102edt

This page is a stub. You can help the Xenharmonic Wiki by expanding it.

← 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	18.6
2	37.3	45/44
3	55.9
4	74.6	23/22
5	93.2	19/18, 39/37
6	111.9
7	130.5	14/13
8	149.2
9	167.8	43/39
10	186.5	39/35
11	205.1
12	223.8	33/29
13	242.4
14	261.1	43/37
15	279.7	27/23
16	298.3	44/37
17	317	6/5
18	335.6	17/14
19	354.3	27/22, 43/35
20	372.9
21	391.6
22	410.2	19/15
23	428.9
24	447.5	22/17, 35/27
25	466.2	17/13
26	484.8	37/28, 41/31, 45/34
27	503.5
28	522.1	23/17
29	540.8	26/19
30	559.4	29/21
31	578
32	596.7
33	615.3
34	634
35	652.6
36	671.3	28/19
37	689.9
38	708.6
39	727.2	35/23, 38/25
40	745.9
41	764.5	14/9
42	783.2	11/7
43	801.8	27/17, 35/22
44	820.5	45/28
45	839.1
46	857.7	23/14
47	876.4
48	895
49	913.7	39/23
50	932.3
51	951	26/15, 45/26
52	969.6
53	988.3	23/13
54	1006.9	34/19
55	1025.6
56	1044.2	42/23
57	1062.9
58	1081.5	28/15, 43/23
59	1100.2	17/9
60	1118.8	21/11
61	1137.4	27/14
62	1156.1	37/19, 41/21
63	1174.7
64	1193.4
65	1212
66	1230.7
67	1249.3	35/17, 37/18
68	1268
69	1286.6
70	1305.3
71	1323.9
72	1342.6
73	1361.2
74	1379.8
75	1398.5
76	1417.1	34/15
77	1435.8	39/17
78	1454.4	44/19
79	1473.1
80	1491.7	45/19
81	1510.4
82	1529
83	1547.7	22/9
84	1566.3	42/17
85	1585	5/2
86	1603.6
87	1622.3	23/9
88	1640.9
89	1659.5
90	1678.2	29/11
91	1696.8
92	1715.5	35/13
93	1734.1
94	1752.8
95	1771.4	39/14
96	1790.1
97	1808.7	37/13
98	1827.4
99	1846
100	1864.7	44/15
101	1883.3
102	1902	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)