184edt

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184 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 184edt or 184ed3), is a nonoctave tuning system that divides the interval of 3/1 into 184 equal parts of about 10.3 ¢ each. Each step represents a frequency ratio of 3^1/184, or the 184th root of 3.

← 183edt

184edt

185edt →

Prime factorization	23 × 23
Step size	10.3367 ¢
Octave	116\184edt (1199.06 ¢) (→ 29\46edt)
Consistency limit	4
Distinct consistency limit	4

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	10.34	7.07
2	20.67	14.13
3	31.01	21.2	57/56, 58/57
4	41.35	28.26	42/41, 43/42
5	51.68	35.33	34/33
6	62.02	42.39	28/27
7	72.36	49.46	49/47
8	82.69	56.52	43/41
9	93.03	63.59	19/18
10	103.37	70.65	52/49
11	113.7	77.72	47/44
12	124.04	84.78	29/27, 43/40
13	134.38	91.85	40/37
14	144.71	98.91	62/57
15	155.05	105.98	47/43
16	165.39	113.04	11/10
17	175.72	120.11	31/28, 52/47
18	186.06	127.17	49/44
19	196.4	134.24
20	206.73	141.3
21	217.07	148.37	17/15
22	227.41	155.43
23	237.74	162.5	39/34
24	248.08	169.57	15/13
25	258.42	176.63	36/31
26	268.75	183.7
27	279.09	190.76	47/40
28	289.43	197.83	13/11
29	299.76	204.89	44/37
30	310.1	211.96
31	320.44	219.02
32	330.77	226.09	23/19
33	341.11	233.15	28/23
34	351.45	240.22	38/31, 49/40, 60/49
35	361.78	247.28
36	372.12	254.35	57/46
37	382.46	261.41
38	392.8	268.48
39	403.13	275.54
40	413.47	282.61	33/26, 47/37
41	423.81	289.67	23/18, 60/47
42	434.14	296.74	9/7
43	444.48	303.8
44	454.82	310.87	13/10
45	465.15	317.93	17/13
46	475.49	325
47	485.83	332.07	45/34, 49/37
48	496.16	339.13
49	506.5	346.2	63/47
50	516.84	353.26	31/23, 66/49
51	527.17	360.33
52	537.51	367.39	15/11
53	547.85	374.46
54	558.18	381.52	29/21
55	568.52	388.59
56	578.86	395.65
57	589.19	402.72	52/37
58	599.53	409.78	41/29, 58/41
59	609.87	416.85	37/26
60	620.2	423.91	63/44
61	630.54	430.98
62	640.88	438.04	42/29
63	651.21	445.11	51/35
64	661.55	452.17	63/43
65	671.89	459.24	28/19
66	682.22	466.3	43/29, 46/31
67	692.56	473.37
68	702.9	480.43	3/2
69	713.23	487.5
70	723.57	494.57	41/27
71	733.91	501.63
72	744.24	508.7	63/41
73	754.58	515.76	17/11
74	764.92	522.83	14/9
75	775.25	529.89	36/23
76	785.59	536.96	63/40
77	795.93	544.02	19/12
78	806.26	551.09	43/27
79	816.6	558.15
80	826.94	565.22
81	837.27	572.28	60/37
82	847.61	579.35	31/19
83	857.95	586.41
84	868.28	593.48	38/23
85	878.62	600.54
86	888.96	607.61
87	899.29	614.67	37/22
88	909.63	621.74	22/13
89	919.97	628.8
90	930.3	635.87
91	940.64	642.93	31/18
92	950.98	650
93	961.31	657.07	54/31
94	971.65	664.13
95	981.99	671.2
96	992.32	678.26	39/22
97	1002.66	685.33	66/37
98	1013	692.39
99	1023.33	699.46	56/31
100	1033.67	706.52
101	1044.01	713.59
102	1054.34	720.65	57/31
103	1064.68	727.72	37/20
104	1075.02	734.78
105	1085.35	741.85	58/31
106	1095.69	748.91
107	1106.03	755.98	36/19
108	1116.36	763.04	40/21
109	1126.7	770.11	23/12
110	1137.04	777.17	27/14
111	1147.38	784.24	33/17
112	1157.71	791.3	41/21
113	1168.05	798.37
114	1178.39	805.43
115	1188.72	812.5
116	1199.06	819.57	2/1
117	1209.4	826.63
118	1219.73	833.7
119	1230.07	840.76	57/28
120	1240.41	847.83	43/21
121	1250.74	854.89	35/17
122	1261.08	861.96	29/14
123	1271.42	869.02
124	1281.75	876.09	44/21
125	1292.09	883.15
126	1302.43	890.22
127	1312.76	897.28
128	1323.1	904.35	58/27
129	1333.44	911.41
130	1343.77	918.48	63/29
131	1354.11	925.54
132	1364.45	932.61	11/5
133	1374.78	939.67
134	1385.12	946.74	49/22
135	1395.46	953.8	47/21
136	1405.79	960.87
137	1416.13	967.93	34/15
138	1426.47	975
139	1436.8	982.07	39/17
140	1447.14	989.13	30/13
141	1457.48	996.2
142	1467.81	1003.26	7/3
143	1478.15	1010.33	47/20, 54/23
144	1488.49	1017.39	26/11
145	1498.82	1024.46
146	1509.16	1031.52
147	1519.5	1038.59
148	1529.83	1045.65	46/19
149	1540.17	1052.72	56/23
150	1550.51	1059.78	49/20
151	1560.84	1066.85
152	1571.18	1073.91	57/23
153	1581.52	1080.98
154	1591.85	1088.04
155	1602.19	1095.11	58/23
156	1612.53	1102.17	33/13
157	1622.86	1109.24
158	1633.2	1116.3
159	1643.54	1123.37	31/12
160	1653.87	1130.43	13/5
161	1664.21	1137.5	34/13
162	1674.55	1144.57
163	1684.88	1151.63	45/17
164	1695.22	1158.7
165	1705.56	1165.76
166	1715.89	1172.83	62/23
167	1726.23	1179.89
168	1736.57	1186.96	30/11
169	1746.9	1194.02
170	1757.24	1201.09
171	1767.58	1208.15
172	1777.91	1215.22
173	1788.25	1222.28
174	1798.59	1229.35
175	1808.92	1236.41	54/19
176	1819.26	1243.48
177	1829.6	1250.54
178	1839.93	1257.61
179	1850.27	1264.67
180	1860.61	1271.74	41/14
181	1870.94	1278.8	56/19
182	1881.28	1285.87
183	1891.62	1292.93
184	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 184edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-0.94	+0.00	-1.88	+4.60	-0.94	+0.94	-2.82	+0.00	+3.66	+4.04	-1.88
	Relative (%)	-9.1	+0.0	-18.2	+44.5	-9.1	+9.1	-27.3	+0.0	+35.4	+39.1	-18.2
Steps (reduced)		116 (116)	184 (0)	232 (48)	270 (86)	300 (116)	326 (142)	348 (164)	368 (0)	386 (18)	402 (34)	416 (48)

Approximation of harmonics in 184edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+4.26	+0.00	+4.60	-3.77	+4.98	-0.94	-1.51	+2.72	+0.94	+3.10	-1.50
	Relative (%)	+41.2	+0.0	+44.5	-36.4	+48.2	-9.1	-14.6	+26.3	+9.1	+30.0	-14.5
Steps (reduced)		430 (62)	442 (74)	454 (86)	464 (96)	475 (107)	484 (116)	493 (125)	502 (134)	510 (142)	518 (150)	525 (157)