210edo

Welcome to 210edo

210edo = 14edo × 15edo

Distinctively interesting choice for an edo, due to its divisibility by both 14 and 15. This means it can be used to play 14edo music and 15edo music at the same time, using the 210/15 and 210/14 vals respectively.

5.714

210edo has a step size of 5.7142857142857 cents. It is a commatonal EDO, because the step size represents commas like 78732/78125, 1728/1715, 121/120.

Selected just intervals by error

The following table shows how some prominent just intervals are represented in 210edo (ordered by absolute error).

Interval, complement	Error (abs., in cents)
7/5, 10/7	0.345
10/9, 9/5	0.453
16/13, 13/8	0.528
15/14, 28/15	0.557
9/7, 14/9	0.798
4/3, 3/2	0.902
6/5, 5/3	1.356
13/12, 24/13	1.43
7/6, 12/7	1.701
9/8, 16/9	1.804
13/11, 22/13	2.219
5/4, 8/5	2.258
18/13, 13/9	2.332
8/7, 7/4	2.603
11/8, 16/11	2.747
13/10, 20/13	2.785
14/13, 13/7	3.13
16/15, 15/8	3.16
12/11, 11/6	3.649
15/13, 26/15	3.688
11/9, 18/11	4.551
11/10, 20/11	5.004
14/11, 11/7	5.349
15/11, 22/15	5.906

Table of 210edo intervals

Step	Five limit	Seven limit	Eleven limit	Thirteen limit
1	78732/78125	1728/1715	121/120	121/120
2	2048/2025	126/125	99/98	99/98
3	15625/15552	245/243	243/242	91/90
4	81/80	64/63	64/63	64/63
5	20000/19683	686/675	55/54	55/54
6	128/125	50/49	50/49	50/49
7	3125/3072	49/48	49/48	49/48
8	6561/6400	36/35	36/35	36/35
9	250/243	250/243	33/32	33/32
10	648/625	405/392	405/392	147/143
11	16875/16384	28/27	28/27	26/25
12	16384/15625	256/245	80/77	27/26
13	25/24	25/24	22/21	22/21
14	6561/6250	360/343	126/121	126/121
15	256/243	21/20	21/20	21/20
16	82944/78125	1296/1225	81/77	81/77
17	135/128	135/128	135/128	52/49
18	62500/59049	343/324	128/121	128/121
19	16/15	16/15	16/15	16/15
20	78125/73728	1225/1152	77/72	77/72
21	2187/2048	15/14	15/14	15/14
22	3125/2916	343/320	121/112	121/112
23	27/25	27/25	27/25	14/13
24	64000/59049	175/162	88/81	13/12
25	2048/1875	160/147	160/147	99/91
26	625/576	49/45	49/45	49/45
27	2187/2000	192/175	12/11	12/11
28	800/729	35/32	11/10	11/10
29	3456/3125	54/49	54/49	54/49
30	1125/1024	441/400	441/400	182/165
31	?	972/875	243/220	72/65
32	10/9	10/9	10/9	10/9
33	17496/15625	384/343	121/108	121/108
34	4096/3645	28/25	28/25	28/25
35	78125/69984	1715/1536	135/121	91/81
36	9/8	9/8	9/8	9/8
37	?	1372/1215	275/243	143/126
38	256/225	256/225	112/99	112/99
39	15625/13824	245/216	154/135	91/80
40	729/640	8/7	8/7	8/7
41	2500/2187	343/300	55/48	55/48
42	144/125	144/125	63/55	63/55
43	9375/8192	147/128	147/128	52/45
44	32768/28125	81/70	81/70	15/13
45	125/108	125/108	125/108	65/56
46	729/625	400/343	64/55	64/55
47	2560/2187	7/6	7/6	7/6
48	18432/15625	288/245	90/77	90/77
49	75/64	75/64	33/28	33/28
50	59049/50000	405/343	324/275	168/143
51	32/27	32/27	32/27	13/11
52	93312/78125	1458/1225	385/324	108/91
53	1215/1024	25/21	25/21	25/21
54	15625/13122	343/288	144/121	144/121
55	6/5	6/5	6/5	6/5
56	78125/65536	875/729	77/64	65/54
57	4096/3375	135/112	135/112	110/91
58	3125/2592	98/81	98/81	91/75
59	243/200	128/105	40/33	40/33
60	8000/6561	175/144	11/9	11/9
61	768/625	60/49	60/49	60/49
62	625/512	49/40	49/40	49/40
63	19683/16000	216/175	27/22	16/13
64	100/81	100/81	99/80	26/21
65	3888/3125	243/196	243/196	225/182
66	8192/6561	56/45	56/45	56/45
67	98304/78125	1536/1225	96/77	81/65
68	5/4	5/4	5/4	5/4
69	19683/15625	432/343	121/96	121/96
70	512/405	63/50	63/50	49/39
71	78125/62208	1225/972	308/243	91/72
72	81/64	80/63	80/63	33/26
73	25000/19683	343/270	242/189	143/112
74	32/25	32/25	14/11	14/11
75	15625/12288	245/192	77/60	77/60
76	6561/5120	9/7	9/7	9/7
77	625/486	625/486	165/128	165/128
78	162/125	162/125	128/99	84/65
79	25600/19683	35/27	35/27	13/10
80	4096/3125	64/49	64/49	64/49
81	125/96	98/75	55/42	55/42
82	6561/5000	450/343	72/55	72/55
83	320/243	21/16	21/16	21/16
84	20736/15625	324/245	324/245	120/91
85	675/512	250/189	250/189	65/49
86	78125/59049	1715/1296	160/121	160/121
87	4/3	4/3	4/3	4/3
88	?	2304/1715	121/90	121/90
89	8192/6075	75/56	66/49	66/49
90	15625/11664	343/256	162/121	162/121
91	27/20	27/20	27/20	27/20
92	80000/59049	875/648	110/81	65/48
93	512/375	200/147	200/147	200/147
94	3125/2304	49/36	49/36	49/36
95	2187/1600	48/35	15/11	15/11
96	1000/729	175/128	11/8	11/8
97	864/625	135/98	135/98	125/91
98	5625/4096	112/81	112/81	91/66
99	65536/46875	243/175	243/175	18/13
100	25/18	25/18	25/18	25/18
101	4374/3125	480/343	168/121	168/121
102	1024/729	7/5	7/5	7/5
103	?	1728/1225	108/77	108/77
104	45/32	45/32	45/32	45/32
105	?	343/243	343/243	343/243
106	64/45	64/45	64/45	64/45
107	78125/55296	1225/864	77/54	77/54
108	729/512	10/7	10/7	10/7
109	3125/2187	343/240	121/84	121/84
110	36/25	36/25	36/25	36/25
111	46875/32768	350/243	231/160	13/9
112	8192/5625	81/56	81/56	75/52
113	625/432	196/135	196/135	143/98
114	729/500	256/175	16/11	16/11
115	3200/2187	35/24	22/15	22/15
116	4608/3125	72/49	72/49	72/49
117	375/256	147/100	147/100	147/100
118	59049/40000	1296/875	81/55	81/55
119	40/27	40/27	40/27	40/27
120	23328/15625	512/343	121/81	121/81
121	6075/4096	112/75	49/33	49/33
122	78125/52488	1715/1152	180/121	180/121
123	3/2	3/2	3/2	3/2
124	?	2401/1600	121/80	121/80
125	1024/675	189/125	189/125	98/65
126	15625/10368	245/162	245/162	91/60
127	243/160	32/21	32/21	32/21
128	10000/6561	343/225	55/36	55/36
129	192/125	75/49	75/49	75/49
130	3125/2048	49/32	49/32	49/32
131	19683/12800	54/35	54/35	20/13
132	125/81	125/81	99/64	65/42
133	972/625	972/625	256/165	256/165
134	10240/6561	14/9	14/9	14/9
135	24576/15625	384/245	120/77	81/52
136	25/16	25/16	11/7	11/7
137	19683/12500	540/343	189/121	189/121
138	128/81	63/40	63/40	52/33
139	?	1944/1225	243/154	143/90
140	405/256	100/63	100/63	78/49
141	31250/19683	343/216	192/121	192/121
142	8/5	8/5	8/5	8/5
143	78125/49152	1225/768	77/48	77/48
144	6561/4096	45/28	45/28	45/28
145	3125/1944	392/243	363/224	363/224
146	81/50	81/50	81/50	21/13
147	32000/19683	175/108	44/27	13/8
148	1024/625	80/49	80/49	80/49
149	625/384	49/30	49/30	49/30
150	6561/4000	288/175	18/11	18/11
151	400/243	105/64	33/20	33/20
152	5184/3125	81/49	81/49	81/49
153	3375/2048	224/135	224/135	91/55
154	?	1458/875	128/77	108/65
155	5/3	5/3	5/3	5/3
156	26244/15625	576/343	121/72	121/72
157	2048/1215	42/25	42/25	42/25
158	78125/46656	1225/729	405/242	91/54
159	27/16	27/16	27/16	22/13
160	?	686/405	275/162	143/84
161	128/75	128/75	56/33	56/33
162	15625/9216	245/144	77/45	77/45
163	2187/1280	12/7	12/7	12/7
164	1250/729	343/200	55/32	55/32
165	216/125	216/125	189/110	112/65
166	28125/16384	140/81	140/81	26/15
167	16384/9375	243/140	243/140	45/26
168	125/72	125/72	110/63	110/63
169	2187/1250	600/343	96/55	96/55
170	1280/729	7/4	7/4	7/4
171	27648/15625	432/245	135/77	135/77
172	225/128	225/128	99/56	99/56
173	?	1215/686	486/275	252/143
174	16/9	16/9	16/9	16/9
175	?	2187/1225	242/135	143/80
176	3645/2048	25/14	25/14	25/14
177	15625/8748	343/192	216/121	216/121
178	9/5	9/5	9/5	9/5
179	?	875/486	231/128	65/36
180	2048/1125	405/224	405/224	165/91
181	3125/1728	49/27	49/27	49/27
182	729/400	64/35	20/11	20/11
183	4000/2187	175/96	11/6	11/6
184	1152/625	90/49	90/49	90/49
185	1875/1024	147/80	147/80	147/80
186	59049/32000	324/175	81/44	24/13
187	50/27	50/27	50/27	13/7
188	5832/3125	640/343	224/121	224/121
189	4096/2187	28/15	28/15	28/15
190	?	2304/1225	144/77	144/77
191	15/8	15/8	15/8	15/8
192	59049/31250	648/343	121/64	121/64
193	256/135	189/100	189/100	49/26
194	78125/41472	1225/648	154/81	91/48
195	243/128	40/21	40/21	40/21
196	12500/6561	343/180	121/63	121/63
197	48/25	48/25	21/11	21/11
198	15625/8192	245/128	77/40	52/27
199	19683/10240	27/14	27/14	25/13
200	625/324	625/324	495/256	286/147
201	243/125	243/125	64/33	64/33
202	12800/6561	35/18	35/18	35/18
203	6144/3125	96/49	96/49	96/49
204	125/64	49/25	49/25	49/25
205	19683/10000	675/343	108/55	108/55
206	160/81	63/32	63/32	63/32
207	31104/15625	486/245	484/243	143/72
208	2025/1024	125/63	125/63	125/63
209	78125/39366	1715/864	240/121	240/121
210	2/1	2/1	2/1	2/1