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	15.1
2	30.2
3	45.4	37/36, 38/37
4	60.5	29/28, 30/29
5	75.6	23/22
6	90.7
7	105.9
8	121	15/14, 44/41
9	136.1
10	151.2
11	166.3
12	181.5
13	196.6	28/25
14	211.7	26/23, 35/31
15	226.8	41/36
16	242
17	257.1	29/25, 36/31
18	272.2	41/35
19	287.3	13/11
20	302.4	31/26, 44/37
21	317.6	6/5
22	332.7	23/19
23	347.8	11/9
24	362.9	37/30
25	378.1
26	393.2
27	408.3	19/15
28	423.4	23/18, 37/29
29	438.5
30	453.7
31	468.8	38/29
32	483.9	37/28, 41/31
33	499
34	514.2	35/26
35	529.3	19/14
36	544.4	26/19
37	559.5
38	574.7
39	589.8
40	604.9	17/12, 44/31
41	620
42	635.1	13/9
43	650.3
44	665.4	22/15, 25/17
45	680.5	37/25
46	695.6
47	710.8
48	725.9	35/23, 38/25
49	741	23/15
50	756.1
51	771.2
52	786.4	41/26
53	801.5	35/22
54	816.6
55	831.7	21/13
56	846.9	31/19
57	862	23/14, 28/17
58	877.1
59	892.2
60	907.3
61	922.5	29/17
62	937.6
63	952.7	26/15
64	967.8
65	983	30/17
66	998.1
67	1013.2
68	1028.3
69	1043.4	42/23
70	1058.6	35/19
71	1073.7	13/7
72	1088.8
73	1103.9	36/19
74	1119.1	21/11
75	1134.2
76	1149.3	35/18
77	1164.4
78	1179.5
79	1194.7
80	1209.8
81	1224.9
82	1240	43/21
83	1255.2	31/15
84	1270.3	25/12
85	1285.4
86	1300.5	36/17
87	1315.6
88	1330.8	41/19
89	1345.9	37/17
90	1361
91	1376.1	31/14
92	1391.3	38/17
93	1406.4
94	1421.5
95	1436.6
96	1451.7	44/19
97	1466.9	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)