94edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:~~keenanpepper~~|~~keenanpepper~~]] and made on <tt>~~2012~~-03-09 03:55:32 UTC</tt>.

: This revision was by author [[User:Gedankenwelt|Gedankenwelt]] and made on <tt>2013-12-30 03:25:35 UTC</tt>.

: The original revision id was <tt>~~309325440~~</tt>.

: The original revision id was <tt>479834206</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

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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.

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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 ... ||

94 solo <<12 -2 20 -6 -42 12 -36 -44 ... || (a rank one temperament!)

Temperaments for which 94 is a [[MOS]]:

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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>.

<h1 id="toc0"><a name="Rank two temperaments"></a>Rank two temperaments</h1>

<tr>

<th>Periods per octave

</th>

<th>Generator

</th>

<th>Cents

</th>

<th>Associated ratio

</th>

<th>Temperament

</th>

</tr>

<tr>

<td style="text-align: right;">1

</td>

<td style="text-align: right;">3\94

</td>

<td style="text-align: right;">38.298

</td>

<td style="text-align: center;">49/48

</td>

<td style="text-align: left;"><a class="wiki_link" href="/Slender">Slender</a>

</td>

</tr>

<tr>

<td style="text-align: right;">1

</td>

<td style="text-align: right;">5\94

</td>

<td style="text-align: right;">63.830

</td>

<td style="text-align: center;">25/24

</td>

<td><a class="wiki_link" href="/Sycamore">Sycamore</a>/<a class="wiki_link" href="/betic">betic</a>

</td>

</tr>

<tr>

<td style="text-align: right;">1

</td>

<td style="text-align: right;">11\94

</td>

<td style="text-align: right;">140.426

</td>

<td style="text-align: center;">243/224

13/12

</td>

<td><a class="wiki_link" href="/Tsaharuk">Tsaharuk</a>

<a class="wiki_link" href="/Quanic">Quanic</a>

</td>

</tr>

<tr>

<td style="text-align: right;">1

</td>

<td style="text-align: right;">19\94

</td>

<td style="text-align: right;">242.553

</td>

<td style="text-align: center;">147/128

</td>

<td><a class="wiki_link" href="/Septiquarter">Septiquarter</a>

</td>

</tr>

<tr>

<td style="text-align: right;">1

</td>

<td style="text-align: right;">39\94

</td>

<td style="text-align: right;">497.872

</td>

<td style="text-align: center;">4/3

</td>

<td><a class="wiki_link" href="/Schismatic">Schismatic</a>/<a class="wiki_link" href="/garibaldi">garibaldi</a>

</td>

</tr>

<tr>

<td style="text-align: right;">2

</td>

<td style="text-align: right;">2\94

</td>

<td style="text-align: right;">25.532

</td>

<td style="text-align: center;">64/63

</td>

<td><a class="wiki_link" href="/Ketchup">Ketchup</a>

</td>

</tr>

<tr>

<td style="text-align: right;">2

</td>

<td style="text-align: right;">43\94

</td>

<td style="text-align: right;">548.936

</td>

<td style="text-align: center;">11/8

</td>

<td><a class="wiki_link" href="/Kleischismic">Kleischismic</a>

</td>

</tr>

<tr>

<td style="text-align: right;">2

</td>

<td style="text-align: right;">11\94

</td>

<td style="text-align: right;">140.426

</td>

<td style="text-align: center;">27/25

</td>

<td><a class="wiki_link" href="/Fifive">Fifive</a>

</td>

</tr>

<tr>

<td style="text-align: right;">2

</td>

<td style="text-align: right;">34\94

</td>

<td style="text-align: right;">434.043

</td>

<td style="text-align: center;">9/7

</td>

<td><a class="wiki_link" href="/Pogo">Pogo</a>, <a class="wiki_link" href="/supers">supers</a>

</td>

</tr>

<tr>

<td style="text-align: right;">2

</td>

<td style="text-align: right;">30\94

</td>

<td style="text-align: right;">382.979

</td>

<td style="text-align: center;">5/4

</td>

<td><a class="wiki_link" href="/Wizard">Wizard</a>/<a class="wiki_link" href="/gizzard">gizzard</a>

</td>

</tr>

</table>

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.

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50&amp;94 &lt;&lt;24 -4 40 -12 10 24 22 6 ... ||

72&amp;94 &lt;&lt;12 -2 20 -6 52 12 -36 -44 ... || (a gizzard extension)

~~94 solo &lt;&lt;12 -2 20 -6 -42 12 -36 -44 ... || ~~

80&amp;94 &lt;&lt;18 44 30 38 -16 18 40 28 ... ||

94 solo &lt;&lt;12 -2 20 -6 -42 12 -36 -44 ... || (a rank one temperament!)

Temperaments for which 94 is a <a class="wiki_link" href="/MOS">MOS</a>:

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422&amp;94 &lt;&lt;8 124 -18 90 -28 102 164 96 ... ||

<h1 id="~~toc0~~"><a name="Scales"></a>Scales</h1>

<h1 id="toc1"><a name="Scales"></a>Scales</h1>

<a class="wiki_link" href="/garibaldi12">garibaldi12</a>

<a class="wiki_link" href="/garibaldi17">garibaldi17</a></body></html></pre></div>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2012-03-09 03:55:32 UTC</tt>.<br>
+: This revision was by author [[User:Gedankenwelt|Gedankenwelt]] and made on <tt>2013-12-30 03:25:35 UTC</tt>.<br>
-: The original revision id was <tt>309325440</tt>.<br>
+: The original revision id was <tt>479834206</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>
@@ Line 9: / Line 9: @@
 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 ||
+||&gt; 1 ||&gt; 3\94 ||&gt; 38.298 ||= 49/48 ||&lt; [[Slender]] ||
+||&gt; 1 ||&gt; 5\94 ||&gt; 63.830 ||= 25/24 || [[Sycamore]]/[[betic]] ||
+||&gt; 1 ||&gt; 11\94 ||&gt; 140.426 ||= 243/224
+/12 || [[Tsaharuk]]
+[[Quanic]] ||
+||&gt; 1 ||&gt; 19\94 ||&gt; 242.553 ||= 147/128 || [[Septiquarter]] ||
+||&gt; 1 ||&gt; 39\94 ||&gt; 497.872 ||= 4/3 || [[Schismatic]]/[[garibaldi]] ||
+||&gt; 2 ||&gt; 2\94 ||&gt; 25.532 ||= 64/63 || [[Ketchup]] ||
+||&gt; 2 ||&gt; 43\94 ||&gt; 548.936 ||= 11/8 || [[Kleischismic]] ||
+||&gt; 2 ||&gt; 11\94 ||&gt; 140.426 ||= 27/25 || [[Fifive]] ||
+||&gt; 2 ||&gt; 34\94 ||&gt; 434.043 ||= 9/7 || [[Pogo]], [[supers]] ||
+||&gt; 2 ||&gt; 30\94 ||&gt; 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.
@@ Line 21: / Line 36: @@
 &amp;94 &lt;&lt;24 -4 40 -12 10 24 22 6 ... ||
 &amp;94 &lt;&lt;12 -2 20 -6 52 12 -36 -44 ... || (a gizzard extension)
-solo &lt;&lt;12 -2 20 -6 -42 12 -36 -44 ... ||
 &amp;94 &lt;&lt;18 44 30 38 -16 18 40 28 ... ||
+solo &lt;&lt;12 -2 20 -6 -42 12 -36 -44 ... || (a rank one temperament!)
 Temperaments for which 94 is a [[MOS]]:
@@ Line 37: / Line 52: @@
 &lt;br /&gt;
 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 &lt;a class="wiki_link" href="/Marvel%20family#Isis"&gt;isis&lt;/a&gt;.&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="Rank two temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Rank two temperaments&lt;/h1&gt;
+&lt;table class="wiki_table"&gt;
+    &lt;tr&gt;
+        &lt;th&gt;Periods per octave&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;Generator&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;Cents&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;Associated ratio&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;Temperament&lt;br /&gt;
+&lt;/th&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: right;"&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;3\94&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;38.298&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;49/48&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/Slender"&gt;Slender&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: right;"&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;5\94&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;63.830&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;25/24&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/Sycamore"&gt;Sycamore&lt;/a&gt;/&lt;a class="wiki_link" href="/betic"&gt;betic&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: right;"&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;11\94&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;140.426&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;243/224&lt;br /&gt;
+/12&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/Tsaharuk"&gt;Tsaharuk&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="/Quanic"&gt;Quanic&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: right;"&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;19\94&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;242.553&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;147/128&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/Septiquarter"&gt;Septiquarter&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: right;"&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;39\94&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;497.872&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;4/3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/Schismatic"&gt;Schismatic&lt;/a&gt;/&lt;a class="wiki_link" href="/garibaldi"&gt;garibaldi&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: right;"&gt;2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;2\94&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;25.532&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;64/63&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/Ketchup"&gt;Ketchup&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: right;"&gt;2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;43\94&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;548.936&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;11/8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/Kleischismic"&gt;Kleischismic&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: right;"&gt;2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;11\94&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;140.426&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;27/25&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/Fifive"&gt;Fifive&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: right;"&gt;2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;34\94&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;434.043&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;9/7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/Pogo"&gt;Pogo&lt;/a&gt;, &lt;a class="wiki_link" href="/supers"&gt;supers&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: right;"&gt;2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;30\94&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;382.979&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;5/4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/Wizard"&gt;Wizard&lt;/a&gt;/&lt;a class="wiki_link" href="/gizzard"&gt;gizzard&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+&lt;/table&gt;
 &lt;br /&gt;
 Below are some 23-limit temperaments supported by 94et. It might be noted that 94, a very good tuning for &lt;a class="wiki_link" href="/garibaldi%20temperament"&gt;garibaldi temperament&lt;/a&gt;, shows us how to extend it to the 23-limit.&lt;br /&gt;
@@ Line 49: / Line 205: @@
 &amp;amp;94 &amp;lt;&amp;lt;24 -4 40 -12 10 24 22 6 ... ||&lt;br /&gt;
 &amp;amp;94 &amp;lt;&amp;lt;12 -2 20 -6 52 12 -36 -44 ... || (a gizzard extension)&lt;br /&gt;
-solo &amp;lt;&amp;lt;12 -2 20 -6 -42 12 -36 -44 ... ||&lt;br /&gt;
 &amp;amp;94 &amp;lt;&amp;lt;18 44 30 38 -16 18 40 28 ... ||&lt;br /&gt;
+solo &amp;lt;&amp;lt;12 -2 20 -6 -42 12 -36 -44 ... || (a rank one temperament!)&lt;br /&gt;
 &lt;br /&gt;
 Temperaments for which 94 is a &lt;a class="wiki_link" href="/MOS"&gt;MOS&lt;/a&gt;:&lt;br /&gt;
@@ Line 57: / Line 213: @@
 &amp;amp;94 &amp;lt;&amp;lt;8 124 -18 90 -28 102 164 96 ... ||&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="Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Scales&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Scales&lt;/h1&gt;
   &lt;br /&gt;
 &lt;a class="wiki_link" href="/garibaldi12"&gt;garibaldi12&lt;/a&gt;&lt;br /&gt;
 &lt;a class="wiki_link" href="/garibaldi17"&gt;garibaldi17&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>