93ed7/3

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93ed7/3

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Prime factorization	3 × 31
Step size	15.7728¢
Octave	76\93ed7/3 (1198.73¢) (semiconvergent)
Twelfth	121\93ed7/3 (1908.51¢)
Consistency limit	3
Distinct consistency limit	3

93 equal divisions of 7/3 (abbreviated 93ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 93 equal parts of about 15.8 ¢ each. Each step represents a frequency ratio of (7/3)^1/93, or the 93rd root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	15.773
2	31.546
3	47.318	36/35, 38/37
4	63.091	29/28
5	78.864	23/22
6	94.637
7	110.41	33/31
8	126.182	14/13, 43/40
9	141.955
10	157.728	34/31
11	173.501
12	189.274	29/26, 39/35
13	205.046
14	220.819
15	236.592
16	252.365	22/19, 37/32
17	268.138	7/6
18	283.91	20/17, 33/28
19	299.683	19/16, 25/21
20	315.456	6/5
21	331.229	23/19, 40/33
22	347.002
23	362.775
24	378.547
25	394.32
26	410.093	33/26
27	425.866
28	441.639	31/24, 40/31
29	457.411	43/33
30	473.184
31	488.957
32	504.73
33	520.503
34	536.275
35	552.048	11/8
36	567.821	25/18, 43/31
37	583.594	7/5
38	599.367	24/17, 41/29
39	615.139	10/7
40	630.912	23/16, 36/25
41	646.685	16/11
42	662.458	41/28
43	678.231	34/23
44	694.003
45	709.776
46	725.549
47	741.322	43/28
48	757.095	31/20
49	772.867
50	788.64	41/26
51	804.413
52	820.186
53	835.959
54	851.731
55	867.504	33/20, 38/23
56	883.277	5/3
57	899.05	37/22, 42/25
58	914.823
59	930.596	12/7
60	946.368	19/11
61	962.141
62	977.914
63	993.687
64	1009.46	34/19, 43/24
65	1025.232
66	1041.005	31/17
67	1056.778
68	1072.551	13/7
69	1088.324
70	1104.096
71	1119.869
72	1135.642
73	1151.415	35/18, 37/19
74	1167.188
75	1182.96
76	1198.733	2/1
77	1214.506
78	1230.279
79	1246.052
80	1261.824	29/14
81	1277.597	23/11
82	1293.37
83	1309.143
84	1324.916	43/20
85	1340.688	13/6
86	1356.461
87	1372.234
88	1388.007	29/13
89	1403.78
90	1419.552
91	1435.325
92	1451.098	37/16
93	1466.871	7/3

Harmonics

Approximation of harmonics in 93ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-1.27	+6.55	-2.53	+5.47	+5.29	+6.55	-3.80	-2.66	+4.21	-3.07	+4.02
	Relative (%)	-8.0	+41.6	-16.1	+34.7	+33.5	+41.6	-24.1	-16.9	+26.7	-19.5	+25.5
Steps (reduced)		76 (76)	121 (28)	152 (59)	177 (84)	197 (11)	214 (28)	228 (42)	241 (55)	253 (67)	263 (77)	273 (87)

Approximation of harmonics in 93ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+7.40	+5.29	-3.75	-5.07	+0.39	-3.93	-2.90	+2.94	-2.66	-4.34	-2.43
	Relative (%)	+46.9	+33.5	-23.7	-32.1	+2.5	-24.9	-18.4	+18.6	-16.9	-27.5	-15.4
Steps (reduced)		282 (3)	290 (11)	297 (18)	304 (25)	311 (32)	317 (38)	323 (44)	329 (50)	334 (55)	339 (60)	344 (65)