182edt

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182edt

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Prime factorization	2 × 7 × 13
Step size	10.4503¢
Octave	115\182edt (1201.78¢)
Consistency limit	5
Distinct consistency limit	5

182 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 182edt or 182ed3), is a nonoctave tuning system that divides the interval of 3/1 into 182 equal parts of about 10.5⁠ ⁠¢ each. Each step represents a frequency ratio of 3^1/182, or the 182nd root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	10.45	7.14
2	20.9	14.29
3	31.35	21.43	55/54, 56/55, 57/56
4	41.8	28.57	42/41, 43/42
5	52.25	35.71	34/33
6	62.7	42.86	28/27, 57/55
7	73.15	50
8	83.6	57.14	43/41
9	94.05	64.29	19/18
10	104.5	71.43
11	114.95	78.57	31/29, 47/44
12	125.4	85.71
13	135.85	92.86
14	146.3	100	37/34, 62/57
15	156.75	107.14	23/21
16	167.2	114.29
17	177.66	121.43	41/37, 51/46
18	188.11	128.57	29/26, 39/35
19	198.56	135.71	37/33, 46/41
20	209.01	142.86	35/31, 44/39
21	219.46	150	42/37
22	229.91	157.14
23	240.36	164.29	31/27, 54/47
24	250.81	171.43	52/45
25	261.26	178.57	43/37
26	271.71	185.71	55/47
27	282.16	192.86
28	292.61	200	45/38
29	303.06	207.14	56/47
30	313.51	214.29
31	323.96	221.43	41/34, 47/39
32	334.41	228.57	57/47
33	344.86	235.71
34	355.31	242.86	27/22, 43/35
35	365.76	250	21/17
36	376.21	257.14	41/33, 46/37
37	386.66	264.29	5/4
38	397.11	271.43	39/31, 44/35
39	407.56	278.57	43/34
40	418.01	285.71	14/11
41	428.46	292.86	32/25
42	438.91	300	58/45
43	449.36	307.14	35/27, 57/44
44	459.81	314.29
45	470.26	321.43
46	480.71	328.57	62/47
47	491.16	335.71
48	501.61	342.86
49	512.06	350	39/29
50	522.52	357.14	23/17
51	532.97	364.29
52	543.42	371.43	26/19, 63/46
53	553.87	378.57	62/45
54	564.32	385.71	18/13
55	574.77	392.86	39/28, 46/33
56	585.22	400
57	595.67	407.14	55/39
58	606.12	414.29	44/31
59	616.57	421.43
60	627.02	428.57	56/39
61	637.47	435.71	13/9
62	647.92	442.86
63	658.37	450
64	668.82	457.14
65	679.27	464.29
66	689.72	471.43
67	700.17	478.57
68	710.62	485.71
69	721.07	492.86	44/29, 47/31
70	731.52	500	29/19
71	741.97	507.14	43/28
72	752.42	514.29	17/11
73	762.87	521.43
74	773.32	528.57	25/16
75	783.77	535.71
76	794.22	542.86
77	804.67	550	35/22, 43/27
78	815.12	557.14
79	825.57	564.29	29/18
80	836.02	571.43	47/29
81	846.47	578.57	31/19, 44/27
82	856.92	585.71
83	867.38	592.86
84	877.83	600
85	888.28	607.14
86	898.73	614.29
87	909.18	621.43
88	919.63	628.57
89	930.08	635.71	65/38
90	940.53	642.86	31/18
91	950.98	650
92	961.43	657.14	54/31
93	971.88	664.29
94	982.33	671.43
95	992.78	678.57	55/31
96	1003.23	685.71
97	1013.68	692.86
98	1024.13	700	47/26, 56/31, 65/36
99	1034.58	707.14
100	1045.03	714.29
101	1055.48	721.43	57/31
102	1065.93	728.57
103	1076.38	735.71	54/29
104	1086.83	742.86
105	1097.28	750
106	1107.73	757.14	55/29
107	1118.18	764.29
108	1128.63	771.43	48/25
109	1139.08	778.57	56/29
110	1149.53	785.71	33/17
111	1159.98	792.86	43/22
112	1170.43	800	57/29
113	1180.88	807.14
114	1191.33	814.29
115	1201.78	821.43
116	1212.24	828.57
117	1222.69	835.71
118	1233.14	842.86
119	1243.59	850
120	1254.04	857.14
121	1264.49	864.29	27/13
122	1274.94	871.43
123	1285.39	878.57
124	1295.84	885.71
125	1306.29	892.86
126	1316.74	900
127	1327.19	907.14	28/13
128	1337.64	914.29	13/6
129	1348.09	921.43
130	1358.54	928.57	46/21, 57/26
131	1368.99	935.71
132	1379.44	942.86	51/23
133	1389.89	950	29/13
134	1400.34	957.14
135	1410.79	964.29
136	1421.24	971.43
137	1431.69	978.57
138	1442.14	985.71
139	1452.59	992.86	44/19
140	1463.04	1000
141	1473.49	1007.14
142	1483.94	1014.29	33/14
143	1494.39	1021.43
144	1504.84	1028.57	31/13
145	1515.29	1035.71	12/5
146	1525.74	1042.86
147	1536.19	1050	17/7
148	1546.64	1057.14	22/9
149	1557.1	1064.29
150	1567.55	1071.43	47/19
151	1578	1078.57
152	1588.45	1085.71
153	1598.9	1092.86
154	1609.35	1100	38/15
155	1619.8	1107.14
156	1630.25	1114.29
157	1640.7	1121.43
158	1651.15	1128.57
159	1661.6	1135.71	47/18
160	1672.05	1142.86
161	1682.5	1150	37/14
162	1692.95	1157.14
163	1703.4	1164.29
164	1713.85	1171.43	35/13
165	1724.3	1178.57	46/17, 65/24
166	1734.75	1185.71
167	1745.2	1192.86	63/23
168	1755.65	1200
169	1766.1	1207.14
170	1776.55	1214.29
171	1787	1221.43
172	1797.45	1228.57
173	1807.9	1235.71	54/19
174	1818.35	1242.86
175	1828.8	1250
176	1839.25	1257.14	55/19
177	1849.7	1264.29
178	1860.15	1271.43	41/14
179	1870.6	1278.57	56/19
180	1881.05	1285.71
181	1891.5	1292.86
182	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 182edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+1.78	+0.00	+3.57	+3.92	+1.78	-3.83	-5.10	+0.00	-4.75	-2.55	+3.57
	Relative (%)	+17.1	+0.0	+34.2	+37.5	+17.1	-36.6	-48.8	+0.0	-45.4	-24.4	+34.2
Steps (reduced)		115 (115)	182 (0)	230 (48)	267 (85)	297 (115)	322 (140)	344 (162)	364 (0)	381 (17)	397 (33)	412 (48)

Approximation of harmonics in 182edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+0.85	-2.04	+3.92	-3.31	-3.76	+1.78	+2.23	-2.96	-3.83	-0.76	-4.57
	Relative (%)	+8.1	-19.6	+37.5	-31.7	-36.0	+17.1	+21.4	-28.4	-36.6	-7.3	-43.7
Steps (reduced)		425 (61)	437 (73)	449 (85)	459 (95)	469 (105)	479 (115)	488 (124)	496 (132)	504 (140)	512 (148)	519 (155)