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	20.5
2	40.9
3	61.4	30/29
4	81.8	21/20, 22/21, 43/41
5	102.3	35/33
6	122.7	29/27
7	143.2	25/23, 38/35
8	163.6	11/10
9	184.1	10/9
10	204.5
11	225	33/29
12	245.4	15/13, 38/33
13	265.9	7/6
14	286.3
15	306.8	31/26, 37/31
16	327.2	35/29
17	347.7	11/9
18	368.1	21/17, 26/21
19	388.6
20	409	19/15
21	429.5
22	449.9	35/27
23	470.4	38/29
24	490.8
25	511.3	39/29
26	531.7
27	552.2
28	572.6
29	593.1	31/22, 38/27
30	613.5
31	634	13/9
32	654.4	19/13
33	674.9	31/21
34	695.3
35	715.8
36	736.2	26/17
37	756.7	31/20
38	777.1
39	797.6
40	818
41	838.5
42	858.9	41/25
43	879.4
44	899.8	37/22
45	920.3	17/10
46	940.8	31/18, 43/25
47	961.2
48	981.7	30/17, 37/21
49	1002.1	41/23
50	1022.6
51	1043
52	1063.5	37/20
53	1083.9	43/23
54	1104.4
55	1124.8
56	1145.3
57	1165.7
58	1186.2
59	1206.6
60	1227.1
61	1247.5	35/17, 37/18, 39/19
62	1268	27/13
63	1288.4
64	1308.9
65	1329.3	41/19
66	1349.8
67	1370.2
68	1390.7	29/13, 38/17
69	1411.1
70	1431.6
71	1452
72	1472.5
73	1492.9
74	1513.4
75	1533.8	17/7
76	1554.3	27/11
77	1574.7
78	1595.2
79	1615.6
80	1636.1	18/7
81	1656.5	13/5
82	1677	29/11
83	1697.4
84	1717.9	27/10
85	1738.3	30/11, 41/15
86	1758.8
87	1779.2
88	1799.7
89	1820.2	20/7
90	1840.6	29/10
91	1861.1
92	1881.5
93	1902	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)