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	19.812
2	39.624	42/41, 43/42
3	59.436
4	79.248
5	99.06	18/17
6	118.872	15/14
7	138.684
8	158.496	23/21
9	178.308	41/37
10	198.12	28/25, 37/33
11	217.932	17/15, 42/37
12	237.744	31/27
13	257.556
14	277.368	27/23
15	297.18
16	316.993	6/5
17	336.805	17/14
18	356.617	43/35
19	376.429	41/33
20	396.241	39/31
21	416.053	14/11
22	435.865	9/7
23	455.677	43/33
24	475.489
25	495.301
26	515.113	31/23, 35/26, 39/29
27	534.925	15/11, 34/25
28	554.737
29	574.549
30	594.361
31	614.173
32	633.985
33	653.797
34	673.609	31/21
35	693.421
36	713.233
37	733.045	26/17, 29/19
38	752.857	17/11
39	772.669
40	792.481
41	812.293
42	832.105	21/13
43	851.917	18/11
44	871.729	38/23, 43/26
45	891.541
46	911.353
47	931.165
48	950.978	26/15
49	970.79
50	990.602
51	1010.414
52	1030.226
53	1050.038	11/6
54	1069.85	13/7
55	1089.662
56	1109.474
57	1129.286
58	1149.098	33/17, 35/18
59	1168.91
60	1188.722
61	1208.534
62	1228.346
63	1248.158	35/17, 37/18
64	1267.97
65	1287.782
66	1307.594
67	1327.406
68	1347.218	37/17
69	1367.03	11/5
70	1386.842	29/13
71	1406.654
72	1426.466	41/18
73	1446.278
74	1466.09	7/3
75	1485.902	33/14
76	1505.714	31/13, 43/18
77	1525.526	41/17
78	1545.338
79	1565.15	37/15, 42/17
80	1584.963	5/2
81	1604.775	43/17
82	1624.587	23/9
83	1644.399
84	1664.211
85	1684.023	37/14
86	1703.835
87	1723.647
88	1743.459
89	1763.271
90	1783.083	14/5
91	1802.895	17/6
92	1822.707	43/15
93	1842.519
94	1862.331	41/14
95	1882.143
96	1901.955	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)