286edo

Welcome to 286edo

286edo = 13edo × 22edo

Distinctively interesting choice for an edo, due to its divisibility by both 13 and 22. This means it can be used to play 13edo music and 22edo music at the same time, using the 286/22 and 286/13 vals respectively.

4.196

286edo has a step size of 4.1958041958042 cents. It is a commatonal EDO, because the step size represents commas like 78732/78125, 225/224. It is also a nanotonal EDO.

Selected just intervals by error

The following table shows how some prominent just intervals are represented in 286edo (ordered by absolute error).

Interval, complement	Error (abs., in cents)
13/12, 24/13	0.111
15/11, 22/15	0.112
15/13, 26/15	0.189
5/4, 8/5	0.3
13/11, 22/13	0.301
8/7, 7/4	0.405
12/11, 11/6	0.412
7/5, 10/7	0.705
11/9, 18/11	0.844
6/5, 5/3	0.956
13/10, 20/13	1.067
18/13, 13/9	1.145
4/3, 3/2	1.256
16/13, 13/8	1.367
11/10, 20/11	1.368
16/15, 15/8	1.555
7/6, 12/7	1.661
11/8, 16/11	1.668
14/13, 13/7	1.772
15/14, 28/15	1.96
14/11, 11/7	2.072
10/9, 9/5	2.212
9/8, 16/9	2.511
9/7, 14/9	2.916

Table of 286edo intervals

Step	Five limit	Seven limit	Eleven limit	Thirteen limit
1	78732/78125	225/224	225/224	225/224
2	32768/32805	1029/1024	176/175	169/168
3	15625/15552	126/125	99/98	99/98
4	81/80	81/80	81/80	81/80
5	?	245/243	100/99	78/77
6	2048/2025	875/864	245/242	65/64
7	3125/3072	64/63	64/63	64/63
8	6561/6400	50/49	50/49	50/49
9	20000/19683	49/48	45/44	45/44
10	128/125	128/125	128/125	128/125
11	16875/16384	36/35	36/35	36/35
12	?	405/392	33/32	33/32
13	250/243	250/243	250/243	65/63
14	648/625	648/625	125/121	91/88
15	?	729/700	512/495	27/26
16	?	28/27	28/27	26/25
17	25/24	25/24	25/24	25/24
18	6561/6250	256/245	256/245	169/162
19	20480/19683	360/343	22/21	22/21
20	16384/15625	21/20	21/20	21/20
21	135/128	135/128	135/128	104/99
22	?	1296/1225	132/125	96/91
23	256/243	256/243	256/243	55/52
24	78125/73728	200/189	128/121	52/49
25	2187/2048	343/324	35/33	35/33
26	62500/59049	1225/1152	375/352	180/169
27	16/15	16/15	16/15	16/15
28	?	15/14	15/14	15/14
29	?	343/320	189/176	189/176
30	3125/2916	672/625	242/225	130/121
31	27/25	27/25	27/25	14/13
32	?	243/224	243/224	225/208
33	32768/30375	175/162	175/162	13/12
34	625/576	625/576	525/484	99/91
35	2187/2000	160/147	88/81	88/81
36	64000/59049	49/45	12/11	12/11
37	2048/1875	35/32	35/32	35/32
38	1125/1024	192/175	192/175	128/117
39	?	54/49	11/10	11/10
40	800/729	441/400	243/220	208/189
41	3456/3125	567/512	400/363	182/165
42	18225/16384	972/875	693/625	72/65
43	?	448/405	256/231	231/208
44	10/9	10/9	10/9	10/9
45	17496/15625	125/112	49/44	49/44
46	65536/59049	384/343	352/315	189/169
47	78125/69984	28/25	28/25	28/25
48	9/8	9/8	9/8	9/8
49	?	2025/1792	704/625	91/81
50	4096/3645	1944/1715	198/175	44/39
51	15625/13824	567/500	363/320	147/130
52	729/640	500/441	112/99	112/99
53	?	245/216	25/22	25/22
54	256/225	256/225	256/225	256/225
55	9375/8192	8/7	8/7	8/7
56	59049/51200	225/196	55/48	55/48
57	2500/2187	147/128	147/128	147/128
58	144/125	144/125	121/105	121/105
59	?	81/70	81/70	15/13
60	?	280/243	280/243	52/45
61	125/108	125/108	125/108	65/56
62	729/625	512/441	512/441	121/104
63	?	400/343	64/55	64/55
64	32768/28125	7/6	7/6	7/6
65	75/64	75/64	75/64	75/64
66	59049/50000	288/245	88/75	88/75
67	2560/2187	147/125	33/28	33/28
68	18432/15625	189/160	189/160	189/160
69	1215/1024	1215/1024	350/297	13/11
70	?	1458/1225	297/250	77/65
71	32/27	32/27	32/27	32/27
72	78125/65536	25/21	25/21	25/21
73	19683/16384	343/288	105/88	105/88
74	15625/13122	448/375	176/147	176/147
75	6/5	6/5	6/5	6/5
76	?	135/112	77/64	77/64
77	65536/54675	875/729	875/729	65/54
78	3125/2592	756/625	121/100	110/91
79	243/200	243/200	243/200	63/52
80	?	98/81	40/33	40/33
81	4096/3375	175/144	147/121	39/32
82	625/512	128/105	128/105	128/105
83	19683/16000	60/49	11/9	11/9
84	8000/6561	49/40	27/22	27/22
85	768/625	315/256	315/256	315/256
86	10125/8192	216/175	121/98	16/13
87	?	243/196	99/80	99/80
88	100/81	100/81	100/81	26/21
89	3888/3125	625/504	150/121	150/121
90	?	1280/1029	704/567	81/65
91	?	56/45	56/45	56/45
92	5/4	5/4	5/4	5/4
93	19683/15625	1125/896	441/352	169/135
94	8192/6561	432/343	44/35	44/35
95	78125/62208	63/50	63/50	49/39
96	81/64	81/64	81/64	81/64
97	?	1225/972	125/99	91/72
98	512/405	512/405	512/405	33/26
99	15625/12288	80/63	80/63	80/63
100	6561/5120	125/98	14/11	14/11
101	25000/19683	245/192	225/176	216/169
102	32/25	32/25	32/25	32/25
103	84375/65536	9/7	9/7	9/7
104	?	1029/800	165/128	104/81
105	625/486	625/486	484/375	156/121
106	162/125	162/125	162/125	84/65
107	?	729/560	128/99	128/99
108	65536/50625	35/27	35/27	13/10
109	125/96	125/96	125/96	125/96
110	6561/5000	64/49	64/49	64/49
111	25600/19683	98/75	55/42	55/42
112	4096/3125	21/16	21/16	21/16
113	675/512	675/512	675/512	130/99
114	?	324/245	33/25	33/25
115	320/243	320/243	297/224	189/143
116	20736/15625	250/189	160/121	65/49
117	10935/8192	1715/1296	175/132	117/88
118	78125/59049	896/675	512/385	225/169
119	4/3	4/3	4/3	4/3
120	?	75/56	75/56	75/56
121	?	343/256	343/256	169/126
122	15625/11664	168/125	66/49	66/49
123	27/20	27/20	27/20	27/20
124	?	980/729	400/297	104/77
125	8192/6075	875/648	490/363	65/48
126	3125/2304	256/189	256/189	256/189
127	2187/1600	200/147	110/81	110/81
128	80000/59049	49/36	15/11	15/11
129	512/375	175/128	175/128	175/128
130	5625/4096	48/35	48/35	48/35
131	?	135/98	11/8	11/8
132	1000/729	441/320	243/176	243/176
133	864/625	864/625	242/175	91/66
134	91125/65536	243/175	243/175	18/13
135	?	112/81	112/81	104/75
136	25/18	25/18	25/18	25/18
137	4374/3125	625/448	245/176	245/176
138	81920/59049	480/343	88/63	88/63
139	65536/46875	7/5	7/5	7/5
140	45/32	45/32	45/32	45/32
141	?	1728/1225	176/125	128/91
142	1024/729	486/343	99/70	55/39
143	78125/55296	567/400	363/256	147/104
144	729/512	343/243	140/99	78/55
145	?	1225/864	125/88	91/64
146	64/45	64/45	64/45	64/45
147	46875/32768	10/7	10/7	10/7
148	59049/40960	343/240	63/44	63/44
149	3125/2187	735/512	352/245	243/169
150	36/25	36/25	36/25	36/25
151	?	81/56	81/56	75/52
152	?	350/243	350/243	13/9
153	625/432	625/432	175/121	132/91
154	729/500	640/441	352/243	189/130
155	?	196/135	16/11	16/11
156	8192/5625	35/24	35/24	35/24
157	375/256	256/175	256/175	256/175
158	59049/40000	72/49	22/15	22/15
159	3200/2187	147/100	81/55	81/55
160	4608/3125	189/128	189/128	189/128
161	6075/4096	1296/875	363/245	65/44
162	?	729/490	297/200	77/52
163	40/27	40/27	40/27	40/27
164	23328/15625	125/84	49/33	49/33
165	98415/65536	512/343	512/343	252/169
166	78125/52488	112/75	112/75	112/75
167	3/2	3/2	3/2	3/2
168	?	675/448	385/256	338/225
169	16384/10935	2592/1715	264/175	169/112
170	15625/10368	189/125	121/80	98/65
171	243/160	243/160	243/160	243/160
172	?	245/162	50/33	50/33
173	1024/675	875/576	735/484	99/65
174	3125/2048	32/21	32/21	32/21
175	19683/12800	75/49	55/36	55/36
176	10000/6561	49/32	49/32	49/32
177	192/125	192/125	192/125	169/110
178	50625/32768	54/35	54/35	20/13
179	?	1120/729	99/64	99/64
180	125/81	125/81	125/81	65/42
181	972/625	972/625	375/242	121/78
182	?	1600/1029	256/165	81/52
183	?	14/9	14/9	14/9
184	25/16	25/16	25/16	25/16
185	19683/12500	384/245	352/225	169/108
186	10240/6561	196/125	11/7	11/7
187	24576/15625	63/40	63/40	63/40
188	405/256	405/256	405/256	52/33
189	?	1944/1225	198/125	144/91
190	128/81	128/81	128/81	128/81
191	78125/49152	100/63	100/63	78/49
192	6561/4096	343/216	35/22	35/22
193	31250/19683	1225/768	704/441	270/169
194	8/5	8/5	8/5	8/5
195	?	45/28	45/28	45/28
196	?	1029/640	567/352	130/81
197	3125/1944	1008/625	121/75	121/75
198	81/50	81/50	81/50	21/13
199	?	392/243	160/99	160/99
200	16384/10125	175/108	125/77	13/8
201	625/384	512/315	512/315	275/169
202	6561/4000	80/49	44/27	44/27
203	32000/19683	49/30	18/11	18/11
204	1024/625	105/64	105/64	105/64
205	3375/2048	288/175	242/147	64/39
206	?	81/49	33/20	33/20
207	400/243	400/243	400/243	104/63
208	5184/3125	625/378	200/121	91/55
209	54675/32768	1458/875	875/528	108/65
210	?	224/135	128/77	128/77
211	5/3	5/3	5/3	5/3
212	26244/15625	375/224	147/88	147/88
213	32768/19683	576/343	176/105	176/105
214	78125/46656	42/25	42/25	42/25
215	27/16	27/16	27/16	27/16
216	?	1225/729	500/297	91/54
217	2048/1215	2048/1215	297/175	22/13
218	15625/9216	320/189	320/189	243/143
219	2187/1280	250/147	56/33	56/33
220	?	245/144	75/44	75/44
221	128/75	128/75	128/75	128/75
222	28125/16384	12/7	12/7	12/7
223	?	343/200	55/32	55/32
224	1250/729	441/256	441/256	169/98
225	216/125	216/125	121/70	112/65
226	?	243/140	243/140	45/26
227	?	140/81	140/81	26/15
228	125/72	125/72	125/72	125/72
229	2187/1250	256/147	256/147	256/147
230	?	392/225	96/55	96/55
231	16384/9375	7/4	7/4	7/4
232	225/128	225/128	225/128	225/128
233	?	432/245	44/25	44/25
234	1280/729	441/250	99/56	99/56
235	27648/15625	567/320	567/320	143/81
236	3645/2048	1715/972	175/99	39/22
237	?	2187/1225	625/352	162/91
238	16/9	16/9	16/9	16/9
239	?	25/14	25/14	25/14
240	59049/32768	343/192	315/176	315/176
241	15625/8748	224/125	88/49	88/49
242	9/5	9/5	9/5	9/5
243	?	405/224	231/128	231/128
244	32768/18225	875/486	875/486	65/36
245	3125/1728	1024/567	363/200	165/91
246	729/400	729/400	440/243	189/104
247	?	49/27	20/11	20/11
248	2048/1125	175/96	175/96	117/64
249	1875/1024	64/35	64/35	64/35
250	59049/32000	90/49	11/6	11/6
251	4000/2187	147/80	81/44	81/44
252	1152/625	945/512	945/512	182/99
253	30375/16384	324/175	231/125	24/13
254	?	448/243	297/160	297/160
255	50/27	50/27	50/27	13/7
256	5832/3125	625/336	225/121	121/65
257	?	640/343	352/189	243/130
258	?	28/15	28/15	28/15
259	15/8	15/8	15/8	15/8
260	59049/31250	2304/1225	704/375	169/90
261	4096/2187	648/343	66/35	66/35
262	78125/41472	189/100	121/64	49/26
263	243/128	243/128	243/128	104/55
264	?	1225/648	125/66	91/48
265	256/135	256/135	256/135	99/52
266	15625/8192	40/21	40/21	40/21
267	19683/10240	343/180	21/11	21/11
268	12500/6561	245/128	245/128	245/128
269	48/25	48/25	48/25	48/25
270	?	27/14	27/14	25/13
271	?	1400/729	495/256	52/27
272	625/324	625/324	242/125	176/91
273	243/125	243/125	243/125	126/65
274	?	784/405	64/33	64/33
275	32768/16875	35/18	35/18	35/18
276	125/64	125/64	125/64	125/64
277	19683/10000	96/49	88/45	88/45
278	12800/6561	49/25	49/25	49/25
279	6144/3125	63/32	63/32	63/32
280	2025/1024	1728/875	484/245	65/33
281	?	486/245	99/50	77/39
282	160/81	160/81	160/81	160/81
283	31104/15625	125/63	125/63	125/63
284	32805/16384	1715/864	175/88	175/88
285	78125/39366	448/225	448/225	448/225
286	2/1	2/1	2/1	2/1