101ed7/3

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

← 100ed7/3

101ed7/3

102ed7/3 →

Prime factorization	101 (prime)
Step size	14.5235¢
Octave	83\101ed7/3 (1205.45¢)
Twelfth	131\101ed7/3 (1902.58¢)
Consistency limit	3
Distinct consistency limit	3

101 equal divisions of 7/3 (abbreviated 101ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 101 equal parts of about 14.5 ¢ each. Each step represents a frequency ratio of (7/3)^1/101, or the 101st root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	14.523
2	29.047
3	43.57	39/38, 42/41
4	58.094
5	72.617
6	87.141	41/39
7	101.664	35/33
8	116.188	31/29
9	130.711	14/13, 41/38
10	145.235	25/23
11	159.758	23/21, 45/41
12	174.282	21/19
13	188.805	39/35
14	203.329
15	217.852	17/15
16	232.376
17	246.899	15/13
18	261.423	43/37
19	275.946	27/23, 41/35
20	290.469	13/11, 45/38
21	304.993	37/31
22	319.516
23	334.04	17/14
24	348.563	11/9
25	363.087
26	377.61	41/33
27	392.134
28	406.657
29	421.181	37/29
30	435.704	9/7
31	450.228	35/27
32	464.751	17/13
33	479.275	33/25
34	493.798
35	508.322
36	522.845	23/17
37	537.369	15/11
38	551.892
39	566.415	25/18, 43/31
40	580.939	7/5
41	595.462
42	609.986	27/19
43	624.509	33/23
44	639.033	13/9
45	653.556
46	668.08	25/17
47	682.603	43/29
48	697.127
49	711.65
50	726.174	35/23, 38/25
51	740.697	23/15
52	755.221	17/11
53	769.744	39/25
54	784.268	11/7
55	798.791	27/17
56	813.315
57	827.838	21/13
58	842.362
59	856.885	41/25
60	871.408	38/23
61	885.932	5/3
62	900.455	42/25
63	914.979	39/23
64	929.502
65	944.026	19/11
66	958.549
67	973.073
68	987.596	23/13
69	1002.12	25/14, 41/23
70	1016.643	9/5
71	1031.167
72	1045.69
73	1060.214
74	1074.737
75	1089.261
76	1103.784
77	1118.308	21/11
78	1132.831	25/13
79	1147.354	33/17
80	1161.878	45/23
81	1176.401
82	1190.925
83	1205.448
84	1219.972
85	1234.495
86	1249.019	35/17
87	1263.542	27/13
88	1278.066	23/11
89	1292.589	19/9
90	1307.113
91	1321.636	15/7
92	1336.16	13/6
93	1350.683
94	1365.207	11/5
95	1379.73
96	1394.254	38/17
97	1408.777
98	1423.3	25/11, 41/18
99	1437.824	39/17
100	1452.347
101	1466.871	7/3

Harmonics

Approximation of harmonics in 101ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+5.45	+0.62	-3.63	+2.19	+6.07	+0.62	+1.82	+1.24	-6.88	+2.40	-3.01
	Relative (%)	+37.5	+4.3	-25.0	+15.1	+41.8	+4.3	+12.5	+8.5	-47.4	+16.5	-20.7
Steps (reduced)		83 (83)	131 (30)	165 (64)	192 (91)	214 (12)	232 (30)	248 (46)	262 (60)	274 (72)	286 (84)	296 (94)

Approximation of harmonics in 101ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+3.66	+6.07	+2.81	-7.25	+3.98	+6.69	+0.23	-1.43	+1.24	-6.68	+3.51
	Relative (%)	+25.2	+41.8	+19.4	-49.9	+27.4	+46.1	+1.6	-9.9	+8.5	-46.0	+24.1
Steps (reduced)		306 (3)	315 (12)	323 (20)	330 (27)	338 (35)	345 (42)	351 (48)	357 (54)	363 (60)	368 (65)	374 (71)