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The 95 equal temperament divides the octave into 12.632 cents each. 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.
{{Infobox ET}}
{{ED intro}}


== Theory ==
95edo is a [[dual-fifth tuning]]. However, the [[patent val]] makes for a reasonable sharp-tending system, and [[tempering out|tempers out]] [[245/243]], [[2401/2400]], and [[4000/3969]] in the 7-limit, [[176/175]], 1331/1323, [[4000/3993]] and [[6250/6237]] in the 11-limit, and [[196/195]], [[325/324]], [[364/363]], [[640/637]], [[847/845]], [[1001/1000]] and [[2200/2197]] in the 13-limit.


Since 95edo has a step of 12.632 cents, 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.
It [[support]]s rank-2 temperaments such as [[enneadecal]], [[magus]], [[gorgik]], [[octacot]], [[quinmite]], [[tetracot]] and [[trisedodge]], and rank-3 temperaments such as [[manwe]] and [[shrusus]]. It provides the [[optimal patent val]] for shrusus.
{| class="wikitable"
 
|+Circulating temperaments in 95edo
=== Odd harmonics ===
!Tones
{{Harmonics in equal|95}}
!Pattern
 
!L:s
=== Subsets and supersets ===
|-
Since 95 factors as {{factorization|95}}, 95edo contains [[5edo]] and [[19edo]] as its subsets.
|5
 
|[[5edo]]
== Intervals ==
|equal
{{Interval table}}
|-
 
|6
[[Category:Shrusus]]
|[[5L 1s]]
 
|16:15
== Instruments ==
|-
 
|7
A [[Lumatone mapping for 95edo]] is available.
|[[4L 3s]]
 
|14:13
== Music ==
|-
; [[Bryan Deister]]
|8
* [https://www.youtube.com/watch?v=io8qp3GA5vU ''microtonal improvisation in 95edo''] (2025)
|[[7L 1s]]
 
|12:11
; [[JUMBLE]]
|-
* [https://youtu.be/6XC5bnu6SwY ''Puget Sound Asleep''] (2024)
|9
|[[5L 4s]]
|11:10
|-
|10
|[[5L 5s]]
|10:9
|-
|11
|[[7L 4s]]
|9:8
|-
|12
|[[11L 1s]]
| rowspan="2" |8:7
|-
|13
|[[3L 10s]]
|-
|14
|[[10L 4s]]
| rowspan="2" |7:6
|-
|15
|[[4L 11s]]
|-
|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
|}

Latest revision as of 08:22, 22 May 2025

← 94edo 95edo 96edo →
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

95 equal divisions of the octave (abbreviated 95edo or 95ed2), also called 95-tone equal temperament (95tet) or 95 equal temperament (95et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 95 equal parts of about 12.6 ¢ each. Each step represents a frequency ratio of 21/95, or the 95th root of 2.

Theory

95edo is a dual-fifth tuning. However, the patent val makes for a reasonable sharp-tending system, and tempers out 245/243, 2401/2400, and 4000/3969 in the 7-limit, 176/175, 1331/1323, 4000/3993 and 6250/6237 in the 11-limit, and 196/195, 325/324, 364/363, 640/637, 847/845, 1001/1000 and 2200/2197 in the 13-limit.

It supports rank-2 temperaments such as enneadecal, magus, gorgik, octacot, quinmite, tetracot and trisedodge, and rank-3 temperaments such as manwe and shrusus. It provides the optimal patent val for shrusus.

Odd harmonics

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)

Subsets and supersets

Since 95 factors as 5 × 19, 95edo contains 5edo and 19edo as its subsets.

Intervals

Steps Cents Approximate ratios Ups and downs notation
(Dual flat fifth 55\95) 		Ups and downs notation
(Dual sharp fifth 56\95)
0 0 1/1 D D
1 12.6 ^D, ^E♭♭♭ ^D, v4E♭
2 25.3 ^^D, ^^E♭♭♭ ^^D, v3E♭
3 37.9 vvD♯, vvE♭♭ ^3D, vvE♭
4 50.5 36/35 vD♯, vE♭♭ ^4D, vE♭
5 63.2 29/28 D♯, E♭♭ ^5D, E♭
6 75.8 23/22, 24/23 ^D♯, ^E♭♭ ^6D, ^E♭
7 88.4 20/19 ^^D♯, ^^E♭♭ v5D♯, ^^E♭
8 101.1 35/33 vvD𝄪, vvE♭ v4D♯, ^3E♭
9 113.7 31/29 vD𝄪, vE♭ v3D♯, ^4E♭
10 126.3 14/13 D𝄪, E♭ vvD♯, ^5E♭
11 138.9 13/12 ^D𝄪, ^E♭ vD♯, v6E
12 151.6 12/11 ^^D𝄪, ^^E♭ D♯, v5E
13 164.2 11/10 vvD♯𝄪, vvE ^D♯, v4E
14 176.8 31/28, 41/37 vD♯𝄪, vE ^^D♯, v3E
15 189.5 29/26, 39/35 E ^3D♯, vvE
16 202.1 ^E, ^F♭♭ ^4D♯, vE
17 214.7 26/23 ^^E, ^^F♭♭ E
18 227.4 vvE♯, vvF♭ ^E, v4F
19 240 23/20 vE♯, vF♭ ^^E, v3F
20 252.6 22/19, 37/32 E♯, F♭ ^3E, vvF
21 265.3 7/6 ^E♯, ^F♭ ^4E, vF
22 277.9 ^^E♯, ^^F♭ F
23 290.5 13/11 vvE𝄪, vvF ^F, v4G♭
24 303.2 25/21, 31/26 vE𝄪, vF ^^F, v3G♭
25 315.8 6/5 F ^3F, vvG♭
26 328.4 23/19, 29/24 ^F, ^G♭♭♭ ^4F, vG♭
27 341.1 28/23 ^^F, ^^G♭♭♭ ^5F, G♭
28 353.7 38/31 vvF♯, vvG♭♭ ^6F, ^G♭
29 366.3 vF♯, vG♭♭ v5F♯, ^^G♭
30 378.9 F♯, G♭♭ v4F♯, ^3G♭
31 391.6 ^F♯, ^G♭♭ v3F♯, ^4G♭
32 404.2 24/19, 43/34 ^^F♯, ^^G♭♭ vvF♯, ^5G♭
33 416.8 14/11 vvF𝄪, vvG♭ vF♯, v6G
34 429.5 41/32 vF𝄪, vG♭ F♯, v5G
35 442.1 31/24, 40/31 F𝄪, G♭ ^F♯, v4G
36 454.7 13/10 ^F𝄪, ^G♭ ^^F♯, v3G
37 467.4 38/29 ^^F𝄪, ^^G♭ ^3F♯, vvG
38 480 29/22, 33/25, 37/28 vvF♯𝄪, vvG ^4F♯, vG
39 492.6 vF♯𝄪, vG G
40 505.3 G ^G, v4A♭
41 517.9 31/23 ^G, ^A♭♭♭ ^^G, v3A♭
42 530.5 19/14 ^^G, ^^A♭♭♭ ^3G, vvA♭
43 543.2 26/19 vvG♯, vvA♭♭ ^4G, vA♭
44 555.8 40/29 vG♯, vA♭♭ ^5G, A♭
45 568.4 25/18 G♯, A♭♭ ^6G, ^A♭
46 581.1 7/5 ^G♯, ^A♭♭ v5G♯, ^^A♭
47 593.7 31/22 ^^G♯, ^^A♭♭ v4G♯, ^3A♭
48 606.3 vvG𝄪, vvA♭ v3G♯, ^4A♭
49 618.9 10/7 vG𝄪, vA♭ vvG♯, ^5A♭
50 631.6 36/25 G𝄪, A♭ vG♯, v6A
51 644.2 29/20 ^G𝄪, ^A♭ G♯, v5A
52 656.8 19/13 ^^G𝄪, ^^A♭ ^G♯, v4A
53 669.5 28/19 vvG♯𝄪, vvA ^^G♯, v3A
54 682.1 vG♯𝄪, vA ^3G♯, vvA
55 694.7 A ^4G♯, vA
56 707.4 ^A, ^B♭♭♭ A
57 720 ^^A, ^^B♭♭♭ ^A, v4B♭
58 732.6 29/19 vvA♯, vvB♭♭ ^^A, v3B♭
59 745.3 20/13 vA♯, vB♭♭ ^3A, vvB♭
60 757.9 31/20 A♯, B♭♭ ^4A, vB♭
61 770.5 39/25 ^A♯, ^B♭♭ ^5A, B♭
62 783.2 11/7 ^^A♯, ^^B♭♭ ^6A, ^B♭
63 795.8 19/12 vvA𝄪, vvB♭ v5A♯, ^^B♭
64 808.4 vA𝄪, vB♭ v4A♯, ^3B♭
65 821.1 37/23 A𝄪, B♭ v3A♯, ^4B♭
66 833.7 ^A𝄪, ^B♭ vvA♯, ^5B♭
67 846.3 31/19 ^^A𝄪, ^^B♭ vA♯, v6B
68 858.9 23/14 vvA♯𝄪, vvB A♯, v5B
69 871.6 38/23 vA♯𝄪, vB ^A♯, v4B
70 884.2 5/3 B ^^A♯, v3B
71 896.8 42/25 ^B, ^C♭♭ ^3A♯, vvB
72 909.5 22/13 ^^B, ^^C♭♭ ^4A♯, vB
73 922.1 vvB♯, vvC♭ B
74 934.7 12/7 vB♯, vC♭ ^B, v4C
75 947.4 19/11 B♯, C♭ ^^B, v3C
76 960 40/23 ^B♯, ^C♭ ^3B, vvC
77 972.6 ^^B♯, ^^C♭ ^4B, vC
78 985.3 23/13 vvB𝄪, vvC C
79 997.9 vB𝄪, vC ^C, v4D♭
80 1010.5 C ^^C, v3D♭
81 1023.2 ^C, ^D♭♭♭ ^3C, vvD♭
82 1035.8 20/11 ^^C, ^^D♭♭♭ ^4C, vD♭
83 1048.4 11/6 vvC♯, vvD♭♭ ^5C, D♭
84 1061.1 24/13 vC♯, vD♭♭ ^6C, ^D♭
85 1073.7 13/7 C♯, D♭♭ v5C♯, ^^D♭
86 1086.3 ^C♯, ^D♭♭ v4C♯, ^3D♭
87 1098.9 ^^C♯, ^^D♭♭ v3C♯, ^4D♭
88 1111.6 19/10 vvC𝄪, vvD♭ vvC♯, ^5D♭
89 1124.2 23/12 vC𝄪, vD♭ vC♯, v6D
90 1136.8 C𝄪, D♭ C♯, v5D
91 1149.5 35/18 ^C𝄪, ^D♭ ^C♯, v4D
92 1162.1 ^^C𝄪, ^^D♭ ^^C♯, v3D
93 1174.7 vvC♯𝄪, vvD ^3C♯, vvD
94 1187.4 vC♯𝄪, vD ^4C♯, vD
95 1200 2/1 D D

Instruments

A Lumatone mapping for 95edo is available.

Music

Bryan Deister
JUMBLE
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