <<24 -4 40 -12 10 24 22 6 ... || 72&94 <<12 -2 20 -6 52 12 -36 -44 ... || (a gizzard extension) 94 solo <<12 -2 20 -6 -42 12 -36 -44 ... || 80&94 <<18 44 30 38 -16 18 40 28 ... || Temperaments for which 94 is a [[MOS]]: 311&94 <<3 70 -42 69 -34 50 85 83...|| 422&94 <<8 124 -18 90 -28 102 164 96 ... || =Scales= [[garibaldi12]] [[garibaldi17]]
Original HTML content:
<html><head><title>94edo</title></head><body>The 94 equal temperament, often abbreviated 94-tET, 94-<a class="wiki_link" href="/EDO">EDO</a>, or 94-ET, is the scale derived by dividing the <a class="wiki_link" href="/octave">octave</a> into 94 equally-sized steps, where each step represents a frequency ratio of 12.766 <a class="wiki_link" href="/cent">cent</a>s. It is a remarkable all-around utility temperament, good from low prime limit to very high prime limit situations. It is the first equal temperament to be<a class="wiki_link" href="/consistent"> consistent</a> though the <a class="wiki_link" href="/23-limit">23-limit</a>, and no other equal temperament is so consistent until 282 and 311 make their appearance.<br /> <br /> The list of 23-limit commas it tempers out is huge, but it's worth noting that it tempers out 32805/32768 and is thus a schismatic system, that it tempers out 225/224 and 385/384 and so is a marvel system, and that it also tempers out 3125/3087, 4000/3969, 5120/5103 and 540/539. It provides the optimal patent val for the rank five temperament tempering out 275/273, and for a number of other temperaments, such as <a class="wiki_link" href="/Marvel%20family#Isis">isis</a>.<br /> <br /> Below are some 23-limit temperaments supported by 94et. It might be noted that 94, a very good tuning for <a class="wiki_link" href="/garibaldi%20temperament">garibaldi temperament</a>, shows us how to extend it to the 23-limit.<br /> <br /> 46&94 <<8 30 -18 -4 -28 8 -24 2 ... ||<br /> 68&94 <<20 28 2 -10 24 20 34 52 ... ||<br /> 53&94 <<1 -8 -14 23 20 -46 -3 -35 ... || (one garibaldi)<br /> 41&94 <<1 -8 -14 23 20 48 -3 -35 ... || (another garibaldi, only differing in the mappings of 17 and 23)<br /> 135&94 <<1 -8 -14 23 20 48 -3 59 ... || (another garibaldi)<br /> 130&94 <<6 -48 10 -50 26 6 -18 -22 ... || (a pogo extension)<br /> 58&94 <<6 46 10 44 26 6 -18 -22 ... || (a supers extension)<br /> 50&94 <<24 -4 40 -12 10 24 22 6 ... ||<br /> 72&94 <<12 -2 20 -6 52 12 -36 -44 ... || (a gizzard extension)<br /> 94 solo <<12 -2 20 -6 -42 12 -36 -44 ... ||<br /> 80&94 <<18 44 30 38 -16 18 40 28 ... ||<br /> <br /> Temperaments for which 94 is a <a class="wiki_link" href="/MOS">MOS</a>:<br /> <br /> 311&94 <<3 70 -42 69 -34 50 85 83...||<br /> 422&94 <<8 124 -18 90 -28 102 164 96 ... ||<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Scales"></a><!-- ws:end:WikiTextHeadingRule:0 -->Scales</h1> <br /> <a class="wiki_link" href="/garibaldi12">garibaldi12</a><br /> <a class="wiki_link" href="/garibaldi17">garibaldi17</a></body></html>