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	26.374
2	52.747	35/34
3	79.121	22/21, 23/22
4	105.495	33/31
5	131.868	41/38
6	158.242	23/21
7	184.615
8	210.989	26/23
9	237.363	31/27
10	263.736
11	290.11	13/11
12	316.484	6/5
13	342.857
14	369.231	26/21
15	395.604	39/31
16	421.978	23/18, 37/29
17	448.352	22/17
18	474.725
19	501.099
20	527.473
21	553.846
22	580.22	7/5
23	606.593	27/19
24	632.967	36/25
25	659.341	19/13
26	685.714
27	712.088
28	738.462	23/15
29	764.835
30	791.209	41/26
31	817.582
32	843.956
33	870.33	38/23
34	896.703	42/25
35	923.077	29/17
36	949.451
37	975.824
38	1002.198	25/14, 41/23
39	1028.571	38/21
40	1054.945
41	1081.319
42	1107.692
43	1134.066
44	1160.44	41/21
45	1186.813
46	1213.187
47	1239.56
48	1265.934	27/13
49	1292.308	19/9
50	1318.681	15/7
51	1345.055	37/17
52	1371.429
53	1397.802
54	1424.176	41/18
55	1450.549
56	1476.923
57	1503.297	31/13
58	1529.67
59	1556.044	27/11
60	1582.418
61	1608.791	38/15
62	1635.165	18/7
63	1661.538
64	1687.912
65	1714.286
66	1740.659	41/15
67	1767.033
68	1793.407	31/11
69	1819.78
70	1846.154
71	1872.527
72	1898.901
73	1925.275
74	1951.648
75	1978.022
76	2004.396
77	2030.769
78	2057.143	23/7
79	2083.516
80	2109.89
81	2136.264
82	2162.637
83	2189.011	39/11
84	2215.385	18/5
85	2241.758
86	2268.132
87	2294.505
88	2320.879
89	2347.253
90	2373.626
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)