189edt

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189edt

190edt →

Prime factorization	33 × 7
Step size	10.0633 ¢
Octave	119\189edt (1197.53 ¢) (→ 17\27edt)
Consistency limit	4
Distinct consistency limit	4

189 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 189edt or 189ed3), is a nonoctave tuning system that divides the interval of 3/1 into 189 equal parts of about 10.1 ¢ each. Each step represents a frequency ratio of 3^1/189, or the 189th root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	10.06	6.88
2	20.13	13.76
3	30.19	20.63
4	40.25	27.51	43/42, 44/43
5	50.32	34.39
6	60.38	41.27	29/28
7	70.44	48.15
8	80.51	55.03	22/21
9	90.57	61.9	39/37
10	100.63	68.78
11	110.7	75.66
12	120.76	82.54
13	130.82	89.42	41/38
14	140.89	96.3	51/47
15	150.95	103.17
16	161.01	110.05	45/41, 56/51
17	171.08	116.93
18	181.14	123.81
19	191.2	130.69
20	201.27	137.57
21	211.33	144.44	26/23
22	221.39	151.32	25/22
23	231.45	158.2
24	241.52	165.08	23/20, 54/47
25	251.58	171.96
26	261.64	178.84	50/43, 57/49
27	271.71	185.71
28	281.77	192.59	20/17
29	291.83	199.47	45/38
30	301.9	206.35	25/21
31	311.96	213.23
32	322.02	220.11	47/39, 65/54
33	332.09	226.98
34	342.15	233.86
35	352.21	240.74	38/31
36	362.28	247.62	37/30
37	372.34	254.5	31/25
38	382.4	261.38
39	392.47	268.25
40	402.53	275.13
41	412.59	282.01
42	422.66	288.89	37/29, 60/47
43	432.72	295.77
44	442.78	302.65
45	452.85	309.52
46	462.91	316.4
47	472.97	323.28
48	483.04	330.16	37/28, 41/31
49	493.1	337.04
50	503.16	343.92
51	513.23	350.79	39/29
52	523.29	357.67	23/17
53	533.35	364.55
54	543.42	371.43
55	553.48	378.31
56	563.54	385.19	18/13
57	573.61	392.06	39/28
58	583.67	398.94	7/5
59	593.73	405.82	31/22
60	603.8	412.7	17/12
61	613.86	419.58
62	623.92	426.46	43/30
63	633.99	433.33	62/43
64	644.05	440.21	29/20, 45/31
65	654.11	447.09	54/37
66	664.17	453.97	22/15
67	674.24	460.85	31/21
68	684.3	467.72	49/33
69	694.36	474.6
70	704.43	481.48
71	714.49	488.36	65/43
72	724.55	495.24	38/25
73	734.62	502.12	26/17
74	744.68	508.99	20/13, 63/41
75	754.74	515.87
76	764.81	522.75	14/9
77	774.87	529.63	36/23
78	784.93	536.51
79	795	543.39
80	805.06	550.26	43/27
81	815.12	557.14
82	825.19	564.02	29/18, 66/41
83	835.25	570.9	47/29
84	845.31	577.78	44/27, 57/35
85	855.38	584.66	41/25
86	865.44	591.53
87	875.5	598.41	63/38
88	885.57	605.29
89	895.63	612.17	47/28
90	905.69	619.05
91	915.76	625.93
92	925.82	632.8
93	935.88	639.68
94	945.95	646.56	19/11
95	956.01	653.44	33/19
96	966.07	660.32
97	976.14	667.2	65/37
98	986.2	674.07
99	996.26	680.95
100	1006.33	687.83
101	1016.39	694.71
102	1026.45	701.59	38/21
103	1036.52	708.47
104	1046.58	715.34
105	1056.64	722.22	35/19
106	1066.7	729.1	50/27
107	1076.77	735.98	41/22, 54/29
108	1086.83	742.86
109	1096.89	749.74
110	1106.96	756.61
111	1117.02	763.49
112	1127.08	770.37	23/12
113	1137.15	777.25	27/14
114	1147.21	784.13
115	1157.27	791.01	39/20, 41/21
116	1167.34	797.88	51/26
117	1177.4	804.76
118	1187.46	811.64
119	1197.53	818.52
120	1207.59	825.4
121	1217.65	832.28
122	1227.72	839.15	63/31
123	1237.78	846.03	45/22, 47/23
124	1247.84	852.91	37/18
125	1257.91	859.79	31/15, 60/29
126	1267.97	866.67
127	1278.03	873.54
128	1288.1	880.42
129	1298.16	887.3	36/17
130	1308.22	894.18	66/31
131	1318.29	901.06	15/7
132	1328.35	907.94	28/13
133	1338.41	914.81	13/6
134	1348.48	921.69
135	1358.54	928.57
136	1368.6	935.45
137	1378.67	942.33	51/23
138	1388.73	949.21	29/13
139	1398.79	956.08
140	1408.86	962.96
141	1418.92	969.84
142	1428.98	976.72
143	1439.05	983.6	62/27
144	1449.11	990.48
145	1459.17	997.35	65/28
146	1469.24	1004.23
147	1479.3	1011.11	47/20
148	1489.36	1017.99
149	1499.42	1024.87
150	1509.49	1031.75
151	1519.55	1038.62
152	1529.61	1045.5
153	1539.68	1052.38	56/23
154	1549.74	1059.26
155	1559.8	1066.14
156	1569.87	1073.02
157	1579.93	1079.89
158	1589.99	1086.77
159	1600.06	1093.65	63/25
160	1610.12	1100.53	38/15
161	1620.18	1107.41	51/20
162	1630.25	1114.29
163	1640.31	1121.16	49/19
164	1650.37	1128.04
165	1660.44	1134.92	47/18, 60/23
166	1670.5	1141.8
167	1680.56	1148.68	66/25
168	1690.63	1155.56
169	1700.69	1162.43
170	1710.75	1169.31
171	1720.82	1176.19
172	1730.88	1183.07
173	1740.94	1189.95	41/15
174	1751.01	1196.83
175	1761.07	1203.7	47/17
176	1771.13	1210.58
177	1781.2	1217.46
178	1791.26	1224.34
179	1801.32	1231.22
180	1811.39	1238.1	37/13
181	1821.45	1244.97	63/22
182	1831.51	1251.85
183	1841.58	1258.73
184	1851.64	1265.61
185	1861.7	1272.49
186	1871.77	1279.37
187	1881.83	1286.24
188	1891.89	1293.12
189	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 189edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-2.47	+0.00	-4.95	+1.21	-2.47	+2.36	+2.64	+0.00	-1.27	+4.81	-4.95
	Relative (%)	-24.6	+0.0	-49.1	+12.0	-24.6	+23.5	+26.3	+0.0	-12.6	+47.8	-49.1
Steps (reduced)		119 (119)	189 (0)	238 (49)	277 (88)	308 (119)	335 (146)	358 (169)	378 (0)	396 (18)	413 (35)	427 (49)

Approximation of harmonics in 189edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	-0.11	+1.21	+0.17	-4.15	-2.47	+4.56	-3.74	+2.36	+2.33	-4.18
	Relative (%)	-26.2	-1.1	+12.0	+1.7	-41.2	-24.6	+45.3	-37.1	+23.5	+23.2	-41.5
Steps (reduced)		441 (63)	454 (76)	466 (88)	477 (99)	487 (109)	497 (119)	507 (129)	515 (137)	524 (146)	532 (154)	539 (161)