94edo
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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]]. =Rank two temperaments= ||~ Periods per octave ||~ Generator ||~ Cents ||~ Associated ratio ||~ Temperament || ||> 1 ||> 3\94 ||> 38.298 ||= 49/48 ||< [[Slender]] || ||> 1 ||> 5\94 ||> 63.830 ||= 25/24 || [[Sycamore]]/[[betic]] || ||> 1 ||> 11\94 ||> 140.426 ||= 243/224 13/12 || [[Tsaharuk]] [[Quanic]] || ||> 1 ||> 19\94 ||> 242.553 ||= 147/128 || [[Septiquarter]] || ||> 1 ||> 39\94 ||> 497.872 ||= 4/3 || [[Schismatic]]/[[garibaldi]] || ||> 2 ||> 2\94 ||> 25.532 ||= 64/63 || [[Ketchup]] || ||> 2 ||> 43\94 ||> 548.936 ||= 11/8 || [[Kleischismic]] || ||> 2 ||> 11\94 ||> 140.426 ||= 27/25 || [[Fifive]] || ||> 2 ||> 34\94 ||> 434.043 ||= 9/7 || [[Pogo]], [[supers]] || ||> 2 ||> 30\94 ||> 382.979 ||= 5/4 || [[Wizard]]/[[gizzard]] || 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) 80&94 <<18 44 30 38 -16 18 40 28 ... || 94 solo <<12 -2 20 -6 -42 12 -36 -44 ... || (a rank one temperament!) 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 />
<!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Rank two temperaments"></a><!-- ws:end:WikiTextHeadingRule:0 -->Rank two temperaments</h1>
<table class="wiki_table">
<tr>
<th>Periods<br />
per<br />
octave<br />
</th>
<th>Generator<br />
</th>
<th>Cents<br />
</th>
<th>Associated<br />
ratio<br />
</th>
<th>Temperament<br />
</th>
</tr>
<tr>
<td style="text-align: right;">1<br />
</td>
<td style="text-align: right;">3\94<br />
</td>
<td style="text-align: right;">38.298<br />
</td>
<td style="text-align: center;">49/48<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="/Slender">Slender</a><br />
</td>
</tr>
<tr>
<td style="text-align: right;">1<br />
</td>
<td style="text-align: right;">5\94<br />
</td>
<td style="text-align: right;">63.830<br />
</td>
<td style="text-align: center;">25/24<br />
</td>
<td><a class="wiki_link" href="/Sycamore">Sycamore</a>/<a class="wiki_link" href="/betic">betic</a><br />
</td>
</tr>
<tr>
<td style="text-align: right;">1<br />
</td>
<td style="text-align: right;">11\94<br />
</td>
<td style="text-align: right;">140.426<br />
</td>
<td style="text-align: center;">243/224<br />
13/12<br />
</td>
<td><a class="wiki_link" href="/Tsaharuk">Tsaharuk</a><br />
<a class="wiki_link" href="/Quanic">Quanic</a><br />
</td>
</tr>
<tr>
<td style="text-align: right;">1<br />
</td>
<td style="text-align: right;">19\94<br />
</td>
<td style="text-align: right;">242.553<br />
</td>
<td style="text-align: center;">147/128<br />
</td>
<td><a class="wiki_link" href="/Septiquarter">Septiquarter</a><br />
</td>
</tr>
<tr>
<td style="text-align: right;">1<br />
</td>
<td style="text-align: right;">39\94<br />
</td>
<td style="text-align: right;">497.872<br />
</td>
<td style="text-align: center;">4/3<br />
</td>
<td><a class="wiki_link" href="/Schismatic">Schismatic</a>/<a class="wiki_link" href="/garibaldi">garibaldi</a><br />
</td>
</tr>
<tr>
<td style="text-align: right;">2<br />
</td>
<td style="text-align: right;">2\94<br />
</td>
<td style="text-align: right;">25.532<br />
</td>
<td style="text-align: center;">64/63<br />
</td>
<td><a class="wiki_link" href="/Ketchup">Ketchup</a><br />
</td>
</tr>
<tr>
<td style="text-align: right;">2<br />
</td>
<td style="text-align: right;">43\94<br />
</td>
<td style="text-align: right;">548.936<br />
</td>
<td style="text-align: center;">11/8<br />
</td>
<td><a class="wiki_link" href="/Kleischismic">Kleischismic</a><br />
</td>
</tr>
<tr>
<td style="text-align: right;">2<br />
</td>
<td style="text-align: right;">11\94<br />
</td>
<td style="text-align: right;">140.426<br />
</td>
<td style="text-align: center;">27/25<br />
</td>
<td><a class="wiki_link" href="/Fifive">Fifive</a><br />
</td>
</tr>
<tr>
<td style="text-align: right;">2<br />
</td>
<td style="text-align: right;">34\94<br />
</td>
<td style="text-align: right;">434.043<br />
</td>
<td style="text-align: center;">9/7<br />
</td>
<td><a class="wiki_link" href="/Pogo">Pogo</a>, <a class="wiki_link" href="/supers">supers</a><br />
</td>
</tr>
<tr>
<td style="text-align: right;">2<br />
</td>
<td style="text-align: right;">30\94<br />
</td>
<td style="text-align: right;">382.979<br />
</td>
<td style="text-align: center;">5/4<br />
</td>
<td><a class="wiki_link" href="/Wizard">Wizard</a>/<a class="wiki_link" href="/gizzard">gizzard</a><br />
</td>
</tr>
</table>
<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 />
80&94 <<18 44 30 38 -16 18 40 28 ... ||<br />
94 solo <<12 -2 20 -6 -42 12 -36 -44 ... || (a rank one temperament!)<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:2:<h1> --><h1 id="toc1"><a name="Scales"></a><!-- ws:end:WikiTextHeadingRule:2 -->Scales</h1>
<br />
<a class="wiki_link" href="/garibaldi12">garibaldi12</a><br />
<a class="wiki_link" href="/garibaldi17">garibaldi17</a></body></html>