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	15.28
2	30.56
3	45.84	37/36
4	61.12	29/28
5	76.4
6	91.679	39/37
7	106.959	33/31
8	122.239
9	137.519	13/12
10	152.799	12/11
11	168.079	43/39
12	183.359
13	198.639	37/33
14	213.919
15	229.199
16	244.478
17	259.758	36/31, 43/37
18	275.038	34/29
19	290.318	13/11
20	305.598	37/31, 43/36
21	320.878
22	336.158	17/14
23	351.438
24	366.718
25	381.998
26	397.278	39/31
27	412.557
28	427.837
29	443.117
30	458.397	30/23, 43/33
31	473.677
32	488.957
33	504.237
34	519.517
35	534.797
36	550.077
37	565.356	43/31
38	580.636	7/5
39	595.916
40	611.196
41	626.476	33/23
42	641.756	29/20
43	657.036	19/13
44	672.316	28/19
45	687.596
46	702.876
47	718.156
48	733.435	29/19
49	748.715
50	763.995
51	779.275
52	794.555	19/12
53	809.835
54	825.115	37/23
55	840.395
56	855.675
57	870.955
58	886.235	5/3
59	901.514
60	916.794	17/10, 39/23
61	932.074
62	947.354	19/11
63	962.634
64	977.914
65	993.194
66	1008.474	34/19
67	1023.754
68	1039.034	31/17
69	1054.313
70	1069.593
71	1084.873	43/23
72	1100.153
73	1115.433
74	1130.713
75	1145.993	33/17
76	1161.273
77	1176.553
78	1191.833
79	1207.113
80	1222.392
81	1237.672
82	1252.952
83	1268.232
84	1283.512
85	1298.792	36/17
86	1314.072
87	1329.352	28/13, 41/19
88	1344.632	37/17
89	1359.912
90	1375.191	31/14
91	1390.471	29/13
92	1405.751
93	1421.031
94	1436.311	39/17
95	1451.591
96	1466.871	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)