272edo

Welcome to 272edo

272edo = 16edo × 17edo

Distinctively interesting choice for an edo, due to its divisibility by both 16 and 17. This means it can be used to play 16edo music and 17edo music at the same time, using the 272/17 and 272/16 vals respectively.

4.412

272edo has a step size of 4.4117647058824 cents. It is a commatonal EDO, because the step size represents commas like 78125/78732, 1728/1715, 176/175. It is also a nanotonal EDO.

Selected just intervals by error

The following table shows how some prominent just intervals are represented in 272edo (ordered by absolute error).

Interval, complement	Error (abs., in cents)
11/8, 16/11	0.153
7/5, 10/7	0.159
13/10, 20/13	0.198
15/14, 28/15	0.325
14/13, 13/7	0.357
4/3, 3/2	0.484
12/11, 11/6	0.637
15/13, 26/15	0.682
9/8, 16/9	0.969
11/9, 18/11	1.121
15/11, 22/15	1.285
16/15, 15/8	1.437
14/11, 11/7	1.61
8/7, 7/4	1.762
11/10, 20/11	1.769
5/4, 8/5	1.922
13/11, 22/13	1.967
16/13, 13/8	2.119
7/6, 12/7	2.247
6/5, 5/3	2.406
13/12, 24/13	2.604
9/7, 14/9	2.731
10/9, 9/5	2.89
18/13, 13/9	3.088

Table of 272edo intervals

Step	Five limit	Seven limit	Eleven limit	Thirteen limit
1	78125/78732	1728/1715	176/175	176/175
2	?	126/125	126/125	126/125
3	?	1029/1024	99/98	99/98
4	81/80	81/80	81/80	81/80
5	15625/15552	245/243	100/99	66/65
6	?	64/63	64/63	64/63
7	?	686/675	56/55	56/55
8	128/125	50/49	50/49	50/49
9	3125/3072	49/48	45/44	45/44
10	?	36/35	36/35	36/35
11	?	525/512	525/512	147/143
12	648/625	405/392	33/32	33/32
13	250/243	250/243	250/243	65/63
14	?	729/700	125/121	27/26
15	?	28/27	28/27	26/25
16	6561/6250	256/245	126/121	126/121
17	25/24	25/24	25/24	25/24
18	?	360/343	22/21	22/21
19	?	21/20	21/20	21/20
20	82944/78125	1296/1225	132/125	96/91
21	135/128	135/128	135/128	135/128
22	?	729/686	128/121	55/52
23	?	200/189	200/189	52/49
24	?	343/324	35/33	35/33
25	16/15	16/15	16/15	16/15
26	62500/59049	1225/1152	294/275	273/256
27	?	15/14	15/14	15/14
28	?	343/320	189/176	189/176
29	27/25	27/25	27/25	14/13
30	3125/2916	784/729	121/112	121/112
31	?	243/224	243/224	225/208
32	?	175/162	175/162	13/12
33	2048/1875	160/147	88/81	88/81
34	625/576	49/45	12/11	12/11
35	?	192/175	192/175	128/117
36	?	35/32	35/32	35/32
37	3456/3125	54/49	11/10	11/10
38	800/729	441/400	243/220	208/189
39	?	972/875	400/363	72/65
40	?	448/405	256/231	256/231
41	17496/15625	2187/1960	672/605	195/176
42	10/9	10/9	10/9	10/9
43	?	384/343	49/44	49/44
44	?	28/25	28/25	28/25
45	?	1715/1536	55/49	55/49
46	9/8	9/8	9/8	9/8
47	78125/69984	1944/1715	198/175	44/39
48	?	567/500	567/500	147/130
49	?	1372/1215	112/99	112/99
50	256/225	256/225	256/225	143/126
51	15625/13824	245/216	25/22	25/22
52	?	8/7	8/7	8/7
53	?	343/300	63/55	63/55
54	144/125	144/125	55/48	55/48
55	2500/2187	147/128	121/105	121/105
56	?	81/70	81/70	15/13
57	?	280/243	280/243	52/45
58	729/625	512/441	140/121	140/121
59	125/108	125/108	64/55	64/55
60	?	400/343	220/189	220/189
61	?	7/6	7/6	7/6
62	18432/15625	288/245	88/75	88/75
63	75/64	75/64	75/64	75/64
64	?	405/343	33/28	33/28
65	?	189/160	189/160	189/160
66	93312/78125	1458/1225	297/250	13/11
67	32/27	32/27	32/27	32/27
68	?	2048/1715	144/121	144/121
69	?	25/21	25/21	25/21
70	?	343/288	105/88	105/88
71	6/5	6/5	6/5	6/5
72	15625/13122	1225/1024	605/504	343/286
73	?	135/112	77/64	77/64
74	?	875/729	121/100	65/54
75	243/200	243/200	243/200	63/52
76	3125/2592	98/81	40/33	40/33
77	?	128/105	128/105	128/105
78	?	175/144	175/144	39/32
79	768/625	60/49	11/9	11/9
80	625/512	49/40	27/22	27/22
81	?	216/175	154/125	16/13
82	?	315/256	121/98	121/98
83	3888/3125	243/196	99/80	99/80
84	100/81	100/81	100/81	26/21
85	?	1280/1029	150/121	81/65
86	?	56/45	56/45	56/45
87	19683/15625	1536/1225	343/275	343/275
88	5/4	5/4	5/4	5/4
89	?	432/343	44/35	44/35
90	?	63/50	63/50	49/39
91	?	2744/2187	121/96	121/96
92	81/64	81/64	81/64	81/64
93	78125/62208	1225/972	125/99	33/26
94	?	80/63	80/63	80/63
95	?	343/270	14/11	14/11
96	32/25	32/25	32/25	32/25
97	15625/12288	245/192	225/176	225/176
98	?	9/7	9/7	9/7
99	?	1029/800	484/375	104/81
100	162/125	162/125	162/125	84/65
101	625/486	625/486	128/99	128/99
102	?	729/560	625/484	135/104
103	?	35/27	35/27	13/10
104	4096/3125	64/49	64/49	64/49
105	125/96	98/75	72/55	72/55
106	?	450/343	55/42	55/42
107	?	21/16	21/16	21/16
108	20736/15625	324/245	33/25	33/25
109	320/243	320/243	320/243	189/143
110	?	3645/2744	160/121	160/121
111	?	250/189	250/189	65/49
112	?	1715/1296	175/132	117/88
113	4/3	4/3	4/3	4/3
114	78125/59049	2304/1715	147/110	147/110
115	?	75/56	75/56	75/56
116	?	343/256	66/49	66/49
117	27/20	27/20	27/20	27/20
118	15625/11664	980/729	400/297	88/65
119	?	256/189	256/189	256/189
120	?	875/648	224/165	65/48
121	512/375	200/147	110/81	110/81
122	3125/2304	49/36	15/11	15/11
123	?	48/35	48/35	48/35
124	?	175/128	175/128	175/128
125	864/625	135/98	11/8	11/8
126	1000/729	441/320	242/175	242/175
127	?	243/175	243/175	18/13
128	?	112/81	112/81	104/75
129	4374/3125	1024/735	168/121	168/121
130	25/18	25/18	25/18	25/18
131	?	480/343	88/63	88/63
132	?	7/5	7/5	7/5
133	?	1728/1225	176/125	128/91
134	45/32	45/32	45/32	45/32
135	?	486/343	99/70	55/39
136	?	567/400	567/400	147/104
137	?	343/243	140/99	78/55
138	64/45	64/45	64/45	64/45
139	78125/55296	1225/864	125/88	91/64
140	?	10/7	10/7	10/7
141	?	343/240	63/44	63/44
142	36/25	36/25	36/25	36/25
143	3125/2187	735/512	121/84	121/84
144	?	81/56	81/56	75/52
145	?	350/243	350/243	13/9
146	729/500	640/441	175/121	175/121
147	625/432	196/135	16/11	16/11
148	?	256/175	256/175	143/98
149	?	35/24	35/24	35/24
150	4608/3125	72/49	22/15	22/15
151	375/256	147/100	81/55	81/55
152	?	1296/875	165/112	96/65
153	?	189/128	189/128	189/128
154	23328/15625	729/490	297/200	65/44
155	40/27	40/27	40/27	40/27
156	?	512/343	49/33	49/33
157	?	112/75	112/75	112/75
158	?	1715/1152	121/81	121/81
159	3/2	3/2	3/2	3/2
160	78125/52488	2401/1600	264/175	176/117
161	?	189/125	189/125	98/65
162	?	3087/2048	121/80	121/80
163	243/160	243/160	243/160	243/160
164	15625/10368	245/162	50/33	50/33
165	?	32/21	32/21	32/21
166	?	343/225	84/55	84/55
167	192/125	75/49	55/36	55/36
168	3125/2048	49/32	49/32	49/32
169	?	54/35	54/35	20/13
170	?	1120/729	605/392	208/135
171	972/625	972/625	99/64	99/64
172	125/81	125/81	125/81	65/42
173	?	1600/1029	375/242	81/52
174	?	14/9	14/9	14/9
175	19683/12500	384/245	189/121	189/121
176	25/16	25/16	25/16	25/16
177	?	540/343	11/7	11/7
178	?	63/40	63/40	63/40
179	?	1944/1225	198/125	52/33
180	128/81	128/81	128/81	128/81
181	?	2187/1372	192/121	165/104
182	?	100/63	100/63	78/49
183	?	343/216	35/22	35/22
184	8/5	8/5	8/5	8/5
185	31250/19683	1225/768	441/275	441/275
186	?	45/28	45/28	45/28
187	?	1029/640	121/75	121/75
188	81/50	81/50	81/50	21/13
189	3125/1944	392/243	160/99	160/99
190	?	512/315	196/121	196/121
191	?	175/108	125/77	13/8
192	1024/625	80/49	44/27	44/27
193	625/384	49/30	18/11	18/11
194	?	288/175	275/168	64/39
195	?	105/64	105/64	105/64
196	5184/3125	81/49	33/20	33/20
197	400/243	400/243	400/243	104/63
198	?	1458/875	200/121	91/55
199	?	224/135	128/77	128/77
200	26244/15625	2048/1225	875/528	572/343
201	5/3	5/3	5/3	5/3
202	?	576/343	147/88	147/88
203	?	42/25	42/25	42/25
204	?	1715/1024	121/72	121/72
205	27/16	27/16	27/16	27/16
206	78125/46656	1225/729	297/175	22/13
207	?	320/189	320/189	243/143
208	?	686/405	56/33	56/33
209	128/75	128/75	128/75	128/75
210	15625/9216	245/144	75/44	75/44
211	?	12/7	12/7	12/7
212	?	343/200	189/110	189/110
213	216/125	216/125	55/32	55/32
214	1250/729	441/256	121/70	121/70
215	?	243/140	243/140	45/26
216	?	140/81	140/81	26/15
217	2187/1250	256/147	210/121	210/121
218	125/72	125/72	96/55	96/55
219	?	600/343	110/63	110/63
220	?	7/4	7/4	7/4
221	27648/15625	432/245	44/25	44/25
222	225/128	225/128	225/128	225/128
223	?	1215/686	99/56	99/56
224	?	567/320	567/320	143/81
225	?	1715/972	175/99	39/22
226	16/9	16/9	16/9	16/9
227	?	2401/1350	98/55	98/55
228	?	25/14	25/14	25/14
229	?	343/192	88/49	88/49
230	9/5	9/5	9/5	9/5
231	15625/8748	3675/2048	605/336	352/195
232	?	405/224	231/128	231/128
233	?	875/486	363/200	65/36
234	729/400	729/400	440/243	189/104
235	3125/1728	49/27	20/11	20/11
236	?	64/35	64/35	64/35
237	?	175/96	175/96	117/64
238	1152/625	90/49	11/6	11/6
239	1875/1024	147/80	81/44	81/44
240	?	324/175	231/125	24/13
241	?	448/243	363/196	363/196
242	5832/3125	729/392	224/121	224/121
243	50/27	50/27	50/27	13/7
244	?	640/343	225/121	225/121
245	?	28/15	28/15	28/15
246	59049/31250	2304/1225	275/147	275/147
247	15/8	15/8	15/8	15/8
248	?	648/343	66/35	66/35
249	?	189/100	189/100	49/26
250	?	1372/729	121/64	104/55
251	243/128	243/128	243/128	243/128
252	78125/41472	1225/648	125/66	91/48
253	?	40/21	40/21	40/21
254	?	343/180	21/11	21/11
255	48/25	48/25	48/25	48/25
256	12500/6561	245/128	121/63	121/63
257	?	27/14	27/14	25/13
258	?	1400/729	242/125	52/27
259	243/125	243/125	243/125	126/65
260	625/324	625/324	64/33	64/33
261	?	1024/525	1024/525	286/147
262	?	35/18	35/18	35/18
263	6144/3125	96/49	88/45	88/45
264	125/64	49/25	49/25	49/25
265	?	675/343	55/28	55/28
266	?	63/32	63/32	63/32
267	31104/15625	486/245	99/50	65/33
268	160/81	160/81	160/81	160/81
269	?	2048/1029	196/99	196/99
270	?	125/63	125/63	125/63
271	?	1715/864	175/88	175/88
272	2/1	2/1	2/1	2/1