221edo

Welcome to 221edo

221edo = 13edo × 17edo

Distinctively interesting choice for an edo, due to its divisibility by both 13 and 17. This means it can be used to play 13edo music and 17edo music at the same time, using the 221/17 and 221/13 vals respectively.

5.430

221edo has a step size of 5.4298642533937 cents. It is a commatonal EDO, because the step size represents commas like 78732/78125, 225/224, 144/143. It is also a nanotonal EDO.

Interval, complement	Error (abs., in cents)
15/14, 28/15	0.014
9/7, 14/9	0.695
6/5, 5/3	0.709
5/4, 8/5	0.793
7/6, 12/7	0.808
16/13, 13/8	1.101
13/11, 22/13	1.427
4/3, 3/2	1.503
7/5, 10/7	1.517
13/10, 20/13	1.895
10/9, 9/5	2.212
16/15, 15/8	2.296
8/7, 7/4	2.31
11/8, 16/11	2.528
13/12, 24/13	2.604
9/8, 16/9	3.005
11/10, 20/11	3.322
15/13, 26/15	3.397
14/13, 13/7	3.411
12/11, 11/6	4.031
18/13, 13/9	4.106
15/11, 22/15	4.824
14/11, 11/7	4.838
11/9, 18/11	5.533

Table of 221edo intervals

Step	Five limit	Seven limit	Eleven limit	Thirteen limit
1	78732/78125	225/224	225/224	144/143
2	15625/15552	126/125	126/125	105/104
3	81/80	81/80	81/80	81/80
4	?	875/864	99/98	78/77
5	2048/2025	686/675	56/55	56/55
6	6561/6400	49/48	45/44	45/44
7	20000/19683	50/49	50/49	50/49
8	128/125	128/125	128/125	40/39
9	?	36/35	36/35	36/35
10	250/243	250/243	33/32	33/32
11	648/625	648/625	126/121	27/26
12	?	28/27	28/27	28/27
13	25/24	25/24	25/24	25/24
14	6561/6250	392/375	288/275	117/112
15	20480/19683	21/20	21/20	21/20
16	135/128	135/128	22/21	22/21
17	?	1323/1250	128/121	96/91
18	256/243	256/243	35/33	35/33
19	2187/2048	200/189	200/189	117/110
20	62500/59049	625/588	294/275	52/49
21	16/15	16/15	16/15	16/15
22	?	15/14	15/14	15/14
23	3125/2916	672/625	275/256	14/13
24	27/25	27/25	27/25	27/25
25	?	175/162	175/162	175/162
26	625/576	625/576	121/112	13/12
27	2187/2000	49/45	12/11	12/11
28	64000/59049	35/32	35/32	35/32
29	1125/1024	375/343	275/252	128/117
30	?	192/175	192/175	100/91
31	800/729	54/49	11/10	11/10
32	3456/3125	625/567	484/441	72/65
33	?	448/405	49/44	49/44
34	10/9	10/9	10/9	10/9
35	17496/15625	125/112	125/112	39/35
36	65536/59049	28/25	28/25	28/25
37	9/8	9/8	9/8	9/8
38	?	2025/1792	55/49	55/49
39	4096/3645	567/500	112/99	44/39
40	729/640	245/216	25/22	25/22
41	?	500/441	275/243	91/80
42	256/225	256/225	63/55	63/55
43	59049/51200	8/7	8/7	8/7
44	2500/2187	225/196	55/48	55/48
45	144/125	144/125	140/121	15/13
46	?	81/70	81/70	81/70
47	125/108	125/108	121/105	52/45
48	729/625	729/625	64/55	64/55
49	?	7/6	7/6	7/6
50	75/64	75/64	75/64	75/64
51	59049/50000	147/125	147/125	147/125
52	2560/2187	189/160	88/75	88/75
53	1215/1024	405/343	33/28	13/11
54	?	2401/2025	144/121	77/65
55	32/27	32/27	32/27	32/27
56	19683/16384	25/21	25/21	25/21
57	15625/13122	448/375	448/375	117/98
58	6/5	6/5	6/5	6/5
59	?	135/112	77/64	77/64
60	3125/2592	756/625	147/121	63/52
61	243/200	98/81	40/33	40/33
62	?	175/144	121/100	91/75
63	625/512	625/512	336/275	39/32
64	19683/16000	49/40	27/22	27/22
65	8000/6561	60/49	11/9	11/9
66	768/625	768/625	275/224	16/13
67	?	216/175	150/121	150/121
68	100/81	100/81	99/80	99/80
69	3888/3125	625/504	121/98	26/21
70	?	56/45	56/45	56/45
71	5/4	5/4	5/4	5/4
72	19683/15625	784/625	550/441	49/39
73	8192/6561	63/50	63/50	63/50
74	81/64	81/64	44/35	44/35
75	?	3969/3125	121/96	91/72
76	512/405	343/270	14/11	14/11
77	6561/5120	80/63	80/63	80/63
78	25000/19683	125/98	125/98	125/98
79	32/25	32/25	32/25	32/25
80	?	9/7	9/7	9/7
81	625/486	625/486	165/128	84/65
82	162/125	162/125	128/99	128/99
83	?	35/27	35/27	35/27
84	125/96	125/96	125/96	13/10
85	6561/5000	98/75	72/55	72/55
86	25600/19683	21/16	21/16	21/16
87	675/512	450/343	55/42	55/42
88	?	1152/875	160/121	120/91
89	320/243	320/243	33/25	33/25
90	10935/8192	250/189	250/189	117/88
91	78125/59049	896/675	147/110	65/49
92	4/3	4/3	4/3	4/3
93	?	75/56	75/56	75/56
94	15625/11664	168/125	168/125	35/26
95	27/20	27/20	27/20	27/20
96	?	875/648	66/49	66/49
97	3125/2304	1701/1250	224/165	65/48
98	2187/1600	49/36	15/11	15/11
99	80000/59049	175/128	110/81	110/81
100	512/375	343/250	343/250	143/105
101	?	48/35	48/35	48/35
102	1000/729	135/98	11/8	11/8
103	864/625	864/625	168/121	18/13
104	?	112/81	112/81	112/81
105	25/18	25/18	25/18	25/18
106	4374/3125	625/448	384/275	39/28
107	81920/59049	7/5	7/5	7/5
108	45/32	45/32	45/32	45/32
109	?	882/625	275/196	128/91
110	1024/729	343/243	140/99	55/39
111	729/512	486/343	99/70	78/55
112	?	625/441	363/256	91/64
113	64/45	64/45	63/44	63/44
114	59049/40960	10/7	10/7	10/7
115	3125/2187	896/625	275/192	56/39
116	36/25	36/25	36/25	36/25
117	?	81/56	81/56	81/56
118	625/432	625/432	121/84	13/9
119	729/500	196/135	16/11	16/11
120	?	35/24	35/24	35/24
121	375/256	375/256	275/189	117/80
122	59049/40000	147/100	81/55	81/55
123	3200/2187	72/49	22/15	22/15
124	4608/3125	2025/1372	165/112	65/44
125	?	1296/875	49/33	49/33
126	40/27	40/27	40/27	40/27
127	23328/15625	125/84	125/84	52/35
128	78125/52488	112/75	112/75	112/75
129	3/2	3/2	3/2	3/2
130	?	675/448	121/81	98/65
131	15625/10368	189/125	189/125	176/117
132	243/160	243/160	50/33	50/33
133	?	875/576	121/80	91/60
134	1024/675	343/225	84/55	84/55
135	19683/12800	32/21	32/21	32/21
136	10000/6561	75/49	55/36	55/36
137	192/125	192/125	192/125	20/13
138	?	54/35	54/35	54/35
139 | | 125/81	125/81	99/64	99/64
140	972/625	972/625	189/121	65/42
141	?	14/9	14/9	14/9
142	25/16	25/16	25/16	25/16
143	19683/12500	196/125	196/125	196/125
144	10240/6561	63/40	63/40	63/40
145	405/256	405/256	11/7	11/7
146	?	3969/2500	192/121	144/91
147	128/81	128/81	35/22	35/22
148	6561/4096	100/63	100/63	100/63
149	31250/19683	625/392	441/275	78/49
150	8/5	8/5	8/5	8/5
151	?	45/28	45/28	45/28
152	3125/1944	1008/625	196/121	21/13
153	81/50	81/50	81/50	81/50
154	?	175/108	121/75	121/75
155	625/384	625/384	363/224	13/8
156	6561/4000	49/30	18/11	18/11
157	32000/19683	80/49	44/27	44/27
158	1024/625	1024/625	275/168	64/39
159	?	288/175	200/121	150/91
160	400/243	81/49	33/20	33/20
161	5184/3125	625/378	242/147	104/63
162	?	224/135	128/77	128/77
163	5/3	5/3	5/3	5/3
164	26244/15625	375/224	375/224	117/70
165	32768/19683	42/25	42/25	42/25
166	27/16	27/16	27/16	27/16
167	?	4050/2401	121/72	91/54
168	2048/1215	686/405	56/33	22/13
169	2187/1280	245/144	75/44	75/44
170	?	250/147	250/147	245/143
171	128/75	128/75	128/75	128/75
172	?	12/7	12/7	12/7
173	1250/729	675/392	55/32	55/32
174	216/125	216/125	210/121	45/26
175	?	140/81	140/81	140/81
176	125/72	125/72	121/70	26/15
177	2187/1250	392/225	96/55	96/55
178	?	7/4	7/4	7/4
179	225/128	225/128	110/63	110/63
180	?	441/250	441/250	160/91
181	1280/729	432/245	44/25	44/25
182	3645/2048	1000/567	99/56	39/22
183	?	2401/1350	98/55	98/55
184	16/9	16/9	16/9	16/9
185	59049/32768	25/14	25/14	25/14
186	15625/8748	224/125	224/125	70/39
187	9/5	9/5	9/5	9/5
188	?	405/224	88/49	88/49
189	3125/1728	1134/625	441/242	65/36
190	729/400	49/27	20/11	20/11
191	?	175/96	175/96	91/50
192	1875/1024	625/343	504/275	117/64
193	59049/32000	64/35	64/35	64/35
194	4000/2187	90/49	11/6	11/6
195	1152/625	1152/625	224/121	24/13
196	?	324/175	225/121	225/121
197	50/27	50/27	50/27	50/27
198	5832/3125	625/336	363/196	13/7
199	?	28/15	28/15	28/15
200	15/8	15/8	15/8	15/8
201	59049/31250	1176/625	275/147	49/26
202	4096/2187	189/100	189/100	169/90
203	243/128	243/128	66/35	66/35
204	?	2500/1323	121/64	91/48
205	256/135	256/135	21/11	21/11
206	19683/10240	40/21	40/21	40/21
207	12500/6561	375/196	275/144	143/75
208	48/25	48/25	48/25	25/13
209	?	27/14	27/14	27/14
210	625/324	625/324	121/63	52/27
211	243/125	243/125	64/33	64/33
212	?	35/18	35/18	35/18
213	125/64	125/64	125/64	39/20
214	19683/10000	49/25	49/25	49/25
215	12800/6561	63/32	63/32	63/32
216	2025/1024	675/343	55/28	55/28
217	?	1728/875	196/99	77/39
218	160/81	160/81	99/50	99/50
219	31104/15625	125/63	125/63	125/63
220	78125/39366	448/225	243/121	143/72
221	2/1	2/1	2/1	2/1