96ed7/3

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96ed7/3

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Prime factorization	25 × 3
Step size	15.2799¢
Octave	79\96ed7/3 (1207.11¢)
Twelfth	124\96ed7/3 (1894.71¢) (→31\24ed7/3)
Consistency limit	2
Distinct consistency limit	2

96 equal divisions of 7/3 (abbreviated 96ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 96 equal parts of about 15.3⁠ ⁠¢ each. Each step represents a frequency ratio of (7/3)^1/96, or the 96th root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	15.3
2	30.6
3	45.8	37/36
4	61.1	29/28
5	76.4
6	91.7	39/37
7	107	33/31
8	122.2
9	137.5	13/12
10	152.8	12/11
11	168.1	43/39
12	183.4
13	198.6	37/33
14	213.9
15	229.2
16	244.5
17	259.8	36/31, 43/37
18	275	34/29
19	290.3	13/11
20	305.6	37/31, 43/36
21	320.9
22	336.2	17/14
23	351.4
24	366.7
25	382
26	397.3	39/31
27	412.6
28	427.8
29	443.1
30	458.4	30/23, 43/33
31	473.7
32	489
33	504.2
34	519.5
35	534.8
36	550.1
37	565.4	43/31
38	580.6	7/5
39	595.9
40	611.2
41	626.5	33/23
42	641.8	29/20
43	657	19/13
44	672.3	28/19
45	687.6
46	702.9
47	718.2
48	733.4	29/19
49	748.7
50	764
51	779.3
52	794.6	19/12
53	809.8
54	825.1	37/23
55	840.4
56	855.7
57	871
58	886.2	5/3
59	901.5
60	916.8	17/10, 39/23
61	932.1
62	947.4	19/11
63	962.6
64	977.9
65	993.2
66	1008.5	34/19
67	1023.8
68	1039	31/17
69	1054.3
70	1069.6
71	1084.9	43/23
72	1100.2
73	1115.4
74	1130.7
75	1146	33/17
76	1161.3
77	1176.6
78	1191.8
79	1207.1
80	1222.4
81	1237.7
82	1253
83	1268.2
84	1283.5
85	1298.8	36/17
86	1314.1
87	1329.4	28/13, 41/19
88	1344.6	37/17
89	1359.9
90	1375.2	31/14
91	1390.5	29/13
92	1405.8
93	1421
94	1436.3	39/17
95	1451.6
96	1466.9	7/3

Harmonics

Approximation of harmonics in 96ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+7.11	-7.25	-1.05	-5.37	-0.13	-7.25	+6.06	+0.79	+1.74	+4.82	+6.98
	Relative (%)	+46.5	-47.4	-6.9	-35.2	-0.9	-47.4	+39.6	+5.1	+11.4	+31.5	+45.7
Steps (reduced)		79 (79)	124 (28)	157 (61)	182 (86)	203 (11)	220 (28)	236 (44)	249 (57)	261 (69)	272 (80)	282 (90)

Approximation of harmonics in 96ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+5.92	-0.13	+2.66	-2.11	-0.11	-7.38	+5.98	-6.43	+0.79	-3.35	-3.91
	Relative (%)	+38.8	-0.9	+17.4	-13.8	-0.7	-48.3	+39.1	-42.1	+5.1	-21.9	-25.6
Steps (reduced)		291 (3)	299 (11)	307 (19)	314 (26)	321 (33)	327 (39)	334 (46)	339 (51)	345 (57)	350 (62)	355 (67)