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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
The 94 equal temperament, often abbreviated 94-tET, 94-[[EDO|EDO]], or 94-ET, is the scale derived by dividing the [[Octave|octave]] into 94 equally-sized steps, where each step represents a frequency ratio of 12.766 [[cent|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|23-limit]], and no other equal temperament is so consistent until 282 and 311 make their appearance.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:Gedankenwelt|Gedankenwelt]] and made on <tt>2013-12-30 04:07:09 UTC</tt>.<br>
: The original revision id was <tt>479837316</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>
<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 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]].
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=
 
{| class="wikitable"
|-
! | Periods


=Rank two temperaments=
||~ Periods
per
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
13/12 || [[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.
octave
! | Generator
! | Cents
! | Associated
 
ratio
! | Temperament
|-
| style="text-align:right;" | 1
| style="text-align:right;" | 3\94
| style="text-align:right;" | 38.298
| style="text-align:center;" | 49/48
| | [[Slender|Slender]]
|-
| style="text-align:right;" | 1
| style="text-align:right;" | 5\94
| style="text-align:right;" | 63.830
| style="text-align:center;" | 25/24
| | [[Sycamore|Sycamore]]/[[betic|betic]]
|-
| style="text-align:right;" | 1
| style="text-align:right;" | 11\94
| style="text-align:right;" | 140.426
| style="text-align:center;" | 243/224
 
13/12
| | [[Tsaharuk|Tsaharuk]]
 
[[Quanic|Quanic]]
|-
| style="text-align:right;" | 1
| style="text-align:right;" | 19\94
| style="text-align:right;" | 242.553
| style="text-align:center;" | 147/128
| | [[Septiquarter|Septiquarter]]
|-
| style="text-align:right;" | 1
| style="text-align:right;" | 39\94
| style="text-align:right;" | 497.872
| style="text-align:center;" | 4/3
| | [[Schismatic|Schismatic]]/[[Garibaldi|garibaldi]]
|-
| style="text-align:right;" | 2
| style="text-align:right;" | 2\94
| style="text-align:right;" | 25.532
| style="text-align:center;" | 64/63
| | [[Ketchup|Ketchup]]
|-
| style="text-align:right;" | 2
| style="text-align:right;" | 43\94
| style="text-align:right;" | 548.936
| style="text-align:center;" | 11/8
| | [[Kleischismic|Kleischismic]]
|-
| style="text-align:right;" | 2
| style="text-align:right;" | 11\94
| style="text-align:right;" | 140.426
| style="text-align:center;" | 27/25
| | [[Fifive|Fifive]]
|-
| style="text-align:right;" | 2
| style="text-align:right;" | 34\94
| style="text-align:right;" | 434.043
| style="text-align:center;" | 9/7
| | [[Pogo|Pogo]], [[supers|supers]]
|-
| style="text-align:right;" | 2
| style="text-align:right;" | 30\94
| style="text-align:right;" | 382.979
| style="text-align:center;" | 5/4
| | [[wizard|Wizard]]/[[gizzard|gizzard]]
|}
 
Below are some 23-limit temperaments supported by 94et. It might be noted that 94, a very good tuning for [[Garibaldi_temperament|garibaldi temperament]], shows us how to extend it to the 23-limit.


46&amp;94 &lt;&lt;8 30 -18 -4 -28 8 -24 2 ... ||
46&amp;94 &lt;&lt;8 30 -18 -4 -28 8 -24 2 ... ||
68&amp;94 &lt;&lt;20 28 2 -10 24 20 34 52 ... ||
68&amp;94 &lt;&lt;20 28 2 -10 24 20 34 52 ... ||
53&amp;94 &lt;&lt;1 -8 -14 23 20 -46 -3 -35 ... || (one garibaldi)
53&amp;94 &lt;&lt;1 -8 -14 23 20 -46 -3 -35 ... || (one garibaldi)
41&amp;94 &lt;&lt;1 -8 -14 23 20 48 -3 -35 ... || (another garibaldi, only differing in the mappings of 17 and 23)
41&amp;94 &lt;&lt;1 -8 -14 23 20 48 -3 -35 ... || (another garibaldi, only differing in the mappings of 17 and 23)
135&amp;94 &lt;&lt;1 -8 -14 23 20 48 -3 59 ... || (another garibaldi)
135&amp;94 &lt;&lt;1 -8 -14 23 20 48 -3 59 ... || (another garibaldi)
130&amp;94 &lt;&lt;6 -48 10 -50 26 6 -18 -22 ... || (a pogo extension)
130&amp;94 &lt;&lt;6 -48 10 -50 26 6 -18 -22 ... || (a pogo extension)
58&amp;94 &lt;&lt;6 46 10 44 26 6 -18 -22 ... || (a supers extension)
58&amp;94 &lt;&lt;6 46 10 44 26 6 -18 -22 ... || (a supers extension)
50&amp;94 &lt;&lt;24 -4 40 -12 10 24 22 6 ... ||
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)
72&amp;94 &lt;&lt;12 -2 20 -6 52 12 -36 -44 ... || (a gizzard extension)
80&amp;94 &lt;&lt;18 44 30 38 -16 18 40 28 ... ||
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!)
94 solo &lt;&lt;12 -2 20 -6 -42 12 -36 -44 ... || (a rank one temperament!)


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


311&amp;94 &lt;&lt;3 70 -42 69 -34 50 85 83...||
311&amp;94 &lt;&lt;3 70 -42 69 -34 50 85 83...||
422&amp;94 &lt;&lt;8 124 -18 90 -28 102 164 96 ... ||
422&amp;94 &lt;&lt;8 124 -18 90 -28 102 164 96 ... ||


=Scales=  
=Scales=
 
[[garibaldi12]]
[[garibaldi17]]</pre></div>
<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;94edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 94 equal temperament, often abbreviated 94-tET, 94-&lt;a class="wiki_link" href="/EDO"&gt;EDO&lt;/a&gt;, or 94-ET, is the scale derived by dividing the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 94 equally-sized steps, where each step represents a frequency ratio of 12.766 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;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&lt;a class="wiki_link" href="/consistent"&gt; consistent&lt;/a&gt; though the &lt;a class="wiki_link" href="/23-limit"&gt;23-limit&lt;/a&gt;, and no other equal temperament is so consistent until 282 and 311 make their appearance.&lt;br /&gt;
&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;
[[garibaldi12|garibaldi12]]
    &lt;tr&gt;
        &lt;th&gt;Periods&lt;br /&gt;
per&lt;br /&gt;
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&lt;br /&gt;
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;
13/12&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;
[[garibaldi17|garibaldi17]]      [[Category:94edo]]
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;
[[Category:edo]]
&lt;br /&gt;
[[Category:garibaldi]]
46&amp;amp;94 &amp;lt;&amp;lt;8 30 -18 -4 -28 8 -24 2 ... ||&lt;br /&gt;
[[Category:marvel]]
68&amp;amp;94 &amp;lt;&amp;lt;20 28 2 -10 24 20 34 52 ... ||&lt;br /&gt;
[[Category:theory]]
53&amp;amp;94 &amp;lt;&amp;lt;1 -8 -14 23 20 -46 -3 -35 ... || (one garibaldi)&lt;br /&gt;
41&amp;amp;94 &amp;lt;&amp;lt;1 -8 -14 23 20 48 -3 -35 ... || (another garibaldi, only differing in the mappings of 17 and 23)&lt;br /&gt;
135&amp;amp;94 &amp;lt;&amp;lt;1 -8 -14 23 20 48 -3 59 ... || (another garibaldi)&lt;br /&gt;
130&amp;amp;94 &amp;lt;&amp;lt;6 -48 10 -50 26 6 -18 -22 ... || (a pogo extension)&lt;br /&gt;
58&amp;amp;94 &amp;lt;&amp;lt;6 46 10 44 26 6 -18 -22 ... || (a supers extension)&lt;br /&gt;
50&amp;amp;94 &amp;lt;&amp;lt;24 -4 40 -12 10 24 22 6 ... ||&lt;br /&gt;
72&amp;amp;94 &amp;lt;&amp;lt;12 -2 20 -6 52 12 -36 -44 ... || (a gizzard extension)&lt;br /&gt;
80&amp;amp;94 &amp;lt;&amp;lt;18 44 30 38 -16 18 40 28 ... ||&lt;br /&gt;
94 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;
&lt;br /&gt;
311&amp;amp;94 &amp;lt;&amp;lt;3 70 -42 69 -34 50 85 83...||&lt;br /&gt;
422&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: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>
Retrieved from "https://en.xen.wiki/w/94edo"