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
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← 95ed4 | 97ed4 | 99ed4 → |
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 41/97, 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
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) |
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) |