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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>2011-07-13 22:03:59 UTC</tt>.<br>
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| : The original revision id was <tt>241267445</tt>.<br>
| | 640edo is [[enfactoring|enfactored]] in the 5-limit, [[tempering out]] the [[vishnuzma]], {{monzo| 23 6 -14 }}, with the same tuning as [[320edo]]. In the 7-limit it tempers out [[19683/19600]] and {{monzo| 16 2 -1 -6 }} and in the 11-limit it tempers out [[540/539]], [[8019/8000]] and {{monzo| 14 -1 -2 -4 1 }}. It provides the [[optimal patent val]] for the rank-3 [[albus]] temperament tempering out 540/539 and 8019/8000, and [[hemipental]], the 255 & 385 temperament. |
| : 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>
| | === Odd harmonics === |
| <h4>Original Wikitext content:</h4>
| | {{Harmonics in equal|640}} |
| <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 //640 equal divisions// divides the octave into 640 equal parts of precisely 1.875 cents each. It is contorted in the 5-limit, tempering out the vishnuzma, |23 6 -14>, with the tuning as 320edo. In the 7-limit it tempers out 19683/19600 and 589824/588245 and in the 11-limit it tempers out 540/539, 8019/8000 and 180224/180075. It provides the [[optimal patent val]] for the rank three [[Cataharry family|albus temperament]] tempering out 540/539 and 8019/8000, and the 125&130 temperament.</pre></div>
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| <h4>Original HTML content:</h4>
| | === Subsets and supersets === |
| <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>640edo</title></head><body>The <em>640 equal divisions</em> divides the octave into 640 equal parts of precisely 1.875 cents each. It is contorted in the 5-limit, tempering out the vishnuzma, |23 6 -14&gt;, with the tuning as 320edo. In the 7-limit it tempers out 19683/19600 and 589824/588245 and in the 11-limit it tempers out 540/539, 8019/8000 and 180224/180075. It provides the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for the rank three <a class="wiki_link" href="/Cataharry%20family">albus temperament</a> tempering out 540/539 and 8019/8000, and the 125&amp;130 temperament.</body></html></pre></div>
| | Since 640 factors into {{factorization|640}}, 640edo has subset edos {{EDOs| 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, and 320 }}. |
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| | [[Category:Albus]] |
| | [[Category:Hemipental]] |
Latest revision as of 15:43, 20 February 2025
| Prime factorization
|
27 × 5
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| Step size
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1.875 ¢
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| Fifth
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374\640 (701.25 ¢) (→ 187\320)
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| Semitones (A1:m2)
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58:50 (108.8 ¢ : 93.75 ¢)
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| Dual sharp fifth
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375\640 (703.125 ¢) (→ 75\128)
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| Dual flat fifth
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374\640 (701.25 ¢) (→ 187\320)
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| Dual major 2nd
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109\640 (204.375 ¢)
|
| Consistency limit
|
5
|
| Distinct consistency limit
|
5
|
640 equal divisions of the octave (abbreviated 640edo or 640ed2), also called 640-tone equal temperament (640tet) or 640 equal temperament (640et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 640 equal parts of about 1.88 ¢ each. Each step represents a frequency ratio of 21/640, or the 640th root of 2.
640edo is enfactored in the 5-limit, tempering out the vishnuzma, [23 6 -14⟩, with the same tuning as 320edo. In the 7-limit it tempers out 19683/19600 and [16 2 -1 -6⟩ and in the 11-limit it tempers out 540/539, 8019/8000 and [14 -1 -2 -4 1⟩. It provides the optimal patent val for the rank-3 albus temperament tempering out 540/539 and 8019/8000, and hemipental, the 255 & 385 temperament.
Odd harmonics
Approximation of odd harmonics in 640edo
| Harmonic
|
3
|
5
|
7
|
9
|
11
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13
|
15
|
17
|
19
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21
|
23
|
| Error
|
Absolute (¢)
|
-0.705
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-0.064
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+0.549
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+0.465
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-0.068
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-0.528
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-0.769
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+0.045
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+0.612
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-0.156
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-0.149
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| Relative (%)
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-37.6
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-3.4
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+29.3
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+24.8
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-3.6
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-28.1
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-41.0
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+2.4
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+32.6
|
-8.3
|
-8.0
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Steps
(reduced)
|
1014
(374)
|
1486
(206)
|
1797
(517)
|
2029
(109)
|
2214
(294)
|
2368
(448)
|
2500
(580)
|
2616
(56)
|
2719
(159)
|
2811
(251)
|
2895
(335)
|
Subsets and supersets
Since 640 factors into 27 × 5, 640edo has subset edos 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, and 320.