93ed4

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93ed4

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Prime factorization	3 × 31
Step size	25.8065¢
Octave	47\93ed4 (1212.9¢)
Twelfth	74\93ed4 (1909.68¢)
Consistency limit	1
Distinct consistency limit	1

93 equal divisions of the 4th harmonic (abbreviated 93ed4) is a nonoctave tuning system that divides the interval of 4/1 into 93 equal parts of about 25.8 ¢ each. Each step represents a frequency ratio of 4^1/93, or the 93rd root of 4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	25.806
2	51.613	34/33, 35/34
3	77.419
4	103.226	35/33
5	129.032
6	154.839
7	180.645	10/9
8	206.452
9	232.258
10	258.065	29/25, 43/37
11	283.871
12	309.677
13	335.484
14	361.29
15	387.097
16	412.903	33/26
17	438.71
18	464.516	17/13
19	490.323
20	516.129	31/23, 35/26
21	541.935	26/19
22	567.742	43/31
23	593.548	38/27
24	619.355	10/7
25	645.161
26	670.968
27	696.774
28	722.581
29	748.387
30	774.194
31	800
32	825.806
33	851.613
34	877.419
35	903.226
36	929.032
37	954.839	26/15, 33/19
38	980.645
39	1006.452	34/19
40	1032.258
41	1058.065	35/19
42	1083.871	43/23
43	1109.677	19/10
44	1135.484	27/14
45	1161.29
46	1187.097
47	1212.903
48	1238.71
49	1264.516
50	1290.323
51	1316.129
52	1341.935
53	1367.742
54	1393.548
55	1419.355	25/11, 34/15
56	1445.161
57	1470.968
58	1496.774
59	1522.581	41/17
60	1548.387	22/9
61	1574.194
62	1600
63	1625.806
64	1651.613	13/5
65	1677.419	29/11
66	1703.226
67	1729.032	19/7
68	1754.839
69	1780.645
70	1806.452
71	1832.258
72	1858.065
73	1883.871
74	1909.677
75	1935.484
76	1961.29
77	1987.097	41/13
78	2012.903
79	2038.71
80	2064.516	33/10
81	2090.323
82	2116.129	17/5
83	2141.935
84	2167.742	7/2
85	2193.548	39/11
86	2219.355
87	2245.161
88	2270.968	26/7
89	2296.774
90	2322.581
91	2348.387
92	2374.194
93	2400

Harmonics

Approximation of harmonics in 93ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+12.9	+7.7	+0.0	+0.8	-5.2	+11.8	+12.9	-10.4	-12.1	+3.5	+7.7
	Relative (%)	+50.0	+29.9	+0.0	+3.0	-20.1	+45.8	+50.0	-40.2	-47.0	+13.6	+29.9
Steps (reduced)		47 (47)	74 (74)	93 (0)	108 (15)	120 (27)	131 (38)	140 (47)	147 (54)	154 (61)	161 (68)	167 (74)

Approximation of harmonics in 93ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-1.8	-1.1	+8.5	+0.0	-1.7	+2.5	+12.2	+0.8	-6.3	-9.4	-8.9
	Relative (%)	-7.0	-4.2	+33.0	+0.0	-6.7	+9.8	+47.1	+3.0	-24.3	-36.4	-34.6
Steps (reduced)		172 (79)	177 (84)	182 (89)	186 (0)	190 (4)	194 (8)	198 (12)	201 (15)	204 (18)	207 (21)	210 (24)