101ed7/3

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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	14.5
2	29
3	43.6	39/38, 42/41
4	58.1
5	72.6
6	87.1	41/39
7	101.7	35/33
8	116.2	31/29
9	130.7	14/13, 41/38
10	145.2	25/23
11	159.8	23/21, 45/41
12	174.3	21/19
13	188.8	39/35
14	203.3
15	217.9	17/15
16	232.4
17	246.9	15/13
18	261.4	43/37
19	275.9	27/23, 41/35
20	290.5	13/11, 45/38
21	305	37/31
22	319.5
23	334	17/14
24	348.6	11/9
25	363.1
26	377.6	41/33
27	392.1
28	406.7
29	421.2	37/29
30	435.7	9/7
31	450.2	35/27
32	464.8	17/13
33	479.3	33/25
34	493.8
35	508.3
36	522.8	23/17
37	537.4	15/11
38	551.9
39	566.4	25/18, 43/31
40	580.9	7/5
41	595.5
42	610	27/19
43	624.5	33/23
44	639	13/9
45	653.6
46	668.1	25/17
47	682.6	43/29
48	697.1
49	711.7
50	726.2	35/23, 38/25
51	740.7	23/15
52	755.2	17/11
53	769.7	39/25
54	784.3	11/7
55	798.8	27/17
56	813.3
57	827.8	21/13
58	842.4
59	856.9	41/25
60	871.4	38/23
61	885.9	5/3
62	900.5	42/25
63	915	39/23
64	929.5
65	944	19/11
66	958.5
67	973.1
68	987.6	23/13
69	1002.1	25/14, 41/23
70	1016.6	9/5
71	1031.2
72	1045.7
73	1060.2
74	1074.7
75	1089.3
76	1103.8
77	1118.3	21/11
78	1132.8	25/13
79	1147.4	33/17
80	1161.9	45/23
81	1176.4
82	1190.9
83	1205.4
84	1220
85	1234.5
86	1249	35/17
87	1263.5	27/13
88	1278.1	23/11
89	1292.6	19/9
90	1307.1
91	1321.6	15/7
92	1336.2	13/6
93	1350.7
94	1365.2	11/5
95	1379.7
96	1394.3	38/17
97	1408.8
98	1423.3	25/11, 41/18
99	1437.8	39/17
100	1452.3
101	1466.9	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)