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	Hekts	Approximate ratios
0	0	0	1/1
1	20.9	14.3
2	41.8	28.6
3	62.7	42.9
4	83.6	57.1
5	104.5	71.4
6	125.4	85.7	29/27
7	146.3	100	37/34
8	167.2	114.3
9	188.1	128.6	39/35
10	209	142.9	35/31
11	229.9	157.1
12	250.8	171.4
13	271.7	185.7
14	292.6	200
15	313.5	214.3	6/5
16	334.4	228.6
17	355.3	242.9	27/22
18	376.2	257.1	41/33
19	397.1	271.4	34/27, 39/31
20	418	285.7
21	438.9	300
22	459.8	314.3
23	480.7	328.6	29/22
24	501.6	342.9
25	522.5	357.1	23/17
26	543.4	371.4	37/27
27	564.3	385.7	18/13
28	585.2	400	7/5
29	606.1	414.3	27/19
30	627	428.6	33/23
31	647.9	442.9
32	668.8	457.1
33	689.7	471.4
34	710.6	485.7
35	731.5	500	29/19
36	752.4	514.3	17/11
37	773.3	528.6
38	794.2	542.9
39	815.1	557.1
40	836	571.4	34/21
41	856.9	585.7
42	877.8	600
43	898.7	614.3	37/22, 42/25
44	919.6	628.6
45	940.5	642.9	31/18
46	961.4	657.1
47	982.3	671.4	37/21
48	1003.2	685.7	25/14, 41/23
49	1024.1	700	38/21
50	1045	714.3
51	1065.9	728.6
52	1086.8	742.9
53	1107.7	757.1
54	1128.6	771.4
55	1149.5	785.7	33/17, 35/18
56	1170.4	800
57	1191.3	814.3
58	1212.2	828.6
59	1233.1	842.9
60	1254	857.1	31/15
61	1274.9	871.4	23/11
62	1295.8	885.7	19/9
63	1316.7	900	15/7
64	1337.6	914.3	13/6
65	1358.5	928.6
66	1379.4	942.9
67	1400.3	957.1
68	1421.2	971.4
69	1442.1	985.7
70	1463	1000
71	1483.9	1014.3
72	1504.8	1028.6	31/13
73	1525.7	1042.9	41/17
74	1546.6	1057.1	22/9
75	1567.5	1071.4
76	1588.4	1085.7	5/2
77	1609.3	1100	38/15
78	1630.2	1114.3
79	1651.1	1128.6
80	1672	1142.9
81	1692.9	1157.1
82	1713.8	1171.4	35/13
83	1734.8	1185.7
84	1755.7	1200
85	1776.6	1214.3
86	1797.5	1228.6
87	1818.4	1242.9
88	1839.3	1257.1
89	1860.2	1271.4
90	1881.1	1285.7
91	1902	1300	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)