102ed7/3

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

← 101ed7/3

102ed7/3

103ed7/3 →

Prime factorization	2 × 3 × 17
Step size	14.3811¢
Octave	83\102ed7/3 (1193.63¢)
Twelfth	132\102ed7/3 (1898.3¢) (→22\17ed7/3)
Consistency limit	3
Distinct consistency limit	3

102 equal divisions of 7/3 (abbreviated 102ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 102 equal parts of about 14.4 ¢ each. Each step represents a frequency ratio of (7/3)^1/102, or the 102nd root of 7/3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	14.381
2	28.762
3	43.143
4	57.524	30/29, 31/30
5	71.905
6	86.287	21/20, 41/39
7	100.668	35/33
8	115.049	31/29
9	129.43
10	143.811
11	158.192	23/21, 34/31
12	172.573	21/19
13	186.954	29/26, 39/35
14	201.335
15	215.716	17/15
16	230.097
17	244.478
18	258.86	43/37
19	273.241	34/29, 41/35
20	287.622	13/11
21	302.003
22	316.384
23	330.765	23/19
24	345.146
25	359.527
26	373.908	41/33
27	388.289
28	402.67	29/23
29	417.052
30	431.433
31	445.814	22/17
32	460.195	30/23, 43/33
33	474.576
34	488.957
35	503.338
36	517.719	27/20, 31/23
37	532.1
38	546.481
39	560.862	29/21
40	575.243
41	589.625	38/27
42	604.006	44/31
43	618.387	10/7
44	632.768
45	647.149	45/31
46	661.53	22/15
47	675.911	31/21, 34/23
48	690.292
49	704.673
50	719.054
51	733.435	26/17, 29/19
52	747.817
53	762.198	45/29
54	776.579
55	790.96	30/19
56	805.341	35/22
57	819.722
58	834.103	34/21
59	848.484	31/19
60	862.865
61	877.246
62	891.627
63	906.009
64	920.39	17/10
65	934.771
66	949.152	45/26
67	963.533
68	977.914
69	992.295	39/22
70	1006.676	34/19
71	1021.057
72	1035.438
73	1049.819
74	1064.2
75	1078.582	41/22
76	1092.963
77	1107.344
78	1121.725	44/23
79	1136.106	27/14
80	1150.487	33/17
81	1164.868
82	1179.249
83	1193.63
84	1208.011
85	1222.392
86	1236.774	45/22
87	1251.155	35/17
88	1265.536
89	1279.917	44/21
90	1294.298	19/9
91	1308.679
92	1323.06
93	1337.441
94	1351.822
95	1366.203	11/5
96	1380.584	20/9
97	1394.965
98	1409.347
99	1423.728	25/11
100	1438.109	39/17
101	1452.49	44/19
102	1466.871	7/3

Harmonics

Approximation of harmonics in 102ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-6.37	-3.65	+1.64	+3.62	+4.36	-3.65	-4.73	+7.08	-2.75	+4.82	-2.01
	Relative (%)	-44.3	-25.4	+11.4	+25.2	+30.3	-25.4	-32.9	+49.2	-19.1	+33.5	-14.0
Steps (reduced)		83 (83)	132 (30)	167 (65)	194 (92)	216 (12)	234 (30)	250 (46)	265 (61)	277 (73)	289 (85)	299 (95)

Approximation of harmonics in 102ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+3.23	+4.36	-0.03	+3.28	-1.00	+0.71	-6.61	+5.26	+7.08	-1.55	-6.60
	Relative (%)	+22.4	+30.3	-0.2	+22.8	-7.0	+4.9	-45.9	+36.6	+49.2	-10.8	-45.9
Steps (reduced)		309 (3)	318 (12)	326 (20)	334 (28)	341 (35)	348 (42)	354 (48)	361 (55)	367 (61)	372 (66)	377 (71)