239edt

← 238edt 239edt 240edt →
Prime factorization	239 (prime)
Step size	7.95797 ¢
Octave	151\239edt (1201.65 ¢)
Consistency limit	4
Distinct consistency limit	4

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239 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 239edt or 239ed3), is a nonoctave tuning system that divides the interval of 3/1 into 239 equal parts of about 7.96 ¢ each. Each step represents a frequency ratio of 3^1/239, or the 239th root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	7.96	5.44
2	15.92	10.88
3	23.87	16.32
4	31.83	21.76	55/54, 56/55
5	39.79	27.2
6	47.75	32.64	37/36
7	55.71	38.08
8	63.66	43.51	28/27
9	71.62	48.95
10	79.58	54.39	45/43
11	87.54	59.83
12	95.5	65.27
13	103.45	70.71	69/65
14	111.41	76.15
15	119.37	81.59	15/14
16	127.33	87.03
17	135.29	92.47	40/37
18	143.24	97.91
19	151.2	103.35	12/11
20	159.16	108.79	34/31, 57/52
21	167.12	114.23
22	175.08	119.67	52/47
23	183.03	125.1	10/9
24	190.99	130.54
25	198.95	135.98	37/33, 46/41
26	206.91	141.42	62/55
27	214.87	146.86	77/68
28	222.82	152.3	33/29
29	230.78	157.74
30	238.74	163.18	31/27
31	246.7	168.62
32	254.66	174.06	22/19
33	262.61	179.5
34	270.57	184.94
35	278.53	190.38	47/40
36	286.49	195.82	46/39
37	294.44	201.26
38	302.4	206.69	25/21
39	310.36	212.13
40	318.32	217.57
41	326.28	223.01
42	334.23	228.45	57/47
43	342.19	233.89
44	350.15	239.33
45	358.11	244.77
46	366.07	250.21	21/17
47	374.02	255.65	36/29
48	381.98	261.09
49	389.94	266.53
50	397.9	271.97	39/31
51	405.86	277.41	43/34
52	413.81	282.85	47/37
53	421.77	288.28	37/29
54	429.73	293.72	50/39
55	437.69	299.16
56	445.65	304.6
57	453.6	310.04	13/10
58	461.56	315.48	47/36
59	469.52	320.92
60	477.48	326.36	29/22, 54/41
61	485.44	331.8	45/34
62	493.39	337.24
63	501.35	342.68
64	509.31	348.12	55/41
65	517.27	353.56	31/23
66	525.23	359	42/31
67	533.18	364.44	34/25
68	541.14	369.87	41/30
69	549.1	375.31	70/51
70	557.06	380.75	40/29, 69/50
71	565.02	386.19
72	572.97	391.63	39/28
73	580.93	397.07
74	588.89	402.51	52/37
75	596.85	407.95
76	604.81	413.39	78/55
77	612.76	418.83	47/33, 57/40
78	620.72	424.27
79	628.68	429.71
80	636.64	435.15	13/9
81	644.6	440.59	45/31
82	652.55	446.03	51/35
83	660.51	451.46	41/28, 63/43
84	668.47	456.9	25/17
85	676.43	462.34	34/23
86	684.39	467.78
87	692.34	473.22
88	700.3	478.66
89	708.26	484.1
90	716.22	489.54	62/41, 65/43
91	724.18	494.98
92	732.13	500.42	29/19
93	740.09	505.86	23/15
94	748.05	511.3	57/37, 77/50
95	756.01	516.74	65/42
96	763.97	522.18
97	771.92	527.62
98	779.88	533.05
99	787.84	538.49	41/26, 52/33
100	795.8	543.93	19/12
101	803.76	549.37
102	811.71	554.81
103	819.67	560.25
104	827.63	565.69	50/31
105	835.59	571.13	47/29
106	843.54	576.57	70/43
107	851.5	582.01
108	859.46	587.45	23/14
109	867.42	592.89	33/20
110	875.38	598.33	68/41
111	883.33	603.77
112	891.29	609.21	77/46
113	899.25	614.64	37/22
114	907.21	620.08
115	915.17	625.52	56/33
116	923.12	630.96	46/27
117	931.08	636.4
118	939.04	641.84	43/25
119	947	647.28	19/11
120	954.96	652.72	33/19
121	962.91	658.16	68/39, 75/43
122	970.87	663.6
123	978.83	669.04
124	986.79	674.48
125	994.75	679.92
126	1002.7	685.36	66/37
127	1010.66	690.79	52/29
128	1018.62	696.23
129	1026.58	701.67
130	1034.54	707.11	20/11
131	1042.49	712.55	42/23
132	1050.45	717.99
133	1058.41	723.43
134	1066.37	728.87	50/27
135	1074.33	734.31
136	1082.28	739.75
137	1090.24	745.19	77/41
138	1098.2	750.63
139	1106.16	756.07	36/19
140	1114.12	761.51	78/41
141	1122.07	766.95	65/34
142	1130.03	772.38
143	1137.99	777.82
144	1145.95	783.26
145	1153.91	788.7	37/19
146	1161.86	794.14	45/23
147	1169.82	799.58	57/29
148	1177.78	805.02	77/39
149	1185.74	810.46
150	1193.7	815.9
151	1201.65	821.34
152	1209.61	826.78
153	1217.57	832.22
154	1225.53	837.66	69/34
155	1233.49	843.1	51/25
156	1241.44	848.54	43/21
157	1249.4	853.97	35/17
158	1257.36	859.41	31/15
159	1265.32	864.85	27/13
160	1273.28	870.29
161	1281.23	875.73	65/31
162	1289.19	881.17	40/19
163	1297.15	886.61	55/26
164	1305.11	892.05
165	1313.07	897.49
166	1321.02	902.93
167	1328.98	908.37	28/13
168	1336.94	913.81
169	1344.9	919.25	50/23
170	1352.86	924.69
171	1360.81	930.13	68/31
172	1368.77	935.56	75/34
173	1376.73	941	31/14
174	1384.69	946.44	69/31
175	1392.64	951.88
176	1400.6	957.32
177	1408.56	962.76
178	1416.52	968.2	34/15
179	1424.48	973.64	41/18, 66/29
180	1432.43	979.08
181	1440.39	984.52
182	1448.35	989.96	30/13
183	1456.31	995.4
184	1464.27	1000.84
185	1472.22	1006.28
186	1480.18	1011.72
187	1488.14	1017.15
188	1496.1	1022.59
189	1504.06	1028.03	31/13
190	1512.01	1033.47
191	1519.97	1038.91
192	1527.93	1044.35	29/12
193	1535.89	1049.79	17/7
194	1543.85	1055.23
195	1551.8	1060.67
196	1559.76	1066.11
197	1567.72	1071.55	47/19
198	1575.68	1076.99	77/31
199	1583.64	1082.43
200	1591.59	1087.87
201	1599.55	1093.31	63/25, 68/27
202	1607.51	1098.74
203	1615.47	1104.18
204	1623.43	1109.62
205	1631.38	1115.06	77/30
206	1639.34	1120.5
207	1647.3	1125.94	57/22
208	1655.26	1131.38
209	1663.22	1136.82
210	1671.17	1142.26
211	1679.13	1147.7	29/11
212	1687.09	1153.14
213	1695.05	1158.58
214	1703.01	1164.02
215	1710.96	1169.46
216	1718.92	1174.9	27/10
217	1726.88	1180.33
218	1734.84	1185.77
219	1742.8	1191.21	52/19
220	1750.75	1196.65	11/4
221	1758.71	1202.09
222	1766.67	1207.53
223	1774.63	1212.97
224	1782.59	1218.41	14/5
225	1790.54	1223.85
226	1798.5	1229.29	65/23
227	1806.46	1234.73
228	1814.42	1240.17	77/27
229	1822.38	1245.61	43/15
230	1830.33	1251.05
231	1838.29	1256.49
232	1846.25	1261.92
233	1854.21	1267.36
234	1862.17	1272.8
235	1870.12	1278.24
236	1878.08	1283.68
237	1886.04	1289.12
238	1894	1294.56
239	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 239edt
Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+1.65	+0.00	+3.31	-1.02	+1.65	-2.60	-3.00	+0.00	+0.63	+2.74	+3.31
Error	Relative (%)	+20.8	+0.0	+41.6	-12.9	+20.8	-32.7	-37.7	+0.0	+7.9	+34.5	+41.6
Steps (reduced)		151 (151)	239 (0)	302 (63)	350 (111)	390 (151)	423 (184)	452 (213)	478 (0)	501 (23)	522 (44)	541 (63)

Approximation of harmonics in 239edt
Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+0.02	-0.95	-1.02	-1.34	-2.85	+1.65	+3.55	+2.28	-2.60	-3.56	-0.94
Error	Relative (%)	+0.3	-11.9	-12.9	-16.9	-35.8	+20.8	+44.6	+28.7	-32.7	-44.8	-11.8
Steps (reduced)		558 (80)	574 (96)	589 (111)	603 (125)	616 (138)	629 (151)	641 (163)	652 (174)	662 (184)	672 (194)	682 (204)