102edt

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← 101edt

102edt

103edt →

Prime factorization	2 × 3 × 17
Step size	18.6466¢
Octave	64\102edt (1193.38¢) (→32\51edt)
Consistency limit	2
Distinct consistency limit	2

102 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 102edt or 102ed3), is a nonoctave tuning system that divides the interval of 3/1 into 102 equal parts of about 18.6 ¢ each. Each step represents a frequency ratio of 3^1/102, or the 102nd root of 3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	18.647
2	37.293	45/44
3	55.94
4	74.586	23/22
5	93.233	19/18, 39/37
6	111.88
7	130.526	14/13
8	149.173
9	167.82	43/39
10	186.466	39/35
11	205.113
12	223.759	33/29
13	242.406
14	261.053	43/37
15	279.699	27/23
16	298.346	44/37
17	316.993	6/5
18	335.639	17/14
19	354.286	27/22, 43/35
20	372.932
21	391.579
22	410.226	19/15
23	428.872
24	447.519	22/17, 35/27
25	466.165	17/13
26	484.812	37/28, 41/31, 45/34
27	503.459
28	522.105	23/17
29	540.752	26/19
30	559.399	29/21
31	578.045
32	596.692
33	615.338
34	633.985
35	652.632
36	671.278	28/19
37	689.925
38	708.571
39	727.218	35/23, 38/25
40	745.865
41	764.511	14/9
42	783.158	11/7
43	801.805	27/17, 35/22
44	820.451	45/28
45	839.098
46	857.744	23/14
47	876.391
48	895.038
49	913.684	39/23
50	932.331
51	950.978	26/15, 45/26
52	969.624
53	988.271	23/13
54	1006.917	34/19
55	1025.564
56	1044.211	42/23
57	1062.857
58	1081.504	28/15, 43/23
59	1100.15	17/9
60	1118.797	21/11
61	1137.444	27/14
62	1156.09	37/19, 41/21
63	1174.737
64	1193.384
65	1212.03
66	1230.677
67	1249.323	35/17, 37/18
68	1267.97
69	1286.617
70	1305.263
71	1323.91
72	1342.556
73	1361.203
74	1379.85
75	1398.496
76	1417.143	34/15
77	1435.79	39/17
78	1454.436	44/19
79	1473.083
80	1491.729	45/19
81	1510.376
82	1529.023
83	1547.669	22/9
84	1566.316	42/17
85	1584.963	5/2
86	1603.609
87	1622.256	23/9
88	1640.902
89	1659.549
90	1678.196	29/11
91	1696.842
92	1715.489	35/13
93	1734.135
94	1752.782
95	1771.429	39/14
96	1790.075
97	1808.722	37/13
98	1827.369
99	1846.015
100	1864.662	44/15
101	1883.308
102	1901.955	3/1

Harmonics

Approximation of harmonics in 102edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-6.62	+0.00	+5.41	-7.97	-6.62	+6.21	-1.20	+0.00	+4.06	+6.88	+5.41
	Relative (%)	-35.5	+0.0	+29.0	-42.7	-35.5	+33.3	-6.5	+0.0	+21.8	+36.9	+29.0
Steps (reduced)		64 (64)	102 (0)	129 (27)	149 (47)	166 (64)	181 (79)	193 (91)	204 (0)	214 (10)	223 (19)	231 (27)

Approximation of harmonics in 102edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	-0.40	-7.97	-7.82	-0.89	-6.62	-6.99	-2.55	+6.21	+0.26	-2.11
	Relative (%)	-14.1	-2.2	-42.7	-41.9	-4.8	-35.5	-37.5	-13.7	+33.3	+1.4	-11.3
Steps (reduced)		238 (34)	245 (41)	251 (47)	257 (53)	263 (59)	268 (64)	273 (69)	278 (74)	283 (79)	287 (83)	291 (87)