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	20.9
2	41.8
3	62.7
4	83.6
5	104.5
6	125.4	29/27
7	146.3	37/34
8	167.2
9	188.1	39/35
10	209	35/31
11	229.9
12	250.8
13	271.7
14	292.6
15	313.5	6/5
16	334.4
17	355.3	27/22
18	376.2	41/33
19	397.1	34/27, 39/31
20	418
21	438.9
22	459.8
23	480.7	29/22
24	501.6
25	522.5	23/17
26	543.4	37/27
27	564.3	18/13
28	585.2	7/5
29	606.1	27/19
30	627	33/23
31	647.9
32	668.8
33	689.7
34	710.6
35	731.5	29/19
36	752.4	17/11
37	773.3
38	794.2
39	815.1
40	836	34/21
41	856.9
42	877.8
43	898.7	37/22, 42/25
44	919.6
45	940.5	31/18
46	961.4
47	982.3	37/21
48	1003.2	25/14, 41/23
49	1024.1	38/21
50	1045
51	1065.9
52	1086.8
53	1107.7
54	1128.6
55	1149.5	33/17, 35/18
56	1170.4
57	1191.3
58	1212.2
59	1233.1
60	1254	31/15
61	1274.9	23/11
62	1295.8	19/9
63	1316.7	15/7
64	1337.6	13/6
65	1358.5
66	1379.4
67	1400.3
68	1421.2
69	1442.1
70	1463
71	1483.9
72	1504.8	31/13
73	1525.7	41/17
74	1546.6	22/9
75	1567.5
76	1588.4	5/2
77	1609.3	38/15
78	1630.2
79	1651.1
80	1672
81	1692.9
82	1713.8	35/13
83	1734.8
84	1755.7
85	1776.6
86	1797.5
87	1818.4
88	1839.3
89	1860.2
90	1881.1
91	1902	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)