11edf: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
 
{{ED intro}} It corresponds to 18.8046[[edo]], is is similar to [[19edo]], and nearly identical to [[Carlos Beta]].
'''11edf''' is the [[EDF|equal division of the just perfect fifth]] into 11 parts of 63.8141 [[cent|cents]] each, corresponding to 18.8046 [[edo]] (similar to every fifth step of [[94edo]]). It is similar to [[19edo]] and nearly identical to [[Carlos Beta]].


While the fifth is just, the fourth is very sharp and significantly less accurate than in 19edo, being about four cents flat of that of [[7edo]].
While the fifth is just, the fourth is very sharp and significantly less accurate than in 19edo, being about four cents flat of that of [[7edo]].
Line 7: Line 6:
11edf represents the upper bound of the [[phoenix]] tuning range. 11edf benefits from all the desirable properties of phoenix tuning systems.
11edf represents the upper bound of the [[phoenix]] tuning range. 11edf benefits from all the desirable properties of phoenix tuning systems.


==Harmonics==
== Harmonics ==
{{Harmonics in equal|11|3|2|prec=2|columns=15}}
{{Harmonics in equal|11|3|2|prec=2|columns=15}}


==Intervals==
== Intervals ==
{| class="wikitable"
{| class="wikitable"
|-
|-
! | Degree
! Degree
! | Cent value
! Cent value
! | Corresponding <br>JI intervals
! Corresponding<br />JI intervals
! | Comments
! Comments
|-
|-
| colspan="2" | 0
| colspan="2" | 0
| | '''exact [[1/1]]'''
| '''exact [[1/1]]'''
| |  
|  
|-
|-
| | 1
| 1
| | 63.8141
| 63.8141
| | ([[28/27]]), ([[27/26]])
| ([[28/27]]), ([[27/26]])
| |  
|  
|-
|-
| | 2
| 2
| | 127.6282
| 127.6282
| | [[14/13]]
| [[14/13]]
| |  
|  
|-
|-
| | 3
| 3
| | 191.4423
| 191.4423
| |  
|  
| |  
|  
|-
|-
| | 4
| 4
| | 255.2564
| 255.2564
| |  
|  
| |  
|  
|-
|-
| | 5
| 5
| | 319.07045
| 319.07045
| | 6/5
| 6/5
| |  
|  
|-
|-
| | 6
| 6
| | 382.8845
| 382.8845
| | 5/4
| 5/4
| |  
|  
|-
|-
| | 7
| 7
| | 446.6986
| 446.6986
| |
|  
| |  
|  
|-
|-
| | 8
| 8
| | 510.5127
| 510.5127
| |  
|  
| |  
|  
|-
|-
| | 9
| 9
| | 574.3268
| 574.3268
| | 39/28
| 39/28
| |  
|  
|-
|-
| | 10
| 10
| | 638.1409
| 638.1409
| | ([[13/9]])
| ([[13/9]])
| |  
|  
|-
|-
| | 11
| 11
| | 701.955
| 701.955
| | '''exact [[3/2]]'''
| '''exact [[3/2]]'''
| | just perfect fifth
| just perfect fifth
|-
|-
| | 12
| 12
| | 765.7691
| 765.7691
| | 14/9, 81/52
| 14/9, 81/52
| |  
|  
|-
|-
| | 13
| 13
| | 828.5732
| 828.5732
| | 21/13
| 21/13
| |  
|  
|-
|-
| | 14
| 14
| | 893.3973
| 893.3973
| |  
|  
| |  
|  
|-
|-
| | 15
| 15
| | 956.2114
| 956.2114
| |  
|  
| |  
|  
|-
|-
| | 16
| 16
| | 1020.0255
| 1020.0255
| | 9/5
| 9/5
| |  
|  
|-
|-
| | 17
| 17
| | 1084.8395
| 1084.8395
| | 15/8
| 15/8
| |  
|  
|-
|-
| | 18
| 18
| | 1148.6536
| 1148.6536
| |  
|  
| |  
|  
|-
|-
| | 19
| 19
| | 1211.4677
| 1211.4677
| |
|  
| |  
|  
|-
|-
| | 20
| 20
| | 1276.2816
| 1276.2816
| | 117/56
| 117/56
| |  
|  
|-
|-
| | 21
| 21
| | 1340.0959
| 1340.0959
| | 13/6
| 13/6
| |  
|  
|-
|-
| | 22
| 22
| | 1403.91
| 1403.91
| | '''exact''' 9/4
| '''exact''' 9/4
| |  
|  
|}
|}


{{todo|expand}}
{{todo|expand}}

Revision as of 13:23, 21 January 2025

← 10edf 11edf 12edf →
Prime factorization 11 (prime)
Step size 63.8141 ¢ 
Octave 19\11edf (1212.47 ¢)
Twelfth 30\11edf (1914.42 ¢)
Consistency limit 7
Distinct consistency limit 7

11 equal divisions of the perfect fifth (abbreviated 11edf or 11ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 11 equal parts of about 63.8 ¢ each. Each step represents a frequency ratio of (3/2)1/11, or the 11th root of 3/2. It corresponds to 18.8046edo, is is similar to 19edo, and nearly identical to Carlos Beta.

While the fifth is just, the fourth is very sharp and significantly less accurate than in 19edo, being about four cents flat of that of 7edo.

11edf represents the upper bound of the phoenix tuning range. 11edf benefits from all the desirable properties of phoenix tuning systems.

Harmonics

Approximation of harmonics in 11edf
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Error Absolute (¢) +12.47 +12.47 +24.94 +21.51 +24.94 +13.32 -26.41 +24.94 -29.84 -3.40 -26.41 +26.46 +25.79 -29.84 -13.94
Relative (%) +19.5 +19.5 +39.1 +33.7 +39.1 +20.9 -41.4 +39.1 -46.8 -5.3 -41.4 +41.5 +40.4 -46.8 -21.8
Steps
(reduced) 		19
(8) 		30
(8) 		38
(5) 		44
(0) 		49
(5) 		53
(9) 		56
(1) 		60
(5) 		62
(7) 		65
(10) 		67
(1) 		70
(4) 		72
(6) 		73
(7) 		75
(9)

Intervals

Degree Cent value Corresponding
JI intervals 		Comments
0 exact 1/1
1 63.8141 (28/27), (27/26)
2 127.6282 14/13
3 191.4423
4 255.2564
5 319.07045 6/5
6 382.8845 5/4
7 446.6986
8 510.5127
9 574.3268 39/28
10 638.1409 (13/9)
11 701.955 exact 3/2 just perfect fifth
12 765.7691 14/9, 81/52
13 828.5732 21/13
14 893.3973
15 956.2114
16 1020.0255 9/5
17 1084.8395 15/8
18 1148.6536
19 1211.4677
20 1276.2816 117/56
21 1340.0959 13/6
22 1403.91 exact 9/4
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