209edo

Welcome to 209edo

209edo = 11edo × 19edo

Distinctively interesting choice for an edo, due to its divisibility by both 11 and 19. This means it can be used to play 11edo music and 19edo music at the same time, using the 209/19 and 209/11 vals respectively.

5.742

209edo has a step size of 5.7416267942584 cents. It is a commatonal EDO, because the step size represents commas like 15625/15552, 1728/1715, 385/384, 169/168.

Selected just intervals by error

The following table shows how some prominent just intervals are represented in 209edo (ordered by absolute error).

Interval, complement	Error (abs., in cents)
11/8, 16/11	0.122
6/5, 5/3	0.148
13/10, 20/13	0.625
18/13, 13/9	0.703
13/12, 24/13	0.774
15/13, 26/15	0.851
10/9, 9/5	1.328
12/11, 11/6	1.355
4/3, 3/2	1.477
11/10, 20/11	1.503
8/7, 7/4	1.509
5/4, 8/5	1.625
14/11, 11/7	1.631
13/11, 22/13	2.128
16/13, 13/8	2.25
11/9, 18/11	2.831
9/8, 16/9	2.953
15/11, 22/15	2.979
7/6, 12/7	2.986
16/15, 15/8	3.101
7/5, 10/7	3.134
14/13, 13/7	3.759
9/7, 14/9	4.462
15/14, 28/15	4.61

Table of 209edo intervals

Step	Five limit	Seven limit	Eleven limit	Thirteen limit
1	15625/15552	1728/1715	385/384	169/168
2	32768/32805	1029/1024	99/98	99/98
3	81/80	81/80	81/80	78/77
4	3125/3072	245/243	245/242	65/64
5	2048/2025	50/49	50/49	50/49
6	6561/6400	5103/5000	45/44	45/44
7	16875/16384	49/48	49/48	49/48
8	128/125	36/35	36/35	36/35
9	250/243	250/243	33/32	33/32
10	?	1029/1000	1029/1000	91/88
11	648/625	648/625	80/77	27/26
12	25/24	25/24	25/24	25/24
13	?	256/245	256/245	169/162
14	6561/6250	2401/2304	22/21	22/21
15	135/128	21/20	21/20	21/20
16	16384/15625	729/686	363/343	96/91
17	256/243	200/189	128/121	52/49
18	2187/2048	1323/1250	35/33	35/33
19	82944/78125	343/324	343/324	180/169
20	16/15	15/14	15/14	15/14
21	3125/2916	2592/2401	77/72	77/72
22	?	343/320	264/245	264/245
23	27/25	27/25	27/25	14/13
24	625/576	175/162	175/162	13/12
25	32768/30375	160/147	160/147	99/91
26	2187/2000	2187/2000	12/11	12/11
27	1125/1024	35/32	35/32	35/32
28	2048/1875	54/49	54/49	54/49
29	800/729	625/567	11/10	11/10
30	18225/16384	441/400	441/400	182/165
31	3456/3125	972/875	256/231	72/65
32	10/9	10/9	10/9	10/9
33	78125/69984	384/343	49/44	49/44
34	17496/15625	1715/1536	55/49	55/49
35	9/8	9/8	9/8	9/8
36	15625/13824	1944/1715	539/480	91/81
37	4096/3645	500/441	198/175	44/39
38	729/640	567/500	25/22	25/22
39	9375/8192	245/216	245/216	91/80
40	256/225	8/7	8/7	8/7
41	2500/2187	2500/2187	55/48	55/48
42	?	147/128	147/128	147/128
43	144/125	81/70	81/70	15/13
44	125/108	125/108	125/108	52/45
45	?	400/343	343/297	343/297
46	729/625	729/625	64/55	64/55
47	75/64	7/6	7/6	7/6
48	32768/28125	288/245	288/245	169/144
49	2560/2187	2000/1701	33/28	33/28
50	1215/1024	147/125	147/125	13/11
51	18432/15625	1458/1225	640/539	108/91
52	32/27	25/21	25/21	25/21
53	15625/13122	2048/1715	105/88	105/88
54	93312/78125	343/288	176/147	176/147
55	6/5	6/5	6/5	6/5
56	3125/2592	875/729	77/64	65/54
57	65536/54675	1250/1029	297/245	110/91
58	243/200	243/200	40/33	40/33
59	625/512	98/81	98/81	39/32
60	4096/3375	60/49	60/49	60/49
61	8000/6561	6250/5103	11/9	11/9
62	10125/8192	49/40	49/40	49/40
63	768/625	216/175	121/98	16/13
64	100/81	100/81	99/80	26/21
65	?	1280/1029	245/198	245/198
66	3888/3125	2187/1750	96/77	81/65
67	5/4	5/4	5/4	5/4
68	78125/62208	432/343	343/275	169/135
69	8192/6561	2401/1920	44/35	44/35
70	81/64	63/50	63/50	49/39
71	15625/12288	1225/972	1225/968	91/72
72	512/405	80/63	80/63	33/26
73	6561/5120	3072/2401	14/11	14/11
74	84375/65536	245/192	245/192	169/132
75	32/25	9/7	9/7	9/7
76	625/486	625/486	77/60	77/60
77	?	1029/800	891/686	352/273
78	162/125	162/125	100/77	84/65
79	125/96	35/27	35/27	13/10
80	65536/50625	64/49	64/49	64/49
81	6561/5000	6561/5000	55/42	55/42
82	675/512	21/16	21/16	21/16
83	4096/3125	324/245	324/245	120/91
84	320/243	250/189	33/25	33/25
85	10935/8192	1323/1000	175/132	117/88
86	20736/15625	1715/1296	512/385	121/91
87	4/3	4/3	4/3	4/3
88	15625/11664	2304/1715	147/110	147/110
89	?	343/256	66/49	66/49
90	27/20	27/20	27/20	27/20
91	3125/2304	875/648	490/363	65/48
92	8192/6075	200/147	200/147	88/65
93	2187/1600	1701/1250	15/11	15/11
94	5625/4096	49/36	49/36	49/36
95	512/375	48/35	48/35	48/35
96	1000/729	1000/729	11/8	11/8
97	91125/65536	343/250	343/250	91/66
98	864/625	243/175	242/175	18/13
99	25/18	25/18	25/18	25/18
100	?	480/343	245/176	169/121
101	4374/3125	2401/1728	88/63	88/63
102	45/32	7/5	7/5	7/5
103	65536/46875	486/343	484/343	128/91
104	1024/729	625/441	99/70	55/39
105	729/512	567/400	125/88	78/55
106	46875/32768	343/243	343/242	91/64
107	64/45	10/7	10/7	10/7
108	3125/2187	3125/2187	63/44	63/44
109	?	343/240	343/240	242/169
110	36/25	36/25	36/25	36/25
111	625/432	350/243	175/121	13/9
112	?	500/343	500/343	132/91
113	729/500	729/500	16/11	16/11
114	375/256	35/24	35/24	35/24
115	8192/5625	72/49	72/49	72/49
116	3200/2187	2500/1701	22/15	22/15
117	6075/4096	147/100	147/100	65/44
118	4608/3125	729/490	363/245	96/65
119	40/27	40/27	40/27	40/27
120	78125/52488	512/343	49/33	49/33
121	23328/15625	1715/1152	220/147	220/147
122	3/2	3/2	3/2	3/2
123	15625/10368	2592/1715	385/256	169/112
124	16384/10935	2000/1323	264/175	176/117
125	243/160	189/125	50/33	50/33
126	3125/2048	245/162	245/162	91/60
127	1024/675	32/21	32/21	32/21
128	10000/6561	10000/6561	55/36	55/36
129	50625/32768	49/32	49/32	49/32
130	192/125	54/35	54/35	20/13
131	125/81	125/81	77/50	65/42
132	?	1600/1029	1225/792	273/176
133	972/625	972/625	120/77	81/52
134	25/16	14/9	14/9	14/9
135	?	384/245	343/220	169/108
136	10240/6561	2401/1536	11/7	11/7
137	405/256	63/40	63/40	52/33
138	24576/15625	1944/1225	1089/686	144/91
139	128/81	100/63	100/63	78/49
140	6561/4096	3840/2401	35/22	35/22
141	?	343/216	343/216	270/169
142	8/5	8/5	8/5	8/5
143	3125/1944	3125/1944	77/48	77/48
144	?	1029/640	396/245	396/245
145	81/50	81/50	81/50	21/13
146	625/384	175/108	175/108	13/8
147	16384/10125	80/49	80/49	80/49
148	6561/4000	5103/3125	18/11	18/11
149	3375/2048	49/30	49/30	49/30
150	1024/625	81/49	81/49	64/39
151	400/243	400/243	33/20	33/20
152	54675/32768	1029/625	490/297	91/55
153	5184/3125	1458/875	128/77	108/65
154	5/3	5/3	5/3	5/3
155	78125/46656	576/343	147/88	147/88
156	26244/15625	1715/1024	165/98	165/98
157	27/16	27/16	27/16	27/16
158	15625/9216	1225/729	539/320	91/54
159	2048/1215	250/147	250/147	22/13
160	2187/1280	1701/1000	56/33	56/33
161	28125/16384	245/144	245/144	169/99
162	128/75	12/7	12/7	12/7
163	1250/729	1250/729	55/32	55/32
164	?	343/200	343/200	343/200
165	216/125	216/125	121/70	45/26
166	125/72	125/72	125/72	26/15
167	?	256/147	256/147	256/147
168	2187/1250	2187/1250	96/55	96/55
169	225/128	7/4	7/4	7/4
170	16384/9375	432/245	432/245	160/91
171	1280/729	1000/567	44/25	44/25
172	3645/2048	441/250	175/99	39/22
173	27648/15625	1715/972	960/539	162/91
174	16/9	16/9	16/9	16/9
175	15625/8748	3072/1715	98/55	98/55
176	?	343/192	88/49	88/49
177	9/5	9/5	9/5	9/5
178	3125/1728	875/486	231/128	65/36
179	32768/18225	625/343	625/343	165/91
180	729/400	729/400	20/11	20/11
181	1875/1024	49/27	49/27	49/27
182	2048/1125	64/35	64/35	64/35
183	4000/2187	3125/1701	11/6	11/6
184	30375/16384	147/80	147/80	147/80
185	1152/625	324/175	324/175	24/13
186	50/27	50/27	50/27	13/7
187	?	640/343	245/132	245/132
188	5832/3125	2401/1296	144/77	121/65
189	15/8	15/8	15/8	15/8
190	78125/41472	648/343	539/288	169/90
191	4096/2187	2401/1280	66/35	66/35
192	243/128	189/100	121/64	49/26
193	15625/8192	1225/648	686/363	91/48
194	256/135	40/21	40/21	40/21
195	12500/6561	4608/2401	21/11	21/11
196	?	245/128	245/128	169/88
197	48/25	27/14	27/14	25/13
198	625/324	625/324	77/40	52/27
199	?	2000/1029	1331/686	176/91
200	243/125	243/125	64/33	64/33
201	125/64	35/18	35/18	35/18
202	32768/16875	96/49	96/49	96/49
203	12800/6561	10000/5103	55/28	55/28
204	2025/1024	49/25	49/25	49/25
205	6144/3125	486/245	484/245	128/65
206	160/81	125/63	99/50	77/39
207	32805/16384	2048/1029	175/88	143/72
208	31104/15625	1715/864	768/385	336/169
209	2/1	2/1	2/1	2/1