97ed7/3

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Prime factorization	97 (prime)
Step size	15.1224¢
Octave	79\97ed7/3 (1194.67¢)
Twelfth	126\97ed7/3 (1905.42¢)
Consistency limit	2
Distinct consistency limit	2

97 equal divisions of 7/3 (abbreviated 97ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 97 equal parts of about 15.1 ¢ each. Each step represents a frequency ratio of (7/3)^1/97, or the 97th root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	15.122
2	30.245
3	45.367	37/36, 38/37
4	60.49	29/28, 30/29
5	75.612	23/22
6	90.734
7	105.857
8	120.979	15/14, 44/41
9	136.101
10	151.224
11	166.346
12	181.469
13	196.591	28/25
14	211.713	26/23, 35/31
15	226.836	41/36
16	241.958
17	257.08	29/25, 36/31
18	272.203	41/35
19	287.325	13/11
20	302.448	31/26, 44/37
21	317.57	6/5
22	332.692	23/19
23	347.815	11/9
24	362.937	37/30
25	378.06
26	393.182
27	408.304	19/15
28	423.427	23/18, 37/29
29	438.549
30	453.671
31	468.794	38/29
32	483.916	37/28, 41/31
33	499.039
34	514.161	35/26
35	529.283	19/14
36	544.406	26/19
37	559.528
38	574.65
39	589.773
40	604.895	17/12, 44/31
41	620.018
42	635.14	13/9
43	650.262
44	665.385	22/15, 25/17
45	680.507	37/25
46	695.63
47	710.752
48	725.874	35/23, 38/25
49	740.997	23/15
50	756.119
51	771.241
52	786.364	41/26
53	801.486	35/22
54	816.609
55	831.731	21/13
56	846.853	31/19
57	861.976	23/14, 28/17
58	877.098
59	892.22
60	907.343
61	922.465	29/17
62	937.588
63	952.71	26/15
64	967.832
65	982.955	30/17
66	998.077
67	1013.199
68	1028.322
69	1043.444	42/23
70	1058.567	35/19
71	1073.689	13/7
72	1088.811
73	1103.934	36/19
74	1119.056	21/11
75	1134.179
76	1149.301	35/18
77	1164.423
78	1179.546
79	1194.668
80	1209.79
81	1224.913
82	1240.035	43/21
83	1255.158	31/15
84	1270.28	25/12
85	1285.402
86	1300.525	36/17
87	1315.647
88	1330.769	41/19
89	1345.892	37/17
90	1361.014
91	1376.137	31/14
92	1391.259	38/17
93	1406.381
94	1421.504
95	1436.626
96	1451.749	44/19
97	1466.871	7/3

Harmonics

Approximation of harmonics in 97ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-5.33	+3.46	+4.46	-3.80	-1.87	+3.46	-0.87	+6.93	+5.99	+7.34	-7.20
	Relative (%)	-35.3	+22.9	+29.5	-25.1	-12.3	+22.9	-5.8	+45.8	+39.6	+48.5	-47.6
Steps (reduced)		79 (79)	126 (29)	159 (62)	184 (87)	205 (11)	223 (29)	238 (44)	252 (58)	264 (70)	275 (81)	284 (90)

Approximation of harmonics in 96ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+5.92	-0.13	+2.66	-2.11	-0.11	-7.38	+5.98	-6.43	+0.79	-3.35	-3.91
	Relative (%)	+38.8	-0.9	+17.4	-13.8	-0.7	-48.3	+39.1	-42.1	+5.1	-21.9	-25.6
Steps (reduced)		291 (3)	299 (11)	307 (19)	314 (26)	321 (33)	327 (39)	334 (46)	339 (51)	345 (57)	350 (62)	355 (67)