102edt

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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	Hekts	Approximate ratios
0	0	0	1/1
1	18.6	12.7
2	37.3	25.5	45/44
3	55.9	38.2
4	74.6	51	23/22
5	93.2	63.7	19/18, 39/37
6	111.9	76.5
7	130.5	89.2	14/13
8	149.2	102
9	167.8	114.7	43/39
10	186.5	127.5	39/35
11	205.1	140.2
12	223.8	152.9	33/29
13	242.4	165.7
14	261.1	178.4	43/37
15	279.7	191.2	27/23
16	298.3	203.9	44/37
17	317	216.7	6/5
18	335.6	229.4	17/14
19	354.3	242.2	27/22, 43/35
20	372.9	254.9
21	391.6	267.6
22	410.2	280.4	19/15
23	428.9	293.1
24	447.5	305.9	22/17, 35/27
25	466.2	318.6	17/13
26	484.8	331.4	37/28, 41/31, 45/34
27	503.5	344.1
28	522.1	356.9	23/17
29	540.8	369.6	26/19
30	559.4	382.4	29/21
31	578	395.1
32	596.7	407.8
33	615.3	420.6
34	634	433.3
35	652.6	446.1
36	671.3	458.8	28/19
37	689.9	471.6
38	708.6	484.3
39	727.2	497.1	35/23, 38/25
40	745.9	509.8
41	764.5	522.5	14/9
42	783.2	535.3	11/7
43	801.8	548	27/17, 35/22
44	820.5	560.8	45/28
45	839.1	573.5
46	857.7	586.3	23/14
47	876.4	599
48	895	611.8
49	913.7	624.5	39/23
50	932.3	637.3
51	951	650	26/15, 45/26
52	969.6	662.7
53	988.3	675.5	23/13
54	1006.9	688.2	34/19
55	1025.6	701
56	1044.2	713.7	42/23
57	1062.9	726.5
58	1081.5	739.2	28/15, 43/23
59	1100.2	752	17/9
60	1118.8	764.7	21/11
61	1137.4	777.5	27/14
62	1156.1	790.2	37/19, 41/21
63	1174.7	802.9
64	1193.4	815.7
65	1212	828.4
66	1230.7	841.2
67	1249.3	853.9	35/17, 37/18
68	1268	866.7
69	1286.6	879.4
70	1305.3	892.2
71	1323.9	904.9
72	1342.6	917.6
73	1361.2	930.4
74	1379.8	943.1
75	1398.5	955.9
76	1417.1	968.6	34/15
77	1435.8	981.4	39/17
78	1454.4	994.1	44/19
79	1473.1	1006.9
80	1491.7	1019.6	45/19
81	1510.4	1032.4
82	1529	1045.1
83	1547.7	1057.8	22/9
84	1566.3	1070.6	42/17
85	1585	1083.3	5/2
86	1603.6	1096.1
87	1622.3	1108.8	23/9
88	1640.9	1121.6
89	1659.5	1134.3
90	1678.2	1147.1	29/11
91	1696.8	1159.8
92	1715.5	1172.5	35/13
93	1734.1	1185.3
94	1752.8	1198
95	1771.4	1210.8	39/14
96	1790.1	1223.5
97	1808.7	1236.3	37/13
98	1827.4	1249
99	1846	1261.8
100	1864.7	1274.5	44/15
101	1883.3	1287.3
102	1902	1300	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)