181edt

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181edt

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Prime factorization	181 (prime)
Step size	10.508 ¢
Octave	114\181edt (1197.92 ¢)
Consistency limit	6
Distinct consistency limit	6

181 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 181edt or 181ed3), is a nonoctave tuning system that divides the interval of 3/1 into 181 equal parts of about 10.5 ¢ each. Each step represents a frequency ratio of 3^1/181, or the 181st root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	10.51	7.18
2	21.02	14.36
3	31.52	21.55	55/54, 56/55, 57/56
4	42.03	28.73	42/41
5	52.54	35.91	34/33
6	63.05	43.09	28/27, 57/55
7	73.56	50.28
8	84.06	57.46
9	94.57	64.64	19/18
10	105.08	71.82
11	115.59	79.01	31/29, 46/43
12	126.1	86.19
13	136.6	93.37
14	147.11	100.55	37/34
15	157.62	107.73	23/21
16	168.13	114.92	43/39
17	178.64	122.1	41/37, 51/46
18	189.14	129.28	29/26
19	199.65	136.46	46/41
20	210.16	143.65	35/31
21	220.67	150.83	25/22, 42/37
22	231.18	158.01
23	241.68	165.19
24	252.19	172.38
25	262.7	179.56
26	273.21	186.74	41/35, 55/47
27	283.72	193.92	33/28
28	294.23	201.1	51/43
29	304.73	208.29	31/26
30	315.24	215.47	6/5
31	325.75	222.65	35/29
32	336.26	229.83	17/14
33	346.77	237.02	11/9
34	357.27	244.2	43/35
35	367.78	251.38	47/38
36	378.29	258.56	51/41, 56/45
37	388.8	265.75
38	399.31	272.93	34/27
39	409.81	280.11	19/15
40	420.32	287.29	65/51
41	430.83	294.48
42	441.34	301.66
43	451.85	308.84
44	462.35	316.02	47/36
45	472.86	323.2	46/35
46	483.37	330.39	37/28, 41/31
47	493.88	337.57
48	504.39	344.75
49	514.89	351.93	35/26
50	525.4	359.12	42/31
51	535.91	366.3	15/11
52	546.42	373.48	37/27
53	556.93	380.66
54	567.43	387.85	43/31
55	577.94	395.03
56	588.45	402.21	52/37
57	598.96	409.39	41/29, 65/46
58	609.47	416.57	27/19
59	619.97	423.76
60	630.48	430.94	36/25
61	640.99	438.12	42/29, 55/38
62	651.5	445.3	51/35
63	662.01	452.49	22/15, 63/43
64	672.51	459.67	28/19
65	683.02	466.85	43/29, 46/31
66	693.53	474.03
67	704.04	481.22
68	714.55	488.4	65/43
69	725.05	495.58	38/25
70	735.56	502.76	26/17
71	746.07	509.94
72	756.58	517.13	65/42
73	767.09	524.31
74	777.59	531.49	47/30, 58/37
75	788.1	538.67	41/26, 52/33
76	798.61	545.86	46/29, 65/41
77	809.12	553.04
78	819.63	560.22
79	830.14	567.4	21/13
80	840.64	574.59
81	851.15	581.77
82	861.66	588.95	51/31
83	872.17	596.13	43/26
84	882.68	603.31
85	893.18	610.5	62/37
86	903.69	617.68
87	914.2	624.86	39/23
88	924.71	632.04	29/17
89	935.22	639.23
90	945.72	646.41	19/11
91	956.23	653.59	33/19
92	966.74	660.77
93	977.25	667.96	51/29, 58/33
94	987.76	675.14	23/13
95	998.26	682.32
96	1008.77	689.5
97	1019.28	696.69
98	1029.79	703.87
99	1040.3	711.05	31/17
100	1050.8	718.23
101	1061.31	725.41
102	1071.82	732.6	13/7
103	1082.33	739.78	43/23
104	1092.84	746.96	47/25, 62/33
105	1103.34	754.14
106	1113.85	761.33
107	1124.36	768.51
108	1134.87	775.69	52/27
109	1145.38	782.87
110	1155.88	790.06
111	1166.39	797.24	51/26
112	1176.9	804.42
113	1187.41	811.6
114	1197.92	818.78
115	1208.42	825.97
116	1218.93	833.15
117	1229.44	840.33	57/28
118	1239.95	847.51	43/21, 45/22
119	1250.46	854.7	35/17
120	1260.96	861.88	29/14
121	1271.47	869.06	25/12
122	1281.98	876.24	65/31
123	1292.49	883.43	19/9
124	1303	890.61
125	1313.5	897.79	47/22
126	1324.01	904.97	58/27
127	1334.52	912.15
128	1345.03	919.34
129	1355.54	926.52
130	1366.05	933.7	11/5
131	1376.55	940.88	31/14
132	1387.06	948.07
133	1397.57	955.25	65/29
134	1408.08	962.43
135	1418.59	969.61
136	1429.09	976.8
137	1439.6	983.98	62/27
138	1450.11	991.16
139	1460.62	998.34
140	1471.13	1005.52
141	1481.63	1012.71
142	1492.14	1019.89	45/19
143	1502.65	1027.07
144	1513.16	1034.25
145	1523.67	1041.44	41/17
146	1534.17	1048.62
147	1544.68	1055.8
148	1555.19	1062.98	27/11
149	1565.7	1070.17	42/17
150	1576.21	1077.35
151	1586.71	1084.53	5/2
152	1597.22	1091.71
153	1607.73	1098.9	43/17
154	1618.24	1106.08	28/11
155	1628.75	1113.26
156	1639.25	1120.44
157	1649.76	1127.62
158	1660.27	1134.81
159	1670.78	1141.99
160	1681.29	1149.17	37/14
161	1691.79	1156.35
162	1702.3	1163.54
163	1712.81	1170.72
164	1723.32	1177.9	46/17
165	1733.83	1185.08
166	1744.33	1192.27	63/23
167	1754.84	1199.45
168	1765.35	1206.63
169	1775.86	1213.81
170	1786.37	1220.99
171	1796.87	1228.18
172	1807.38	1235.36	54/19
173	1817.89	1242.54
174	1828.4	1249.72
175	1838.91	1256.91	55/19
176	1849.41	1264.09
177	1859.92	1271.27	41/14
178	1870.43	1278.45	56/19
179	1880.94	1285.64
180	1891.45	1292.82
181	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 181edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-2.08	+0.00	-4.17	-1.68	-2.08	+4.25	+4.26	+0.00	-3.77	-0.64	-4.17
	Relative (%)	-19.8	+0.0	-39.7	-16.0	-19.8	+40.5	+40.5	+0.0	-35.8	-6.1	-39.7
Steps (reduced)		114 (114)	181 (0)	228 (47)	265 (84)	295 (114)	321 (140)	343 (162)	362 (0)	379 (17)	395 (33)	409 (47)

Approximation of harmonics in 181edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+4.37	+2.17	-1.68	+2.17	+2.30	-2.08	-1.11	+4.66	+4.25	-2.73	+4.38
	Relative (%)	+41.6	+20.7	-16.0	+20.7	+21.9	-19.8	-10.6	+44.3	+40.5	-25.9	+41.7
Steps (reduced)		423 (61)	435 (73)	446 (84)	457 (95)	467 (105)	476 (114)	485 (123)	494 (132)	502 (140)	509 (147)	517 (155)