204edo

Welcome to 204edo

204edo = 12edo × 17edo

Distinctively interesting choice for an edo, due to its divisibility by both 12 and 17. This means it can be used to play 12edo music and 17edo music at the same time, using the 204/17 and 204/12 vals respectively.

5.882

204edo has a step size of 5.8823529411765 cents. It is a commatonal EDO, because the step size represents commas like 126/125, 225/224.

Selected just intervals by error

The following table shows how some prominent just intervals are represented in 204edo (ordered by absolute error).

Interval, complement	Error (abs., in cents)
16/15, 15/8	0.033
14/11, 11/7	0.139
7/5, 10/7	0.159
11/10, 20/11	0.298
16/13, 13/8	0.649
15/13, 26/15	0.682
13/11, 22/13	0.974
14/13, 13/7	1.114
13/10, 20/13	1.273
11/8, 16/11	1.623
15/11, 22/15	1.657
8/7, 7/4	1.762
15/14, 28/15	1.796
5/4, 8/5	1.922
4/3, 3/2	1.955
13/12, 24/13	2.604
12/11, 11/6	3.578
7/6, 12/7	3.717
6/5, 5/3	3.877
9/8, 16/9	3.91
18/13, 13/9	4.559
11/9, 18/11	5.533
9/7, 14/9	5.672
10/9, 9/5	5.832

Table of 204edo intervals

Step	Five limit	Seven limit	Eleven limit	Thirteen limit
1	?	126/125	126/125	126/125
2	81/80	81/80	81/80	81/80
3	78125/78732	3645/3584	121/120	78/77
4	2048/2025	2048/2025	100/99	66/65
5	15625/15552	64/63	56/55	56/55
6	128/125	50/49	45/44	45/44
7	3125/3072	36/35	36/35	36/35
8	648/625	405/392	77/75	40/39
9	16875/16384	729/700	33/32	33/32
10	6561/6250	2240/2187	125/121	27/26
11	250/243	250/243	80/77	26/25
12	16384/15625	28/27	28/27	28/27
13	25/24	25/24	25/24	25/24
14	82944/78125	21/20	21/20	21/20
15	135/128	135/128	132/125	96/91
16	?	1701/1600	128/121	128/121
17	256/243	256/243	256/243	52/49
18	?	200/189	35/33	35/33
19	16/15	16/15	16/15	16/15
20	78125/73728	15/14	15/14	15/14
21	27/25	27/25	27/25	27/25
22	62500/59049	243/224	243/224	14/13
23	2187/2000	2187/2000	121/112	121/112
24	3125/2916	784/729	250/231	13/12
25	2048/1875	160/147	12/11	12/11
26	625/576	49/45	49/45	49/45
27	3456/3125	35/32	35/32	35/32
28	1125/1024	441/400	11/10	11/10
29	17496/15625	567/512	400/363	72/65
30	800/729	800/729	256/231	195/176
31	?	448/405	135/121	39/35
32	10/9	10/9	10/9	10/9
33	?	28/25	28/25	28/25
34	9/8	9/8	9/8	9/8
35	?	567/500	121/108	121/108
36	729/640	729/640	729/640	44/39
37	78125/69984	640/567	112/99	112/99
38	256/225	256/225	25/22	25/22
39	15625/13824	8/7	8/7	8/7
40	144/125	144/125	144/125	144/125
41	9375/8192	81/70	55/48	55/48
42	729/625	729/625	121/105	15/13
43	2500/2187	2500/2187	140/121	52/45
44	32768/28125	280/243	64/55	64/55
45	125/108	125/108	90/77	90/77
46	18432/15625	7/6	7/6	7/6
47	75/64	75/64	75/64	75/64
48	93312/78125	189/160	33/28	33/28
49	1215/1024	1215/1024	297/250	13/11
50	?	2000/1701	144/121	77/65
51	32/27	32/27	32/27	32/27
52	?	25/21	25/21	25/21
53	6/5	6/5	6/5	6/5
54	78125/65536	135/112	135/112	135/112
55	243/200	243/200	77/64	77/64
56	15625/13122	2048/1701	121/100	63/52
57	4096/3375	875/729	40/33	40/33
58	3125/2592	98/81	98/81	39/32
59	768/625	60/49	27/22	27/22
60	625/512	49/40	11/9	11/9
61	3888/3125	243/196	154/125	16/13
62	8000/6561	2187/1750	99/80	99/80
63	19683/15625	896/729	150/121	26/21
64	100/81	100/81	96/77	96/77
65	98304/78125	56/45	56/45	56/45
66	5/4	5/4	5/4	5/4
67	?	63/50	44/35	44/35
68	81/64	81/64	81/64	49/39
69	?	5103/4000	121/96	121/96
70	512/405	512/405	125/99	33/26
71	78125/62208	80/63	14/11	14/11
72	32/25	32/25	32/25	32/25
73	15625/12288	9/7	9/7	9/7
74	162/125	162/125	77/60	50/39
75	25000/19683	729/560	165/128	84/65
76	6561/5000	2800/2187	128/99	128/99
77	625/486	625/486	100/77	13/10
78	4096/3125	35/27	35/27	35/27
79	125/96	98/75	98/75	98/75
80	20736/15625	21/16	21/16	21/16
81	675/512	675/512	33/25	33/25
82	?	1701/1280	160/121	154/117
83	320/243	320/243	320/243	65/49
84	?	250/189	162/121	121/91
85	4/3	4/3	4/3	4/3
86	?	75/56	75/56	75/56
87	27/20	27/20	27/20	27/20
88	78125/59049	1215/896	121/90	35/26
89	2187/1600	2187/1600	400/297	88/65
90	15625/11664	256/189	224/165	65/48
91	512/375	200/147	15/11	15/11
92	3125/2304	48/35	48/35	48/35
93	864/625	135/98	135/98	135/98
94	5625/4096	243/175	11/8	11/8
95	4374/3125	2187/1568	242/175	18/13
96	1000/729	1000/729	168/121	104/75
97	65536/46875	112/81	112/81	39/28
98	25/18	25/18	25/18	25/18
99	?	7/5	7/5	7/5
100	45/32	45/32	45/32	45/32
101	?	567/400	99/70	99/70
102	729/512	729/512	729/512	55/39
103	?	800/567	140/99	140/99
104	64/45	64/45	64/45	64/45
105	78125/55296	10/7	10/7	10/7
106	36/25	36/25	36/25	36/25
107	46875/32768	81/56	81/56	56/39
108	729/500	729/500	121/84	75/52
109	3125/2187	3125/2187	175/121	13/9
110	8192/5625	350/243	16/11	16/11
111	625/432	196/135	196/135	117/80
112	4608/3125	35/24	35/24	35/24
113	375/256	147/100	22/15	22/15
114	23328/15625	189/128	165/112	96/65
115	3200/2187	3200/2187	297/200	65/44
116	?	1792/1215	180/121	52/35
117	40/27	40/27	40/27	40/27
118	?	112/75	112/75	112/75
119	3/2	3/2	3/2	3/2
120	?	189/125	121/81	121/81
121	243/160	243/160	243/160	98/65
122	78125/52488	2560/1701	121/80	117/77
123	1024/675	1024/675	50/33	50/33
124	15625/10368	32/21	32/21	32/21
125	192/125	75/49	75/49	75/49
126	3125/2048	49/32	49/32	49/32
127	972/625	972/625	77/50	20/13
128	10000/6561	2187/1400	99/64	99/64
129	19683/12500	1120/729	256/165	65/42
130	125/81	125/81	120/77	39/25
131	24576/15625	14/9	14/9	14/9
132	25/16	25/16	25/16	25/16
133	?	63/40	11/7	11/7
134	405/256	405/256	198/125	52/33
135	?	5103/3200	192/121	192/121
136	128/81	128/81	128/81	78/49
137	?	100/63	35/22	35/22
138	8/5	8/5	8/5	8/5
139	78125/49152	45/28	45/28	45/28
140	81/50	81/50	77/48	77/48
141	31250/19683	729/448	121/75	21/13
142	6561/4000	3500/2187	160/99	160/99
143	3125/1944	392/243	125/77	13/8
144	1024/625	80/49	18/11	18/11
145	625/384	49/30	44/27	44/27
146	5184/3125	81/49	81/49	64/39
147	3375/2048	1323/800	33/20	33/20
148	26244/15625	1701/1024	200/121	91/55
149	400/243	400/243	128/77	128/77
150	?	224/135	224/135	117/70
151	5/3	5/3	5/3	5/3
152	?	42/25	42/25	42/25
153	27/16	27/16	27/16	27/16
154	?	1701/1000	121/72	121/72
155	2048/1215	2048/1215	500/297	22/13
156	78125/46656	320/189	56/33	56/33
157	128/75	128/75	75/44	75/44
158	15625/9216	12/7	12/7	12/7
159	216/125	216/125	77/45	77/45
160	28125/16384	243/140	55/32	55/32
161	2187/1250	2187/1250	121/70	45/26
162	1250/729	1250/729	210/121	26/15
163	16384/9375	140/81	96/55	96/55
164	125/72	125/72	125/72	125/72
165	27648/15625	7/4	7/4	7/4
166	225/128	225/128	44/25	44/25
167	?	567/320	99/56	99/56
168	1280/729	1280/729	847/480	39/22
169	?	1000/567	175/99	143/81
170	16/9	16/9	16/9	16/9
171	?	25/14	25/14	25/14
172	9/5	9/5	9/5	9/5
173	?	405/224	242/135	70/39
174	729/400	729/400	231/128	231/128
175	15625/8748	1024/567	363/200	65/36
176	2048/1125	800/441	20/11	20/11
177	3125/1728	49/27	49/27	49/27
178	1152/625	90/49	81/44	81/44
179	1875/1024	147/80	11/6	11/6
180	5832/3125	729/392	231/125	24/13
181	4000/2187	4000/2187	224/121	224/121
182	59049/31250	448/243	225/121	13/7
183	50/27	50/27	50/27	50/27
184	?	28/15	28/15	28/15
185	15/8	15/8	15/8	15/8
186	?	189/100	66/35	66/35
187	243/128	243/128	243/128	49/26
188	?	3200/1701	121/64	121/64
189	256/135	256/135	125/66	91/48
190	78125/41472	40/21	21/11	21/11
191	48/25	48/25	48/25	48/25
192	15625/8192	27/14	27/14	27/14
193	243/125	243/125	77/40	25/13
194	12500/6561	2187/1120	242/125	52/27
195	19683/10000	1400/729	64/33	64/33
196	625/324	625/324	150/77	39/20
197	6144/3125	35/18	35/18	35/18
198	125/64	49/25	49/25	49/25
199	31104/15625	63/32	55/28	55/28
200	2025/1024	2025/1024	99/50	65/33
201	?	5103/2560	240/121	77/39
202	160/81	160/81	160/81	160/81
203	?	125/63	125/63	125/63
204	2/1	2/1	2/1	2/1