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	Hekts	Approximate ratios
0	0	0	1/1
1	19.8	13.5
2	39.6	27.1	42/41, 43/42
3	59.4	40.6
4	79.2	54.2
5	99.1	67.7	18/17
6	118.9	81.3	15/14
7	138.7	94.8
8	158.5	108.3	23/21
9	178.3	121.9	41/37
10	198.1	135.4	28/25, 37/33
11	217.9	149	17/15, 42/37
12	237.7	162.5	31/27
13	257.6	176
14	277.4	189.6	27/23
15	297.2	203.1
16	317	216.7	6/5
17	336.8	230.2	17/14
18	356.6	243.8	43/35
19	376.4	257.3	41/33
20	396.2	270.8	39/31
21	416.1	284.4	14/11
22	435.9	297.9	9/7
23	455.7	311.5	43/33
24	475.5	325
25	495.3	338.5
26	515.1	352.1	31/23, 35/26, 39/29
27	534.9	365.6	15/11, 34/25
28	554.7	379.2
29	574.5	392.7
30	594.4	406.3
31	614.2	419.8
32	634	433.3
33	653.8	446.9
34	673.6	460.4	31/21
35	693.4	474
36	713.2	487.5
37	733	501	26/17, 29/19
38	752.9	514.6	17/11
39	772.7	528.1
40	792.5	541.7
41	812.3	555.2
42	832.1	568.8	21/13
43	851.9	582.3	18/11
44	871.7	595.8	38/23, 43/26
45	891.5	609.4
46	911.4	622.9
47	931.2	636.5
48	951	650	26/15
49	970.8	663.5
50	990.6	677.1
51	1010.4	690.6
52	1030.2	704.2
53	1050	717.7	11/6
54	1069.8	731.3	13/7
55	1089.7	744.8
56	1109.5	758.3
57	1129.3	771.9
58	1149.1	785.4	33/17, 35/18
59	1168.9	799
60	1188.7	812.5
61	1208.5	826
62	1228.3	839.6
63	1248.2	853.1	35/17, 37/18
64	1268	866.7
65	1287.8	880.2
66	1307.6	893.8
67	1327.4	907.3
68	1347.2	920.8	37/17
69	1367	934.4	11/5
70	1386.8	947.9	29/13
71	1406.7	961.5
72	1426.5	975	41/18
73	1446.3	988.5
74	1466.1	1002.1	7/3
75	1485.9	1015.6	33/14
76	1505.7	1029.2	31/13, 43/18
77	1525.5	1042.7	41/17
78	1545.3	1056.3
79	1565.2	1069.8	37/15, 42/17
80	1585	1083.3	5/2
81	1604.8	1096.9	43/17
82	1624.6	1110.4	23/9
83	1644.4	1124
84	1664.2	1137.5
85	1684	1151	37/14
86	1703.8	1164.6
87	1723.6	1178.1
88	1743.5	1191.7
89	1763.3	1205.2
90	1783.1	1218.8	14/5
91	1802.9	1232.3	17/6
92	1822.7	1245.8	43/15
93	1842.5	1259.4
94	1862.3	1272.9	41/14
95	1882.1	1286.5
96	1902	1300	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)