220edo

Welcome to 220edo

220edo = 11edo × 20edo

Distinctively interesting choice for an edo, due to its divisibility by both 11 and 20. This means it can be used to play 11edo music and 20edo music at the same time, using the 220/20 and 220/11 vals respectively.

5.455

220edo has a step size of 5.4545454545455 cents. It is a commatonal EDO, because the step size represents commas like 15625/15552, 2401/2400, 176/175, 169/168. It is also a nanotonal EDO.

Selected just intervals by error

The following table shows how some prominent just intervals are represented in 220edo (ordered by absolute error).

Interval, complement	Error (abs., in cents)
13/11, 22/13	0.119
7/6, 12/7	0.402
11/8, 16/11	0.409
16/13, 13/8	0.528
15/14, 28/15	0.557
6/5, 5/3	0.722
5/4, 8/5	0.959
7/5, 10/7	1.124
9/7, 14/9	1.28
11/10, 20/11	1.368
13/10, 20/13	1.487
4/3, 3/2	1.681
8/7, 7/4	2.083
12/11, 11/6	2.09
13/12, 24/13	2.209
10/9, 9/5	2.404
14/11, 11/7	2.492
14/13, 13/7	2.611
16/15, 15/8	2.64
15/11, 22/15	3.049
15/13, 26/15	3.168
9/8, 16/9	3.363
11/9, 18/11	3.772
18/13, 13/9	3.89

Table of 220edo intervals

Step	Five limit	Seven limit	Eleven limit	Thirteen limit
1	15625/15552	2401/2400	176/175	169/168
2	2048/2025	225/224	121/120	121/120
3	20000/19683	126/125	99/98	91/90
4	78732/78125	64/63	64/63	64/63
5	81/80	81/80	55/54	55/54
6	3125/3072	50/49	50/49	50/49
7	128/125	49/48	49/48	49/48
8	250/243	250/243	45/44	40/39
9	?	36/35	36/35	36/35
10	6561/6400	1029/1000	33/32	33/32
11	16875/16384	28/27	28/27	28/27
12	648/625	648/625	80/77	26/25
13	25/24	25/24	25/24	25/24
14	16384/15625	392/375	22/21	22/21
15	256/243	256/243	256/243	104/99
16	62500/59049	21/20	21/20	21/20
17	6561/6250	200/189	81/77	81/77
18	135/128	135/128	128/121	52/49
19	78125/73728	625/588	35/33	35/33
20	16/15	16/15	16/15	16/15
21	3125/2916	1701/1600	77/72	77/72
22	32768/30375	15/14	15/14	15/14
23	2187/2048	343/320	264/245	130/121
24	?	175/162	121/112	14/13
25	27/25	27/25	27/25	13/12
26	625/576	160/147	160/147	160/147
27	2048/1875	49/45	49/45	49/45
28	800/729	375/343	12/11	12/11
29	?	35/32	35/32	35/32
30	2187/2000	625/567	11/10	11/10
31	1125/1024	54/49	54/49	54/49
32	3456/3125	441/400	256/231	256/231
33	10/9	10/9	10/9	10/9
34	78125/69984	567/512	352/315	39/35
35	4096/3645	125/112	49/44	49/44
36	18225/16384	28/25	28/25	28/25
37	17496/15625	640/567	432/385	169/150
38	9/8	9/8	9/8	9/8
39	15625/13824	500/441	112/99	112/99
40	256/225	245/216	245/216	147/130
41	2500/2187	567/500	25/22	25/22
42	?	8/7	8/7	8/7
43	729/640	343/300	55/48	55/48
44	9375/8192	225/196	63/55	63/55
45	144/125	144/125	144/125	52/45
46	125/108	125/108	125/108	15/13
47	32768/28125	81/70	81/70	65/56
48	2560/2187	400/343	64/55	64/55
49	?	7/6	7/6	7/6
50	729/625	729/625	88/75	88/75
51	75/64	75/64	75/64	75/64
52	18432/15625	147/125	33/28	33/28
53	32/27	32/27	32/27	13/11
54	15625/13122	189/160	189/160	77/65
55	59049/50000	25/21	25/21	25/21
56	1215/1024	343/288	144/121	117/98
57	78125/65536	875/729	105/88	105/88
58	6/5	6/5	6/5	6/5
59	3125/2592	1600/1323	77/64	77/64
60	4096/3375	98/81	98/81	98/81
61	8000/6561	756/625	40/33	40/33
62	?	128/105	128/105	63/52
63	243/200	243/200	11/9	11/9
64	625/512	60/49	60/49	60/49
65	768/625	49/40	49/40	49/40
66	100/81	100/81	27/22	16/13
67	?	216/175	216/175	26/21
68	8192/6561	625/504	99/80	99/80
69	10125/8192	56/45	56/45	56/45
70	3888/3125	3000/2401	96/77	96/77
71	5/4	5/4	5/4	5/4
72	78125/62208	784/625	44/35	44/35
73	512/405	432/343	121/96	49/39
74	25000/19683	63/50	63/50	63/50
75	19683/15625	80/63	80/63	80/63
76	81/64	81/64	81/64	33/26
77	15625/12288	125/98	14/11	14/11
78	32/25	32/25	32/25	32/25
79	625/486	625/486	77/60	50/39
80	65536/50625	9/7	9/7	9/7
81	6561/5120	1029/800	128/99	128/99
82	84375/65536	35/27	35/27	35/27
83	162/125	162/125	100/77	13/10
84	125/96	64/49	64/49	64/49
85	4096/3125	98/75	55/42	55/42
86	320/243	320/243	72/55	72/55
87	78125/59049	21/16	21/16	21/16
88	6561/5000	250/189	33/25	33/25
89	675/512	324/245	160/121	65/49
90	20736/15625	1323/1000	175/132	121/91
91	4/3	4/3	4/3	4/3
92	15625/11664	1701/1280	385/288	169/126
93	8192/6075	75/56	75/56	75/56
94	10935/8192	168/125	66/49	66/49
95	?	256/189	256/189	35/26
96	27/20	27/20	27/20	27/20
97	3125/2304	200/147	200/147	143/105
98	512/375	49/36	49/36	49/36
99	1000/729	1000/729	15/11	15/11
100	?	48/35	48/35	48/35
101	2187/1600	343/250	11/8	11/8
102	5625/4096	112/81	112/81	91/66
103	864/625	441/320	320/231	104/75
104	25/18	25/18	25/18	18/13
105	65536/46875	243/175	88/63	39/28
106	1024/729	480/343	245/176	169/121
107	91125/65536	7/5	7/5	7/5
108	4374/3125	800/567	108/77	108/77
109	45/32	45/32	45/32	45/32
110	78125/55296	625/441	99/70	99/70
111	64/45	64/45	64/45	64/45
112	3125/2187	567/400	77/54	77/54
113	?	10/7	10/7	10/7
114	729/512	343/240	275/192	242/169
115	46875/32768	350/243	63/44	56/39
116	36/25	36/25	36/25	13/9
117	625/432	625/432	231/160	75/52
118	8192/5625	81/56	81/56	81/56
119	3200/2187	500/343	16/11	16/11
120	?	35/24	35/24	35/24
121	729/500	729/500	22/15	22/15
122	375/256	72/49	72/49	72/49
123	4608/3125	147/100	147/100	147/100
124	40/27	40/27	40/27	40/27
125	78125/52488	189/128	189/128	52/35
126	16384/10935	125/84	49/33	49/33
127	6075/4096	112/75	112/75	112/75
128	23328/15625	2560/1701	525/352	175/117
129	3/2	3/2	3/2	3/2
130	15625/10368	2000/1323	264/175	169/112
131	1024/675	245/162	121/80	98/65
132	10000/6561	189/125	50/33	50/33
133	?	32/21	32/21	32/21
134	243/160	243/160	55/36	55/36
135	3125/2048	75/49	75/49	75/49
136	192/125	49/32	49/32	49/32
137	125/81	125/81	77/50	20/13
138	?	54/35	54/35	54/35
139	10240/6561	1600/1029	99/64	99/64
140	50625/32768	14/9	14/9	14/9
141	972/625	972/625	120/77	39/25
142	25/16	25/16	25/16	25/16
143	24576/15625	196/125	11/7	11/7
144	128/81	128/81	128/81	52/33
145	31250/19683	63/40	63/40	63/40
146	19683/12500	100/63	100/63	100/63
147	405/256	343/216	192/121	78/49
148	78125/49152	625/392	35/22	35/22
149	8/5	8/5	8/5	8/5
150	3125/1944	2401/1500	77/48	77/48
151	16384/10125	45/28	45/28	45/28
152	6561/4096	1008/625	160/99	160/99
153	?	175/108	175/108	21/13
154	81/50	81/50	44/27	13/8
155	625/384	80/49	80/49	80/49
156	1024/625	49/30	49/30	49/30
157	400/243	400/243	18/11	18/11
158	?	105/64	105/64	104/63
159	6561/4000	625/378	33/20	33/20
160	3375/2048	81/49	81/49	81/49
161	5184/3125	1323/800	128/77	128/77
162	5/3	5/3	5/3	5/3
163	78125/46656	1458/875	176/105	117/70
164	2048/1215	375/224	121/72	121/72
165	54675/32768	42/25	42/25	42/25
166	26244/15625	320/189	320/189	130/77
167	27/16	27/16	27/16	22/13
168	15625/9216	250/147	56/33	56/33
169	128/75	128/75	128/75	128/75
170	1250/729	1250/729	75/44	75/44
171	?	12/7	12/7	12/7
172	2187/1280	343/200	55/32	55/32
173	28125/16384	140/81	121/70	112/65
174	216/125	216/125	216/125	26/15
175	125/72	125/72	125/72	45/26
176	16384/9375	243/140	110/63	110/63
177	1280/729	600/343	96/55	96/55
178	?	7/4	7/4	7/4
179	2187/1250	1000/567	44/25	44/25
180	225/128	225/128	225/128	225/128
181	27648/15625	441/250	99/56	99/56
182	16/9	16/9	16/9	16/9
183	15625/8748	567/320	385/216	231/130
184	32768/18225	25/14	25/14	25/14
185	3645/2048	224/125	88/49	88/49
186	?	875/486	315/176	70/39
187	9/5	9/5	9/5	9/5
188	3125/1728	800/441	231/128	231/128
189	2048/1125	49/27	49/27	49/27
190	4000/2187	625/343	20/11	20/11
191	?	64/35	64/35	64/35
192	729/400	686/375	11/6	11/6
193	1875/1024	90/49	90/49	90/49
194	1152/625	147/80	147/80	147/80
195	50/27	50/27	50/27	24/13
196	?	324/175	224/121	13/7
197	4096/2187	625/336	245/132	121/65
198	30375/16384	28/15	28/15	28/15
199	5832/3125	3200/1701	144/77	144/77
200	15/8	15/8	15/8	15/8
201	78125/41472	1176/625	66/35	66/35
202	256/135	256/135	121/64	49/26
203	12500/6561	189/100	125/66	91/48
204	59049/31250	40/21	40/21	40/21
205	243/128	243/128	243/128	99/52
206	15625/8192	375/196	21/11	21/11
207	48/25	48/25	48/25	48/25
208	625/324	625/324	77/40	25/13
209	32768/16875	27/14	27/14	27/14
210	12800/6561	2000/1029	64/33	64/33
211	?	35/18	35/18	35/18
212	243/125	243/125	88/45	39/20
213	125/64	96/49	96/49	96/49
214	6144/3125	49/25	49/25	49/25
215	160/81	160/81	108/55	65/33
216	78125/39366	63/32	63/32	63/32
217	19683/10000	125/63	99/50	99/50
218	2025/1024	448/225	240/121	195/98
219	31104/15625	3125/1568	175/88	175/88
220	2/1	2/1	2/1	2/1