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45edt: Difference between revisions

VisualWikitext
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**Imported revision 250635956 - Original comment: **
 
m Text replacement - "[[the Riemann zeta function and tuning" to "[[Riemann zeta function"
 
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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>
'''45EDT''' is the [[Edt|equal division of the third harmonic]] into 45 parts of 42.2657 [[cent|cents]] each, corresponding to 28.3918 [[edo]]. It makes for a strong no-twos 17-limit system, particularly with respect to the tuning of 5, 13, and 17. It tempers out 3125/3087 in the 7-limit, 891/875 and 2475/2401 in the 11-limit, 275/273, 351/343, 847/845 and 2197/2187 in the 13-limit, and 121/119, 459/455 and 2025/2023 in the 17-limit (no-twos subgroup). It is the tenth [[Riemann zeta function#Removing primes|no-twos zeta peak edt]].
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-04 14:03:51 UTC</tt>.<br>
 
: The original revision id was <tt>250635956</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 = 45
<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">The 45 equal division of 3, the tritave, divides it into 45 equal parts of 42.266 cents each, corresponding to 28.392 edo. It makes for a strong 17-limit no-twos system, particularly with respect to the tuning of 5, 13, and 17. It tempers out 3125/3087 in the 7-limit, 891/875 and 2475/2401 in the 11-limit, 275/273, 351/343, 847/845 and 2197/2187 in the 13-limit, and 121/119, 459/455 and 2025/2023 in the 17-limit. It is the tenth [[The Riemann Zeta Function and Tuning#Removing primes|no-twos zeta peak edt]].</pre></div>
| denom = 1
<h4>Original HTML content:</h4>
| intervals = integer
<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;45edt&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 45 equal division of 3, the tritave, divides it into 45 equal parts of 42.266 cents each, corresponding to 28.392 edo. It makes for a strong 17-limit no-twos system, particularly with respect to the tuning of 5, 13, and 17. It tempers out 3125/3087 in the 7-limit, 891/875 and 2475/2401 in the 11-limit, 275/273, 351/343, 847/845 and 2197/2187 in the 13-limit, and 121/119, 459/455 and 2025/2023 in the 17-limit. It is the tenth &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Removing primes"&gt;no-twos zeta peak edt&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
}}
{{Harmonics in equal
| steps = 45
| num = 3
| denom = 1
| start = 12
| collapsed = 1
| intervals = integer
}}
 
== Intervals ==
{| class="wikitable"
|-
! Degrees
! [[Cent]]s
! [[Hekt]]s
! Approximate ratios
|-
! colspan="3" | 0
| <span style="color: #660000;">[[1/1]]</span>
|-
| 1
| 42.266
| 28.889
|
|-
| 2
| 84.531
| 57.778
| [[21/20]]
|-
| 3
| 126.797
| 86.667
| [[14/13]], [[15/14]], [[16/15]], 29/27
|-
| 4
| 169.063
| 115.556
| 11/10
|-
| 5
| 211.328
| 144.444
| 9/8
|-
| 6
| 253.594
| 173.333
| [[15/13]]
|-
| 7
| 295.86
| 202.222
| 19/16
|-
| 8
| 338.125
| 231.111
| 17/14
|-
| 9
| 380.391
| 260
| <span style="color: #660000;">[[5/4]]</span>
|-
| 10
| 422.657
| 288.889
| 14/11
|-
| 11
| 464.922
| 317.778
| [[21/16]], [[17/13]]
|-
| 12
| 507.188
| 336.667
| [[4/3]]
|-
| 13
| 549.454
| 375.556
| 11/8
|-
| 14
| 591.719
| 304.444
| 7/5
|-
| 15
| 633.985
| 433.333
| [[13/9]]
|-
| 16
| 676.251
| 462.222
| 40/27. 189/128
|-
| 17
| 718.516
| 491.111
| 50/33
|-
| 18
| 760.782
| 520
| <span style="color: #660000;">[[14/9]]</span>
|-
| 19
| 803.048
| 548.889
| 8/5
|-
| 20
| 845.313
| 577.778
| 13/8
|-
| 21
| 887.579
| 606.667
| [[5/3]], 17/11
|-
| 22
| 929.845
| 635.556
| 12/7
|-
| 23
| 972.110
| 664.444
| 7/4
|-
| 24
| 1014.376
| 693.333
| [[9/5]], 33/17
|-
| 25
| 1056.642
| 722.222
| 24/13
|-
| 26
| 1098.907
| 751.111
| 17/9
|-
| 27
| 1141.173
| 780
| <span style="color: #660000;">[[27/14]]</span>
|-
| 28
| 1183.439
| 808.889
| 99/50
|-
| 29
| 1225.704
| 837.778
| 81/40, 128/63
|-
| 30
| 1267.97
| 866.667
| <span style="color: #660000;">[[27/26|27/13]]</span>
|-
| 31
| 1310.236
| 895.556
| 32/15
|-
| 32
| 1352.501
| 924.444
| 24/11
|-
| 33
| 1394.767
| 953.333
| <span style="color: #660000;">[[9/4]]</span> ([[9/8]] plus an octave)
|-
| 34
| 1437.033
| 982.222
| 16/7, 39/17
|-
| 35
| 1479.298
| 1011.111
| 33/14
|-
| 36
| 1521.564
| 1040
| <span style="color: #660000;">[[12/5]]</span> (<span style="color: #660000;">[[6/5]]</span> plus an octave)
|-
| 37
| 1563.83
| 1068.889
| 42/17
|-
| 38
| 1606.095
| 1097.778
| 48/19
|-
| 39
| 1648.361
| 1126.667
| <span style="color: #660000;">[[13/5]]</span> ([[13/10]] plus an octave)
|-
| 40
| 1690.627
| 1155.556
| [[8/3]]
|-
| 41
| 1732.892
| 1184.444
| 30/11
|-
| 42
| 1775.158
| 1213.333
| <span style="color: #660000;">39/14, [[14/5]]</span> ([[7/5]] plus an octave), 45/16, 81/29
|-
| 43
| 1817.424
| 1242.222
| [[10/7|20/7]]
|-
| 44
| 1859.689
| 1271.111
|
|-
| 45
| 1901.955
| 1300
| <span style="color: #660000;">[[3/1]]</span>
|}
 
{{todo|expand}}
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