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]].
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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
| |  
|  
|}
|}


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