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32edt: Difference between revisions

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**Imported revision 250569378 - Original comment: **
 
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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>
'''32EDT''' is the [[Edt|equal division of the third harmonic]] into 32 parts of 59.4361 [[cent]]s each, corresponding to 20.1898 [[edo]]. It has a distinct sharp tendency, in the sense that if 3 is pure, 5, 7, 11, 13, 17, and 19 are all sharp. It tempers out 3125/3087 and 885735/823543 in the 7-limit; 891/875, 1331/1323, and 2475/2401 in the 11-limit; 275/273, 351/343, 729/715, and 847/845 in the 13-limit; 121/119, 189/187, 225/221, 459/455, and 845/833 in the 17-limit; 135/133, 171/169, 247/245, 325/323, and 363/361 in the 19-limit (no-twos subgroup). It is the eighth [[the Riemann zeta function and tuning#Removing primes|zeta peak tritave division]].
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-04 01:20:59 UTC</tt>.<br>
 
: The original revision id was <tt>250569378</tt>.<br>
== Harmonics ==
: The revision comment was: <tt></tt><br>
{{Harmonics in equal
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| steps = 32
<h4>Original Wikitext content:</h4>
| num = 3
<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">//32edt// means the division of 3, the tritave, into 32 equal parts of 59.463 cents each. It has a distinct sharp tendency, in the sense that if 3 is pure, 5, 7, 11, 13, 17 and 19 are all sharp. It tempers out 3125/3087 in the 7-limit, 891/875, 1331/1323 and 2475/2401 in the 11-limit, 275/273, 351/343, 729/714, 847/845 and 1575/1573 in the 13-limit, 121/119, 189/197 and 225/221 in the 17-limit. It is the eighth [[The Riemann Zeta Function and Tuning#Removing primes|zeta peak tritave division]].</pre></div>
| denom = 1
<h4>Original HTML content:</h4>
| columns = 9
<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;32edt&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;em&gt;32edt&lt;/em&gt; means the division of 3, the tritave, into 32 equal parts of 59.463 cents each. It has a distinct sharp tendency, in the sense that if 3 is pure, 5, 7, 11, 13, 17 and 19 are all sharp. It tempers out 3125/3087 in the 7-limit, 891/875, 1331/1323 and 2475/2401 in the 11-limit, 275/273, 351/343, 729/714, 847/845 and 1575/1573 in the 13-limit, 121/119, 189/197 and 225/221 in the 17-limit. It is the eighth &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Removing primes"&gt;zeta peak tritave division&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
| intervals = prime
}}
{{Harmonics in equal
| steps = 32
| num = 3
| denom = 1
| start = 12
| collapsed = 1
| intervals = odd
}}
 
== Intervals ==
{| class="wikitable"
|-
! Step
! [[Cent]]s
! [[Hekt]]s
|-
| 1
| 59.436
| 40.625
|-
| 2
| 118.872
| 81.25
|-
| 3
| 178.308
| 121.875
|-
| 4
| 237.744
| 162.5
|-
| 5
| 297.180
| 203.125
|-
| 6
| 356.617
| 243.75
|-
| 7
| 416.053
| 284.375
|-
| 8
| 475.489
| 325
|-
| 9
| 534.925
| 365.625
|-
| 10
| 594.361
| 406.25
|-
| 11
| 653.797
| 446.875
|-
| 12
| 713.233
| 487.5
|-
| 13
| 772.669
| 528.125
|-
| 14
| 832.105
| 568.75
|-
| 15
| 891.541
| 609.375
|-
| 16
| 950.978
| 650
|-
| 17
| 1010.414
| 690.625
|-
| 18
| 1069.85
| 731.25
|-
| 19
| 1129.286
| 774.875
|-
| 20
| 1188.722
| 812.5
|-
| 21
| 1248.158
| 853.125.
|-
| 22
| 1307.594
| 893.75
|-
| 23
| 1367.03
| 934.375
|-
| 24
| 1426.466
| 975
|-
| 25
| 1485.902
| 1015.625
|-
| 26
| 1545.338
| 1056.25
|-
| 27
| 1604.775
| 1096.875
|-
| 28
| 1664.211
| 1137.5
|-
| 29
| 1723.647
| 1178.125
|-
| 30
| 1783.083
| 1218.75
|-
| 31
| 1842.519
| 1259.375
|-
| 32
| 1901.955
| 1300
|}
 
{{todo|expand}}
Retrieved from "https://en.xen.wiki/w/32edt"