User:Overthink/The 7-limit in 171edo

An excellent system for approximating the 7-limit is 171edo. The 9-odd-limit tonality diamond is approximated with just over 0.4 cents of error, and all 7-limit intervals with odd limit up to 10,000,000 are consistent (first odd to cause inconsistencies is 13671875). 171edo is thus an excellent system for classifying intervals and commas simply and accurately.

Approximation of prime harmonics in 171edo

Harmonic		2	3	5	7
Error	Absolute (¢)	+0.00000	-0.20061	-0.34880	-0.40485
	Relative (%)	+0.0	-2.9	-5.0	-5.8
Steps (reduced)		171 (0)	271 (100)	397 (55)	480 (138)

7-limit intervals in 171edo

Steps	Cents	Approximate ratios	Name
0	0.00	1/1	Unison
1	7.02	225/224, 5120/5103, 15625/15552	Kleisma
2	14.04	126/125, 245/243, 78732/78125	Semicomma
3	21.05	81/80, 875/864, 3125/3087
4	28.07	64/63, 3125/3072, 20000/19683
5	35.09	49/48, 50/49
6	42.11	128/125, 525/512
7	49.12	36/35, 250/243
8	56.14	405/392, 1323/1280
9	63.16	28/27, 648/625
10	70.18	25/24, 20480/19683
11	77.19	256/245
12	84.21	21/20
13	91.23	135/128, 256/243
14	98.25
15	105.26
16	112.28	16/15, 2187/2048
17	119.30
18	126.32
19	133.33
20	140.35
21	147.37
22	154.39
23	161.40
24	168.42
25	175.44
26	182.46	10/9
27	189.47
28	196.49
29	203.51	9/8
30	210.53
31	217.54
32	224.56
33	231.58	8/7
34	238.60
35	245.61
36	252.63
37	259.65
38	266.67	7/6
39	273.68
40	280.70
41	287.72
42	294.74
43	301.75
44	308.77
45	315.79	6/5
46	322.81
47	329.82
48	336.84
49	343.86
50	350.88
51	357.89
52	364.91
53	371.93
54	378.95
55	385.96	5/4
56	392.98
57	400.00
58	407.02
59	414.04
60	421.05
61	428.07
62	435.09	9/7
63	442.11
64	449.12
65	456.14
66	463.16
67	470.18
68	477.19
69	484.21
70	491.23
71	498.25	4/3
72	505.26
73	512.28
74	519.30
75	526.32
76	533.33
77	540.35
78	547.37
79	554.39
80	561.40
81	568.42
82	575.44
83	582.46	7/5
84	589.47
85	596.49
86	603.51
87	610.53
88	617.54	10/7
89	624.56
90	631.58
91	638.60
92	645.61
93	652.63
94	659.65
95	666.67
96	673.68
97	680.70
98	687.72
99	694.74
100	701.75	3/2
101	708.77
102	715.79
103	722.81
104	729.82
105	736.84
106	743.86
107	750.88
108	757.89
109	764.91	14/9
110	771.93
111	778.95
112	785.96
113	792.98
114	800.00
115	807.02
116	814.04	8/5
117	821.05
118	828.07
119	835.09
120	842.11
121	849.12
122	856.14
123	863.16
124	870.18
125	877.19
126	884.21	5/3
127	891.23
128	898.25
129	905.26
130	912.28
131	919.30
132	926.32
133	933.33	12/7
134	940.35
135	947.37
136	954.39
137	961.40
138	968.42	7/4
139	975.44
140	982.46
141	989.47
142	996.49	16/9
143	1003.51
144	1010.53
145	1017.54	9/5
146	1024.56
147	1031.58
148	1038.60
149	1045.61
150	1052.63
151	1059.65
152	1066.67
153	1073.68
154	1080.70
155	1087.72
156	1094.74
157	1101.75
158	1108.77
159	1115.79
160	1122.81
161	1129.82
162	1136.84
163	1143.86
164	1150.88
165	1157.89
166	1164.91
167	1171.93
168	1178.95
169	1185.96
170	1192.98
171	1200.00	2/1