97edt

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97edt

98edt →

Prime factorization	97 (prime)
Step size	19.6078¢
Octave	61\97edt (1196.07¢)
Consistency limit	5
Distinct consistency limit	5

Division of the third harmonic into 97 equal parts (97EDT) is related to 61 edo, but with the 3/1 rather than the 2/1 being just; in fact, 97edt is close to 61.2002edo, meaning that its step is very accurately represented by 5 steps of 306edo. The octave is about 3.9252 cents compressed and the step size is about 19.6078 cents.

Lookalikes: 61edo, 141ed5, 158ed6

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	19.608
2	39.216	42/41, 43/42, 44/43
3	58.823	29/28, 30/29, 31/30
4	78.431	22/21, 23/22
5	98.039	18/17, 37/35
6	117.647	15/14, 31/29
7	137.254	13/12
8	156.862	23/21
9	176.47	31/28, 41/37
10	196.078	28/25, 37/33
11	215.686	17/15, 43/38
12	235.293	39/34
13	254.901	22/19, 29/25
14	274.509	34/29, 41/35
15	294.117
16	313.725	6/5
17	333.332	23/19
18	352.94	27/22, 38/31
19	372.548	31/25, 36/29
20	392.156
21	411.763	19/15
22	431.371
23	450.979	35/27
24	470.587
25	490.195
26	509.802
27	529.41	19/14
28	549.018
29	568.626	25/18, 43/31
30	588.234
31	607.841	27/19, 44/31
32	627.449	33/23
33	647.057
34	666.665	25/17
35	686.272
36	705.88
37	725.488	35/23, 38/25, 41/27
38	745.096	20/13, 43/28
39	764.704	14/9
40	784.311	11/7
41	803.919	35/22, 43/27
42	823.527	29/18, 37/23
43	843.135	44/27
44	862.742	28/17
45	882.35	5/3
46	901.958	37/22
47	921.566
48	941.174	31/18, 43/25
49	960.781
50	980.389	37/21, 44/25
51	999.997	41/23
52	1019.605	9/5
53	1039.213	31/17
54	1058.82	35/19
55	1078.428	28/15, 41/22
56	1098.036
57	1117.644	21/11
58	1137.251	27/14
59	1156.859	39/20, 41/21
60	1176.467
61	1196.075
62	1215.683
63	1235.29
64	1254.898	31/15
65	1274.506	23/11
66	1294.114	19/9
67	1313.721
68	1333.329	41/19
69	1352.937
70	1372.545	42/19
71	1392.153	38/17
72	1411.76	43/19
73	1431.368
74	1450.976
75	1470.584
76	1490.192
77	1509.799	43/18
78	1529.407	29/12
79	1549.015	22/9
80	1568.623
81	1588.23	5/2
82	1607.838	38/15, 43/17
83	1627.446
84	1647.054	44/17
85	1666.662	34/13
86	1686.269
87	1705.877
88	1725.485
89	1745.093
90	1764.701	36/13
91	1784.308	14/5
92	1803.916	17/6
93	1823.524	43/15
94	1843.132	29/10
95	1862.739	41/14, 44/15
96	1882.347
97	1901.955	3/1

Harmonics

Approximation of prime harmonics in 97edt

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-3.93	+0.00	-2.01	+3.71	+5.53	-9.17	-3.01	+0.51	+3.08	-6.07	-3.88
	Relative (%)	-20.0	+0.0	-10.2	+18.9	+28.2	-46.8	-15.3	+2.6	+15.7	-30.9	-19.8
Steps (reduced)		61 (61)	97 (0)	142 (45)	172 (75)	212 (18)	226 (32)	250 (56)	260 (66)	277 (83)	297 (6)	303 (12)

Approximation of prime harmonics in 97edt

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+3.54	+2.29	-1.73	+1.14	+8.83	-0.37	+0.74	-4.82	-7.17	+3.56	+4.07
	Relative (%)	+18.0	+11.7	-8.8	+5.8	+45.0	-1.9	+3.8	-24.6	-36.6	+18.2	+20.7
Steps (reduced)		319 (28)	328 (37)	332 (41)	340 (49)	351 (60)	360 (69)	363 (72)	371 (80)	376 (85)	379 (88)	386 (95)

Music

• Imagination by Francium