180edt

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180edt

181edt →

Prime factorization	22 × 32 × 5
Step size	10.5664 ¢
Octave	114\180edt (1204.57 ¢) (→ 19\30edt)
Consistency limit	3
Distinct consistency limit	3
Special properties	Highly composite

180 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 180edt or 180ed3), is a nonoctave tuning system that divides the interval of 3/1 into 180 equal parts of about 10.6 ¢ each. Each step represents a frequency ratio of 3^1/180, or the 180th root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	10.57	7.22
2	21.13	14.44
3	31.7	21.67	55/54
4	42.27	28.89
5	52.83	36.11	34/33
6	63.4	43.33
7	73.96	50.56
8	84.53	57.78
9	95.1	65	37/35
10	105.66	72.22
11	116.23	79.44	31/29
12	126.8	86.67
13	137.36	93.89
14	147.93	101.11	49/45
15	158.5	108.33	23/21
16	169.06	115.56	43/39, 54/49
17	179.63	122.78
18	190.2	130	29/26
19	200.76	137.22	55/49
20	211.33	144.44	26/23, 35/31
21	221.89	151.67	25/22
22	232.46	158.89
23	243.03	166.11	38/33
24	253.59	173.33
25	264.16	180.56
26	274.73	187.78	34/29
27	285.29	195
28	295.86	202.22	51/43
29	306.43	209.44	37/31
30	316.99	216.67
31	327.56	223.89
32	338.13	231.11	45/37
33	348.69	238.33
34	359.26	245.56
35	369.82	252.78	26/21
36	380.39	260
37	390.96	267.22
38	401.52	274.44	29/23
39	412.09	281.67	33/26
40	422.66	288.89	37/29
41	433.22	296.11
42	443.79	303.33
43	454.36	310.56
44	464.92	317.78	17/13
45	475.49	325
46	486.06	332.22	45/34, 49/37
47	496.62	339.44
48	507.19	346.67	63/47
49	517.75	353.89	31/23
50	528.32	361.11
51	538.89	368.33
52	549.45	375.56
53	560.02	382.78	29/21, 47/34
54	570.59	390	57/41
55	581.15	397.22
56	591.72	404.44	38/27
57	602.29	411.67
58	612.85	418.89	47/33
59	623.42	426.11
60	633.99	433.33
61	644.55	440.56	45/31
62	655.12	447.78	54/37
63	665.68	455
64	676.25	462.22	34/23
65	686.82	469.44	55/37
66	697.38	476.67
67	707.95	483.89
68	718.52	491.11
69	729.08	498.33
70	739.65	505.56	23/15
71	750.22	512.78	54/35
72	760.78	520	45/29
73	771.35	527.22
74	781.91	534.44	11/7
75	792.48	541.67	49/31
76	803.05	548.89	35/22
77	813.61	556.11
78	824.18	563.33	37/23
79	834.75	570.56	34/21, 47/29
80	845.31	577.78
81	855.88	585
82	866.45	592.22
83	877.01	599.44
84	887.58	606.67
85	898.15	613.89	42/25
86	908.71	621.11	49/29
87	919.28	628.33
88	929.84	635.56	65/38
89	940.41	642.78	31/18
90	950.98	650
91	961.54	657.22	54/31
92	972.11	664.44
93	982.68	671.67
94	993.24	678.89	55/31
95	1003.81	686.11	25/14
96	1014.38	693.33
97	1024.94	700.56	47/26
98	1035.51	707.78
99	1046.08	715
100	1056.64	722.22	46/25
101	1067.21	729.44	63/34
102	1077.77	736.67
103	1088.34	743.89
104	1098.91	751.11
105	1109.47	758.33
106	1120.04	765.56	21/11
107	1130.61	772.78
108	1141.17	780	29/15
109	1151.74	787.22	35/18
110	1162.31	794.44	45/23
111	1172.87	801.67	65/33
112	1183.44	808.89
113	1194.01	816.11
114	1204.57	823.33
115	1215.14	830.56
116	1225.7	837.78
117	1236.27	845	47/23
118	1246.84	852.22	37/18
119	1257.4	859.44	31/15
120	1267.97	866.67	52/25
121	1278.54	873.89
122	1289.1	881.11
123	1299.67	888.33
124	1310.24	895.56	49/23
125	1320.8	902.78
126	1331.37	910	41/19
127	1341.93	917.22	63/29
128	1352.5	924.44
129	1363.07	931.67
130	1373.63	938.89
131	1384.2	946.11
132	1394.77	953.33	47/21
133	1405.33	960.56
134	1415.9	967.78	34/15
135	1426.47	975
136	1437.03	982.22	39/17
137	1447.6	989.44
138	1458.17	996.67	58/25
139	1468.73	1003.89
140	1479.3	1011.11
141	1489.86	1018.33	26/11
142	1500.43	1025.56
143	1511	1032.78
144	1521.56	1040	65/27
145	1532.13	1047.22	63/26
146	1542.7	1054.44
147	1553.26	1061.67
148	1563.83	1068.89	37/15
149	1574.4	1076.11
150	1584.96	1083.33
151	1595.53	1090.56
152	1606.1	1097.78	43/17
153	1616.66	1105
154	1627.23	1112.22
155	1637.79	1119.44
156	1648.36	1126.67
157	1658.93	1133.89
158	1669.49	1141.11
159	1680.06	1148.33
160	1690.63	1155.56
161	1701.19	1162.78
162	1711.76	1170
163	1722.33	1177.22
164	1732.89	1184.44	49/18
165	1743.46	1191.67	63/23
166	1754.03	1198.89
167	1764.59	1206.11
168	1775.16	1213.33
169	1785.72	1220.56
170	1796.29	1227.78
171	1806.86	1235
172	1817.42	1242.22
173	1827.99	1249.44
174	1838.56	1256.67
175	1849.12	1263.89
176	1859.69	1271.11
177	1870.26	1278.33
178	1880.82	1285.56
179	1891.39	1292.78
180	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 180edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+4.57	+0.00	-1.42	+3.22	+4.57	+1.86	+3.15	+0.00	-2.77	+1.28	-1.42
	Relative (%)	+43.3	+0.0	-13.5	+30.5	+43.3	+17.6	+29.8	+0.0	-26.3	+12.1	-13.5
Steps (reduced)		114 (114)	180 (0)	227 (47)	264 (84)	294 (114)	319 (139)	341 (161)	360 (0)	377 (17)	393 (33)	407 (47)

Approximation of harmonics in 180edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	-4.13	+3.22	-2.85	-2.14	+4.57	-4.50	+1.80	+1.86	-4.71	+2.86
	Relative (%)	-24.9	-39.1	+30.5	-26.9	-20.2	+43.3	-42.6	+17.0	+17.6	-44.6	+27.1
Steps (reduced)		420 (60)	432 (72)	444 (84)	454 (94)	464 (104)	474 (114)	482 (122)	491 (131)	499 (139)	506 (146)	514 (154)