91edt

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91edt

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Prime factorization	7 × 13
Step size	20.9006¢
Octave	57\91edt (1191.33¢)
Consistency limit	2
Distinct consistency limit	2

91 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 91edt or 91ed3), is a nonoctave tuning system that divides the interval of 3/1 into 91 equal parts of about 20.9 ¢ each. Each step represents a frequency ratio of 3^1/91, or the 91st root of 3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	20.901
2	41.801
3	62.702
4	83.602
5	104.503
6	125.404	29/27
7	146.304	37/34
8	167.205
9	188.105	39/35
10	209.006	35/31
11	229.907
12	250.807
13	271.708
14	292.608
15	313.509	6/5
16	334.41
17	355.31	27/22
18	376.211	41/33
19	397.111	34/27, 39/31
20	418.012
21	438.913
22	459.813
23	480.714	29/22
24	501.615
25	522.515	23/17
26	543.416	37/27
27	564.316	18/13
28	585.217	7/5
29	606.118	27/19
30	627.018	33/23
31	647.919
32	668.819
33	689.72
34	710.621
35	731.521	29/19
36	752.422	17/11
37	773.322
38	794.223
39	815.124
40	836.024	34/21
41	856.925
42	877.825
43	898.726	37/22, 42/25
44	919.627
45	940.527	31/18
46	961.428
47	982.328	37/21
48	1003.229	25/14, 41/23
49	1024.13	38/21
50	1045.03
51	1065.931
52	1086.831
53	1107.732
54	1128.633
55	1149.533	33/17, 35/18
56	1170.434
57	1191.334
58	1212.235
59	1233.136
60	1254.036	31/15
61	1274.937	23/11
62	1295.837	19/9
63	1316.738	15/7
64	1337.639	13/6
65	1358.539
66	1379.44
67	1400.34
68	1421.241
69	1442.142
70	1463.042
71	1483.943
72	1504.844	31/13
73	1525.744	41/17
74	1546.645	22/9
75	1567.545
76	1588.446	5/2
77	1609.347	38/15
78	1630.247
79	1651.148
80	1672.048
81	1692.949
82	1713.85	35/13
83	1734.75
84	1755.651
85	1776.551
86	1797.452
87	1818.353
88	1839.253
89	1860.154
90	1881.054
91	1901.955	3/1

Harmonics

Approximation of harmonics in 91edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-8.67	+0.00	+3.57	-6.53	-8.67	-3.83	-5.10	+0.00	+5.70	+7.90	+3.57
	Relative (%)	-41.5	+0.0	+17.1	-31.3	-41.5	-18.3	-24.4	+0.0	+27.3	+37.8	+17.1
Steps (reduced)		57 (57)	91 (0)	115 (24)	133 (42)	148 (57)	161 (70)	172 (81)	182 (0)	191 (9)	199 (17)	206 (24)

Approximation of harmonics in 91edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-9.60	+8.41	-6.53	+7.14	+6.69	-8.67	+2.23	-2.96	-3.83	-0.76	+5.88
	Relative (%)	-45.9	+40.2	-31.3	+34.2	+32.0	-41.5	+10.7	-14.2	-18.3	-3.7	+28.1
Steps (reduced)		212 (30)	219 (37)	224 (42)	230 (48)	235 (53)	239 (57)	244 (62)	248 (66)	252 (70)	256 (74)	260 (78)