133edo

Welcome to 133edo

133edo = 7edo × 19edo

Distinctively interesting choice for an edo, due to its divisibility by both 7 and 19. This means it can be used to play 7edo music and 19edo music at the same time, using the 133/19 and 133/7 vals respectively.

9.023

133edo has a step size of 9.0225563909774 cents. It is a commatonal EDO, because the step size represents commas like 2048/2025, 126/125, 121/120, 91/90.

Selected just intervals by error

The following table shows how some prominent just intervals are represented in 133edo (ordered by absolute error).

Interval, complement	Error (abs., in cents)
6/5, 5/3	0.148
13/11, 22/13	0.488
11/8, 16/11	0.942
16/13, 13/8	1.43
5/4, 8/5	1.656
4/3, 3/2	1.804
10/9, 9/5	1.953
14/13, 13/7	1.982
14/11, 11/7	2.47
11/10, 20/11	2.598
12/11, 11/6	2.746
13/10, 20/13	3.086
13/12, 24/13	3.234
8/7, 7/4	3.412
16/15, 15/8	3.461
9/8, 16/9	3.609
15/11, 22/15	4.403
11/9, 18/11	4.551
15/13, 26/15	4.891
18/13, 13/9	5.039
7/5, 10/7	5.069
7/6, 12/7	5.217
15/14, 28/15	6.873
9/7, 14/9	7.021

Table of 133edo intervals

Step	Five limit	Seven limit	Eleven limit	Thirteen limit
1	2048/2025	126/125	121/120	91/90
2	20000/19683	225/224	100/99	100/99
3	81/80	49/48	49/48	49/48
4	128/125	128/125	77/75	77/75
5	250/243	50/49	45/44	40/39
6	6561/6400	28/27	28/27	28/27
7	648/625	392/375	125/121	26/25
8	25/24	25/24	25/24	25/24
9	256/243	21/20	21/20	21/20
10	6561/6250	1323/1250	132/125	132/125
11	135/128	135/128	35/33	35/33
12	16/15	16/15	16/15	16/15
13	3125/2916	625/588	242/225	125/117
14	2187/2048	15/14	15/14	14/13
15	27/25	27/25	27/25	13/12
16	625/576	625/576	250/231	225/208
17	800/729	35/32	12/11	12/11
18	2187/2000	192/175	11/10	11/10
19	1125/1024	375/343	375/343	100/91
20	10/9	10/9	10/9	10/9
21	4096/3645	28/25	28/25	28/25
22	17496/15625	125/112	125/112	125/112
23	9/8	9/8	9/8	9/8
24	256/225	256/225	154/135	91/80
25	2500/2187	500/441	25/22	25/22
26	729/640	8/7	8/7	8/7
27	144/125	144/125	121/105	52/45
28	125/108	125/108	125/108	15/13
29	2560/2187	7/6	7/6	7/6
30	729/625	147/125	88/75	88/75
31	75/64	75/64	75/64	75/64
32	32/27	32/27	32/27	13/11
33	15625/13122	448/375	297/250	143/120
34	1215/1024	25/21	25/21	25/21
35	6/5	6/5	6/5	6/5
36	3125/2592	756/625	121/100	91/75
37	8000/6561	135/112	40/33	40/33
38	243/200	49/40	11/9	11/9
39	625/512	625/512	154/125	154/125
40	100/81	60/49	27/22	16/13
41	8192/6561	56/45	56/45	26/21
42	3888/3125	625/504	150/121	150/121
43	5/4	5/4	5/4	5/4
44	512/405	63/50	44/35	44/35
45	19683/15625	1125/896	125/99	125/99
46	81/64	80/63	14/11	14/11
47	32/25	32/25	32/25	32/25
48	625/486	125/98	125/98	50/39
49	6561/5120	9/7	9/7	9/7
50	162/125	98/75	98/75	13/10
51	125/96	125/96	100/77	100/77
52	320/243	21/16	21/16	21/16
53	6561/5000	896/675	33/25	33/25
54	675/512	250/189	160/121	120/91
55	4/3	4/3	4/3	4/3
56	8192/6075	168/125	121/90	121/90
57	10935/8192	75/56	75/56	35/26
58	27/20	27/20	27/20	27/20
59	512/375	343/250	308/225	143/105
60	1000/729	175/128	15/11	15/11
61	2187/1600	48/35	11/8	11/8
62	864/625	864/625	242/175	104/75
63	25/18	25/18	25/18	18/13
64	1024/729	7/5	7/5	7/5
65	4374/3125	625/448	176/125	169/120
66	45/32	45/32	45/32	45/32
67	64/45	64/45	64/45	64/45
68	3125/2187	625/441	125/88	125/88
69	729/512	10/7	10/7	10/7
70	36/25	36/25	36/25	13/9
71	625/432	625/432	175/121	75/52
72	3200/2187	35/24	16/11	16/11
73	729/500	147/100	22/15	22/15
74	375/256	375/256	225/154	210/143
75	40/27	40/27	40/27	40/27
76	16384/10935	112/75	112/75	52/35
77	6075/4096	125/84	125/84	125/84
78	3/2	3/2	3/2	3/2
79	1024/675	189/125	121/80	91/60
80	10000/6561	675/448	50/33	50/33
81	243/160	32/21	32/21	32/21
82	192/125	192/125	77/50	77/50
83	125/81	75/49	75/49	20/13
84	10240/6561	14/9	14/9	14/9
85	972/625	196/125	196/125	39/25
86	25/16	25/16	25/16	25/16
87	128/81	63/40	11/7	11/7
88	19683/12500	1792/1125	198/125	143/90
89	405/256	100/63	35/22	35/22
90	8/5	8/5	8/5	8/5
91	3125/1944	625/392	121/75	121/75
92	6561/4096	45/28	45/28	21/13
93	81/50	49/30	44/27	13/8
94	625/384	625/384	125/77	125/77
95	400/243	80/49	18/11	18/11
96	6561/4000	224/135	33/20	33/20
97	3375/2048	625/378	200/121	150/91
98	5/3	5/3	5/3	5/3
99	2048/1215	42/25	42/25	42/25
100	26244/15625	375/224	375/224	169/100
101	27/16	27/16	27/16	22/13
102	128/75	128/75	77/45	77/45
103	1250/729	250/147	75/44	75/44
104	2187/1280	12/7	12/7	12/7
105	216/125	216/125	121/70	26/15
106	125/72	125/72	125/72	45/26
107	1280/729	7/4	7/4	7/4
108	2187/1250	441/250	44/25	44/25
109	225/128	225/128	135/77	135/77
110	16/9	16/9	16/9	16/9
111	15625/8748	224/125	224/125	143/80
112	3645/2048	25/14	25/14	25/14
113	9/5	9/5	9/5	9/5
114	2048/1125	686/375	363/200	91/50
115	4000/2187	175/96	20/11	20/11
116	729/400	64/35	11/6	11/6
117	1152/625	625/343	231/125	231/125
118	50/27	50/27	50/27	24/13
119	4096/2187	28/15	28/15	13/7
120	5832/3125	625/336	225/121	169/90
121	15/8	15/8	15/8	15/8
122	256/135	189/100	66/35	66/35
123	12500/6561	2401/1250	125/66	125/66
124	243/128	40/21	21/11	21/11
125	48/25	48/25	48/25	48/25
126	625/324	375/196	242/125	25/13
127	12800/6561	27/14	27/14	27/14
128	243/125	49/25	49/25	39/20
129	125/64	125/64	125/64	125/64
130	160/81	63/32	55/28	55/28
131	19683/10000	448/225	99/50	99/50
132	2025/1024	125/63	125/63	125/63
133	2/1	2/1	2/1	2/1