95edo

← 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 2^1/95, 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	12.632		^D, v4E♭♭	^D, v4E♭
2	25.263		^^D, v3E♭♭	^^D, v3E♭
3	37.895		^3D, vvE♭♭	^3D, vvE♭
4	50.526	36/35	^4D, vE♭♭	^4D, vE♭
5	63.158	29/28	D♯, E♭♭	^5D, E♭
6	75.789	23/22, 24/23	^D♯, v4E♭	^6D, v11E
7	88.421	20/19	^^D♯, v3E♭	^7D, v10E
8	101.053	35/33	^3D♯, vvE♭	^8D, v9E
9	113.684	31/29	^4D♯, vE♭	^9D, v8E
10	126.316	14/13	D𝄪, E♭	^10D, v7E
11	138.947	13/12	^D𝄪, v4E	^11D, v6E
12	151.579	12/11	^^D𝄪, v3E	D♯, v5E
13	164.211	11/10	^3D𝄪, vvE	^D♯, v4E
14	176.842	31/28, 41/37	^4D𝄪, vE	^^D♯, v3E
15	189.474	29/26, 39/35	E	^3D♯, vvE
16	202.105		^E, v4F♭	^4D♯, vE
17	214.737	26/23	^^E, v3F♭	E
18	227.368		^3E, vvF♭	^E, v4F
19	240	23/20	^4E, vF♭	^^E, v3F
20	252.632	22/19, 37/32	E♯, F♭	^3E, vvF
21	265.263	7/6	^E♯, v4F	^4E, vF
22	277.895		^^E♯, v3F	F
23	290.526	13/11	^3E♯, vvF	^F, v4G♭
24	303.158	25/21, 31/26	^4E♯, vF	^^F, v3G♭
25	315.789	6/5	F	^3F, vvG♭
26	328.421	23/19, 29/24	^F, v4G♭♭	^4F, vG♭
27	341.053	28/23	^^F, v3G♭♭	^5F, G♭
28	353.684	38/31	^3F, vvG♭♭	^6F, v11G
29	366.316		^4F, vG♭♭	^7F, v10G
30	378.947		F♯, G♭♭	^8F, v9G
31	391.579		^F♯, v4G♭	^9F, v8G
32	404.211	24/19, 43/34	^^F♯, v3G♭	^10F, v7G
33	416.842	14/11	^3F♯, vvG♭	^11F, v6G
34	429.474	41/32	^4F♯, vG♭	F♯, v5G
35	442.105	31/24, 40/31	F𝄪, G♭	^F♯, v4G
36	454.737	13/10	^F𝄪, v4G	^^F♯, v3G
37	467.368	38/29	^^F𝄪, v3G	^3F♯, vvG
38	480	29/22, 33/25, 37/28	^3F𝄪, vvG	^4F♯, vG
39	492.632		^4F𝄪, vG	G
40	505.263		G	^G, v4A♭
41	517.895	31/23	^G, v4A♭♭	^^G, v3A♭
42	530.526	19/14	^^G, v3A♭♭	^3G, vvA♭
43	543.158	26/19	^3G, vvA♭♭	^4G, vA♭
44	555.789	40/29	^4G, vA♭♭	^5G, A♭
45	568.421	25/18	G♯, A♭♭	^6G, v11A
46	581.053	7/5	^G♯, v4A♭	^7G, v10A
47	593.684	31/22	^^G♯, v3A♭	^8G, v9A
48	606.316		^3G♯, vvA♭	^9G, v8A
49	618.947	10/7	^4G♯, vA♭	^10G, v7A
50	631.579	36/25	G𝄪, A♭	^11G, v6A
51	644.211	29/20	^G𝄪, v4A	G♯, v5A
52	656.842	19/13	^^G𝄪, v3A	^G♯, v4A
53	669.474	28/19	^3G𝄪, vvA	^^G♯, v3A
54	682.105		^4G𝄪, vA	^3G♯, vvA
55	694.737		A	^4G♯, vA
56	707.368		^A, v4B♭♭	A
57	720		^^A, v3B♭♭	^A, v4B♭
58	732.632	29/19	^3A, vvB♭♭	^^A, v3B♭
59	745.263	20/13	^4A, vB♭♭	^3A, vvB♭
60	757.895	31/20	A♯, B♭♭	^4A, vB♭
61	770.526	39/25	^A♯, v4B♭	^5A, B♭
62	783.158	11/7	^^A♯, v3B♭	^6A, v11B
63	795.789	19/12	^3A♯, vvB♭	^7A, v10B
64	808.421		^4A♯, vB♭	^8A, v9B
65	821.053	37/23	A𝄪, B♭	^9A, v8B
66	833.684		^A𝄪, v4B	^10A, v7B
67	846.316	31/19	^^A𝄪, v3B	^11A, v6B
68	858.947	23/14	^3A𝄪, vvB	A♯, v5B
69	871.579	38/23	^4A𝄪, vB	^A♯, v4B
70	884.211	5/3	B	^^A♯, v3B
71	896.842	42/25	^B, v4C♭	^3A♯, vvB
72	909.474	22/13	^^B, v3C♭	^4A♯, vB
73	922.105		^3B, vvC♭	B
74	934.737	12/7	^4B, vC♭	^B, v4C
75	947.368	19/11	B♯, C♭	^^B, v3C
76	960	40/23	^B♯, v4C	^3B, vvC
77	972.632		^^B♯, v3C	^4B, vC
78	985.263	23/13	^3B♯, vvC	C
79	997.895		^4B♯, vC	^C, v4D♭
80	1010.526		C	^^C, v3D♭
81	1023.158		^C, v4D♭♭	^3C, vvD♭
82	1035.789	20/11	^^C, v3D♭♭	^4C, vD♭
83	1048.421	11/6	^3C, vvD♭♭	^5C, D♭
84	1061.053	24/13	^4C, vD♭♭	^6C, v11D
85	1073.684	13/7	C♯, D♭♭	^7C, v10D
86	1086.316		^C♯, v4D♭	^8C, v9D
87	1098.947		^^C♯, v3D♭	^9C, v8D
88	1111.579	19/10	^3C♯, vvD♭	^10C, v7D
89	1124.211	23/12	^4C♯, vD♭	^11C, v6D
90	1136.842		C𝄪, D♭	C♯, v5D
91	1149.474	35/18	^C𝄪, v4D	^C♯, v4D
92	1162.105		^^C𝄪, v3D	^^C♯, v3D
93	1174.737		^3C𝄪, vvD	^3C♯, vvD
94	1187.368		^4C𝄪, vD	^4C♯, vD
95	1200	2/1	D	D

Music

JUMBLE

• Puget Sound Asleep (2024)