Table of 167edo intervals

This table of 167edo intervals assumes 13-limit patent val ⟨167 265 388 469 578 618].

Intervals highlighted in bold are prime harmonics or subharmonics. Intervals that differ from their assigned steps by more than 50%, but no more than 100%, are shown in italic. Intervals that differ by more than 100% or with odd limit over 800 are not shown. For clarity, an entry can contain multiple intervals if they are of comparable complexity.

#	Cents	Marks	5-limit	7-limit	11-limit	13-limit
0	0.00	P1	1/1
1	7.186			126/125, 225/224	121/120, 176/175, 243/242	144/143, 169/168, 196/195
2	14.371		81/80		99/98, 100/99, 121/120	91/90, 105/104
3	21.557		81/80	64/63		65/64, 66/65, 78/77
4	28.743			49/48, 50/49, 64/63, 686/675	55/54, 56/55	648/637
5	35.928			49/48	45/44
6	43.114			36/35, 525/512		40/39, 693/676
7	50.299		250/243	36/35	33/32, 605/588
8	57.485			28/27	33/32	65/63, 91/88, 336/325
9	64.671		25/24			26/25, 27/26
10	71.856		25/24		704/675	715/686
11	79.042			21/20	22/21	245/234
12	86.228			21/20	81/77	104/99
13	93.413	m2				55/52, 96/91, 325/308, 343/325
14	100.599				35/33	143/135, 441/416, 675/637
15	107.784		16/15			117/110, 484/455, 715/672
16	114.970		16/15	15/14	77/72, 576/539	125/117
17	122.156			15/14	189/176	14/13, 130/121, 338/315
18	129.341				264/245	14/13
19	136.527				250/231	13/12, 225/208
20	143.713			49/45	12/11, 88/81	13/12
21	150.898				12/11
22	158.084			35/32, 192/175	11/10, 675/616	128/117, 325/297, 351/320, 385/351, 429/392
23	165.269				11/10	845/768
24	172.455			54/49	243/220, 495/448, 875/792	182/165
25	179.641		10/9		256/231	72/65, 195/176, 231/208, 375/338, 416/375
26	186.826		10/9		49/44, 891/800	39/35
27	194.012			28/25		143/128, 160/143, 189/169
28	201.198	M2	9/8		55/49	91/81, 702/625
29	208.383		9/8			44/39, 273/242
30	215.569				25/22, 112/99	162/143
31	222.754				25/22	91/80
32	229.940			8/7		297/260, 490/429
33	237.126			8/7	55/48	416/363, 650/567
34	244.311		144/125		121/105	15/13, 539/468
35	251.497			81/70	140/121	15/13, 52/45
36	258.683			512/441	64/55	65/56
37	265.868			7/6, 400/343
38	273.054		75/64	7/6		117/100
39	280.240			147/125, 288/245	33/28, 88/75
40	287.425			189/160, 405/343		13/11
41	294.611	m3	32/27			13/11
42	301.796			25/21
43	308.982		6/5	448/375	105/88, 484/405	117/98, 140/117
44	316.168		6/5		605/504
45	323.353			135/112		65/54
46	330.539			98/81	40/33, 121/100	63/52
47	337.725			175/144	40/33, 147/121	39/32, 91/75
48	344.910		625/512	128/105	11/9, 336/275	39/32, 825/676
49	352.096			49/40	11/9, 27/22	364/297
50	359.281					16/13
51	366.467		100/81		99/80, 121/98	16/13, 26/21, 225/182
52	373.653				150/121	26/21, 242/195, 273/220
53	380.838		5/4	56/45		81/65
54	388.024		5/4			169/135, 429/343, 1001/800
55	395.210				44/35	49/39
56	402.395			63/50	44/35, 121/96, 125/99, 486/385	525/416
57	409.581	M3	81/64		308/243, 792/625	33/26, 195/154
58	416.766				14/11
59	423.952		32/25	125/98	14/11	143/112, 216/169
60	431.138		32/25	9/7	77/60, 440/343	50/39
61	438.323			9/7	165/128, 567/440	156/121, 676/525
62	445.509			35/27	128/99	84/65, 507/392
63	452.695				100/77, 891/686	13/10
64	459.880			64/49	176/135	13/10, 441/338, 845/648
65	467.066			21/16	55/42
66	474.251			21/16	405/308	130/99, 154/117
67	481.437				33/25	169/128, 416/315
68	488.623				175/132, 297/224	65/49
69	495.808	P4	4/3			225/169
70	502.994		4/3	75/56	147/110	234/175
71	510.180			75/56, 168/125	121/90	35/26, 192/143
72	517.365		27/20		66/49	182/135
73	524.551		27/20			65/48, 88/65
74	531.737			49/36, 200/147	15/11, 110/81	495/364, 972/715
75	538.922		512/375		15/11	273/200
76	546.108			48/35	11/8	196/143, 351/256, 891/650
77	553.293			135/98	11/8, 500/363	260/189
78	560.479		864/625	112/81		18/13, 539/390
79	567.665		25/18		168/121	18/13
80	574.850		25/18	1024/735	675/484	39/28
81	582.036			7/5, 480/343
82	589.222	d5	45/32, 1024/729	7/5
83	596.407		45/32	343/243, 882/625	484/343	55/39
84	603.593		64/45	625/441	343/242	78/55
85	610.778	A4	64/45, 729/512	10/7		845/594
86	617.964			10/7, 343/240
87	625.150		36/25	735/512, 1125/784		56/39
88	632.335		36/25		121/84	13/9
89	639.521		625/432	81/56		13/9
90	646.707				16/11, 363/250	189/130
91	653.892			35/24	16/11	143/98, 512/351
92	661.078		375/256		22/15	343/234
93	668.263			[72/49]], 147/100	22/15, 81/55	715/486
94	675.449		40/27			65/44
95	682.635		40/27		49/33	135/91
96	689.820			112/75, 125/84	49/33	52/35, 143/96
97	697.006		3/2	112/75	121/81	175/117
98	704.192	P5	3/2			338/225
99	711.377				264/175, 448/297	98/65
100	718.563			50/33	256/169, 315/208
101	725.749			32/21	616/405	99/65, 117/77
102	732.934			32/21	55/36, 84/55
103	740.120			49/32	135/88	20/13, 676/441
104	747.305				77/50	20/13
105	754.491			54/35	99/64	65/42, 784/507
106	761.677			14/9	256/165	121/78, 525/338
107	768.862		25/16	14/9	120/77, 343/220	39/25
108	776.048		25/16		11/7	169/108
109	783.234				11/7
110	790.419	m6	128/81		243/154, 625/396	52/33
111	797.605			100/63	35/22, 198/125, 385/243	165/104, 507/320, 832/525
112	804.790				35/22	78/49
113	811.976		8/5		1125/704	270/169, 686/429
114	819.162		8/5	45/28	77/48	130/81
115	826.347				121/75	21/13, 195/121, 440/273
116	833.533		81/50		196/121	13/8, 21/13, 364/225
117	840.719					13/8
118	847.904			49/30, 80/49	18/11, 44/27	297/182
119	855.090		1024/625	105/64	18/11, 275/168	64/39, 819/500
120	862.275			288/175	33/20, 242/147	150/91
121	869.461			81/49	33/20, 200/121	945/572
122	876.647			81/49, 224/135		91/55, 108/65
123	883.832		5/3		1008/605	693/416
124	891.018		5/3	375/224	405/242	117/70
125	898.204			42/25
126	905.389	M6	27/16		1225/726	22/13
127	912.575			320/189, 686/405	847/500	22/13
128	919.760			245/144	56/33, 75/44, 1029/605	143/84
129	926.946		128/75	12/7, 875/512	75/44, 77/45	169/99, 1155/676
130	934.132			12/7, 343/200
131	941.317			441/256	55/32	112/65
132	948.503				121/70	26/15, 45/26
133	955.689		125/72			26/15, 936/539
134	962.874			7/4	96/55	363/208, 567/325
135	970.060			7/4		429/245
136	977.246				44/25	160/91
137	984.431				44/25, 99/56	39/22, 143/81, 1125/637
138	991.617		16/9			39/22, 484/273
139	998.802	m7	16/9		98/55	162/91, 625/351
140	1005.988			25/14		143/80, 338/189
141	1013.174		9/5		88/49	70/39
142	1020.359		9/5		231/128	65/36, 375/208
143	1027.545			49/27, 405/224	440/243, 896/495	165/91
144	1034.731				20/11
145	1041.916			64/35, 175/96	20/11, 1125/616	117/64, 594/325, 640/351, 702/385, 715/392, 1183/648
146	1049.102				11/6
147	1056.287				11/6, 81/44	24/13
148	1063.473				231/125	24/13, 1183/640
149	1070.659				245/132	13/7
150	1077.844			28/15		13/7, 121/65, 315/169
151	1085.030		15/8		144/77, 539/288	234/125
152	1092.216		15/8		1323/704	169/90, 220/117, 455/242
153	1099.401				66/35	49/26, 270/143, 832/441, 1274/675
154	1106.587	M7				91/48, 616/325, 650/343
155	1113.772			40/21	21/11	99/52
156	1120.958				21/11, 275/144	468/245
157	1128.144		48/25		675/352	25/13, 1372/715
158	1135.329			27/14		25/13, 52/27
159	1142.515			27/14	64/33	126/65, 176/91, 325/168
160	1149.701		243/125	35/18	1176/605
161	1156.886			35/18, 1024/525		39/20, 1352/693
162	1164.072			49/25, 96/49		1375/702
163	1171.257			49/25, 63/32, 675/343	55/28	637/324, 1125/572
164	1178.443		160/81	63/32		65/33, 77/39
165	1185.629			125/63	99/50, 240/121
166	1192.814			125/63, 448/225	175/88, 484/243	143/72, 195/98
167	1200.000	P8	2/1