273edo

Welcome to 273edo

273edo = 13edo × 21edo

Distinctively interesting choice for an edo, due to its divisibility by both 13 and 21. This means it can be used to play 13edo music and 21edo music at the same time, using the 273/21 and 273/13 vals respectively.

4.396

273edo has a step size of 4.3956043956044 cents. It is a commatonal EDO, because the step size represents commas like 15625/15552, 245/243, 196/195. It is also a nanotonal EDO.

Selected just intervals by error

The following table shows how some prominent just intervals are represented in 273edo (ordered by absolute error).

Interval, complement	Error (abs., in cents)
14/11, 11/7	0.074
5/4, 8/5	0.499
14/13, 13/7	0.826
6/5, 5/3	0.842
13/11, 22/13	0.9
16/13, 13/8	0.967
4/3, 3/2	1.342
13/10, 20/13	1.467
8/7, 7/4	1.793
16/15, 15/8	1.841
11/8, 16/11	1.867
10/9, 9/5	2.184
7/5, 10/7	2.292
13/12, 24/13	2.309
11/10, 20/11	2.367
9/8, 16/9	2.683
15/13, 26/15	2.808
7/6, 12/7	3.135
12/11, 11/6	3.209
15/14, 28/15	3.634
18/13, 13/9	3.651
15/11, 22/15	3.709
9/7, 14/9	4.476
11/9, 18/11	4.551

Table of 273edo intervals

Step	Five limit	Seven limit	Eleven limit	Thirteen limit
1	15625/15552	245/243	245/243	196/195
2	?	2400/2401	121/120	121/120
3	2048/2025	126/125	126/125	91/90
4	20000/19683	686/675	100/99	100/99
5	78732/78125	1728/1715	99/98	99/98
6	81/80	64/63	55/54	55/54
7	3125/3072	49/48	49/48	49/48
8	?	2430/2401	891/875	143/140
9	128/125	50/49	50/49	50/49
10	250/243	250/243	45/44	40/39
11	?	8748/8575	352/343	147/143
12	6561/6400	36/35	33/32	33/32
13	16875/16384	28/27	28/27	28/27
14	?	2401/2304	125/121	125/121
15	648/625	405/392	405/392	26/25
16	25/24	25/24	25/24	25/24
17	?	6125/5832	126/121	126/121
18	16384/15625	256/245	22/21	22/21
19	256/243	21/20	21/20	21/20
20	62500/59049	343/324	343/324	150/143
21	6561/6250	360/343	132/125	132/125
22	135/128	135/128	81/77	55/52
23	78125/73728	1225/1152	35/33	35/33
24	82944/78125	1296/1225	297/280	52/49
25	16/15	16/15	16/15	16/15
26	3125/2916	343/320	294/275	125/117
27	?	729/686	242/225	242/225
28	2187/2048	15/14	15/14	15/14
29	64000/59049	175/162	175/162	14/13
30	?	6561/6125	121/112	121/112
31	27/25	27/25	27/25	13/12
32	625/576	49/45	49/45	49/45
33	?	2401/2187	525/484	525/484
34	2048/1875	160/147	160/147	99/91
35	800/729	35/32	12/11	12/11
36	?	8575/7776	484/441	343/312
37	2187/2000	192/175	11/10	11/10
38	1125/1024	441/400	441/400	100/91
39	?	2401/2160	400/363	315/286
40	3456/3125	54/49	54/49	54/49
41	10/9	10/9	10/9	10/9
42	78125/69984	1715/1536	49/44	49/44
43	?	972/875	121/108	39/35
44	4096/3645	28/25	28/25	28/25
45	?	1372/1215	135/121	135/121
46	17496/15625	384/343	55/49	55/49
47	9/8	9/8	9/8	9/8
48	15625/13824	245/216	112/99	112/99
49	?	2700/2401	198/175	143/126
50	256/225	256/225	154/135	91/80
51	2500/2187	343/300	25/22	25/22
52	?	1944/1715	891/784	143/125
53	729/640	8/7	8/7	8/7
54	9375/8192	147/128	63/55	63/55
55	?	10935/9604	121/105	121/105
56	144/125	144/125	144/125	52/45
57	125/108	125/108	125/108	15/13
58	?	13824/12005	140/121	140/121
59	32768/28125	81/70	81/70	65/56
60	2560/2187	7/6	7/6	7/6
61	?	1715/1458	1029/880	286/245
62	729/625	400/343	88/75	88/75
63	75/64	75/64	75/64	75/64
64	?	2401/2025	350/297	168/143
65	18432/15625	288/245	33/28	33/28
66	32/27	32/27	32/27	13/11
67	15625/13122	343/288	196/165	196/165
68	59049/50000	405/343	297/250	143/120
69	1215/1024	25/21	25/21	25/21
70	78125/65536	875/729	105/88	105/88
71	93312/78125	1458/1225	176/147	117/98
72	6/5	6/5	6/5	6/5
73	3125/2592	98/81	98/81	98/81
74	?	2880/2401	121/100	121/100
75	4096/3375	135/112	135/112	91/75
76	8000/6561	175/144	40/33	40/33
77	?	10368/8575	147/121	147/121
78	243/200	128/105	11/9	11/9
79	625/512	49/40	49/40	49/40
80	?	2401/1944	1331/1080	175/143
81	768/625	60/49	60/49	60/49
82	100/81	100/81	27/22	16/13
83	?	8575/6912	121/98	121/98
84	19683/16000	216/175	99/80	26/21
85	8192/6561	56/45	56/45	56/45
86	?	2401/1920	150/121	150/121
87	3888/3125	243/196	243/196	156/125
88	5/4	5/4	5/4	5/4
89	78125/62208	1225/972	441/352	49/39
90	98304/78125	1536/1225	44/35	44/35
91	512/405	63/50	63/50	63/50
92	25000/19683	343/270	125/99	125/99
93	19683/15625	432/343	432/343	286/225
94	81/64	80/63	80/63	33/26
95	15625/12288	245/192	14/11	14/11
96	?	6075/4802	242/189	143/112
97	32/25	32/25	32/25	32/25
98	625/486	625/486	225/176	50/39
99	?	2187/1715	440/343	440/343
100	6561/5120	9/7	9/7	9/7
101	25600/19683	35/27	35/27	35/27
102	?	8575/6561	343/264	343/264
103	162/125	162/125	162/125	13/10
104	125/96	98/75	98/75	98/75
105	?	4802/3645	315/242	315/242
106	4096/3125	64/49	55/42	55/42
107	320/243	21/16	21/16	21/16
108	78125/59049	1715/1296	392/297	343/260
109	6561/5000	450/343	33/25	33/25
110	675/512	250/189	250/189	120/91
111	?	2401/1800	160/121	160/121
112	20736/15625	324/245	297/224	65/49
113	4/3	4/3	4/3	4/3
114	15625/11664	343/256	147/110	147/110
115	?	3200/2401	121/90	121/90
116	8192/6075	75/56	75/56	75/56
117	80000/59049	875/648	162/121	35/26
118	?	2304/1715	66/49	66/49
119	27/20	27/20	27/20	27/20
120	3125/2304	49/36	49/36	49/36
121	?	3240/2401	1089/800	143/105
122	512/375	200/147	200/147	200/147
123	1000/729	175/128	15/11	15/11
124	?	11664/8575	605/441	196/143
125	2187/1600	48/35	11/8	11/8
126	5625/4096	112/81	112/81	91/66
127	?	2401/1728	242/175	242/175
128	864/625	135/98	135/98	104/75
129	25/18	25/18	25/18	18/13
130	?	6125/4374	168/121	168/121
131	65536/46875	243/175	88/63	39/28
132	1024/729	7/5	7/5	7/5
133	?	343/243	343/243	200/143
134	4374/3125	480/343	176/125	169/120
135	45/32	45/32	45/32	45/32
136	78125/55296	1225/864	140/99	140/99
137	?	1728/1225	99/70	99/70
138	64/45	64/45	64/45	64/45
139	3125/2187	343/240	125/88	125/88
140	?	486/343	486/343	143/100
141	729/512	10/7	10/7	10/7
142	46875/32768	350/243	63/44	56/39
143	?	8748/6125	121/84	121/84
144	36/25	36/25	36/25	13/9
145	625/432	196/135	196/135	75/52
146	?	3456/2401	175/121	175/121
147	8192/5625	81/56	81/56	81/56
148	3200/2187	35/24	16/11	16/11
149	?	8575/5832	882/605	143/98
150	729/500	256/175	22/15	22/15
151	375/256	147/100	147/100	147/100
152	?	2401/1620	875/594	210/143
153	4608/3125	72/49	72/49	72/49
154	40/27	40/27	40/27	40/27
155	78125/52488	1715/1152	49/33	49/33
156	59049/40000	1296/875	121/81	52/35
157	6075/4096	112/75	112/75	112/75
158	?	2401/1600	180/121	175/117
159	23328/15625	512/343	220/147	220/147
160	3/2	3/2	3/2	3/2
161	15625/10368	245/162	245/162	98/65
162	?	3600/2401	121/80	121/80
163	1024/675	189/125	189/125	91/60
164	10000/6561	343/225	50/33	50/33
165	?	2592/1715	297/196	297/196
166	243/160	32/21	32/21	32/21
167	3125/2048	49/32	49/32	49/32
168	?	3645/2401	484/315	429/280
169	192/125	75/49	75/49	75/49
170	125/81	125/81	125/81	20/13
171	?	13122/8575	528/343	441/286
172	19683/12800	54/35	54/35	54/35
173	10240/6561	14/9	14/9	14/9
174	?	2401/1536	343/220	343/220
175	972/625	972/625	352/225	39/25
176	25/16	25/16	25/16	25/16
177	?	6125/3888	189/121	189/121
178	24576/15625	384/245	11/7	11/7
179	128/81	63/40	63/40	52/33
180	31250/19683	343/216	343/216	225/143
181	19683/12500	540/343	198/125	143/90
182	405/256	100/63	100/63	100/63
183	78125/49152	1225/768	35/22	35/22
184	?	1944/1225	605/378	78/49
185	8/5	8/5	8/5	8/5
186	3125/1944	392/243	392/243	125/78
187	?	2187/1372	121/75	121/75
188	6561/4096	45/28	45/28	45/28
189	32000/19683	175/108	160/99	21/13
190	?	13824/8575	196/121	196/121
191	81/50	81/50	44/27	13/8
192	625/384	49/30	49/30	49/30
193	?	2401/1458	1331/810	286/175
194	1024/625	80/49	80/49	80/49
195	400/243	105/64	18/11	18/11
196	?	8575/5184	242/147	242/147
197	6561/4000	288/175	33/20	33/20
198	3375/2048	224/135	224/135	91/55
199	?	2401/1440	200/121	200/121
200	5184/3125	81/49	81/49	81/49
201	5/3	5/3	5/3	5/3
202	78125/46656	1225/729	147/88	147/88
203	?	1458/875	121/72	117/70
204	2048/1215	42/25	42/25	42/25
205	?	686/405	405/242	175/104
206	26244/15625	576/343	165/98	165/98
207	27/16	27/16	27/16	22/13
208	15625/9216	245/144	56/33	56/33
209	?	4050/2401	297/175	143/84
210	128/75	128/75	77/45	77/45
211	1250/729	343/200	75/44	75/44
212	?	2916/1715	1760/1029	245/143
213	2187/1280	12/7	12/7	12/7
214	28125/16384	140/81	140/81	112/65
215	?	12005/6912	121/70	121/70
216	216/125	216/125	216/125	26/15
217	125/72	125/72	125/72	45/26
218	?	16807/9600	210/121	210/121
219	16384/9375	243/140	110/63	110/63
220	1280/729	7/4	7/4	7/4
221	?	1715/972	1331/756	250/143
222	2187/1250	600/343	44/25	44/25
223	225/128	225/128	135/77	135/77
224	?	2401/1350	175/99	175/99
225	27648/15625	432/245	99/56	99/56
226	16/9	16/9	16/9	16/9
227	15625/8748	343/192	98/55	98/55
228	?	1215/686	242/135	143/80
229	3645/2048	25/14	25/14	25/14
230	?	875/486	216/121	70/39
231	?	2187/1225	88/49	88/49
232	9/5	9/5	9/5	9/5
233	3125/1728	49/27	49/27	49/27
234	?	4320/2401	363/200	363/200
235	2048/1125	405/224	405/224	91/50
236	4000/2187	175/96	20/11	20/11
237	?	15552/8575	441/242	441/242
238	729/400	64/35	11/6	11/6
239	1875/1024	147/80	147/80	147/80
240	?	2401/1296	968/525	525/286
241	1152/625	90/49	90/49	90/49
242	50/27	50/27	50/27	24/13
243	?	8575/4608	224/121	224/121
244	59049/32000	324/175	297/160	13/7
245	4096/2187	28/15	28/15	28/15
246	?	1372/729	225/121	225/121
247	5832/3125	640/343	275/147	169/90
248	15/8	15/8	15/8	15/8
249	78125/41472	1225/648	560/297	49/26
250	?	2304/1225	66/35	66/35
251	256/135	189/100	154/81	91/48
252	12500/6561	343/180	125/66	125/66
253	59049/31250	648/343	648/343	143/75
254	243/128	40/21	40/21	40/21
255	15625/8192	245/128	21/11	21/11
256	?	11664/6125	121/63	121/63
257	48/25	48/25	48/25	48/25
258	625/324	625/324	625/324	25/13
259	?	4608/2401	242/125	242/125
260	19683/10240	27/14	27/14	27/14
261	12800/6561	35/18	35/18	35/18
262	?	8575/4374	343/176	286/147
263	243/125	243/125	88/45	39/20
264	125/64	49/25	49/25	49/25
265	?	2401/1215	945/484	280/143
266	6144/3125	96/49	55/28	55/28
267	160/81	63/32	63/32	63/32
268	78125/39366	1715/864	196/99	196/99
269	19683/10000	675/343	99/50	99/50
270	2025/1024	125/63	125/63	125/63
271	?	2401/1200	175/88	175/88
272	31104/15625	486/245	486/245	195/98
273	2/1	2/1	2/1	2/1