188edt

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188edt

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Prime factorization	22 × 47
Step size	10.1168 ¢
Octave	119\188edt (1203.9 ¢)
Consistency limit	3
Distinct consistency limit	3

188 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 188edt or 188ed3), is a nonoctave tuning system that divides the interval of 3/1 into 188 equal parts of about 10.1 ¢ each. Each step represents a frequency ratio of 3^1/188, or the 188th root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	10.12	6.91
2	20.23	13.83
3	30.35	20.74	58/57
4	40.47	27.66	43/42, 44/43
5	50.58	34.57
6	60.7	41.49
7	70.82	48.4
8	80.93	55.32	22/21
9	91.05	62.23	39/37
10	101.17	69.15	35/33
11	111.28	76.06
12	121.4	82.98
13	131.52	89.89
14	141.63	96.81	51/47
15	151.75	103.72
16	161.87	110.64	45/41
17	171.99	117.55
18	182.1	124.47	10/9
19	192.22	131.38	19/17
20	202.34	138.3
21	212.45	145.21	26/23
22	222.57	152.13	33/29, 58/51
23	232.69	159.04
24	242.8	165.96	23/20
25	252.92	172.87	22/19
26	263.04	179.79
27	273.15	186.7	41/35
28	283.27	193.62
29	293.39	200.53
30	303.5	207.45	31/26
31	313.62	214.36
32	323.74	221.28	47/39
33	333.85	228.19	57/47
34	343.97	235.11	50/41
35	354.09	242.02	27/22
36	364.2	248.94	37/30, 58/47
37	374.32	255.85
38	384.44	262.77
39	394.55	269.68	49/39, 54/43
40	404.67	276.6
41	414.79	283.51	47/37
42	424.9	290.43	23/18
43	435.02	297.34	9/7
44	445.14	304.26
45	455.26	311.17	13/10
46	465.37	318.09	17/13
47	475.49	325
48	485.61	331.91	49/37
49	495.72	338.83
50	505.84	345.74
51	515.96	352.66	31/23, 66/49
52	526.07	359.57	42/31
53	536.19	366.49	15/11
54	546.31	373.4	37/27
55	556.42	380.32	51/37
56	566.54	387.23	43/31
57	576.66	394.15	60/43
58	586.77	401.06	66/47
59	596.89	407.98
60	607.01	414.89	44/31
61	617.12	421.81	10/7
62	627.24	428.72
63	637.36	435.64	13/9
64	647.47	442.55
65	657.59	449.47	19/13
66	667.71	456.38
67	677.82	463.3	34/23
68	687.94	470.21	58/39
69	698.06	477.13
70	708.17	484.04
71	718.29	490.96	50/33
72	728.41	497.87
73	738.53	504.79
74	748.64	511.7	57/37
75	758.76	518.62	31/20
76	768.88	525.53
77	778.99	532.45	58/37
78	789.11	539.36
79	799.23	546.28
80	809.34	553.19
81	819.46	560.11
82	829.58	567.02	21/13
83	839.69	573.94
84	849.81	580.85	49/30
85	859.93	587.77	23/14
86	870.04	594.68	38/23, 43/26
87	880.16	601.6
88	890.28	608.51
89	900.39	615.43	37/22
90	910.51	622.34	22/13
91	920.63	629.26	63/37
92	930.74	636.17
93	940.86	643.09	31/18
94	950.98	650
95	961.09	656.91	54/31
96	971.21	663.83
97	981.33	670.74	37/21
98	991.44	677.66	39/22
99	1001.56	684.57	66/37
100	1011.68	691.49
101	1021.79	698.4
102	1031.91	705.32	49/27
103	1042.03	712.23	42/23
104	1052.15	719.15
105	1062.26	726.06
106	1072.38	732.98	13/7
107	1082.5	739.89	43/23
108	1092.61	746.81
109	1102.73	753.72
110	1112.85	760.64
111	1122.96	767.55	44/23
112	1133.08	774.47
113	1143.2	781.38	60/31
114	1153.31	788.3	37/19
115	1163.43	795.21
116	1173.55	802.13	65/33
117	1183.66	809.04
118	1193.78	815.96
119	1203.9	822.87
120	1214.01	829.79
121	1224.13	836.7
122	1234.25	843.62
123	1244.36	850.53	39/19
124	1254.48	857.45
125	1264.6	864.36	27/13
126	1274.71	871.28
127	1284.83	878.19	21/10
128	1294.95	885.11
129	1305.06	892.02
130	1315.18	898.94	47/22
131	1325.3	905.85	43/20
132	1335.42	912.77
133	1345.53	919.68	37/17
134	1355.65	926.6
135	1365.77	933.51	11/5
136	1375.88	940.43	31/14
137	1386	947.34	49/22
138	1396.12	954.26	65/29
139	1406.23	961.17
140	1416.35	968.09
141	1426.47	975
142	1436.58	981.91	39/17
143	1446.7	988.83	30/13
144	1456.82	995.74
145	1466.93	1002.66	7/3
146	1477.05	1009.57	54/23
147	1487.17	1016.49
148	1497.28	1023.4
149	1507.4	1030.32	43/18
150	1517.52	1037.23
151	1527.63	1044.15
152	1537.75	1051.06
153	1547.87	1057.98	22/9
154	1557.98	1064.89
155	1568.1	1071.81	47/19
156	1578.22	1078.72
157	1588.33	1085.64
158	1598.45	1092.55
159	1608.57	1099.47
160	1618.69	1106.38
161	1628.8	1113.3
162	1638.92	1120.21
163	1649.04	1127.13	57/22
164	1659.15	1134.04	60/23
165	1669.27	1140.96
166	1679.39	1147.87	29/11
167	1689.5	1154.79
168	1699.62	1161.7
169	1709.74	1168.62	51/19
170	1719.85	1175.53	27/10
171	1729.97	1182.45
172	1740.09	1189.36	41/15
173	1750.2	1196.28
174	1760.32	1203.19	47/17
175	1770.44	1210.11
176	1780.55	1217.02
177	1790.67	1223.94
178	1800.79	1230.85
179	1810.9	1237.77	37/13
180	1821.02	1244.68	63/22
181	1831.14	1251.6
182	1841.25	1258.51
183	1851.37	1265.43
184	1861.49	1272.34
185	1871.6	1279.26
186	1881.72	1286.17
187	1891.84	1293.09
188	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 188edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+3.90	+0.00	-2.32	-4.20	+3.90	+0.06	+1.57	+0.00	-0.30	-3.44	-2.32
	Relative (%)	+38.5	+0.0	-23.0	-41.5	+38.5	+0.6	+15.6	+0.0	-3.0	-34.0	-23.0
Steps (reduced)		119 (119)	188 (0)	237 (49)	275 (87)	307 (119)	333 (145)	356 (168)	376 (0)	394 (18)	410 (34)	425 (49)

Approximation of harmonics in 188edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+0.74	+3.96	-4.20	-4.65	+1.68	+3.90	+1.35	+3.60	+0.06	+0.46	+4.44
	Relative (%)	+7.3	+39.1	-41.5	-45.9	+16.6	+38.5	+13.3	+35.5	+0.6	+4.5	+43.9
Steps (reduced)		439 (63)	452 (76)	463 (87)	474 (98)	485 (109)	495 (119)	504 (128)	513 (137)	521 (145)	529 (153)	537 (161)