96ed7

← 95ed7

96ed7

97ed7 →

Prime factorization	25 × 3
Step size	35.0919¢
Octave	34\96ed7 (1193.13¢) (→17\48ed7)
Twelfth	54\96ed7 (1894.96¢) (→9\16ed7)
Consistency limit	6
Distinct consistency limit	6

Division of the 7th harmonic into 96 equal parts (96ed7) is related to the Carlos Gamma, but with the 7/1 rather than the 3/2 being just. The step size is about 35.0919 cents, corresponding to every fifth step of 171edo.

Intervals

Intervals of 96ed7

degree	cents value	corresponding JI intervals	comments
0	0.0000	exact 1/1
1	35.0919	50/49, 49/48
2	70.1839	25/24
3	105.2758	17/16
4	140.3677
5	175.4597
6	210.5516
7	245.6436	144/125
8	280.7355	20/17
9	315.8274	6/5
10	350.9194
11	386.0113	5/4
12	421.1032	51/40
13	456.1952	125/96
14	491.2871
15	526.3790
16	561.4710
17	596.5629	24/17
18	631.6549	36/25
19	666.7468	72/49
20	701.8387	3/2
21	736.9307
22	772.0226	25/16
23	807.1145	51/32
24	842.2065
25	877.2984
26	912.3903
27	947.4823	216/125, 140/81
28	982.5742	30/17
29	1017.6662	9/5
30	1052.7581
31	1087.8500	15/4
32	1122.9420
33	1158.0339	125/64
34	1193.1258
35	1228.2178	128/63
36	1263.3097	1296/625, 56/27
37	1298.4017	36/17
38	1333.4936	54/25
39	1368.5855
40	1403.6775	9/4
41	1438.7694
42	1473.8613	225/96
43	1508.9533
44	1544.0452
45	1579.1371
46	1614.2291
47	1649.3210	70/27
48	1684.4130	119/45, 45/17
49	1719.5049	27/10
50	1754.5968
51	1789.6888	45/16
52	1824.7807
53	1859.8726
54	1894.9646
55	1930.0565	64/21
56	1965.1484	28/9
57	2000.2404
58	2035.3323
59	2070.4243
60	2105.5162	27/8
61	2140.6081
62	2175.7001
63	2210.7920
64	2245.8839
65	2280.9759	28/15
66	2316.0678
67	2351.1597	35/9
68	2386.2517	119/30
69	2421.3436	81/20
70	2456.4356
71	2491.5275
72	2526.6194
73	2961.7114
74	2596.8033	112/25
75	2631.8952	32/7
76	2666.9872	14/3
77	2702.0791
78	2737.1710	175/36
79	2772.2630
80	2807.3549
81	2842.4469
82	2877.5388
83	2912.6307
84	2947.7227	192/35
85	2982.8146	28/5
86	3017.9065	40/7
87	3052.9985	35/6
88	3088.0904	119/20
89	3123.1824
90	3158.2743
91	3193.3662
92	3228.4582
93	3263.5501
94	3298.6420	168/25
95	3333.7340	48/7
96	3368.8259	exact 7/1	harmonic seventh plus two octaves

Harmonics

Approximation of prime harmonics in 96ed7

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-6.9	-7.0	-14.1	+0.0	-10.5	+16.1	+7.9	-9.2	+11.0	-4.3	-14.5
	Relative (%)	-19.6	-19.9	-40.0	+0.0	-29.8	+46.0	+22.6	-26.2	+31.3	-12.3	-41.3
Steps (reduced)		34 (34)	54 (54)	79 (79)	96 (0)	118 (22)	127 (31)	140 (44)	145 (49)	155 (59)	166 (70)	169 (73)

Approximation of prime harmonics in 96ed7

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-5.0	-7.2	+15.6	+2.0	+4.5	-5.7	+6.8	-15.3	-10.4	+11.7	+15.3
	Relative (%)	-14.2	-20.6	+44.4	+5.6	+12.9	-16.2	+19.3	-43.5	-29.6	+33.3	+43.7
Steps (reduced)		178 (82)	183 (87)	186 (90)	190 (94)	196 (4)	201 (9)	203 (11)	207 (15)	210 (18)	212 (20)	216 (24)

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