247edt

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247 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 247edt or 247ed3), is a nonoctave tuning system that divides the interval of 3/1 into 247 equal parts of about 7.7 ¢ each. Each step represents a frequency ratio of 3^1/247, or the 247th root of 3.

← 246edt

247edt

248edt →

Prime factorization	13 × 19
Step size	7.70022 ¢
Octave	156\247edt (1201.23 ¢) (→ 12\19edt)
Consistency limit	6
Distinct consistency limit	6

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	7.7	5.26
2	15.4	10.53
3	23.1	15.79	75/74, 76/75
4	30.8	21.05	56/55, 57/56, 58/57
5	38.5	26.32	45/44, 46/45
6	46.2	31.58	38/37
7	53.9	36.84
8	61.6	42.11	29/28, 57/55
9	69.3	47.37
10	77	52.63	23/22
11	84.7	57.89
12	92.4	63.16	58/55
13	100.1	68.42
14	107.8	73.68	33/31, 50/47
15	115.5	78.95	31/29
16	123.2	84.21	29/27
17	130.9	89.47	41/38, 55/51
18	138.6	94.74	13/12
19	146.3	100	37/34, 62/57
20	154	105.26	47/43
21	161.7	110.53	45/41, 56/51
22	169.4	115.79	43/39, 75/68
23	177.11	121.05	41/37, 72/65
24	184.81	126.32	69/62
25	192.51	131.58	19/17
26	200.21	136.84
27	207.91	142.11	62/55
28	215.61	147.37
29	223.31	152.63	33/29, 58/51
30	231.01	157.89
31	238.71	163.16	31/27
32	246.41	168.42
33	254.11	173.68	22/19
34	261.81	178.95	50/43
35	269.51	184.21
36	277.21	189.47	27/23
37	284.91	194.74	33/28
38	292.61	200	45/38
39	300.31	205.26	44/37, 69/58
40	308.01	210.53	43/36
41	315.71	215.79	6/5
42	323.41	221.05	41/34, 47/39
43	331.11	226.32	23/19
44	338.81	231.58	45/37, 62/51
45	346.51	236.84
46	354.21	242.11	27/22
47	361.91	247.37	69/56
48	369.61	252.63
49	377.31	257.89	46/37, 51/41
50	385.01	263.16
51	392.71	268.42	69/55
52	400.41	273.68
53	408.11	278.95
54	415.81	284.21
55	423.51	289.47	23/18, 60/47
56	431.21	294.74
57	438.91	300	58/45
58	446.61	305.26	22/17
59	454.31	310.53	13/10
60	462.01	315.79	47/36, 81/62
61	469.71	321.05
62	477.41	326.32	29/22, 54/41
63	485.11	331.58	45/34
64	492.81	336.84
65	500.51	342.11
66	508.21	347.37	55/41
67	515.91	352.63	31/23
68	523.62	357.89	23/17
69	531.32	363.16
70	539.02	368.42	56/41
71	546.72	373.68
72	554.42	378.95	62/45
73	562.12	384.21	65/47
74	569.82	389.47	57/41
75	577.52	394.74	60/43, 81/58
76	585.22	400
77	592.92	405.26	31/22
78	600.62	410.53	58/41
79	608.32	415.79	27/19
80	616.02	421.05
81	623.72	426.32	43/30
82	631.42	431.58	36/25
83	639.12	436.84	68/47, 81/56
84	646.82	442.11
85	654.52	447.37	54/37
86	662.22	452.63	22/15
87	669.92	457.89	81/55
88	677.62	463.16
89	685.32	468.42
90	693.02	473.68
91	700.72	478.95
92	708.42	484.21
93	716.12	489.47	62/41, 65/43
94	723.82	494.74	41/27
95	731.52	500	29/19
96	739.22	505.26	23/15, 72/47
97	746.92	510.53
98	754.62	515.79
99	762.32	521.05
100	770.02	526.32	39/25
101	777.72	531.58	47/30, 58/37
102	785.42	536.84	74/47
103	793.12	542.11	68/43
104	800.82	547.37	27/17
105	808.52	552.63	75/47
106	816.22	557.89
107	823.92	563.16	37/23, 66/41
108	831.62	568.42	76/47
109	839.32	573.68
110	847.02	578.95	31/19, 75/46
111	854.72	584.21
112	862.42	589.47	51/31
113	870.13	594.74
114	877.83	600	78/47
115	885.53	605.26
116	893.23	610.53	62/37, 72/43
117	900.93	615.79	69/41
118	908.63	621.05
119	916.33	626.32	56/33
120	924.03	631.58	29/17, 75/44
121	931.73	636.84
122	939.43	642.11	43/25, 74/43
123	947.13	647.37
124	954.83	652.63
125	962.53	657.89	68/39, 75/43
126	970.23	663.16
127	977.93	668.42	44/25, 51/29
128	985.63	673.68	76/43
129	993.33	678.95	55/31
130	1001.03	684.21	41/23
131	1008.73	689.47	43/24
132	1016.43	694.74
133	1024.13	700	47/26, 56/31
134	1031.83	705.26
135	1039.53	710.53	31/17
136	1047.23	715.79
137	1054.93	721.05	46/25, 57/31
138	1062.63	726.32
139	1070.33	731.58
140	1078.03	736.84	41/22, 69/37
141	1085.73	742.11
142	1093.43	747.37	47/25
143	1101.13	752.63	17/9
144	1108.83	757.89	55/29, 74/39
145	1116.53	763.16
146	1124.23	768.42
147	1131.93	773.68	25/13
148	1139.63	778.95	56/29
149	1147.33	784.21
150	1155.03	789.47	76/39
151	1162.73	794.74	45/23, 47/24
152	1170.43	800	57/29
153	1178.13	805.26	81/41
154	1185.83	810.53
155	1193.53	815.79
156	1201.23	821.05
157	1208.93	826.32
158	1216.64	831.58
159	1224.34	836.84
160	1232.04	842.11	55/27
161	1239.74	847.37	45/22
162	1247.44	852.63	37/18
163	1255.14	857.89
164	1262.84	863.16	56/27
165	1270.54	868.42	25/12
166	1278.24	873.68
167	1285.94	878.95
168	1293.64	884.21	19/9
169	1301.34	889.47	70/33
170	1309.04	894.74	66/31
171	1316.74	900
172	1324.44	905.26	43/20, 58/27
173	1332.14	910.53	41/19
174	1339.84	915.79
175	1347.54	921.05
176	1355.24	926.32
177	1362.94	931.58
178	1370.64	936.84
179	1378.34	942.11	51/23
180	1386.04	947.37	69/31
181	1393.74	952.63
182	1401.44	957.89
183	1409.14	963.16
184	1416.84	968.42	34/15
185	1424.54	973.68	41/18, 66/29
186	1432.24	978.95
187	1439.94	984.21	62/27
188	1447.64	989.47	30/13
189	1455.34	994.74	51/22
190	1463.04	1000
191	1470.74	1005.26
192	1478.44	1010.53	47/20, 54/23
193	1486.14	1015.79
194	1493.84	1021.05
195	1501.54	1026.32
196	1509.24	1031.58	55/23
197	1516.94	1036.84
198	1524.64	1042.11	41/17
199	1532.34	1047.37
200	1540.04	1052.63	56/23
201	1547.74	1057.89	22/9
202	1555.44	1063.16
203	1563.15	1068.42	37/15
204	1570.85	1073.68	57/23
205	1578.55	1078.95
206	1586.25	1084.21	5/2
207	1593.95	1089.47
208	1601.65	1094.74	58/23
209	1609.35	1100	38/15
210	1617.05	1105.26	28/11
211	1624.75	1110.53	23/9
212	1632.45	1115.79
213	1640.15	1121.05
214	1647.85	1126.32	57/22
215	1655.55	1131.58
216	1663.25	1136.84	81/31
217	1670.95	1142.11
218	1678.65	1147.37	29/11
219	1686.35	1152.63
220	1694.05	1157.89
221	1701.75	1163.16
222	1709.45	1168.42	51/19
223	1717.15	1173.68	62/23
224	1724.85	1178.95	65/24
225	1732.55	1184.21	68/25
226	1740.25	1189.47	41/15
227	1747.95	1194.74
228	1755.65	1200
229	1763.35	1205.26	36/13
230	1771.05	1210.53
231	1778.75	1215.79	81/29
232	1786.45	1221.05
233	1794.15	1226.32	31/11
234	1801.85	1231.58
235	1809.55	1236.84
236	1817.25	1242.11
237	1824.95	1247.37	66/23
238	1832.65	1252.63
239	1840.35	1257.89	55/19
240	1848.05	1263.16
241	1855.75	1268.42
242	1863.45	1273.68	44/15
243	1871.15	1278.95	56/19
244	1878.85	1284.21	74/25
245	1886.55	1289.47
246	1894.25	1294.74
247	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 247edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+1.23	+0.00	+2.47	+1.17	+1.23	-3.83	+3.70	+0.00	+2.40	-0.90	+2.47
	Relative (%)	+16.0	+0.0	+32.1	+15.2	+16.0	-49.7	+48.1	+0.0	+31.2	-11.7	+32.1
Steps (reduced)		156 (156)	247 (0)	312 (65)	362 (115)	403 (156)	437 (190)	468 (221)	494 (0)	518 (24)	539 (45)	559 (65)

Approximation of harmonics in 247edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+2.50	-2.59	+1.17	-2.76	+0.09	+1.23	+0.03	+3.64	-3.83	+0.34	+0.38
	Relative (%)	+32.5	-33.7	+15.2	-35.9	+1.1	+16.0	+0.4	+47.2	-49.7	+4.4	+5.0
Steps (reduced)		577 (83)	593 (99)	609 (115)	623 (129)	637 (143)	650 (156)	662 (168)	674 (180)	684 (190)	695 (201)	705 (211)