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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:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2011-07-12 01:29:20 UTC</tt>.<br>
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| : The original revision id was <tt>240943537</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>
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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;white-space: pre-wrap ! important" class="old-revision-html">=<span style="color: #630080; font-family: 'Times New Roman',Times,serif; font-size: 113%;">253 tone equal temperament</span>=
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| **//253-EDO//** or **253-tET** divides the octave into 253 equal steps of 4.743083 Cents, each one. It approximates the fifth by **148\253**, which is 701.976285 Cents, a **0.004487 Cents sharp**. The primes from 5 to 17 are all slightly flat. It tempers out 32805/32768 in the 5-limit; 2401/2400 in the 7-limit; 385/384, 1375/1372 and 4000/3993 in the 11-limit; 325/324, 1575/1573 and 2200/2197 in the 13-limit; 375/374 and 595/594 in the 17-limit. It provides a good tuning for higher-limit [[Schismatic family|sesquiquartififths]] temperament.
| | == Theory == |
| | 253edo is [[consistent]] to the [[17-odd-limit]], approximating the fifth by 148\253 (0.021284 cents sharper than the just 3/2), and the [[prime harmonic]]s from 5 to 17 are all slightly flat. As an equal temperament, it [[tempering out|tempers out]] [[32805/32768]] in the [[5-limit]]; [[2401/2400]] in the [[7-limit]]; [[385/384]], [[1375/1372]] and [[4000/3993]] in the [[11-limit]]; [[325/324]], [[1575/1573]] and [[2200/2197]] in the [[13-limit]]; [[375/374]] and [[595/594]] in the [[17-limit]]. It provides the [[optimal patent val]] for the [[tertiaschis]] temperament, and a good tuning for the [[sesquiquartififths]] temperament in the higher limits. |
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| __**253 tone equal modes**__
| | === Prime harmonics === |
| 63 32 63 63 32: [[3L 2s]] MOS ([[Sub-diatonic]] Tuning)
| | {{Harmonics in equal|253}} |
| 43 43 19 43 43 43 19: [[5L 2s]] MOS ([[Pythagoric]] Tuning)
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| 41 41 24 41 41 41 24: [[5L 2s]] MOS ([[Meantonic]] Tuning)
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| 35 35 35 35 35 35 35 8: [[7L 1s]] MOS (Perfect [[Porcupine-8]] Tuning [Octal Monatonic scale])
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| 33 33 33 11 33 33 33 33 11: [[7L 2s]] MOS ([[Armodue-Hornbostel]] Tuning)
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| 31 31 31 18 31 31 31 31 18: [[7L 2s]] MOS ([[Armodue-Mesotonic]] Tuning)
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| 26 26 15 26 26 26 15 26 26 26 15: [[8L 3s]] MOS ([[sensi11|Sensi-11]] [or Undecimal Triatonic])
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| 20 20 20 11 20 20 20 20 11 20 20 20 20 11: [[11L 3s]] MOS [[[WITNOTS]] Tuning (Tetradecimal Triatonic scale)]
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| **PRIME FACTORIZATION:**
| | === Subsets and supersets === |
| 253 = [[11edo|11]] * [[23edo|23]]</pre></div> | | Since 253 factors into 11 × 23, and has subset edos [[11edo]] and [[23edo]]. [[1012edo]] divides 253edo's step size into 4 equal parts and provides a good approximation of the 13-limit. |
| <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>253edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x253 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #630080; font-family: 'Times New Roman',Times,serif; font-size: 113%;">253 tone equal temperament</span></h1>
| | == Regular temperament properties == |
| <br />
| | {| class="wikitable center-4 center-5 center-6" |
| <strong><em>253-EDO</em></strong> or <strong>253-tET</strong> divides the octave into 253 equal steps of 4.743083 Cents, each one. It approximates the fifth by <strong>148\253</strong>, which is 701.976285 Cents, a <strong>0.004487 Cents sharp</strong>. The primes from 5 to 17 are all slightly flat. It tempers out 32805/32768 in the 5-limit; 2401/2400 in the 7-limit; 385/384, 1375/1372 and 4000/3993 in the 11-limit; 325/324, 1575/1573 and 2200/2197 in the 13-limit; 375/374 and 595/594 in the 17-limit. It provides a good tuning for higher-limit <a class="wiki_link" href="/Schismatic%20family">sesquiquartififths</a> temperament.<br />
| | |- |
| <br />
| | ! rowspan="2" | [[Subgroup]] |
| <u><strong>253 tone equal modes</strong></u><br />
| | ! rowspan="2" | [[Comma list]] |
| 63 32 63 63 32: <a class="wiki_link" href="/3L%202s">3L 2s</a> MOS (<a class="wiki_link" href="/Sub-diatonic">Sub-diatonic</a> Tuning)<br /> | | ! rowspan="2" | [[Mapping]] |
| 43 43 19 43 43 43 19: <a class="wiki_link" href="/5L%202s">5L 2s</a> MOS (<a class="wiki_link" href="/Pythagoric">Pythagoric</a> Tuning)<br /> | | ! rowspan="2" | Optimal<br />8ve stretch (¢) |
| 41 41 24 41 41 41 24: <a class="wiki_link" href="/5L%202s">5L 2s</a> MOS (<a class="wiki_link" href="/Meantonic">Meantonic</a> Tuning)<br /> | | ! colspan="2" | Tuning error |
| 35 35 35 35 35 35 35 8: <a class="wiki_link" href="/7L%201s">7L 1s</a> MOS (Perfect <a class="wiki_link" href="/Porcupine-8">Porcupine-8</a> Tuning [Octal Monatonic scale])<br /> | | |- |
| 33 33 33 11 33 33 33 33 11: <a class="wiki_link" href="/7L%202s">7L 2s</a> MOS (<a class="wiki_link" href="/Armodue-Hornbostel">Armodue-Hornbostel</a> Tuning)<br /> | | ! [[TE error|Absolute]] (¢) |
| 31 31 31 18 31 31 31 31 18: <a class="wiki_link" href="/7L%202s">7L 2s</a> MOS (<a class="wiki_link" href="/Armodue-Mesotonic">Armodue-Mesotonic</a> Tuning)<br /> | | ! [[TE simple badness|Relative]] (%) |
| 26 26 15 26 26 26 15 26 26 26 15: <a class="wiki_link" href="/8L%203s">8L 3s</a> MOS (<a class="wiki_link" href="/sensi11">Sensi-11</a> [or Undecimal Triatonic])<br /> | | |- |
| 20 20 20 11 20 20 20 20 11 20 20 20 20 11: <a class="wiki_link" href="/11L%203s">11L 3s</a> MOS [<a class="wiki_link" href="/WITNOTS">WITNOTS</a> Tuning (Tetradecimal Triatonic scale)]<br /> | | | 2.3 |
| <br />
| | | {{monzo| 401 -253 }} |
| <strong>PRIME FACTORIZATION:</strong><br />
| | | {{mapping| 253 401 }} |
| 253 = <a class="wiki_link" href="/11edo">11</a> * <a class="wiki_link" href="/23edo">23</a></body></html></pre></div>
| | | −0.007 |
| | | 0.007 |
| | | 0.14 |
| | |- |
| | | 2.3.5 |
| | | 32805/32768, {{monzo| -4 -37 27 }} |
| | | {{mapping| 253 401 587 }} |
| | | +0.300 |
| | | 0.435 |
| | | 9.16 |
| | |- |
| | | 2.3.5.7 |
| | | 2401/2400, 32805/32768, 390625/387072 |
| | | {{mapping| 253 401 587 710 }} |
| | | +0.335 |
| | | 0.381 |
| | | 8.03 |
| | |- |
| | | 2.3.5.7.11 |
| | | 385/384, 1375/1372, 4000/3993, 19712/19683 |
| | | {{mapping| 253 401 587 710 875 }} |
| | | +0.333 |
| | | 0.341 |
| | | 7.19 |
| | |- |
| | | 2.3.5.7.11.13 |
| | | 325/324, 385/384, 1375/1372, 1575/1573, 2200/2197 |
| | | {{mapping| 253 401 587 710 875 936 }} |
| | | +0.323 |
| | | 0.312 |
| | | 6.58 |
| | |- |
| | | 2.3.5.7.11.13.17 |
| | | 325/324, 375/374, 385/384, 595/594, 1275/1274, 2200/2197 |
| | | {{mapping| 253 401 587 710 875 936 1034 }} |
| | | +0.298 |
| | | 0.295 |
| | | 6.22 |
| | |} |
| | |
| | === Rank-2 temperaments === |
| | {| class="wikitable center-all left-5" |
| | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator |
| | |- |
| | ! Periods<br />per 8ve |
| | ! Generator* |
| | ! Cents* |
| | ! Associated<br />ratio* |
| | ! Temperaments |
| | |- |
| | | 1 |
| | | 35\253 |
| | | 166.01 |
| | | 11/10 |
| | | [[Tertiaschis]] |
| | |- |
| | | 1 |
| | | 37\253 |
| | | 175.49 |
| | | 448/405 |
| | | [[Sesquiquartififths]] |
| | |- |
| | | 1 |
| | | 105\253 |
| | | 498.02 |
| | | 4/3 |
| | | [[Helmholtz (temperament)|Helmholtz]] |
| | |- |
| | | 1 |
| | | 123\253 |
| | | 583.40 |
| | | 7/5 |
| | | [[Cotritone]] |
| | |} |
| | <nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct |
| | |
| | == Scales == |
| | * 63 32 63 63 32: One of many [[3L 2s|pentic]] scales available |
| | * 43 43 19 43 43 43 19: [[Helmholtz (temperament)|Helmholtz]][7] |
| | * 41 41 24 41 41 41 24: [[Meantone]][7] |
| | * 35 35 35 35 35 35 35 8: [[Porcupine]][8] |
| | * 33 33 33 11 33 33 33 33 11: [[23edo|"The Hendecapliqued superdiatonic of the Icositriphony"]] |
| | * 31 31 31 18 31 31 31 31 18: [[Mavila]][9] |
| | * 26 26 15 26 26 26 15 26 26 26 15: [[Sensi]][11] |
| | * 20 20 20 11 20 20 20 20 11 20 20 20 20 11: [[11L 3s|Ketradektriatoh scale]] |
| | |
| | [[Category:3-limit record edos|###]] <!-- 3-digit number --> |
| | [[Category:Tertiaschis]] |