138edo

Welcome to 138edo

138edo = 6edo × 23edo

Distinctively interesting choice for an edo, due to its divisibility by both 6 and 23. This means it can be used to play 6edo music and 23edo music at the same time, using the 138/23 and 138/6 vals respectively.

8.696

138edo has a step size of 8.695652173913 cents. It is a commatonal EDO, because the step size represents commas like 3125/3072, 225/224, 100/99.

Selected just intervals by error

The following table shows how some prominent just intervals are represented in 138edo (ordered by absolute error).

Interval, complement	Error (abs., in cents)
7/5, 10/7	0.097
14/11, 11/7	0.117
11/10, 20/11	0.213
13/12, 24/13	0.558
16/15, 15/8	1.312
18/13, 13/9	1.835
15/11, 22/15	2.18
15/14, 28/15	2.296
4/3, 3/2	2.393
16/13, 13/8	2.951
11/8, 16/11	3.492
8/7, 7/4	3.609
5/4, 8/5	3.705
15/13, 26/15	4.263
9/8, 16/9	4.786
12/11, 11/6	5.885
7/6, 12/7	6.001
6/5, 5/3	6.098
13/11, 22/13	6.442
14/13, 13/7	6.559
13/10, 20/13	6.656
11/9, 18/11	8.278
9/7, 14/9	8.394
10/9, 9/5	8.491

Table of 138edo intervals

Step	Five limit	Seven limit	Eleven limit	Thirteen limit
1	3125/3072	225/224	100/99	100/99
2	2048/2025	686/675	55/54	55/54
3	250/243	49/48	49/48	49/48
4	81/80	50/49	50/49	40/39
5	16875/16384	2430/2401	45/44	45/44
6	128/125	28/27	28/27	28/27
7	25/24	25/24	25/24	25/24
8	6561/6400	405/392	80/77	27/26
9	256/243	256/243	22/21	22/21
10	648/625	21/20	21/20	21/20
11	135/128	135/128	35/33	35/33
12	16384/15625	784/729	77/72	77/72
13	16/15	16/15	16/15	16/15
14	625/576	15/14	15/14	14/13
15	2187/2048	729/686	88/81	88/81
16	800/729	49/45	49/45	13/12
17	27/25	27/25	27/25	27/25
18	1125/1024	243/224	12/11	12/11
19	2048/1875	448/405	11/10	11/10
20	10/9	10/9	10/9	10/9
21	2187/2000	54/49	49/44	49/44
22	4096/3645	1372/1215	243/220	91/81
23	2500/2187	28/25	28/25	28/25
24	9/8	9/8	9/8	9/8
25	9375/8192	2025/1792	25/22	25/22
26	256/225	256/225	55/48	55/48
27	125/108	8/7	8/7	8/7
28	729/640	225/196	63/55	15/13
29	2560/2187	784/675	140/121	52/45
30	144/125	7/6	7/6	7/6
31	75/64	75/64	64/55	64/55
32	32768/28125	2401/2025	88/75	88/75
33	32/27	32/27	32/27	32/27
34	729/625	25/21	25/21	13/11
35	1215/1024	405/343	105/88	105/88
36	8000/6561	98/81	77/64	65/54
37	6/5	6/5	6/5	6/5
38	625/512	135/112	40/33	40/33
39	4096/3375	896/729	11/9	11/9
40	100/81	49/40	49/40	39/32
41	243/200	60/49	60/49	16/13
42	8192/6561	2187/1792	27/22	27/22
43	768/625	56/45	56/45	26/21
44	5/4	5/4	5/4	5/4
45	15625/12288	243/196	96/77	81/65
46	512/405	343/270	44/35	44/35
47	625/486	63/50	63/50	33/26
48	81/64	81/64	14/11	14/11
49	25600/19683	1568/1215	77/60	77/60
50	32/25	32/25	32/25	32/25
51	125/96	9/7	9/7	9/7
52	6561/5120	2025/1568	100/77	100/77
53	320/243	98/75	55/42	13/10
54	162/125	21/16	21/16	21/16
55	675/512	450/343	72/55	72/55
56	4096/3125	896/675	33/25	33/25
57	4/3	4/3	4/3	4/3
58	3125/2304	75/56	75/56	35/26
59	8192/6075	2744/2025	110/81	110/81
60	1000/729	49/36	49/36	49/36
61	27/20	27/20	27/20	27/20
62	5625/4096	1215/896	15/11	15/11
63	512/375	112/81	11/8	11/8
64	25/18	25/18	25/18	25/18
65	2187/1600	135/98	135/98	18/13
66	1024/729	343/243	88/63	88/63
67	864/625	7/5	7/5	7/5
68	45/32	45/32	45/32	45/32
69	46875/32768	2187/1568	77/54	77/54
70	64/45	64/45	64/45	64/45
71	625/432	10/7	10/7	10/7
72	729/512	486/343	63/44	63/44
73	3200/2187	196/135	175/121	13/9
74	36/25	35/24	35/24	35/24
75	375/256	81/56	16/11	16/11
76	8192/5625	1792/1215	22/15	22/15
77	40/27	40/27	40/27	40/27
78	729/500	72/49	49/33	49/33
79	6075/4096	2025/1372	81/55	81/55
80	4608/3125	112/75	112/75	52/35
81	3/2	3/2	3/2	3/2
82	3125/2048	675/448	50/33	50/33
83	1024/675	343/225	55/36	55/36
84	125/81	32/21	32/21	32/21
85	243/160	75/49	75/49	20/13
86	10240/6561	3136/2025	77/50	77/50
87	192/125	14/9	14/9	14/9
88	25/16	25/16	25/16	25/16
89	19683/12800	1215/784	120/77	81/52
90	128/81	128/81	11/7	11/7
91	972/625	63/40	63/40	52/33
92	405/256	405/256	35/22	35/22
93	24576/15625	392/243	77/48	77/48
94	8/5	8/5	8/5	8/5
95	625/384	45/28	45/28	21/13
96	6561/4096	2187/1372	44/27	44/27
97	400/243	49/30	49/30	13/8
98	81/50	80/49	80/49	64/39
99	3375/2048	729/448	18/11	18/11
100	1024/625	224/135	33/20	33/20
101	5/3	5/3	5/3	5/3
102	6561/4000	81/49	81/49	81/49
103	2048/1215	686/405	176/105	91/54
104	1250/729	42/25	42/25	22/13
105	27/16	27/16	27/16	27/16
106	28125/16384	4050/2401	75/44	75/44
107	128/75	128/75	55/32	55/32
108	125/72	12/7	12/7	12/7
109	2187/1280	675/392	121/70	45/26
110	1280/729	392/225	110/63	26/15
111	216/125	7/4	7/4	7/4
112	225/128	225/128	96/55	96/55
113	16384/9375	2401/1350	44/25	44/25
114	16/9	16/9	16/9	16/9
115	2187/1250	25/14	25/14	25/14
116	3645/2048	1215/686	315/176	143/80
117	4000/2187	49/27	49/27	49/27
118	9/5	9/5	9/5	9/5
119	1875/1024	405/224	20/11	20/11
120	2048/1125	448/243	11/6	11/6
121	50/27	50/27	50/27	50/27
122	729/400	90/49	90/49	24/13
123	4096/2187	1372/729	81/44	81/44
124	1152/625	28/15	28/15	13/7
125	15/8	15/8	15/8	15/8
126	15625/8192	729/392	121/64	121/64
127	256/135	256/135	66/35	66/35
128	625/324	40/21	40/21	40/21
129	243/128	243/128	21/11	21/11
130	12800/6561	784/405	77/40	52/27
131	48/25	35/18	35/18	35/18
132	125/64	27/14	27/14	27/14
133	19683/10240	2401/1215	88/45	88/45
134	160/81	49/25	49/25	39/20
135	243/125	63/32	63/32	63/32
136	2025/1024	675/343	108/55	108/55
137	6144/3125	448/225	99/50	99/50
138	2/1	2/1	2/1	2/1