183edt

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183edt

184edt →

Prime factorization	3 × 61
Step size	10.3932¢
Octave	115\183edt (1195.22¢)
Consistency limit	2
Distinct consistency limit	2

183 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 183edt or 183ed3), is a nonoctave tuning system that divides the interval of 3/1 into 183 equal parts of about 10.4⁠ ⁠¢ each. Each step represents a frequency ratio of 3^1/183, or the 183rd root of 3. The major chord is 0-37-68.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	10.39	7.1
2	20.79	14.21
3	31.18	21.31	55/54, 58/57
4	41.57	28.42
5	51.97	35.52	34/33
6	62.36	42.62	57/55
7	72.75	49.73	49/47
8	83.15	56.83	43/41
9	93.54	63.93	19/18
10	103.93	71.04
11	114.33	78.14	31/29
12	124.72	85.25	29/27
13	135.11	92.35
14	145.5	99.45	25/23, 37/34, 62/57
15	155.9	106.56
16	166.29	113.66
17	176.68	120.77
18	187.08	127.87	39/35
19	197.47	134.97	37/33, 65/58
20	207.86	142.08	62/55
21	218.26	149.18	42/37
22	228.65	156.28
23	239.04	163.39	31/27
24	249.44	170.49
25	259.83	177.6
26	270.22	184.7
27	280.62	191.8
28	291.01	198.91	58/49
29	301.4	206.01	25/21
30	311.8	213.11
31	322.19	220.22	47/39, 65/54
32	332.58	227.32
33	342.98	234.43
34	353.37	241.53
35	363.76	248.63	37/30, 58/47
36	374.16	255.74
37	384.55	262.84
38	394.94	269.95	49/39
39	405.33	277.05
40	415.73	284.15
41	426.12	291.26
42	436.51	298.36
43	446.91	305.46
44	457.3	312.57
45	467.69	319.67	55/42
46	478.09	326.78
47	488.48	333.88	65/49
48	498.87	340.98
49	509.27	348.09	47/35
50	519.66	355.19
51	530.05	362.3
52	540.45	369.4
53	550.84	376.5
54	561.23	383.61	47/34, 65/47
55	571.63	390.71
56	582.02	397.81	7/5
57	592.41	404.92
58	602.81	412.02
59	613.2	419.13	47/33
60	623.59	426.23
61	633.99	433.33
62	644.38	440.44	45/31
63	654.77	447.54	54/37
64	665.16	454.64
65	675.56	461.75	34/23
66	685.95	468.85	55/37, 58/39
67	696.34	475.96
68	706.74	483.06
69	717.13	490.16
70	727.52	497.27	35/23
71	737.92	504.37
72	748.31	511.48	57/37
73	758.7	518.58
74	769.1	525.68	39/25
75	779.49	532.79
76	789.88	539.89	30/19
77	800.28	546.99	27/17
78	810.67	554.1
79	821.06	561.2
80	831.46	568.31	21/13, 55/34
81	841.85	575.41
82	852.24	582.51	18/11
83	862.64	589.62	51/31
84	873.03	596.72
85	883.42	603.83	5/3
86	893.81	610.93	57/34, 62/37
87	904.21	618.03
88	914.6	625.14	39/23
89	924.99	632.24	29/17
90	935.39	639.34
91	945.78	646.45	19/11
92	956.17	653.55	33/19
93	966.57	660.66
94	976.96	667.76	51/29, 58/33
95	987.35	674.86	23/13
96	997.75	681.97
97	1008.14	689.07	34/19
98	1018.53	696.17	9/5
99	1028.93	703.28
100	1039.32	710.38	31/17
101	1049.71	717.49	11/6
102	1060.11	724.59
103	1070.5	731.69	13/7
104	1080.89	738.8
105	1091.29	745.9	62/33
106	1101.68	753.01	17/9
107	1112.07	760.11	19/10
108	1122.47	767.21	65/34
109	1132.86	774.32	25/13
110	1143.25	781.42
111	1153.64	788.52	37/19
112	1164.04	795.63	49/25
113	1174.43	802.73	65/33
114	1184.82	809.84
115	1195.22	816.94
116	1205.61	824.04
117	1216	831.15
118	1226.4	838.25
119	1236.79	845.36	47/23
120	1247.18	852.46	37/18
121	1257.58	859.56	31/15
122	1267.97	866.67
123	1278.36	873.77
124	1288.76	880.87
125	1299.15	887.98
126	1309.54	895.08	49/23
127	1319.94	902.19	15/7
128	1330.33	909.29
129	1340.72	916.39
130	1351.12	923.5
131	1361.51	930.6
132	1371.9	937.7
133	1382.3	944.81
134	1392.69	951.91
135	1403.08	959.02
136	1413.47	966.12
137	1423.87	973.22
138	1434.26	980.33
139	1444.65	987.43
140	1455.05	994.54
141	1465.44	1001.64
142	1475.83	1008.74
143	1486.23	1015.85
144	1496.62	1022.95
145	1507.01	1030.05
146	1517.41	1037.16
147	1527.8	1044.26
148	1538.19	1051.37
149	1548.59	1058.47
150	1558.98	1065.57
151	1569.37	1072.68
152	1579.77	1079.78
153	1590.16	1086.89
154	1600.55	1093.99	58/23, 63/25
155	1610.95	1101.09
156	1621.34	1108.2
157	1631.73	1115.3
158	1642.13	1122.4
159	1652.52	1129.51
160	1662.91	1136.61
161	1673.3	1143.72
162	1683.7	1150.82	37/14
163	1694.09	1157.92
164	1704.48	1165.03
165	1714.88	1172.13	35/13
166	1725.27	1179.23
167	1735.66	1186.34
168	1746.06	1193.44
169	1756.45	1200.55
170	1766.84	1207.65
171	1777.24	1214.75
172	1787.63	1221.86
173	1798.02	1228.96	65/23
174	1808.42	1236.07	54/19
175	1818.81	1243.17
176	1829.2	1250.27
177	1839.6	1257.38	55/19
178	1849.99	1264.48
179	1860.38	1271.58
180	1870.78	1278.69
181	1881.17	1285.79
182	1891.56	1292.9
183	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 183edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-4.78	+0.00	+0.83	-0.94	-4.78	-1.43	-3.95	+0.00	+4.67	-4.43	+0.83
	Relative (%)	-46.0	+0.0	+8.0	-9.0	-46.0	-13.8	-38.0	+0.0	+45.0	-42.6	+8.0
Steps (reduced)		115 (115)	183 (0)	231 (48)	268 (85)	298 (115)	324 (141)	346 (163)	366 (0)	384 (18)	399 (33)	414 (48)

Approximation of harmonics in 183edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	+4.18	-0.94	+1.66	+0.63	-4.78	-4.85	-0.11	-1.43	+1.18	-3.03
	Relative (%)	-25.3	+40.2	-9.0	+15.9	+6.1	-46.0	-46.6	-1.0	-13.8	+11.3	-29.1
Steps (reduced)		427 (61)	440 (74)	451 (85)	462 (96)	472 (106)	481 (115)	490 (124)	499 (133)	507 (141)	515 (149)	522 (156)