190edt

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← 189edt

190edt

191edt →

Prime factorization	2 × 5 × 19
Step size	10.0103¢
Octave	120\190edt (1201.23¢) (→12\19edt)
Consistency limit	4
Distinct consistency limit	4

190 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 190edt or 190ed3), is a nonoctave tuning system that divides the interval of 3/1 into 190 equal parts of about 10⁠ ⁠¢ each. Each step represents a frequency ratio of 3^1/190, or the 190th root of 3.

Theory

This tuning tempers out 531441/524288 (Pythagorean comma) in the 3-limit.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	10.01	6.84
2	20.02	13.68
3	30.03	20.53	58/57
4	40.04	27.37
5	50.05	34.21	35/34
6	60.06	41.05
7	70.07	47.89
8	80.08	54.74	22/21
9	90.09	61.58
10	100.1	68.42	18/17
11	110.11	75.26
12	120.12	82.11
13	130.13	88.95	55/51
14	140.14	95.79
15	150.15	102.63	12/11
16	160.16	109.47	34/31, 45/41
17	170.17	116.32
18	180.19	123.16
19	190.2	130
20	200.21	136.84	46/41
21	210.22	143.68	35/31
22	220.23	150.53
23	230.24	157.37	8/7
24	240.25	164.21	31/27, 54/47
25	250.26	171.05
26	260.27	177.89	43/37, 50/43
27	270.28	184.74
28	280.29	191.58	20/17, 47/40
29	290.3	198.42	13/11
30	300.31	205.26
31	310.32	212.11	55/46
32	320.33	218.95	65/54
33	330.34	225.79	23/19
34	340.35	232.63
35	350.36	239.47
36	360.37	246.32	16/13
37	370.38	253.16	26/21, 57/46
38	380.39	260
39	390.4	266.84
40	400.41	273.68	29/23
41	410.42	280.53
42	420.43	287.37	51/40, 65/51
43	430.44	294.21
44	440.45	301.05	40/31, 58/45
45	450.46	307.89
46	460.47	314.74	30/23, 47/36
47	470.48	321.58	21/16
48	480.49	328.42	62/47
49	490.5	335.26
50	500.51	342.11
51	510.52	348.95	47/35, 51/38
52	520.54	355.79	27/20, 50/37
53	530.55	362.63
54	540.56	369.47	41/30
55	550.57	376.32	11/8
56	560.58	383.16	47/34, 65/47
57	570.59	390	57/41
58	580.6	396.84
59	590.61	403.68	38/27
60	600.62	410.53	41/29, 58/41
61	610.63	417.37
62	620.64	424.21	63/44
63	630.65	431.05
64	640.66	437.89	55/38
65	650.67	444.74	51/35
66	660.68	451.58
67	670.69	458.42
68	680.7	465.26	40/27
69	690.71	472.11
70	700.72	478.95
71	710.73	485.79
72	720.74	492.63	47/31
73	730.75	499.47
74	740.76	506.32	23/15
75	750.77	513.16	54/35
76	760.78	520	45/29
77	770.79	526.84
78	780.8	533.68
79	790.81	540.53	30/19
80	800.82	547.37	27/17
81	810.83	554.21
82	820.84	561.05
83	830.85	567.89	21/13
84	840.86	574.74	13/8
85	850.87	581.58
86	860.88	588.42	51/31
87	870.9	595.26
88	880.91	602.11
89	890.92	608.95
90	900.93	615.79
91	910.94	622.63	22/13
92	920.95	629.47
93	930.96	636.32
94	940.97	643.16	31/18
95	950.98	650
96	960.99	656.84	54/31
97	971	663.68
98	981.01	670.53
99	991.02	677.37	39/22, 62/35
100	1001.03	684.21	41/23
101	1011.04	691.05
102	1021.05	697.89
103	1031.06	704.74
104	1041.07	711.58	31/17
105	1051.08	718.42
106	1061.09	725.26	24/13
107	1071.1	732.11	13/7
108	1081.11	738.95
109	1091.12	745.79	62/33
110	1101.13	752.63	17/9
111	1111.14	759.47	19/10
112	1121.15	766.32	65/34
113	1131.16	773.16
114	1141.17	780	29/15
115	1151.18	786.84	35/18
116	1161.19	793.68	45/23
117	1171.2	800.53
118	1181.21	807.37
119	1191.22	814.21
120	1201.23	821.05
121	1211.25	827.89
122	1221.26	834.74
123	1231.27	841.58	55/27
124	1241.28	848.42
125	1251.29	855.26	35/17
126	1261.3	862.11
127	1271.31	868.95
128	1281.32	875.79	44/21, 65/31
129	1291.33	882.63
130	1301.34	889.47
131	1311.35	896.32
132	1321.36	903.16
133	1331.37	910	41/19
134	1341.38	916.84
135	1351.39	923.68	24/11
136	1361.4	930.53
137	1371.41	937.37
138	1381.42	944.21	20/9
139	1391.43	951.05	38/17
140	1401.44	957.89
141	1411.45	964.74
142	1421.46	971.58
143	1431.47	978.42	16/7
144	1441.48	985.26	23/10
145	1451.49	992.11
146	1461.5	998.95
147	1471.51	1005.79
148	1481.52	1012.63	40/17
149	1491.53	1019.47
150	1501.54	1026.32
151	1511.55	1033.16
152	1521.56	1040	65/27
153	1531.57	1046.84	46/19, 63/26
154	1541.58	1053.68	39/16
155	1551.59	1060.53
156	1561.61	1067.37
157	1571.62	1074.21	57/23
158	1581.63	1081.05
159	1591.64	1087.89
160	1601.65	1094.74	58/23
161	1611.66	1101.58	33/13
162	1621.67	1108.42	51/20
163	1631.68	1115.26
164	1641.69	1122.11
165	1651.7	1128.95
166	1661.71	1135.79	47/18
167	1671.72	1142.63	21/8
168	1681.73	1149.47
169	1691.74	1156.32
170	1701.75	1163.16
171	1711.76	1170
172	1721.77	1176.84
173	1731.78	1183.68
174	1741.79	1190.53	41/15
175	1751.8	1197.37	11/4
176	1761.81	1204.21
177	1771.82	1211.05
178	1781.83	1217.89
179	1791.84	1224.74
180	1801.85	1231.58	17/6
181	1811.86	1238.42
182	1821.87	1245.26	63/22
183	1831.88	1252.11
184	1841.89	1258.95
185	1851.9	1265.79
186	1861.91	1272.63
187	1871.92	1279.47
188	1881.93	1286.32
189	1891.94	1293.16
190	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 190edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+1.23	+0.00	+2.47	-3.45	+1.23	+4.64	+3.70	+0.00	-2.22	+2.95	+2.47
	Relative (%)	+12.3	+0.0	+24.7	-34.5	+12.3	+46.4	+37.0	+0.0	-22.2	+29.5	+24.7
Steps (reduced)		120 (120)	190 (0)	240 (50)	278 (88)	310 (120)	337 (147)	360 (170)	380 (0)	398 (18)	415 (35)	430 (50)

Approximation of harmonics in 190edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+4.04	-4.13	-3.45	+4.94	+0.09	+1.23	-2.28	-0.98	+4.64	+4.19	-2.70
	Relative (%)	+40.4	-41.3	-34.5	+49.3	+0.9	+12.3	-22.7	-9.8	+46.4	+41.8	-26.9
Steps (reduced)		444 (64)	456 (76)	468 (88)	480 (100)	490 (110)	500 (120)	509 (129)	518 (138)	527 (147)	535 (155)	542 (162)