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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox ET}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | {{ED intro}} |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-07-03 15:04:44 UTC</tt>.<br>
| | |
| : The original revision id was <tt>239839467</tt>.<br>
| | == Theory == |
| : The revision comment was: <tt></tt><br>
| | 127edo is interesting because of its approximations, defined by the [[comma]]s it [[tempering out|tempers out]]: |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| | * In the [[5-limit]], it tempers out 393216/390625 ([[würschmidt comma]]) and hence [[support]]s the [[würschmidt]] temperament. |
| <h4>Original Wikitext content:</h4>
| | * In the [[7-limit]], it also tempers out [[225/224]], and is an excellent tuning for the 7-limit extension of würschmidt which tempers this out also. |
| <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">**127edo**, which divides the [[octave]] into 127 parts of 9.45 [[cents]] each, is another equal division interesting because of its approximations, defined by the [[comma]]s it [[tempering out|tempers out]]. In the [[5-limit]], it tempers out the wuerschmidt comma, 393216/390625 and hence supports [[Wuerschmidt family|wuerschmidt temperament]]. In the [[7-limit]], it also tempers out 225/224, and is an excellent tuning for the 7-limit extension ("wurschmidt") of wuerschmidt which tempers this out also. In the [[11-limit]], it tempers out 99/98, 176/175 and 243/242, and is an excellent tuning for the 11-limit version of wurschmidt, as well as minerva, the rank three temperament tempering out 99/98 and 176/175, for which it is the [[optimal patent val]] and the rank four temperament tempering out 99/98, for which it also provides the optimal patent val.</pre></div>
| | * In the [[11-limit]], it tempers out [[99/98]], [[176/175]] and [[243/242]], and is an excellent tuning for the 11-limit version of würschmidt, as well as [[minerva]], the [[rank-3 temperament]] tempering out 99/98 and 176/175, for which it is the [[optimal patent val]] and the rank-4 temperament tempering out 99/98, for which it also provides the optimal patent val. |
| <h4>Original HTML content:</h4>
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| <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>127edo</title></head><body><strong>127edo</strong>, which divides the <a class="wiki_link" href="/octave">octave</a> into 127 parts of 9.45 <a class="wiki_link" href="/cents">cents</a> each, is another equal division interesting because of its approximations, defined by the <a class="wiki_link" href="/comma">comma</a>s it <a class="wiki_link" href="/tempering%20out">tempers out</a>. In the <a class="wiki_link" href="/5-limit">5-limit</a>, it tempers out the wuerschmidt comma, 393216/390625 and hence supports <a class="wiki_link" href="/Wuerschmidt%20family">wuerschmidt temperament</a>. In the <a class="wiki_link" href="/7-limit">7-limit</a>, it also tempers out 225/224, and is an excellent tuning for the 7-limit extension (&quot;wurschmidt&quot;) of wuerschmidt which tempers this out also. In the <a class="wiki_link" href="/11-limit">11-limit</a>, it tempers out 99/98, 176/175 and 243/242, and is an excellent tuning for the 11-limit version of wurschmidt, as well as minerva, the rank three temperament tempering out 99/98 and 176/175, for which it is the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> and the rank four temperament tempering out 99/98, for which it also provides the optimal patent val.</body></html></pre></div>
| | === Odd harmonics === |
| | {{Harmonics in equal|127}} |
| | |
| | === Subsets and supersets === |
| | 127edo is the 31st [[prime edo]], following [[113edo]] and before [[131edo]]. |
| | |
| | == Scales == |
| | === MOS scales === |
| | See [[List of MOS scales in 127edo]]. |
| | |
| | == Instruments == |
| | * [[Lumatone mapping for 127edo]] |
| | |
| | [[Category:Würschmidt]] |
| | [[Category:Hemiwürschmidt]] |
| | [[Category:Minerva]] |
| Prime factorization
|
127 (prime)
|
| Step size
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9.44882 ¢
|
| Fifth
|
74\127 (699.213 ¢)
|
| Semitones (A1:m2)
|
10:11 (94.49 ¢ : 103.9 ¢)
|
| Consistency limit
|
5
|
| Distinct consistency limit
|
5
|
127 equal divisions of the octave (abbreviated 127edo or 127ed2), also called 127-tone equal temperament (127tet) or 127 equal temperament (127et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 127 equal parts of about 9.45 ¢ each. Each step represents a frequency ratio of 21/127, or the 127th root of 2.
Theory
127edo is interesting because of its approximations, defined by the commas it tempers out:
- In the 5-limit, it tempers out 393216/390625 (würschmidt comma) and hence supports the würschmidt temperament.
- In the 7-limit, it also tempers out 225/224, and is an excellent tuning for the 7-limit extension of würschmidt which tempers this out also.
- In the 11-limit, it tempers out 99/98, 176/175 and 243/242, and is an excellent tuning for the 11-limit version of würschmidt, as well as minerva, the rank-3 temperament tempering out 99/98 and 176/175, for which it is the optimal patent val and the rank-4 temperament tempering out 99/98, for which it also provides the optimal patent val.
Odd harmonics
Approximation of odd harmonics in 127edo
| Harmonic
|
3
|
5
|
7
|
9
|
11
|
13
|
15
|
17
|
19
|
21
|
23
|
| Error
|
Absolute (¢)
|
-2.74
|
+1.09
|
+4.40
|
+3.96
|
-3.29
|
+0.42
|
-1.65
|
-1.02
|
-4.60
|
+1.66
|
-4.65
|
| Relative (%)
|
-29.0
|
+11.5
|
+46.6
|
+42.0
|
-34.8
|
+4.4
|
-17.5
|
-10.8
|
-48.7
|
+17.6
|
-49.2
|
Steps
(reduced)
|
201
(74)
|
295
(41)
|
357
(103)
|
403
(22)
|
439
(58)
|
470
(89)
|
496
(115)
|
519
(11)
|
539
(31)
|
558
(50)
|
574
(66)
|
Subsets and supersets
127edo is the 31st prime edo, following 113edo and before 131edo.
Scales
MOS scales
See List of MOS scales in 127edo.
Instruments