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

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 (%)	+43	+42	+30	-14	+35	+46	-15	-31	+45	-27	+26
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 supports the rank 2 temperaments enneadecal, magus, gorgik, octacot, quinmite, tetracot and trisedodge.

It supports the rank 3 temperaments breed, manwe, octagari, octarod and shrusus.

It provides the optimal patent val for the rank 3 shrusus temperament.

95 factors as 5*19, so it contains both 5edo and 19edo. It is also a dual-fifth tuning.

Intervals

Steps	Cents	Ups and downs notation (dual flat fifth 55\95)	Ups and downs notation (dual sharp fifth 56\95)	Approximate ratios
0	0	D	D	1/1
1	12.6316	↑D, ↓4E♭♭	↑D, ↓4E♭
2	25.2632	↑↑D, ↓3E♭♭	↑↑D, ↓3E♭	66/65, 78/77
3	37.8947	↑3D, ↓↓E♭♭	↑3D, ↓↓E♭	49/48, 50/49
4	50.5263	↑4D, ↓E♭♭	↑4D, ↓E♭	36/35, 65/63
5	63.1579	D♯, E♭♭	↑5D, E♭	26/25, 80/77
6	75.7895	↑D♯, ↓4E♭	↑6D, ↓11E	22/21
7	88.4211	↑↑D♯, ↓3E♭	↑7D, ↓10E	21/20
8	101.053	↑3D♯, ↓↓E♭	↑8D, ↓9E	35/33, 52/49, 55/52
9	113.684	↑4D♯, ↓E♭	↑9D, ↓8E	77/72
10	126.316	D𝄪, E♭	↑10D, ↓7E	14/13
11	138.947	↑D𝄪, ↓4E	↑11D, ↓6E	13/12
12	151.579	↑↑D𝄪, ↓3E	D♯, ↓5E	12/11
13	164.211	↑3D𝄪, ↓↓E	↑D♯, ↓4E	11/10
14	176.842	↑4D𝄪, ↓E	↑↑D♯, ↓3E	72/65
15	189.474	E	↑3D♯, ↓↓E	39/35, 49/44
16	202.105	↑E, ↓4F♭	↑4D♯, ↓E	55/49
17	214.737	↑↑E, ↓3F♭	E
18	227.368	↑3E, ↓↓F♭	↑E, ↓4F	8/7
19	240	↑4E, ↓F♭	↑↑E, ↓3F	55/48, 63/55
20	252.632	E♯, F♭	↑3E, ↓↓F	15/13
21	265.263	↑E♯, ↓4F	↑4E, ↓F	7/6
22	277.895	↑↑E♯, ↓3F	F
23	290.526	↑3E♯, ↓↓F	↑F, ↓4G♭	13/11, 77/65
24	303.158	↑4E♯, ↓F	↑↑F, ↓3G♭	25/21
25	315.789	F	↑3F, ↓↓G♭	6/5
26	328.421	↑F, ↓4G♭♭	↑4F, ↓G♭	40/33
27	341.053	↑↑F, ↓3G♭♭	↑5F, G♭
28	353.684	↑3F, ↓↓G♭♭	↑6F, ↓11G	49/40, 60/49
29	366.316	↑4F, ↓G♭♭	↑7F, ↓10G	26/21
30	378.947	F♯, G♭♭	↑8F, ↓9G
31	391.579	↑F♯, ↓4G♭	↑9F, ↓8G	44/35, 49/39
32	404.211	↑↑F♯, ↓3G♭	↑10F, ↓7G	63/50
33	416.842	↑3F♯, ↓↓G♭	↑11F, ↓6G	14/11, 33/26
34	429.474	↑4F♯, ↓G♭	F♯, ↓5G	50/39, 77/60
35	442.105	F𝄪, G♭	↑F♯, ↓4G
36	454.737	↑F𝄪, ↓4G	↑↑F♯, ↓3G	13/10
37	467.368	↑↑F𝄪, ↓3G	↑3F♯, ↓↓G	55/42, 72/55
38	480	↑3F𝄪, ↓↓G	↑4F♯, ↓G	33/25
39	492.632	↑4F𝄪, ↓G	G	65/49
40	505.263	G	↑G, ↓4A♭
41	517.895	↑G, ↓4A♭♭	↑↑G, ↓3A♭	35/26, 66/49
42	530.526	↑↑G, ↓3A♭♭	↑3G, ↓↓A♭	49/36
43	543.158	↑3G, ↓↓A♭♭	↑4G, ↓A♭	48/35
44	555.789	↑4G, ↓A♭♭	↑5G, A♭	11/8
45	568.421	G♯, A♭♭	↑6G, ↓11A	18/13, 25/18
46	581.053	↑G♯, ↓4A♭	↑7G, ↓10A	7/5
47	593.684	↑↑G♯, ↓3A♭	↑8G, ↓9A	55/39
48	606.316	↑3G♯, ↓↓A♭	↑9G, ↓8A	78/55
49	618.947	↑4G♯, ↓A♭	↑10G, ↓7A	10/7
50	631.579	G𝄪, A♭	↑11G, ↓6A	13/9, 36/25
51	644.211	↑G𝄪, ↓4A	G♯, ↓5A	16/11
52	656.842	↑↑G𝄪, ↓3A	↑G♯, ↓4A	35/24
53	669.474	↑3G𝄪, ↓↓A	↑↑G♯, ↓3A	72/49
54	682.105	↑4G𝄪, ↓A	↑3G♯, ↓↓A	49/33, 52/35, 77/52
55	694.737	A	↑4G♯, ↓A
56	707.368	↑A, ↓4B♭♭	A
57	720	↑↑A, ↓3B♭♭	↑A, ↓4B♭	50/33
58	732.632	↑3A, ↓↓B♭♭	↑↑A, ↓3B♭	55/36
59	745.263	↑4A, ↓B♭♭	↑3A, ↓↓B♭	20/13, 77/50
60	757.895	A♯, B♭♭	↑4A, ↓B♭	65/42
61	770.526	↑A♯, ↓4B♭	↑5A, B♭	39/25
62	783.158	↑↑A♯, ↓3B♭	↑6A, ↓11B	11/7, 52/33
63	795.789	↑3A♯, ↓↓B♭	↑7A, ↓10B
64	808.421	↑4A♯, ↓B♭	↑8A, ↓9B	35/22, 78/49
65	821.053	A𝄪, B♭	↑9A, ↓8B	77/48
66	833.684	↑A𝄪, ↓4B	↑10A, ↓7B	21/13
67	846.316	↑↑A𝄪, ↓3B	↑11A, ↓6B	49/30, 80/49
68	858.947	↑3A𝄪, ↓↓B	A♯, ↓5B
69	871.579	↑4A𝄪, ↓B	↑A♯, ↓4B	33/20
70	884.211	B	↑↑A♯, ↓3B	5/3
71	896.842	↑B, ↓4C♭	↑3A♯, ↓↓B	42/25
72	909.474	↑↑B, ↓3C♭	↑4A♯, ↓B	22/13
73	922.105	↑3B, ↓↓C♭	B
74	934.737	↑4B, ↓C♭	↑B, ↓4C	12/7
75	947.368	B♯, C♭	↑↑B, ↓3C	26/15
76	960	↑B♯, ↓4C	↑3B, ↓↓C
77	972.632	↑↑B♯, ↓3C	↑4B, ↓C	7/4
78	985.263	↑3B♯, ↓↓C	C
79	997.895	↑4B♯, ↓C	↑C, ↓4D♭
80	1010.53	C	↑↑C, ↓3D♭	70/39
81	1023.16	↑C, ↓4D♭♭	↑3C, ↓↓D♭	65/36
82	1035.79	↑↑C, ↓3D♭♭	↑4C, ↓D♭	20/11
83	1048.42	↑3C, ↓↓D♭♭	↑5C, D♭	11/6
84	1061.05	↑4C, ↓D♭♭	↑6C, ↓11D	24/13
85	1073.68	C♯, D♭♭	↑7C, ↓10D	13/7
86	1086.32	↑C♯, ↓4D♭	↑8C, ↓9D
87	1098.95	↑↑C♯, ↓3D♭	↑9C, ↓8D	49/26, 66/35
88	1111.58	↑3C♯, ↓↓D♭	↑10C, ↓7D	40/21
89	1124.21	↑4C♯, ↓D♭	↑11C, ↓6D	21/11
90	1136.84	C𝄪, D♭	C♯, ↓5D	25/13, 77/40
91	1149.47	↑C𝄪, ↓4D	↑C♯, ↓4D	35/18
92	1162.11	↑↑C𝄪, ↓3D	↑↑C♯, ↓3D	49/25
93	1174.74	↑3C𝄪, ↓↓D	↑3C♯, ↓↓D	65/33, 77/39
94	1187.37	↑4C𝄪, ↓D	↑4C♯, ↓D
95	1200	D	D	2/1