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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>
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| : The original revision id was <tt>479837316</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| 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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| <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.
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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]]. | | 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 ||
| |
| ||> 1 ||> 3\94 ||> 38.298 ||= 49/48 ||< [[Slender]] ||
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| ||> 1 ||> 5\94 ||> 63.830 ||= 25/24 || [[Sycamore]]/[[betic]] ||
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| ||> 1 ||> 11\94 ||> 140.426 ||= 243/224
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| 13/12 || [[Tsaharuk]]
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| [[Quanic]] ||
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| ||> 1 ||> 19\94 ||> 242.553 ||= 147/128 || [[Septiquarter]] ||
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| ||> 1 ||> 39\94 ||> 497.872 ||= 4/3 || [[Schismatic]]/[[garibaldi]] ||
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| ||> 2 ||> 2\94 ||> 25.532 ||= 64/63 || [[Ketchup]] ||
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| ||> 2 ||> 43\94 ||> 548.936 ||= 11/8 || [[Kleischismic]] ||
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| ||> 2 ||> 11\94 ||> 140.426 ||= 27/25 || [[Fifive]] ||
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| ||> 2 ||> 34\94 ||> 434.043 ||= 9/7 || [[Pogo]], [[supers]] ||
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| ||> 2 ||> 30\94 ||> 382.979 ||= 5/4 || [[Wizard]]/[[gizzard]] ||
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| 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. |
|
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| 46&94 <<8 30 -18 -4 -28 8 -24 2 ... || | | 46&94 <<8 30 -18 -4 -28 8 -24 2 ... || |
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| 68&94 <<20 28 2 -10 24 20 34 52 ... || | | 68&94 <<20 28 2 -10 24 20 34 52 ... || |
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| 53&94 <<1 -8 -14 23 20 -46 -3 -35 ... || (one garibaldi) | | 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) | | 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) | | 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) | | 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) | | 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 ... || (a gizzard extension) | | 72&94 <<12 -2 20 -6 52 12 -36 -44 ... || (a gizzard extension) |
| | |
| 80&94 <<18 44 30 38 -16 18 40 28 ... || | | 80&94 <<18 44 30 38 -16 18 40 28 ... || |
| | |
| 94 solo <<12 -2 20 -6 -42 12 -36 -44 ... || (a rank one temperament!) | | 94 solo <<12 -2 20 -6 -42 12 -36 -44 ... || (a rank one temperament!) |
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| Temperaments for which 94 is a [[MOS]]: | | Temperaments for which 94 is a [[MOS|MOS]]: |
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| 311&94 <<3 70 -42 69 -34 50 85 83...|| | | 311&94 <<3 70 -42 69 -34 50 85 83...|| |
| | |
| 422&94 <<8 124 -18 90 -28 102 164 96 ... || | | 422&94 <<8 124 -18 90 -28 102 164 96 ... || |
|
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|
| =Scales= | | =Scales= |
| | |
| [[garibaldi12]]
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| [[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"><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 />
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| <br />
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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>.<br />
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| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Rank two temperaments"></a><!-- ws:end:WikiTextHeadingRule:0 -->Rank two temperaments</h1>
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|
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|
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|
| <table class="wiki_table">
| | [[garibaldi12|garibaldi12]] |
| <tr>
| |
| <th>Periods<br />
| |
| per<br />
| |
| octave<br />
| |
| </th>
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| <th>Generator<br />
| |
| </th>
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| <th>Cents<br />
| |
| </th>
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| <th>Associated<br />
| |
| ratio<br />
| |
| </th>
| |
| <th>Temperament<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
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| <td style="text-align: right;">1<br />
| |
| </td>
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| <td style="text-align: right;">3\94<br />
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| </td>
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| <td style="text-align: right;">38.298<br />
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| </td>
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| <td style="text-align: center;">49/48<br />
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| </td>
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| <td style="text-align: left;"><a class="wiki_link" href="/Slender">Slender</a><br />
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| </td>
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| </tr>
| |
| <tr>
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| <td style="text-align: right;">1<br />
| |
| </td>
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| <td style="text-align: right;">5\94<br />
| |
| </td>
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| <td style="text-align: right;">63.830<br />
| |
| </td>
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| <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 />
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| </td>
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| </tr>
| |
| <tr>
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| <td style="text-align: right;">1<br />
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| </td>
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| <td style="text-align: right;">19\94<br />
| |
| </td>
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| <td style="text-align: right;">242.553<br />
| |
| </td>
| |
| <td style="text-align: center;">147/128<br />
| |
| </td>
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| <td><a class="wiki_link" href="/Septiquarter">Septiquarter</a><br />
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| </td>
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| </tr>
| |
| <tr>
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| <td style="text-align: right;">1<br />
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| </td>
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| <td style="text-align: right;">39\94<br />
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| </td>
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| <td style="text-align: right;">497.872<br />
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| </td>
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| <td style="text-align: center;">4/3<br />
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| </td>
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| <td><a class="wiki_link" href="/Schismatic">Schismatic</a>/<a class="wiki_link" href="/garibaldi">garibaldi</a><br />
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| </td>
| |
| </tr>
| |
| <tr>
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| <td style="text-align: right;">2<br />
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| </td>
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| <td style="text-align: right;">2\94<br />
| |
| </td>
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| <td style="text-align: right;">25.532<br />
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| </td>
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| <td style="text-align: center;">64/63<br />
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| </td>
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| <td><a class="wiki_link" href="/Ketchup">Ketchup</a><br />
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| </td>
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| </tr>
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| <tr>
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| <td style="text-align: right;">2<br />
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| </td>
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| <td style="text-align: right;">43\94<br />
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| </td>
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| <td style="text-align: right;">548.936<br />
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| </td>
| |
| <td style="text-align: center;">11/8<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/Kleischismic">Kleischismic</a><br />
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| </td>
| |
| </tr>
| |
| <tr>
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| <td style="text-align: right;">2<br />
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| </td>
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| <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 />
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| </td>
| |
| </tr>
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| <tr>
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| <td style="text-align: right;">2<br />
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| </td>
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| <td style="text-align: right;">34\94<br />
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| </td>
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| <td style="text-align: right;">434.043<br />
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| </td>
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| <td style="text-align: center;">9/7<br />
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| </td>
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| <td><a class="wiki_link" href="/Pogo">Pogo</a>, <a class="wiki_link" href="/supers">supers</a><br />
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| </td>
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| </tr>
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| <tr>
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| <td style="text-align: right;">2<br />
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| </td>
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| <td style="text-align: right;">30\94<br />
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| </td>
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| <td style="text-align: right;">382.979<br />
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| </td>
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| <td style="text-align: center;">5/4<br />
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| </td>
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| <td><a class="wiki_link" href="/Wizard">Wizard</a>/<a class="wiki_link" href="/gizzard">gizzard</a><br />
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| </td>
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| </tr>
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| </table>
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|
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|
| <br />
| | [[garibaldi17|garibaldi17]] [[Category:94edo]] |
| 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 />
| | [[Category:edo]] |
| <br />
| | [[Category:garibaldi]] |
| 46&amp;94 &lt;&lt;8 30 -18 -4 -28 8 -24 2 ... ||<br />
| | [[Category:marvel]] |
| 68&amp;94 &lt;&lt;20 28 2 -10 24 20 34 52 ... ||<br />
| | [[Category:theory]] |
| 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 ... || (another garibaldi, only differing in the mappings of 17 and 23)<br />
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| 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 ... || (a pogo extension)<br />
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| 58&amp;94 &lt;&lt;6 46 10 44 26 6 -18 -22 ... || (a supers extension)<br />
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| 50&amp;94 &lt;&lt;24 -4 40 -12 10 24 22 6 ... ||<br />
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| 72&amp;94 &lt;&lt;12 -2 20 -6 52 12 -36 -44 ... || (a gizzard extension)<br />
| |
| 80&amp;94 &lt;&lt;18 44 30 38 -16 18 40 28 ... ||<br />
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| 94 solo &lt;&lt;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&amp;94 &lt;&lt;3 70 -42 69 -34 50 85 83...||<br />
| |
| 422&amp;94 &lt;&lt;8 124 -18 90 -28 102 164 96 ... ||<br />
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| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><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></pre></div>
| |
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 cents. 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 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 isis.
Rank two temperaments
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