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	25.8
2	51.6	34/33, 35/34
3	77.4
4	103.2	35/33
5	129
6	154.8
7	180.6	10/9
8	206.5
9	232.3
10	258.1	29/25, 43/37
11	283.9
12	309.7
13	335.5
14	361.3
15	387.1
16	412.9	33/26
17	438.7
18	464.5	17/13
19	490.3
20	516.1	31/23, 35/26
21	541.9	26/19
22	567.7	43/31
23	593.5	38/27
24	619.4	10/7
25	645.2
26	671
27	696.8
28	722.6
29	748.4
30	774.2
31	800
32	825.8
33	851.6
34	877.4
35	903.2
36	929
37	954.8	26/15, 33/19
38	980.6
39	1006.5	34/19
40	1032.3
41	1058.1	35/19
42	1083.9	43/23
43	1109.7	19/10
44	1135.5	27/14
45	1161.3
46	1187.1
47	1212.9
48	1238.7
49	1264.5
50	1290.3
51	1316.1
52	1341.9
53	1367.7
54	1393.5
55	1419.4	25/11, 34/15
56	1445.2
57	1471
58	1496.8
59	1522.6	41/17
60	1548.4	22/9
61	1574.2
62	1600
63	1625.8
64	1651.6	13/5
65	1677.4	29/11
66	1703.2
67	1729	19/7
68	1754.8
69	1780.6
70	1806.5
71	1832.3
72	1858.1
73	1883.9
74	1909.7
75	1935.5
76	1961.3
77	1987.1	41/13
78	2012.9
79	2038.7
80	2064.5	33/10
81	2090.3
82	2116.1	17/5
83	2141.9
84	2167.7	7/2
85	2193.5	39/11
86	2219.4
87	2245.2
88	2271	26/7
89	2296.8
90	2322.6
91	2348.4
92	2374.2
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)