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 the nearest step by more than 3.5 cents will be in italics, while intervals that differ from assigned steps by a rate of 50% or more, multiples of such intervals, or else, intervals that have an odd limit higher than 1024, will not be included in the chart at all. 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.

Step	Cents	5 limit	7 limit	11 limit	13 limit	17 limit
0	0	1/1
1	7.5471698	?	225/224	243/242	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	?	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	?	?	?	?	289/256
29	218.8679245	?	?	?	?	17/15
30	226.4150943	256/225	?	?	?	?
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	?	?	?	?	512/425
44	332.0754717	?	?	?	?	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	?	?	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	?	?
60	452.8301887	?	?	?	13/10	?
61	460.3773585	?	?	176/135	?	?
62	467.9245283	?	21/16	?	?	?
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	?	?	?	?
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	?	?	?	?
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	?	?	?	?
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	?	?	?	?
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	?	?	?
98	739.6226415	?	?	135/88	?	?
99	747.1698113	?	?	?	20/13	?
100	754.7169811	?	?	99/64	?	?
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	?	?	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	?	?	?	?	119/72, 272/165
116	875.4716981	?	?	?	?	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	?	?	?	?
130	981.1320755	?	?	?	?	30/17
131	988.6792458	?	?	?	?	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	?	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	700/351	255/128
159	1200	2/1