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	Hekts	Approximate ratios
0	0	0	1/1
1	20.5	14
2	40.9	28
3	61.4	41.9	30/29
4	81.8	55.9	21/20, 22/21, 43/41
5	102.3	69.9	35/33
6	122.7	83.9	29/27
7	143.2	97.8	25/23, 38/35
8	163.6	111.8	11/10
9	184.1	125.8	10/9
10	204.5	139.8
11	225	153.8	33/29
12	245.4	167.7	15/13, 38/33
13	265.9	181.7	7/6
14	286.3	195.7
15	306.8	209.7	31/26, 37/31
16	327.2	223.7	35/29
17	347.7	237.6	11/9
18	368.1	251.6	21/17, 26/21
19	388.6	265.6
20	409	279.6	19/15
21	429.5	293.5
22	449.9	307.5	35/27
23	470.4	321.5	38/29
24	490.8	335.5
25	511.3	349.5	39/29
26	531.7	363.4
27	552.2	377.4
28	572.6	391.4
29	593.1	405.4	31/22, 38/27
30	613.5	419.4
31	634	433.3	13/9
32	654.4	447.3	19/13
33	674.9	461.3	31/21
34	695.3	475.3
35	715.8	489.2
36	736.2	503.2	26/17
37	756.7	517.2	31/20
38	777.1	531.2
39	797.6	545.2
40	818	559.1
41	838.5	573.1
42	858.9	587.1	41/25
43	879.4	601.1
44	899.8	615.1	37/22
45	920.3	629	17/10
46	940.8	643	31/18, 43/25
47	961.2	657
48	981.7	671	30/17, 37/21
49	1002.1	684.9	41/23
50	1022.6	698.9
51	1043	712.9
52	1063.5	726.9	37/20
53	1083.9	740.9	43/23
54	1104.4	754.8
55	1124.8	768.8
56	1145.3	782.8
57	1165.7	796.8
58	1186.2	810.8
59	1206.6	824.7
60	1227.1	838.7
61	1247.5	852.7	35/17, 37/18, 39/19
62	1268	866.7	27/13
63	1288.4	880.6
64	1308.9	894.6
65	1329.3	908.6	41/19
66	1349.8	922.6
67	1370.2	936.6
68	1390.7	950.5	29/13, 38/17
69	1411.1	964.5
70	1431.6	978.5
71	1452	992.5
72	1472.5	1006.5
73	1492.9	1020.4
74	1513.4	1034.4
75	1533.8	1048.4	17/7
76	1554.3	1062.4	27/11
77	1574.7	1076.3
78	1595.2	1090.3
79	1615.6	1104.3
80	1636.1	1118.3	18/7
81	1656.5	1132.3	13/5
82	1677	1146.2	29/11
83	1697.4	1160.2
84	1717.9	1174.2	27/10
85	1738.3	1188.2	30/11, 41/15
86	1758.8	1202.2
87	1779.2	1216.1
88	1799.7	1230.1
89	1820.2	1244.1	20/7
90	1840.6	1258.1	29/10
91	1861.1	1272
92	1881.5	1286
93	1902	1300	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)