96edt

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96edt

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Prime factorization	25 × 3
Step size	19.812¢
Octave	61\96edt (1208.53¢)
Consistency limit	2
Distinct consistency limit	2

96 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 96edt or 96ed3), is a nonoctave tuning system that divides the interval of 3/1 into 96 equal parts of about 19.8 ¢ each. Each step represents a frequency ratio of 3^1/96, or the 96th root of 3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	19.8
2	39.6	42/41, 43/42
3	59.4
4	79.2
5	99.1	18/17
6	118.9	15/14
7	138.7
8	158.5	23/21
9	178.3	41/37
10	198.1	28/25, 37/33
11	217.9	17/15, 42/37
12	237.7	31/27
13	257.6
14	277.4	27/23
15	297.2
16	317	6/5
17	336.8	17/14
18	356.6	43/35
19	376.4	41/33
20	396.2	39/31
21	416.1	14/11
22	435.9	9/7
23	455.7	43/33
24	475.5
25	495.3
26	515.1	31/23, 35/26, 39/29
27	534.9	15/11, 34/25
28	554.7
29	574.5
30	594.4
31	614.2
32	634
33	653.8
34	673.6	31/21
35	693.4
36	713.2
37	733	26/17, 29/19
38	752.9	17/11
39	772.7
40	792.5
41	812.3
42	832.1	21/13
43	851.9	18/11
44	871.7	38/23, 43/26
45	891.5
46	911.4
47	931.2
48	951	26/15
49	970.8
50	990.6
51	1010.4
52	1030.2
53	1050	11/6
54	1069.8	13/7
55	1089.7
56	1109.5
57	1129.3
58	1149.1	33/17, 35/18
59	1168.9
60	1188.7
61	1208.5
62	1228.3
63	1248.2	35/17, 37/18
64	1268
65	1287.8
66	1307.6
67	1327.4
68	1347.2	37/17
69	1367	11/5
70	1386.8	29/13
71	1406.7
72	1426.5	41/18
73	1446.3
74	1466.1	7/3
75	1485.9	33/14
76	1505.7	31/13, 43/18
77	1525.5	41/17
78	1545.3
79	1565.2	37/15, 42/17
80	1585	5/2
81	1604.8	43/17
82	1624.6	23/9
83	1644.4
84	1664.2
85	1684	37/14
86	1703.8
87	1723.6
88	1743.5
89	1763.3
90	1783.1	14/5
91	1802.9	17/6
92	1822.7	43/15
93	1842.5
94	1862.3	41/14
95	1882.1
96	1902	3/1

Harmonics

Approximation of harmonics in 96edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+8.53	+0.00	-2.74	+7.18	+8.53	-0.78	+5.79	+0.00	-4.10	+9.21	-2.74
	Relative (%)	+43.1	+0.0	-13.9	+36.3	+43.1	-3.9	+29.2	+0.0	-20.7	+46.5	-13.9
Steps (reduced)		61 (61)	96 (0)	121 (25)	141 (45)	157 (61)	170 (74)	182 (86)	192 (0)	201 (9)	210 (18)	217 (25)

Approximation of harmonics in 96edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	+7.75	+7.18	-5.49	+8.43	+8.53	-5.82	+4.44	-0.78	-2.07	+0.22
	Relative (%)	-13.3	+39.1	+36.3	-27.7	+42.5	+43.1	-29.4	+22.4	-3.9	-10.4	+1.1
Steps (reduced)		224 (32)	231 (39)	237 (45)	242 (50)	248 (56)	253 (61)	257 (65)	262 (70)	266 (74)	270 (78)	274 (82)