247edo

Welcome to 247edo

247edo = 13edo × 19edo

Distinctively interesting choice for an edo, due to its divisibility by both 13 and 19. This means it can be used to play 13edo music and 19edo music at the same time, using the 247/19 and 247/13 vals respectively.

4.858

247edo has a step size of 4.8582995951417 cents. It is a commatonal EDO, because the step size represents commas like 176/175. It is also a nanotonal EDO.

Selected just intervals by error

The following table shows how some prominent just intervals are represented in 247edo (ordered by absolute error).

Interval, complement	Error (abs., in cents)
16/15, 15/8	0.01
12/11, 11/6	0.03
15/13, 26/15	0.032
16/13, 13/8	0.042
14/11, 11/7	0.306
7/6, 12/7	0.336
14/13, 13/7	1.982
15/14, 28/15	2.015
8/7, 7/4	2.024
13/11, 22/13	2.288
13/12, 24/13	2.318
15/11, 22/15	2.32
11/8, 16/11	2.33
5/4, 8/5	2.35
4/3, 3/2	2.36
11/9, 18/11	2.39
13/10, 20/13	2.392
9/7, 14/9	2.695
7/5, 10/7	4.375
18/13, 13/9	4.678
11/10, 20/11	4.68
6/5, 5/3	4.71
9/8, 16/9	4.72
10/9, 9/5	7.07

Table of 247edo intervals

Step	Five limit	Seven limit	Eleven limit	Thirteen limit
1	?	?	176/175	176/175
2	81/80	81/80	81/80	81/80
3	32768/32805	10976/10935	99/98	99/98
4	6561/6400	2430/2401	896/891	66/65
5	2048/2025	245/243	245/242	78/77
6	?	19683/19208	56/55	56/55
7	128/125	49/48	49/48	49/48
8	?	?	45/44	45/44
9	648/625	36/35	36/35	36/35
10	?	33614/32805	33/32	33/32
11	6561/6250	405/392	363/350	363/350
12	20000/19683	2240/2187	1120/1089	27/26
13	?	6561/6272	343/330	26/25
14	250/243	28/27	28/27	28/27
15	?	?	80/77	80/77
16	25/24	21/20	21/20	21/20
17	?	?	22/21	22/21
18	135/128	135/128	135/128	135/128
19	20480/19683	6860/6561	297/280	96/91
20	2187/2048	729/686	363/343	55/52
21	256/243	256/243	128/121	117/110
22	?	59049/54880	35/33	35/33
23	16/15	16/15	16/15	16/15
24	?	?	77/72	77/72
25	27/25	15/14	15/14	15/14
26	?	62720/59049	264/245	14/13
27	2187/2000	243/224	121/112	121/112
28	32768/30375	784/729	392/363	225/208
29	?	13122/12005	320/297	13/12
30	2048/1875	49/45	49/45	49/45
31	?	?	12/11	12/11
32	625/576	35/32	35/32	35/32
33	?	?	11/10	11/10
34	1125/1024	54/49	54/49	54/49
35	64000/59049	2401/2187	495/448	72/65
36	18225/16384	2187/1960	980/891	208/189
37	800/729	448/405	400/363	195/176
38	?	98415/87808	49/44	39/35
39	10/9	10/9	10/9	10/9
40	?	?	352/315	352/315
41	9/8	9/8	9/8	9/8
42	65536/59049	21952/19683	55/49	55/49
43	729/640	729/640	363/320	44/39
44	4096/3645	1372/1215	686/605	260/231
45	59049/51200	10935/9604	112/99	91/80
46	256/225	245/216	245/216	143/125
47	?	?	25/22	25/22
48	144/125	8/7	8/7	8/7
49	?	67228/59049	55/48	55/48
50	729/625	81/70	81/70	81/70
51	?	12544/10935	297/256	15/13
52	59049/50000	3645/3136	343/297	52/45
53	2500/2187	280/243	140/121	121/104
54	?	19683/16807	64/55	64/55
55	125/108	7/6	7/6	7/6
56	?	?	88/75	88/75
57	75/64	75/64	75/64	75/64
58	?	38416/32805	33/28	33/28
59	1215/1024	405/343	405/343	77/65
60	2560/2187	1715/1458	1280/1089	13/11
61	19683/16384	6561/5488	196/165	196/165
62	32/27	32/27	32/27	32/27
63	?	?	105/88	105/88
64	6/5	6/5	6/5	6/5
65	?	?	77/64	77/64
66	243/200	135/112	121/100	121/100
67	65536/54675	7840/6561	297/245	63/52
68	19683/16000	2187/1792	1089/896	65/54
69	4096/3375	98/81	98/81	98/81
70	?	59049/48020	40/33	39/32
71	768/625	49/40	49/40	49/40
72	?	?	11/9	11/9
73	625/512	60/49	60/49	60/49
74	?	24010/19683	99/80	16/13
75	10125/8192	243/196	121/98	121/98
76	8000/6561	896/729	448/363	81/65
77	?	19683/15680	245/198	26/21
78	100/81	56/45	56/45	56/45
79	?	?	96/77	96/77
80	5/4	5/4	5/4	5/4
81	?	?	44/35	44/35
82	81/64	81/64	81/64	81/64
83	8192/6561	2744/2187	495/392	208/165
84	6561/5120	2187/1715	1120/891	33/26
85	512/405	343/270	343/270	195/154
86	?	98415/76832	14/11	14/11
87	32/25	32/25	32/25	32/25
88	?	?	77/60	77/60
89	162/125	9/7	9/7	9/7
90	?	16807/13122	165/128	50/39
91	6561/5000	729/560	363/280	104/81
92	25000/19683	1568/1215	784/605	135/104
93	?	21870/16807	128/99	13/10
94	625/486	35/27	35/27	35/27
95	?	?	72/55	72/55
96	125/96	21/16	21/16	21/16
97	?	76832/59049	33/25	33/25
98	675/512	324/245	324/245	154/117
99	25600/19683	4802/3645	297/224	120/91
100	10935/8192	3645/2744	392/297	224/169
101	320/243	320/243	160/121	117/88
102	?	59049/43904	147/110	65/49
103	4/3	4/3	4/3	4/3
104	?	?	385/288	385/288
105	27/20	27/20	27/20	27/20
106	?	43904/32805	66/49	35/26
107	2187/1600	1215/896	605/448	88/65
108	8192/6075	980/729	490/363	104/77
109	?	6561/4802	224/165	65/48
110	512/375	49/36	49/36	49/36
111	?	?	15/11	15/11
112	864/625	48/35	48/35	48/35
113	?	?	11/8	11/8
114	4374/3125	135/98	135/98	135/98
115	80000/59049	8960/6561	891/640	18/13
116	91125/65536	2187/1568	686/495	104/75
117	1000/729	112/81	112/81	112/81
118	?	?	245/176	39/28
119	25/18	7/5	7/5	7/5
120	?	?	88/63	88/63
121	45/32	45/32	45/32	45/32
122	81920/59049	27440/19683	99/70	99/70
123	729/512	486/343	363/256	55/39
124	1024/729	343/243	343/242	78/55
125	59049/40960	19683/13720	140/99	91/64
126	64/45	64/45	64/45	64/45
127	?	?	63/44	63/44
128	36/25	10/7	10/7	10/7
129	?	84035/59049	231/160	56/39
130	729/500	81/56	81/56	81/56
131	?	3136/2187	495/343	75/52
132	59049/40000	6561/4480	1280/891	13/9
133	3125/2187	196/135	175/121	175/121
134	?	98415/67228	16/11	16/11
135	625/432	35/24	35/24	35/24
136	?	?	22/15	22/15
137	375/256	72/49	72/49	72/49
138	?	9604/6561	165/112	96/65
139	6075/4096	729/490	363/245	77/52
140	3200/2187	1792/1215	896/605	65/44
141	98415/65536	32805/21952	49/33	49/33
142	40/27	40/27	40/27	40/27
143	?	?	525/352	525/352
144	3/2	3/2	3/2	3/2
145	?	87808/59049	220/147	98/65
146	243/160	243/160	121/80	121/80
147	16384/10935	5488/3645	297/196	169/112
148	19683/12800	3645/2401	448/297	91/60
149	1024/675	245/162	245/162	117/77
150	?	59049/38416	50/33	50/33
151	192/125	32/21	32/21	32/21
152	?	?	55/36	55/36
153	972/625	54/35	54/35	54/35
154	?	16807/10935	99/64	20/13
155	19683/12500	1215/784	605/392	208/135
156	10000/6561	1120/729	560/363	81/52
157	?	19683/12544	256/165	39/25
158	125/81	14/9	14/9	14/9
159	?	?	120/77	120/77
160	25/16	25/16	25/16	25/16
161	?	?	11/7	11/7
162	405/256	405/256	405/256	225/143
163	10240/6561	3430/2187	891/560	52/33
164	6561/4096	2187/1372	784/495	165/104
165	128/81	128/81	128/81	128/81
166	?	?	35/22	35/22
167	8/5	8/5	8/5	8/5
168	?	?	77/48	77/48
169	81/50	45/28	45/28	45/28
170	?	31360/19683	396/245	21/13
171	6561/4000	729/448	363/224	130/81
172	16384/10125	392/243	196/121	196/121
173	?	19683/12005	160/99	13/8
174	1024/625	49/30	49/30	49/30
175	?	?	18/11	18/11
176	625/384	80/49	80/49	80/49
177	?	96040/59049	33/20	33/20
178	3375/2048	81/49	81/49	81/49
179	32000/19683	2401/1458	1331/800	91/55
180	54675/32768	6561/3920	490/297	104/63
181	400/243	224/135	200/121	200/121
182	?	?	128/77	117/70
183	5/3	5/3	5/3	5/3
184	?	?	176/105	176/105
185	27/16	27/16	27/16	27/16
186	32768/19683	10976/6561	165/98	165/98
187	2187/1280	2187/1280	1089/640	22/13
188	2048/1215	686/405	686/405	130/77
189	?	32805/19208	56/33	56/33
190	128/75	128/75	128/75	128/75
191	?	?	75/44	75/44
192	216/125	12/7	12/7	12/7
193	?	33614/19683	55/32	55/32
194	2187/1250	243/140	121/70	121/70
195	?	6272/3645	594/343	45/26
196	?	10935/6272	343/198	26/15
197	1250/729	140/81	140/81	140/81
198	?	59049/33614	96/55	96/55
199	125/72	7/4	7/4	7/4
200	?	?	44/25	44/25
201	225/128	225/128	225/128	225/128
202	?	19208/10935	99/56	99/56
203	3645/2048	1215/686	605/343	231/130
204	1280/729	1280/729	640/363	39/22
205	59049/32768	19683/10976	98/55	98/55
206	16/9	16/9	16/9	16/9
207	?	?	315/176	315/176
208	9/5	9/5	9/5	9/5
209	?	?	88/49	70/39
210	729/400	405/224	363/200	352/195
211	32768/18225	3920/2187	891/490	189/104
212	59049/32000	4374/2401	896/495	65/36
213	2048/1125	49/27	49/27	49/27
214	?	?	20/11	20/11
215	1152/625	64/35	64/35	64/35
216	?	?	11/6	11/6
217	1875/1024	90/49	90/49	90/49
218	?	12005/6561	297/160	24/13
219	30375/16384	729/392	363/196	363/196
220	4000/2187	448/243	224/121	121/65
221	?	59049/31360	245/132	13/7
222	50/27	28/15	28/15	28/15
223	?	?	144/77	144/77
224	15/8	15/8	15/8	15/8
225	?	?	66/35	49/26
226	243/128	243/128	121/64	121/64
227	4096/2187	1372/729	686/363	104/55
228	19683/10240	6561/3430	560/297	91/48
229	256/135	256/135	256/135	143/75
230	?	?	21/11	21/11
231	48/25	40/21	40/21	40/21
232	?	?	77/40	77/40
233	243/125	27/14	27/14	27/14
234	?	12544/6561	495/256	25/13
235	19683/10000	2187/1120	1089/560	52/27
236	12500/6561	784/405	700/363	405/208
237	?	32805/16807	64/33	39/20
238	625/324	35/18	35/18	35/18
239	?	?	88/45	88/45
240	125/64	63/32	63/32	63/32
241	?	38416/19683	55/28	55/28
242	2025/1024	486/245	484/245	77/39
243	12800/6561	2401/1215	891/448	65/33
244	32805/16384	10935/5488	196/99	196/99
245	160/81	160/81	160/81	143/72
246	?	?	175/88	175/88
247	2/1	2/1	2/1	2/1