192edt

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192 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 192edt or 192ed3), is a nonoctave tuning system that divides the interval of 3/1 into 192 equal parts of about 9.91 ¢ each. Each step represents a frequency ratio of 3^1/192, or the 192nd root of 3.

← 191edt

192edt

193edt →

Prime factorization	26 × 3
Step size	9.90602 ¢
Octave	121\192edt (1198.63 ¢)
Consistency limit	15
Distinct consistency limit	15

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	9.91	6.77
2	19.81	13.54
3	29.72	20.31
4	39.62	27.08	43/42, 44/43, 45/44
5	49.53	33.85	35/34, 36/35
6	59.44	40.63	30/29
7	69.34	47.4	51/49
8	79.25	54.17	45/43, 68/65
9	89.15	60.94
10	99.06	67.71	18/17
11	108.97	74.48	33/31, 49/46
12	118.87	81.25	15/14
13	128.78	88.02	14/13
14	138.68	94.79	13/12
15	148.59	101.56
16	158.5	108.33	23/21
17	168.4	115.1	43/39, 54/49
18	178.31	121.88	41/37, 51/46
19	188.21	128.65	29/26, 39/35
20	198.12	135.42	37/33, 46/41, 65/58
21	208.03	142.19	44/39, 62/55
22	217.93	148.96
23	227.84	155.73
24	237.74	162.5	39/34
25	247.65	169.27	15/13
26	257.56	176.04	29/25, 65/56
27	267.46	182.81	7/6
28	277.37	189.58	27/23
29	287.27	196.35
30	297.18	203.13
31	307.09	209.9	37/31, 43/36
32	316.99	216.67
33	326.9	223.44	29/24
34	336.8	230.21	17/14
35	346.71	236.98	11/9
36	356.62	243.75	43/35
37	366.52	250.52	21/17, 68/55
38	376.43	257.29	41/33, 46/37
39	386.33	264.06	5/4
40	396.24	270.83	44/35, 49/39
41	406.15	277.6	43/34
42	416.05	284.38
43	425.96	291.15	55/43
44	435.86	297.92	9/7
45	445.77	304.69	22/17
46	455.68	311.46
47	465.58	318.23	17/13
48	475.49	325
49	485.39	331.77	45/34, 49/37
50	495.3	338.54
51	505.21	345.31
52	515.11	352.08	35/26, 66/49
53	525.02	358.85	42/31, 65/48
54	534.92	365.63
55	544.83	372.4	37/27, 63/46
56	554.74	379.17	51/37, 62/45
57	564.64	385.94
58	574.55	392.71	39/28, 46/33
59	584.45	399.48
60	594.36	406.25	31/22, 55/39
61	604.27	413.02
62	614.17	419.79
63	624.08	426.56	33/23, 43/30
64	633.99	433.33	62/43
65	643.89	440.1	29/20
66	653.8	446.88	35/24, 54/37
67	663.7	453.65	22/15
68	673.61	460.42	31/21
69	683.52	467.19	46/31, 49/33
70	693.42	473.96
71	703.33	480.73
72	713.23	487.5
73	723.14	494.27	41/27
74	733.05	501.04	55/36
75	742.95	507.81	43/28, 63/41
76	752.86	514.58	17/11
77	762.76	521.35
78	772.67	528.13	25/16
79	782.58	534.9	11/7
80	792.48	541.67	49/31, 68/43
81	802.39	548.44	62/39
82	812.29	555.21
83	822.2	561.98	37/23, 45/28
84	832.11	568.75	55/34
85	842.01	575.52
86	851.92	582.29	18/11
87	861.82	589.06	51/31
88	871.73	595.83	43/26, 48/29
89	881.64	602.6
90	891.54	609.38
91	901.45	616.15
92	911.35	622.92	22/13
93	921.26	629.69	46/27, 63/37
94	931.17	636.46
95	941.07	643.23	31/18
96	950.98	650
97	960.88	656.77	54/31
98	970.79	663.54
99	980.7	670.31	37/21
100	990.6	677.08	39/22, 62/35
101	1000.51	683.85	41/23
102	1010.41	690.63	43/24, 52/29
103	1020.32	697.4
104	1030.23	704.17	29/16
105	1040.13	710.94	31/17
106	1050.04	717.71	11/6
107	1059.94	724.48
108	1069.85	731.25
109	1079.76	738.02	28/15
110	1089.66	744.79
111	1099.57	751.56
112	1109.47	758.33
113	1119.38	765.1	21/11
114	1129.29	771.88	48/25
115	1139.19	778.65	56/29
116	1149.1	785.42	33/17, 68/35
117	1159	792.19	41/21
118	1168.91	798.96	55/28
119	1178.82	805.73
120	1188.72	812.5
121	1198.63	819.27
122	1208.53	826.04
123	1218.44	832.81
124	1228.35	839.58	63/31
125	1238.25	846.35	45/22, 47/23
126	1248.16	853.13	37/18
127	1258.06	859.9	60/29
128	1267.97	866.67	52/25
129	1277.88	873.44	23/11
130	1287.78	880.21
131	1297.69	886.98	55/26
132	1307.59	893.75	66/31
133	1317.5	900.52
134	1327.41	907.29	28/13
135	1337.31	914.06
136	1347.22	920.83	37/17
137	1357.12	927.6	46/21
138	1367.03	934.38
139	1376.94	941.15	31/14
140	1386.84	947.92	49/22
141	1396.75	954.69	56/25, 65/29
142	1406.65	961.46
143	1416.56	968.23	34/15
144	1426.47	975
145	1436.37	981.77	39/17, 55/24
146	1446.28	988.54
147	1456.18	995.31	51/22, 58/25
148	1466.09	1002.08	7/3
149	1476	1008.85	68/29
150	1485.9	1015.63
151	1495.81	1022.4
152	1505.71	1029.17
153	1515.62	1035.94	12/5
154	1525.53	1042.71
155	1535.43	1049.48	17/7
156	1545.34	1056.25
157	1555.24	1063.02	27/11
158	1565.15	1069.79	42/17
159	1575.06	1076.56
160	1584.96	1083.33
161	1594.87	1090.1
162	1604.77	1096.88
163	1614.68	1103.65
164	1624.59	1110.42	23/9
165	1634.49	1117.19	18/7
166	1644.4	1123.96
167	1654.3	1130.73	13/5
168	1664.21	1137.5	34/13
169	1674.12	1144.27
170	1684.02	1151.04
171	1693.93	1157.81
172	1703.83	1164.58
173	1713.74	1171.35	35/13
174	1723.65	1178.13	46/17
175	1733.55	1184.9	49/18
176	1743.46	1191.67	63/23
177	1753.36	1198.44
178	1763.27	1205.21	36/13
179	1773.18	1211.98	39/14
180	1783.08	1218.75	14/5
181	1792.99	1225.52	31/11
182	1802.89	1232.29	17/6
183	1812.8	1239.06
184	1822.71	1245.83	43/15
185	1832.61	1252.6	49/17
186	1842.52	1259.38	29/10
187	1852.42	1266.15	35/12
188	1862.33	1272.92	44/15
189	1872.24	1279.69
190	1882.14	1286.46
191	1892.05	1293.23
192	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 192edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-1.37	+0.00	-2.74	-2.72	-1.37	-0.78	-4.12	+0.00	-4.10	-0.70	-2.74
	Relative (%)	-13.9	+0.0	-27.7	-27.5	-13.9	-7.9	-41.6	+0.0	-41.3	-7.0	-27.7
Steps (reduced)		121 (121)	192 (0)	242 (50)	281 (89)	313 (121)	340 (148)	363 (171)	384 (0)	402 (18)	419 (35)	434 (50)

Approximation of harmonics in 192edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	-2.15	-2.72	+4.42	-1.48	-1.37	+4.09	+4.44	-0.78	-2.07	+0.22
	Relative (%)	-26.6	-21.7	-27.5	+44.6	-14.9	-13.9	+41.2	+44.8	-7.9	-20.9	+2.2
Steps (reduced)		448 (64)	461 (77)	473 (89)	485 (101)	495 (111)	505 (121)	515 (131)	524 (140)	532 (148)	540 (156)	548 (164)