11ed5: 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>
'''11ED5''' is the [[Ed5|equal division of the 5th harmonic]] into 11 parts of 252.3012 [[cent|cents]] each. It is related to the [[Meantone family|godzilla temperament]], which tempers out 49/48, 81/80, and 91/90 in the 2.3.5.7.13 subgroup.
: This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2011-11-21 14:56:23 UTC</tt>.<br>
 
: The original revision id was <tt>277820172</tt>.<br>
== Intervals ==
: The revision comment was: <tt></tt><br>
{| class="wikitable"
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>
! | degree
<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">0: 1/1 0.000 unison, perfect prime
! | cents value
1: 253.301 cents 8/7, 7/6
! | corresponding <br>JI intervals
2: 506.602 cents 4/3
! | comments
3: 759.904 cents 14/9
|-
4: 1013.205 cents 9/5
| | 0
5: 1266.506 cents
| | 0.0000
6: 1519.807 cents 12/5
| | '''exact [[1/1]]'''
7: 1773.109 cents 14/5
| |
8: 2026.410 cents 16/5
|-
9: 2279.711 cents
| | 1
10: 2533.012 cents
| | 253.3012
11: 5/1</pre></div>
| | [[8/7]], [[15/13]], [[7/6]]
<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;11ed5&lt;/title&gt;&lt;/head&gt;&lt;body&gt;0: 1/1 0.000 unison, perfect prime&lt;br /&gt;
|-
1: 253.301 cents 8/7, 7/6&lt;br /&gt;
| | 2
2: 506.602 cents 4/3&lt;br /&gt;
| | 506.6025
3: 759.904 cents 14/9&lt;br /&gt;
| | [[4/3]]
4: 1013.205 cents 9/5&lt;br /&gt;
| |
5: 1266.506 cents&lt;br /&gt;
|-
6: 1519.807 cents 12/5&lt;br /&gt;
| | 3
7: 1773.109 cents 14/5&lt;br /&gt;
| | 759.9037
8: 2026.410 cents 16/5&lt;br /&gt;
| | [[14/9]]
9: 2279.711 cents&lt;br /&gt;
| |
10: 2533.012 cents&lt;br /&gt;
|-
11: 5/1&lt;/body&gt;&lt;/html&gt;</pre></div>
| | 4
| | 1013.2050
| | [[9/5]]
| |
|-
| | 5
| | 1266.5062
| | [[27/26|27/13]], [[25/24|25/12]], [[21/20|21/10]]
| |
|-
| | 6
| | 1519.8075
| | [[12/5]]
| |
|-
| | 7
| | 1773.1087
| | [[14/5]]
| |
|-
| | 8
| | 2026.4100
| | [[16/5]], [[13/4]]
| |
|-
| | 9
| | 2279.7112
| | [[15/4]]
| |
|-
| | 10
| | 2533.0125
| | [[15/14|30/7]], [[13/3]], [[35/32|35/8]]
| |
|-
| | 11
| | 2786.3137
| | '''exact [[5/1]]'''
| | just major third plus two octaves
|}
 
== Harmonics ==
{{Harmonics in equal
| steps = 11
| num = 5
| denom = 1
}}
{{Harmonics in equal
| steps = 11
| num = 5
| denom = 1
| start = 12
| collapsed = 1
}}

Latest revision as of 19:20, 1 August 2025

← 10ed5 11ed5 12ed5 →
Prime factorization 11 (prime)
Step size 253.301 ¢ 
Octave 5\11ed5 (1266.51 ¢)
Twelfth 8\11ed5 (2026.41 ¢)
Consistency limit 3
Distinct consistency limit 3

11ED5 is the equal division of the 5th harmonic into 11 parts of 252.3012 cents each. It is related to the godzilla temperament, which tempers out 49/48, 81/80, and 91/90 in the 2.3.5.7.13 subgroup.

Intervals

degree cents value corresponding
JI intervals 		comments
0 0.0000 exact 1/1
1 253.3012 8/7, 15/13, 7/6
2 506.6025 4/3
3 759.9037 14/9
4 1013.2050 9/5
5 1266.5062 27/13, 25/12, 21/10
6 1519.8075 12/5
7 1773.1087 14/5
8 2026.4100 16/5, 13/4
9 2279.7112 15/4
10 2533.0125 30/7, 13/3, 35/8
11 2786.3137 exact 5/1 just major third plus two octaves

Harmonics

Approximation of harmonics in 11ed5
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +67 +124 -120 +0 -62 -76 -54 -4 +67 -98 +4
Relative (%) +26.3 +49.1 -47.5 +0.0 -24.6 -30.0 -21.2 -1.7 +26.3 -38.9 +1.6
Steps
(reduced) 		5
(5) 		8
(8) 		9
(9) 		11
(0) 		12
(1) 		13
(2) 		14
(3) 		15
(4) 		16
(5) 		16
(5) 		17
(6)
Approximation of harmonics in 11ed5
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +119 -9 +124 +13 -92 +62 -31 -120 +49 -32 -109
Relative (%) +46.9 -3.7 +49.1 +5.0 -36.4 +24.5 -12.4 -47.5 +19.2 -12.6 -43.0
Steps
(reduced) 		18
(7) 		18
(7) 		19
(8) 		19
(8) 		19
(8) 		20
(9) 		20
(9) 		20
(9) 		21
(10) 		21
(10) 		21
(10)
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