91ed4

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91ed4

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Prime factorization	7 × 13
Step size	26.3736¢
Octave	46\91ed4 (1213.19¢)
Twelfth	72\91ed4 (1898.9¢)
Consistency limit	1
Distinct consistency limit	1

91 equal divisions of the 4th harmonic (abbreviated 91ed4) is a nonoctave tuning system that divides the interval of 4/1 into 91 equal parts of about 26.4 ¢ each. Each step represents a frequency ratio of 4^1/91, or the 91st root of 4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	26.4
2	52.7	35/34
3	79.1	22/21, 23/22
4	105.5	33/31
5	131.9	41/38
6	158.2	23/21
7	184.6
8	211	26/23
9	237.4	31/27
10	263.7
11	290.1	13/11
12	316.5	6/5
13	342.9
14	369.2	26/21
15	395.6	39/31
16	422	23/18, 37/29
17	448.4	22/17
18	474.7
19	501.1
20	527.5
21	553.8
22	580.2	7/5
23	606.6	27/19
24	633	36/25
25	659.3	19/13
26	685.7
27	712.1
28	738.5	23/15
29	764.8
30	791.2	41/26
31	817.6
32	844
33	870.3	38/23
34	896.7	42/25
35	923.1	29/17
36	949.5
37	975.8
38	1002.2	25/14, 41/23
39	1028.6	38/21
40	1054.9
41	1081.3
42	1107.7
43	1134.1
44	1160.4	41/21
45	1186.8
46	1213.2
47	1239.6
48	1265.9	27/13
49	1292.3	19/9
50	1318.7	15/7
51	1345.1	37/17
52	1371.4
53	1397.8
54	1424.2	41/18
55	1450.5
56	1476.9
57	1503.3	31/13
58	1529.7
59	1556	27/11
60	1582.4
61	1608.8	38/15
62	1635.2	18/7
63	1661.5
64	1687.9
65	1714.3
66	1740.7	41/15
67	1767
68	1793.4	31/11
69	1819.8
70	1846.2
71	1872.5
72	1898.9
73	1925.3
74	1951.6
75	1978
76	2004.4
77	2030.8
78	2057.1	23/7
79	2083.5
80	2109.9
81	2136.3
82	2162.6
83	2189	39/11
84	2215.4	18/5
85	2241.8
86	2268.1
87	2294.5
88	2320.9
89	2347.3
90	2373.6
91	2400

Harmonics

Approximation of harmonics in 91ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+13.2	-3.1	+0.0	+9.3	+10.1	+7.0	+13.2	-6.1	-3.9	-10.7	-3.1
	Relative (%)	+50.0	-11.6	+0.0	+35.2	+38.4	+26.5	+50.0	-23.2	-14.8	-40.4	-11.6
Steps (reduced)		46 (46)	72 (72)	91 (0)	106 (15)	118 (27)	128 (37)	137 (46)	144 (53)	151 (60)	157 (66)	163 (72)

Approximation of harmonics in 91ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-9.8	-6.2	+6.2	+0.0	+0.5	+7.1	-7.4	+9.3	+3.9	+2.5	+4.7
	Relative (%)	-37.0	-23.5	+23.6	+0.0	+2.0	+26.8	-28.1	+35.2	+15.0	+9.6	+17.8
Steps (reduced)		168 (77)	173 (82)	178 (87)	182 (0)	186 (4)	190 (8)	193 (11)	197 (15)	200 (18)	203 (21)	206 (24)