|
|
| Line 5: |
Line 5: |
| {{Harmonics in equal|95}} | | {{Harmonics in equal|95}} |
| It tempers out 245/243, 4000/3969 and 2401/2400 in the 7-limit, 1331/1323, 176/175, 6250/6237 and 4000/3993 in the 11-limit, and 196/195, 640/637, 325/324, 364/363, 847/845, 1001/1000 and 2200/2197 in the 13-limit. It provides the optimal patent val for the rank 3 [[Sensamagic_family#Shrusus|shrusus temperament]]. 95 factors as 5*19. | | It tempers out 245/243, 4000/3969 and 2401/2400 in the 7-limit, 1331/1323, 176/175, 6250/6237 and 4000/3993 in the 11-limit, and 196/195, 640/637, 325/324, 364/363, 847/845, 1001/1000 and 2200/2197 in the 13-limit. It provides the optimal patent val for the rank 3 [[Sensamagic_family#Shrusus|shrusus temperament]]. 95 factors as 5*19. |
|
| |
| == Temperament properties ==
| |
| Since 95edo has a step of 12.632{{cent}}, it also allows one to use its MOS scales as circulating temperaments. As 5*[[19edo]], it is also the first edo to have multiple circulating temperaments which reduce to other edos, called [[superenneadecal]].
| |
| {| class="wikitable"
| |
| |+Circulating temperaments in 95edo
| |
| !Tones
| |
| !Pattern
| |
| !L:s
| |
| |-
| |
| |5
| |
| |[[5edo]]
| |
| |equal
| |
| |-
| |
| |6
| |
| |[[5L 1s]]
| |
| |16:15
| |
| |-
| |
| |7
| |
| |[[4L 3s]]
| |
| |14:13
| |
| |-
| |
| |8
| |
| |[[7L 1s]]
| |
| |12:11
| |
| |-
| |
| |9
| |
| |[[5L 4s]]
| |
| |11:10
| |
| |-
| |
| |10
| |
| |[[5L 5s]]
| |
| |10:9
| |
| |-
| |
| |11
| |
| |[[7L 4s]]
| |
| |9:8
| |
| |-
| |
| |12
| |
| |[[11L 1s]]
| |
| | rowspan="2" |8:7
| |
| |-
| |
| |13
| |
| |[[4L 9s]]
| |
| |-
| |
| |14
| |
| |[[11L 3s]]
| |
| | rowspan="2" |7:6
| |
| |-
| |
| |15
| |
| |[[3L 12s]]
| |
| |-
| |
| |16
| |
| |15L 1s
| |
| | rowspan="3" |6:5
| |
| |-
| |
| |17
| |
| |[[10L 7s]]
| |
| |-
| |
| |18
| |
| |5L 13s
| |
| |-
| |
| |19
| |
| |[[19edo]]
| |
| |equal
| |
| |-
| |
| |20
| |
| |15L 5s
| |
| | rowspan="4" |5:4
| |
| |-
| |
| |21
| |
| |11L 10s
| |
| |-
| |
| |22
| |
| |[[7L 15s]]
| |
| |-
| |
| |23
| |
| |[[3L 20s]]
| |
| |-
| |
| |24
| |
| |23L 1s
| |
| | rowspan="8" |4:3
| |
| |-
| |
| |25
| |
| |20L 5s
| |
| |-
| |
| |26
| |
| |17L 9s
| |
| |-
| |
| |27
| |
| |[[14L 13s]]
| |
| |-
| |
| |28
| |
| |11L 17s
| |
| |-
| |
| |29
| |
| |[[8L 21s]]
| |
| |-
| |
| |30
| |
| |5L 25s
| |
| |-
| |
| |31
| |
| |2L 29s
| |
| |-
| |
| |32
| |
| |31L 1s
| |
| | rowspan="16" |3:2
| |
| |-
| |
| |33
| |
| |29L 4s
| |
| |-
| |
| |34
| |
| |27L 7s
| |
| |-
| |
| |35
| |
| |25L 10s
| |
| |-
| |
| |36
| |
| |23L 13s
| |
| |-
| |
| |37
| |
| |21L 16s
| |
| |-
| |
| |38
| |
| |19L 19s
| |
| |-
| |
| |39
| |
| |17L 22s
| |
| |-
| |
| |40
| |
| |15L 25s
| |
| |-
| |
| |41
| |
| |13L 28s
| |
| |-
| |
| |42
| |
| |11L 31s
| |
| |-
| |
| |43
| |
| |9L 34s
| |
| |-
| |
| |44
| |
| |7L 37s
| |
| |-
| |
| |45
| |
| |5L 40s
| |
| |-
| |
| |46
| |
| |3L 43s
| |
| |-
| |
| |47
| |
| |1L 46s
| |
| |-
| |
| |48
| |
| |47L 1s
| |
| | rowspan="28" |2:1
| |
| |-
| |
| |49
| |
| |46L 3s
| |
| |-
| |
| |50
| |
| |45L 5s
| |
| |-
| |
| |51
| |
| |44L 7s
| |
| |-
| |
| |52
| |
| |43L 9s
| |
| |-
| |
| |53
| |
| |42L 11s
| |
| |-
| |
| |54
| |
| |41L 13s
| |
| |-
| |
| |55
| |
| |40L 15s
| |
| |-
| |
| |56
| |
| |39L 17s
| |
| |-
| |
| |57
| |
| |38L 19s
| |
| |-
| |
| |58
| |
| |37L 21s
| |
| |-
| |
| |59
| |
| |36L 23s
| |
| |-
| |
| |60
| |
| |35L 25s
| |
| |-
| |
| |61
| |
| |34L 27s
| |
| |-
| |
| |62
| |
| |33L 29s
| |
| |-
| |
| |63
| |
| |32L 31s
| |
| |-
| |
| |64
| |
| |31L 33s
| |
| |-
| |
| |65
| |
| |30L 35s
| |
| |-
| |
| |66
| |
| |29L 37s
| |
| |-
| |
| |67
| |
| |28L 39s
| |
| |-
| |
| |68
| |
| |27L 41s
| |
| |-
| |
| |69
| |
| |26L 43s
| |
| |-
| |
| |70
| |
| |25L 45s
| |
| |-
| |
| |71
| |
| |24L 47s
| |
| |-
| |
| |72
| |
| |23L 49s
| |
| |-
| |
| |73
| |
| |22L 51s
| |
| |-
| |
| |74
| |
| |21L 53s
| |
| |-
| |
| |75
| |
| |20L 55s
| |
| |}
| |
|
| |
|
| [[Category:Equal divisions of the octave|##]] <!-- 2-digit number --> | | [[Category:Equal divisions of the octave|##]] <!-- 2-digit number --> |
Revision as of 13:43, 30 May 2023
| Prime factorization
|
5 × 19
|
| Step size
|
12.6316 ¢
|
| Fifth
|
56\95 (707.368 ¢)
|
| Semitones (A1:m2)
|
12:5 (151.6 ¢ : 63.16 ¢)
|
| Dual sharp fifth
|
56\95 (707.368 ¢)
|
| Dual flat fifth
|
55\95 (694.737 ¢) (→ 11\19)
|
| Dual major 2nd
|
16\95 (202.105 ¢)
|
| Consistency limit
|
7
|
| Distinct consistency limit
|
7
|
Template:EDO intro
Theory
Approximation of odd harmonics in 95edo
| Harmonic
|
3
|
5
|
7
|
9
|
11
|
13
|
15
|
17
|
19
|
21
|
23
|
| Error
|
Absolute (¢)
|
+5.41
|
+5.27
|
+3.81
|
-1.80
|
+4.47
|
+5.79
|
-1.95
|
-3.90
|
+5.64
|
-3.41
|
+3.30
|
| Relative (%)
|
+42.9
|
+41.7
|
+30.1
|
-14.3
|
+35.4
|
+45.8
|
-15.5
|
-30.9
|
+44.7
|
-27.0
|
+26.2
|
Steps
(reduced)
|
151
(56)
|
221
(31)
|
267
(77)
|
301
(16)
|
329
(44)
|
352
(67)
|
371
(86)
|
388
(8)
|
404
(24)
|
417
(37)
|
430
(50)
|
It tempers out 245/243, 4000/3969 and 2401/2400 in the 7-limit, 1331/1323, 176/175, 6250/6237 and 4000/3993 in the 11-limit, and 196/195, 640/637, 325/324, 364/363, 847/845, 1001/1000 and 2200/2197 in the 13-limit. It provides the optimal patent val for the rank 3 shrusus temperament. 95 factors as 5*19.