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12edf: Difference between revisions

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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>
'''12EDF''' is the [[EDF|equal division of the just perfect fifth]] into 12 parts of 58.49625 [[cent|cents]] each, corresponding to 20.5141 [[edo]] (similar to every second step of [[41edo]]). It is an intersection of [[3edf]]~[[5edo]] and [[4edf]]~[[7edo]] relations, and could pass as both [[20edo]] and [[21edo]], with both relations nearly breaking down by this point. It is related to the [[Tetracot family#Dodecacot|dodecacot temperament]], which tempers out 3087/3125 and 10976/10935 in the 7-limit.
: This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2011-12-26 16:14:28 UTC</tt>.<br>
: The original revision id was <tt>288516036</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<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">=12 ED 3/2=


It is a strong [[half-prime subgroup|3/2.5/2.7/2 subgroup]] system, a fact first noted by [[User:CompactStar|CompactStar]], tempering out the commas [[10976/10935]] and [[3125/3087]], although the representation of [[11/2]] is more questionable. [[24edf]] (effectively 41edo) provides a correction for 11/2. It contains the [[macrodiatonic and microdiatonic scales|microdiatonic]] scale that corresponds to 12edo's [[5L 2s|diatonic scale]] with [[2/1]] compressed to [[3/2]].
==Harmonics==
{{Harmonics in equal|12|3|2}}
{{Harmonics in equal|12|3|2|start=12|collapsed=1}}
==Intervals==
{| class="wikitable"
|-
! | degree
! | cents value
! | corresponding <br>JI intervals
! | comments
|-
! colspan="2" | 0
| | '''exact [[1/1]]'''
| |
|-
| | 1
| | 58.49625
| | [[28/27]], 91/88, 88/85
| |
|-
| | 2
| | 116.9925
| | [[15/14]]
| |
|-
| | 3
| | 175.48875
| | [[10/9]], [[21/19]]
| |
|-
| | 4
| | 233.9850
| | [[8/7]]
| |
|-
| | 5
| | 292.48125
| | 45/38
| |
|-
| | 6
| | 350.9775
| | [[11/9]], [[27/22]]
| |
|-
| | 7
| | 409.47375
| | [[19/15]], [[63/50]]
| |
|-
| | 8
| | 467.9700
| | [[21/16]]
| |
|-
| | 9
| | 526.46625
| | [[19/14]]
| |
|-
| | 10
| | 584.9625
| | [[7/5]]
| |
|-
| | 11
| | 643.4588
| | [[13/9]]
| |
|-
| | 12
| | 701.9550
| | '''exact [[3/2]]'''
| | just perfect fifth
|-
|13
|760.45125
|273/176, 132/85
|
|-
|14
|818.9475
|8/5
|
|-
|15
|877.44375
|63/38
|
|-
|16
|935.94
|12/7
|
|-
|17
|994.43625
|135/76
|
|-
|18
|1052.9325
|11/6, 81/44
|
|-
|19
|1111.42875
|19/10
|
|-
|20
|1169.925
|63/32
|
|-
|21
|1228.42125
|57/28
|
|-
|22
|1286.9175
|21/10
|
|-
|23
|1345.41375
|13/6
|
|-
|24
|1403.91
|'''exact''' 9/4
|
|
0: 1/1 0.000 unison, perfect prime
|}
1: 58.496 cents 58.496
2: 116.993 cents 116.993
3: 175.489 cents 175.489
4: 233.985 cents 233.985
5: 292.481 cents 292.481
6: 350.978 cents 350.978
7: 409.474 cents 409.474
8: 467.970 cents 467.970
9: 526.466 cents 526.466
10: 584.963 cents 584.963
11: 643.459 cents 643.459
12: 3/2 701.955 perfect fifth


Lookalikes:</pre></div>
{{todo|expand}}
<h4>Original HTML content:</h4>
<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;12edf&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x12 ED 3/2"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;12 ED 3/2&lt;/h1&gt;
&lt;br /&gt;
|&lt;br /&gt;
0: 1/1 0.000 unison, perfect prime&lt;br /&gt;
1: 58.496 cents 58.496&lt;br /&gt;
2: 116.993 cents 116.993&lt;br /&gt;
3: 175.489 cents 175.489&lt;br /&gt;
4: 233.985 cents 233.985&lt;br /&gt;
5: 292.481 cents 292.481&lt;br /&gt;
6: 350.978 cents 350.978&lt;br /&gt;
7: 409.474 cents 409.474&lt;br /&gt;
8: 467.970 cents 467.970&lt;br /&gt;
9: 526.466 cents 526.466&lt;br /&gt;
10: 584.963 cents 584.963&lt;br /&gt;
11: 643.459 cents 643.459&lt;br /&gt;
12: 3/2 701.955 perfect fifth&lt;br /&gt;
&lt;br /&gt;
Lookalikes:&lt;/body&gt;&lt;/html&gt;</pre></div>
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