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	24.7
2	49.5	34/33, 35/34
3	74.2
4	99
5	123.7	29/27
6	148.5	37/34
7	173.2	21/19
8	197.9	28/25, 37/33
9	222.7	25/22, 33/29
10	247.4
11	272.2	41/35
12	296.9
13	321.6	41/34
14	346.4	11/9
15	371.1	26/21
16	395.9	39/31
17	420.6	37/29
18	445.4
19	470.1	38/29
20	494.8
21	519.6
22	544.3	26/19, 37/27
23	569.1	25/18
24	593.8	38/27
25	618.6
26	643.3	42/29
27	668
28	692.8
29	717.5
30	742.3
31	767	14/9
32	791.8
33	816.5
34	841.2
35	866
36	890.7
37	915.5	39/23
38	940.2
39	964.9
40	989.7	23/13
41	1014.4
42	1039.2	31/17
43	1063.9
44	1088.7
45	1113.4
46	1138.1	27/14
47	1162.9
48	1187.6
49	1212.4
50	1237.1
51	1261.9	29/14
52	1286.6
53	1311.3
54	1336.1
55	1360.8
56	1385.6
57	1410.3
58	1435.1	39/17
59	1459.8
60	1484.5	33/14
61	1509.3
62	1534	17/7
63	1558.8
64	1583.5
65	1608.2	38/15, 43/17
66	1633
67	1657.7
68	1682.5	37/14
69	1707.2
70	1732
71	1756.7
72	1781.4	14/5
73	1806.2
74	1830.9
75	1855.7
76	1880.4
77	1905.2
78	1929.9
79	1954.6	34/11
80	1979.4
81	2004.1	35/11
82	2028.9
83	2053.6
84	2078.4
85	2103.1
86	2127.8
87	2152.6
88	2177.3
89	2202.1
90	2226.8
91	2251.5	11/3
92	2276.3	41/11
93	2301	34/9
94	2325.8
95	2350.5	35/9
96	2375.3
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)