97ed4

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97ed4

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Prime factorization	97 (prime)
Step size	24.7423¢
Octave	49\97ed4 (1212.37¢)
Twelfth	77\97ed4 (1905.15¢)
Consistency limit	1
Distinct consistency limit	1

97 equal divisions of the 4th harmonic (abbreviated 97ed4) is a nonoctave tuning system that divides the interval of 4/1 into 97 equal parts of about 24.7 ¢ each. Each step represents a frequency ratio of 4^1/97, or the 97th root of 4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	24.742
2	49.485	34/33, 35/34
3	74.227
4	98.969
5	123.711	29/27
6	148.454	37/34
7	173.196	21/19
8	197.938	28/25, 37/33
9	222.68	25/22, 33/29
10	247.423
11	272.165	41/35
12	296.907
13	321.649	41/34
14	346.392	11/9
15	371.134	26/21
16	395.876	39/31
17	420.619	37/29
18	445.361
19	470.103	38/29
20	494.845
21	519.588
22	544.33	26/19, 37/27
23	569.072	25/18
24	593.814	38/27
25	618.557
26	643.299	42/29
27	668.041
28	692.784
29	717.526
30	742.268
31	767.01	14/9
32	791.753
33	816.495
34	841.237
35	865.979
36	890.722
37	915.464	39/23
38	940.206
39	964.948
40	989.691	23/13
41	1014.433
42	1039.175	31/17
43	1063.918
44	1088.66
45	1113.402
46	1138.144	27/14
47	1162.887
48	1187.629
49	1212.371
50	1237.113
51	1261.856	29/14
52	1286.598
53	1311.34
54	1336.082
55	1360.825
56	1385.567
57	1410.309
58	1435.052	39/17
59	1459.794
60	1484.536	33/14
61	1509.278
62	1534.021	17/7
63	1558.763
64	1583.505
65	1608.247	38/15, 43/17
66	1632.99
67	1657.732
68	1682.474	37/14
69	1707.216
70	1731.959
71	1756.701
72	1781.443	14/5
73	1806.186
74	1830.928
75	1855.67
76	1880.412
77	1905.155
78	1929.897
79	1954.639	34/11
80	1979.381
81	2004.124	35/11
82	2028.866
83	2053.608
84	2078.351
85	2103.093
86	2127.835
87	2152.577
88	2177.32
89	2202.062
90	2226.804
91	2251.546	11/3
92	2276.289	41/11
93	2301.031	34/9
94	2325.773
95	2350.515	35/9
96	2375.258
97	2400

Harmonics

Approximation of harmonics in 97ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+12.4	+3.2	+0.0	+9.6	-9.2	-3.9	+12.4	+6.4	-2.8	+5.4	+3.2
	Relative (%)	+50.0	+12.9	+0.0	+38.6	-37.1	-15.7	+50.0	+25.9	-11.4	+21.8	+12.9
Steps (reduced)		49 (49)	77 (77)	97 (0)	113 (16)	125 (28)	136 (39)	146 (49)	154 (57)	161 (64)	168 (71)	174 (77)

Approximation of harmonics in 97ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-11.7	+8.5	-12.0	+0.0	-6.0	-6.0	-0.6	+9.6	-0.7	-7.0	-9.7
	Relative (%)	-47.1	+34.3	-48.4	+0.0	-24.2	-24.1	-2.4	+38.6	-2.7	-28.2	-39.3
Steps (reduced)		179 (82)	185 (88)	189 (92)	194 (0)	198 (4)	202 (8)	206 (12)	210 (16)	213 (19)	216 (22)	219 (25)