238edo

Welcome to 238edo

238edo = 14edo × 17edo

Distinctively interesting choice for an edo, due to its divisibility by both 14 and 17. This means it can be used to play 14edo music and 17edo music at the same time, using the 238/17 and 238/14 vals respectively.

5.042

238edo has a step size of 5.0420168067227 cents. It is a commatonal EDO, because the step size represents commas like 32768/32805, 126/125. It is also a nanotonal EDO.

Selected just intervals by error

The following table shows how some prominent just intervals are represented in 238edo (ordered by absolute error).

Interval, complement	Error (abs., in cents)
7/6, 12/7	0.356
13/10, 20/13	0.432
11/9, 18/11	0.491
12/11, 11/6	0.623
15/13, 26/15	0.682
8/7, 7/4	0.759
16/15, 15/8	0.807
14/11, 11/7	0.979
4/3, 3/2	1.115
9/7, 14/9	1.471
16/13, 13/8	1.489
15/14, 28/15	1.566
11/8, 16/11	1.738
5/4, 8/5	1.922
9/8, 16/9	2.229
14/13, 13/7	2.248
15/11, 22/15	2.545
13/12, 24/13	2.604
7/5, 10/7	2.68
6/5, 5/3	3.036
13/11, 22/13	3.227
11/10, 20/11	3.66
18/13, 13/9	3.718
10/9, 9/5	4.151

Table of 238edo intervals

Step	Five limit	Seven limit	Eleven limit	Thirteen limit
1	32768/32805	126/125	126/125	126/125
2	78125/78732	225/224	121/120	121/120
3	81/80	81/80	81/80	81/80
4	2048/2025	245/243	245/243	66/65
5	15625/15552	686/675	100/99	78/77
6	6561/6400	64/63	56/55	56/55
7	128/125	49/48	49/48	49/48
8	3125/3072	50/49	45/44	45/44
9	20000/19683	36/35	36/35	36/35
10	648/625	648/625	33/32	33/32
11	16875/16384	405/392	363/350	121/117
12	250/243	250/243	250/243	27/26
13	6561/6250	28/27	28/27	26/25
14	16384/15625	392/375	80/77	80/77
15	25/24	25/24	25/24	25/24
16	20480/19683	21/20	21/20	21/20
17	82944/78125	360/343	81/77	81/77
18	135/128	135/128	135/128	96/91
19	256/243	256/243	256/243	55/52
20	?	343/324	128/121	128/121
21	2187/2048	200/189	35/33	35/33
22	16/15	16/15	16/15	16/15
23	78125/73728	343/320	77/72	77/72
24	62500/59049	15/14	15/14	15/14
25	27/25	27/25	27/25	14/13
26	32768/30375	784/729	121/112	121/112
27	3125/2916	243/224	243/224	225/208
28	2187/2000	175/162	175/162	13/12
29	2048/1875	49/45	49/45	49/45
30	625/576	160/147	12/11	12/11
31	64000/59049	35/32	35/32	35/32
32	3456/3125	375/343	11/10	11/10
33	1125/1024	54/49	54/49	54/49
34	800/729	567/512	495/448	72/65
35	17496/15625	448/405	400/363	231/208
36	18225/16384	625/567	256/231	195/176
37	10/9	10/9	10/9	10/9
38	65536/59049	28/25	28/25	28/25
39	?	125/112	121/108	121/108
40	9/8	9/8	9/8	9/8
41	4096/3645	567/500	198/175	44/39
42	78125/69984	1372/1215	363/320	162/143
43	729/640	640/567	112/99	112/99
44	256/225	245/216	245/216	91/80
45	15625/13824	343/300	25/22	25/22
46	59049/51200	8/7	8/7	8/7
47	144/125	144/125	55/48	55/48
48	9375/8192	225/196	121/105	121/105
49	2500/2187	81/70	81/70	15/13
50	729/625	280/243	280/243	52/45
51	32768/28125	784/675	140/121	121/104
52	125/108	125/108	64/55	64/55
53	59049/50000	7/6	7/6	7/6
54	18432/15625	147/125	88/75	88/75
55	75/64	75/64	75/64	75/64
56	2560/2187	189/160	33/28	33/28
57	93312/78125	405/343	297/250	77/65
58	1215/1024	1215/1024	350/297	13/11
59	32/27	32/27	32/27	32/27
60	?	343/288	144/121	143/120
61	19683/16384	25/21	25/21	25/21
62	6/5	6/5	6/5	6/5
63	65536/54675	756/625	77/64	77/64
64	15625/13122	135/112	121/100	121/100
65	243/200	243/200	243/200	63/52
66	4096/3375	98/81	98/81	91/75
67	3125/2592	1372/1125	40/33	40/33
68	19683/16000	128/105	128/105	39/32
69	768/625	49/40	11/9	11/9
70	625/512	60/49	27/22	27/22
71	8000/6561	216/175	216/175	16/13
72	3888/3125	896/729	99/80	99/80
73	10125/8192	243/196	243/196	225/182
74	100/81	100/81	100/81	26/21
75	19683/15625	56/45	56/45	56/45
76	98304/78125	625/504	96/77	96/77
77	5/4	5/4	5/4	5/4
78	8192/6561	63/50	44/35	44/35
79	?	432/343	121/96	121/96
80	81/64	81/64	81/64	81/64
81	512/405	512/405	512/405	33/26
82	78125/62208	343/270	125/99	125/99
83	6561/5120	80/63	14/11	14/11
84	32/25	32/25	32/25	32/25
85	15625/12288	125/98	77/60	77/60
86	25000/19683	9/7	9/7	9/7
87	162/125	162/125	162/125	84/65
88	65536/50625	1568/1215	363/280	156/121
89	625/486	625/486	128/99	128/99
90	6561/5000	35/27	35/27	13/10
91	4096/3125	98/75	98/75	98/75
92	125/96	64/49	64/49	64/49
93	25600/19683	21/16	21/16	21/16
94	20736/15625	450/343	33/25	33/25
95	675/512	324/245	324/245	120/91
96	320/243	320/243	297/224	169/128
97	?	896/675	160/121	121/91
98	10935/8192	250/189	175/132	65/49
99	4/3	4/3	4/3	4/3
100	?	168/125	162/121	162/121
101	78125/59049	75/56	75/56	75/56
102	27/20	27/20	27/20	27/20
103	8192/6075	980/729	605/448	88/65
104	15625/11664	1215/896	400/297	104/77
105	2187/1600	256/189	224/165	65/48
106	512/375	49/36	49/36	49/36
107	3125/2304	200/147	15/11	15/11
108	80000/59049	48/35	48/35	48/35
109	864/625	441/320	11/8	11/8
110	5625/4096	135/98	135/98	125/91
111	1000/729	243/175	243/175	18/13
112	4374/3125	112/81	112/81	104/75
113	65536/46875	1568/1125	168/121	168/121
114	25/18	25/18	25/18	25/18
115	81920/59049	7/5	7/5	7/5
116	?	480/343	108/77	108/77
117	45/32	45/32	45/32	45/32
118	1024/729	567/400	99/70	55/39
119	?	343/243	343/243	325/231
120	729/512	729/512	140/99	78/55
121	64/45	64/45	64/45	64/45
122	78125/55296	343/240	77/54	77/54
123	59049/40960	10/7	10/7	10/7
124	36/25	36/25	36/25	36/25
125	46875/32768	1125/784	121/84	121/84
126	3125/2187	81/56	81/56	75/52
127	729/500	350/243	350/243	13/9
128	8192/5625	196/135	175/121	175/121
129	625/432	625/432	16/11	16/11
130	59049/40000	35/24	35/24	35/24
131	4608/3125	147/100	22/15	22/15
132	375/256	72/49	72/49	72/49
133	3200/2187	189/128	165/112	96/65
134	23328/15625	1792/1215	297/200	77/52
135	6075/4096	729/490	729/490	65/44
136	40/27	40/27	40/27	40/27
137	?	112/75	112/75	112/75
138	98415/65536	125/84	121/81	121/81
139	3/2	3/2	3/2	3/2
140	16384/10935	189/125	189/125	98/65
141	78125/52488	675/448	121/80	121/80
142	243/160	243/160	243/160	169/112
143	1024/675	245/162	245/162	91/60
144	15625/10368	343/225	50/33	50/33
145	19683/12800	32/21	32/21	32/21
146	192/125	49/32	49/32	49/32
147	3125/2048	75/49	75/49	75/49
148	10000/6561	54/35	54/35	20/13
149	972/625	972/625	99/64	99/64
150	50625/32768	1215/784	560/363	121/78
151	125/81	125/81	125/81	65/42
152	19683/12500	14/9	14/9	14/9
153	24576/15625	196/125	120/77	120/77
154	25/16	25/16	25/16	25/16
155	10240/6561	63/40	11/7	11/7
156	?	540/343	198/125	198/125
157	405/256	405/256	405/256	52/33
158	128/81	128/81	128/81	128/81
159	?	343/216	192/121	143/90
160	6561/4096	100/63	35/22	35/22
161	8/5	8/5	8/5	8/5
162	78125/49152	625/392	77/48	77/48
163	31250/19683	45/28	45/28	45/28
164	81/50	81/50	81/50	21/13
165	16384/10125	392/243	363/224	195/121
166	3125/1944	729/448	160/99	160/99
167	6561/4000	175/108	175/108	13/8
168	1024/625	49/30	44/27	44/27
169	625/384	80/49	18/11	18/11
170	32000/19683	105/64	105/64	64/39
171	5184/3125	1125/686	33/20	33/20
172	3375/2048	81/49	81/49	81/49
173	400/243	400/243	400/243	91/55
174	26244/15625	224/135	200/121	200/121
175	54675/32768	625/378	128/77	128/77
176	5/3	5/3	5/3	5/3
177	32768/19683	42/25	42/25	42/25
178	?	375/224	121/72	121/72
179	27/16	27/16	27/16	27/16
180	2048/1215	1225/729	297/175	22/13
181	78125/46656	686/405	500/297	130/77
182	2187/1280	320/189	56/33	56/33
183	128/75	128/75	128/75	128/75
184	15625/9216	250/147	75/44	75/44
185	?	12/7	12/7	12/7
186	216/125	216/125	55/32	55/32
187	28125/16384	675/392	121/70	121/70
188	1250/729	243/140	243/140	45/26
189	2187/1250	140/81	140/81	26/15
190	16384/9375	392/225	210/121	210/121
191	125/72	125/72	96/55	96/55
192	?	7/4	7/4	7/4
193	27648/15625	441/250	44/25	44/25
194	225/128	225/128	225/128	160/91
195	1280/729	567/320	99/56	99/56
196	?	1215/686	640/363	143/81
197	3645/2048	1000/567	175/99	39/22
198	16/9	16/9	16/9	16/9
199	?	224/125	216/121	143/80
200	59049/32768	25/14	25/14	25/14
201	9/5	9/5	9/5	9/5
202	32768/18225	1134/625	231/128	231/128
203	15625/8748	405/224	363/200	363/200
204	729/400	729/400	729/400	65/36
205	2048/1125	49/27	49/27	49/27
206	3125/1728	686/375	20/11	20/11
207	59049/32000	64/35	64/35	64/35
208	1152/625	147/80	11/6	11/6
209	1875/1024	90/49	81/44	81/44
210	4000/2187	324/175	324/175	24/13
211	5832/3125	448/243	297/160	297/160
212	30375/16384	729/392	224/121	121/65
213	50/27	50/27	50/27	13/7
214	59049/31250	28/15	28/15	28/15
215	?	625/336	144/77	144/77
216	15/8	15/8	15/8	15/8
217	4096/2187	189/100	66/35	49/26
218	?	648/343	121/64	121/64
219	243/128	243/128	243/128	104/55
220	256/135	256/135	256/135	91/48
221	78125/41472	343/180	125/66	125/66
222	19683/10240	40/21	21/11	21/11
223	48/25	48/25	48/25	48/25
224	15625/8192	375/196	77/40	77/40
225	12500/6561	27/14	27/14	25/13
226	243/125	243/125	243/125	52/27
227	32768/16875	784/405	700/363	234/121
228	625/324	625/324	64/33	64/33
229	19683/10000	35/18	35/18	35/18
230	6144/3125	49/25	49/25	49/25
231	125/64	96/49	96/49	96/49
232	12800/6561	63/32	55/28	55/28
233	31104/15625	675/343	99/50	77/39
234	2025/1024	486/245	486/245	65/33
235	160/81	160/81	160/81	160/81
236	?	448/225	240/121	143/72
237	32805/16384	125/63	125/63	125/63
238	2/1	2/1	2/1	2/1