93edt

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93edt

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Prime factorization	3 × 31
Step size	20.4511¢
Octave	59\93edt (1206.62¢)
Consistency limit	2
Distinct consistency limit	2

93 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 93edt or 93ed3), is a nonoctave tuning system that divides the interval of 3/1 into 93 equal parts of about 20.5 ¢ each. Each step represents a frequency ratio of 3^1/93, or the 93rd root of 3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	20.451
2	40.902
3	61.353	30/29
4	81.805	21/20, 22/21, 43/41
5	102.256	35/33
6	122.707	29/27
7	143.158	25/23, 38/35
8	163.609	11/10
9	184.06	10/9
10	204.511
11	224.962	33/29
12	245.414	15/13, 38/33
13	265.865	7/6
14	286.316
15	306.767	31/26, 37/31
16	327.218	35/29
17	347.669	11/9
18	368.12	21/17, 26/21
19	388.571
20	409.023	19/15
21	429.474
22	449.925	35/27
23	470.376	38/29
24	490.827
25	511.278	39/29
26	531.729
27	552.18
28	572.632
29	593.083	31/22, 38/27
30	613.534
31	633.985	13/9
32	654.436	19/13
33	674.887	31/21
34	695.338
35	715.79
36	736.241	26/17
37	756.692	31/20
38	777.143
39	797.594
40	818.045
41	838.496
42	858.947	41/25
43	879.399
44	899.85	37/22
45	920.301	17/10
46	940.752	31/18, 43/25
47	961.203
48	981.654	30/17, 37/21
49	1002.105	41/23
50	1022.556
51	1043.008
52	1063.459	37/20
53	1083.91	43/23
54	1104.361
55	1124.812
56	1145.263
57	1165.714
58	1186.165
59	1206.617
60	1227.068
61	1247.519	35/17, 37/18, 39/19
62	1267.97	27/13
63	1288.421
64	1308.872
65	1329.323	41/19
66	1349.775
67	1370.226
68	1390.677	29/13, 38/17
69	1411.128
70	1431.579
71	1452.03
72	1472.481
73	1492.932
74	1513.384
75	1533.835	17/7
76	1554.286	27/11
77	1574.737
78	1595.188
79	1615.639
80	1636.09	18/7
81	1656.541	13/5
82	1676.993	29/11
83	1697.444
84	1717.895	27/10
85	1738.346	30/11, 41/15
86	1758.797
87	1779.248
88	1799.699
89	1820.15	20/7
90	1840.602	29/10
91	1861.053
92	1881.504
93	1901.955	3/1

Harmonics

Approximation of harmonics in 93edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+6.62	+0.00	-7.22	-4.96	+6.62	+5.61	-0.60	+0.00	+1.66	+0.26	-7.22
	Relative (%)	+32.4	+0.0	-35.3	-24.3	+32.4	+27.4	-2.9	+0.0	+8.1	+1.3	-35.3
Steps (reduced)		59 (59)	93 (0)	117 (24)	136 (43)	152 (59)	165 (72)	176 (83)	186 (0)	195 (9)	203 (17)	210 (24)

Approximation of harmonics in 93edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	-8.22	-4.96	+6.02	+3.32	+6.62	-5.18	+8.27	+5.61	+6.88	-8.73
	Relative (%)	-12.9	-40.2	-24.3	+29.4	+16.2	+32.4	-25.3	+40.5	+27.4	+33.6	-42.7
Steps (reduced)		217 (31)	223 (37)	229 (43)	235 (49)	240 (54)	245 (59)	249 (63)	254 (68)	258 (72)	262 (76)	265 (79)