Table of 159edo Intervals

This table of 159edo intervals assumes 17-limit patent val ⟨159 252 369 446 550 588 650].

Intervals highlighted in bold are prime harmonics or subharmonics, while other well-known intervals will likely have links to their respective pages. In addition, intervals that differ from assigned steps by more than 50%, multiples of such intervals, and intervals of odd limit higher than 1024, are not shown. Furthermore, when multiple well-known intervals for a given prime-limit share a step size, they may share a cell in the chart; conversely, a "?" in the chart means that no known interval meets the criteria for inclusion. Note that no 5-limit intervals can be represented by degrees other than multiples of 3, so those entries are left blank.

Step	Cents	5 limit	7 limit	11 limit	13 limit	17 limit
0	0	1/1
1	7.5471698		225/224	243/242	196/195, 351/350	256/255
2	15.0943396		?	121/120, 100/99	144/143	120/119
3	22.6415094	81/80	?	?	78/77	85/84
4	30.1886792		64/63	56/55, 55/54	?	52/51
5	37.7358491		?	45/44	?	51/50
6	45.2830189	?	?	?	40/39	192/187
7	52.8301887		?	33/32	?	34/33
8	60.3773585		28/27	?	?	88/85
9	67.9245283	25/24	?	?	26/25, 27/26	?
10	75.4716981		?	?	?	160/153
11	83.0188679		21/20	22/21	?	?
12	90.5660377	256/243, 135/128	?	?	?	?
13	98.1132075		?	128/121	55/52	18/17
14	105.6603774		?	?	?	17/16
15	113.2075472	16/15	?	?	?	?
16	120.7547170		15/14	275/256	?	?
17	128.3018868		?	?	14/13	128/119
18	135.8490566	27/25	?	?	13/12	?
19	143.3962264		?	88/81	?	?
20	150.9433962		?	12/11	?	?
21	158.4905660	?	?	?	128/117	561/512, 1024/935
22	166.0377358		?	11/10	?	?
23	173.5849057		567/512	243/220	?	425/384
24	181.1320755	10/9	?	256/231	?	?
25	188.6792458		?	?	143/128	512/459
26	196.2264151		28/25	?	?	?
27	203.7735849	9/8	?	?	?	?
28	211.3207547		?	?	44/39	289/256
29	218.8679245		?	?	?	17/15
30	226.4150943	256/225	?	154/135	?	?
31	233.9622642		8/7	55/48	?	?
32	241.5094340		?	1024/891	?	?
33	249.0566038	?	?	?	15/13	?
34	256.6037736		?	297/256	?	?
35	264.1509434		7/6	64/55	?	?
36	271.6981132	75/64	?	?	?	?
37	279.2452830		?	?	?	20/17
38	286.7924528		?	33/28	13/11	85/72
39	294.3396226	32/27	?	?	?	?
40	301.8867925		25/21	?	?	?
41	309.4339622		?	?	512/429	153/128
42	316.9811321	6/5	?	77/64	?	?
43	324.5283019		135/112	?	?	512/425
44	332.0754717		?	40/33, 121/100	?	144/119, 165/136
45	339.6226415	?	?	?	39/32	?
46	347.1698113		?	11/9	?	?
47	354.7169811		?	27/22	?	?
48	362.2641509	?	?	?	16/13	?
49	369.8113208		?	?	?	68/55
50	377.3584906		56/45	1024/825	?	?
51	384.9056604	5/4	?	96/77	?	?
52	392.4528302		?	?	?	64/51
53	400		63/50	?	?	?
54	407.5471698	81/64	?	?	?	?
55	415.0943396		?	14/11	33/26	108/85
56	422.6415094		?	?	?	51/40
57	430.1886792	32/25	?	?	?	?
58	437.7358491		9/7	165/128	?	?
59	445.2830189		?	128/99	?	22/17
60	452.8301887	?	?	?	13/10	?
61	460.3773585		?	176/135	?	?
62	467.9245283		21/16	55/42, 72/55	?	17/13
63	475.4716981	320/243, 675/512	?	?	?	?
64	483.0188679		?	33/25	?	45/34
65	490.5660377		?	?	?	85/64
66	498.1132075	4/3	?	?	?	?
67	505.6603774		75/56	?	?	?
68	513.2075472		?	121/90	?	?
69	520.7547170	27/20	?	?	104/77	?
70	528.3018868		?	110/81	?	?
71	535.8490566		?	15/11	?	?
72	543.3962264	?	?	?	?	256/187
73	550.9433962		?	11/8	?	?
74	558.4905660		112/81	?	?	?
75	566.0377358	25/18	?	?	18/13	?
76	573.5849057		?	?	?	357/256
77	581.1320755		7/5	?	?	?
78	588.6792458	1024/729, 45/32	?	?	?	?
79	596.2264151		?	?	?	24/17
80	603.7735849		?	?	?	17/12
81	611.3207547	729/512, 64/45	?	?	?	?
82	618.8679245		10/7	?	?	?
83	626.4150943		?	?	?	512/357
84	633.9622642	36/25	?	?	13/9	?
85	641.5094340		81/56	?	?	?
86	649.0566038		?	16/11	?	?
87	656.6037736	?	?	?	?	187/128
88	664.1509434		?	22/15	?	?
89	671.6981132		?	81/55	?	?
90	679.2452830	40/27	?	?	77/52	?
91	686.7924528		?	180/121	?	?
92	694.3396226		112/75	?	?	?
93	701.8867925	3/2	?	?	?	?
94	709.4339622		?	?	?	128/85
95	716.9811321		?	50/33	?	68/45
96	724.5283019	243/160, 1024/675	?	?	?	?
97	732.0754717		32/21	84/55, 55/36	?	26/17
98	739.6226415		?	135/88	?	?
99	747.1698113	?	?	?	20/13	?
100	754.7169811		?	99/64	?	17/11
101	762.2641509		14/9	256/165	?	?
102	769.8113208	25/16	?	?	?	?
103	777.3584906		?	?	?	80/51
104	784.9056604		?	11/7	52/33	85/54
105	792.4528302	128/81	?	?	?	?
106	800		100/63	?	?	?
107	807.5471698		?	?	?	51/32
108	815.0943396	8/5	?	77/48	?	?
109	822.6415094		45/28	825/512	?	?
110	830.1886792		?	?	?	55/34
111	837.7358491	?	?	?	13/8	?
112	845.2830189		?	44/27	?	?
113	852.8301887		?	18/11	?	?
114	860.3773585	?	?	?	64/39	?
115	867.9245283		?	33/20, 200/121	?	119/72, 272/165
116	875.4716981		224/135	?	?	425/256
117	883.0188679	5/3	?	128/77	?	?
118	890.5660377		?	?	429/256	256/153
119	898.1132075		42/25	?	?	?
120	905.6603774	27/16	?	?	?	?
121	913.2075472		?	56/33	22/13	144/85
122	920.7547170		?	?	?	17/10
123	928.3018868	128/75	?	?	?	?
124	935.8490566		12/7	55/32	?	?
125	943.3962264		?	512/297	?	?
126	950.9433962	?	?	?	26/15	?
127	958.4905660		?	891/512	?	?
128	966.0377358		7/4	96/55	?	?
129	973.5849057	225/128	?	135/77	?	?
130	981.1320755		?	?	?	30/17
131	988.6792458		?	?	39/22	512/289
132	996.2264151	16/9	?	?	?	?
133	1003.7735849		25/14	?	?	?
134	1011.3207547		?	?	256/143	459/256
135	1018.8679245	9/5	?	231/128	?	?
136	1026.4150943		1024/567	440/243	?	768/425
137	1033.9622642		?	20/11	?	?
138	1041.5094340	?	?	?	117/64	1024/561, 935/512
139	1049.0566038		?	11/6	?	?
140	1056.6037736		?	81/44	?	?
141	1064.1509434	50/27	?	?	24/13	?
142	1071.6981132		?	?	13/7	119/64
143	1079.2452830		28/15	512/275	?	?
144	1086.7924528	15/8	?	?	?	?
145	1094.3396226		?	?	?	32/17
146	1101.8867925		?	121/64	104/55	17/9
147	1109.4339622	243/128, 256/135	?	?	?	?
148	1116.9811321		40/21	21/11	?	?
149	1124.5283019		?	?	?	153/80
150	1132.0754717	48/25	?	?	25/13, 52/27	?
151	1139.6226415		27/14	?	?	85/44
152	1147.1698113		?	64/33	?	33/17
153	1154.7169811	?	?	?	39/20	187/96
154	1162.2641509		?	88/45	?	100/51
155	1169.8113208		63/32	55/28, 108/55	?	51/26
156	1177.3584906	160/81	?	?	77/39	168/85
157	1184.9056604		?	240/121, 99/50	143/72	119/60
158	1192.4528302		448/225	484/243	195/98, 700/351	255/128
159	1200	2/1