124ed8

124 equal divisions of the 8th harmonic (abbreviated 124ed8), is the tuning system that divides the 8th harmonic into 124 equal parts of about 29.03226 ¢ each. Each step represents a frequency ratio of [math]\displaystyle{ 8^{\frac{1}{124}} }[/math], or the 124th root of 8.

Context

124ed8 is an alternative version of 143ed11, the best 5.7.8.9.11.13.17.23 equal step tuning in the world. 124ed8 is for people who absolutely need a locked pure 8/1 when using some software or hardware. As a trade-off, 124ed8 has a slightly sharp tendency above the optimal 5.7.8.9.11.13.17.23 tuning. Comparared to 143ed11, 124ed8 stretches the 11th harmonic by about 0.295 ¢ and the mapping of the 8th harmonic (now pure) by about 0.256 ¢.

Intervals and approximation to JI

124ed8 degree	Cents	Ratios in the 5.7.8.9.11.13.17.23 subgroup	Error (abs, ¢)	Error (rel, %)
5	145.2	25/23	0.808	2.8
7	203.2	9/8	-0.684	-2.4
8	232.3	8/7	1.084	3.7
10	290.3	13/11	1.113	3.8
12	348.4	11/9	0.979	3.4
15	435.5	9/7	0.4	1.4
16	464.5	17/13	0.088	0.3
18	522.6	23/17	-0.738	-2.5
19	551.6	11/8	0.295	1.0
20	580.6	7/5	-1.867	-6.4
22	638.7	13/9	2.092	7.2
23	667.7	25/17	0.07	0.2
26	754.8	17/11	1.201	4.1
27	783.9	11/7	1.379	4.7
28	812.9	8/5	-0.783	-2.7
29	841.9	13/8	1.408	4.8
34	987.1	23/13	-0.65	-2.2
35	1016.1	9/5	-1.467	-5.1
37	1074.2	13/7	2.492	8.6
38	1103.2	17/9	2.18	7.5
39	1132.3	25/13	0.158	0.5
44	1277.4	23/11	0.463	1.6
45	1306.5	17/8	1.496	5.2
47	1364.5	11/5	-0.488	-1.7
49	1422.6	25/11	1.271	4.4
53	1538.7	17/7	2.58	8.9
56	1625.8	23/9	1.442	5.0
57	1654.8	13/5	0.625	2.2
61	1771.0	25/9	2.25	7.8
63	1829.0	23/8	0.758	2.6
68	1974.2	25/8	1.566	5.4
71	2061.3	23/7	1.842	6.3
73	2119.4	17/5	0.713	2.5
76	2206.5	25/7	2.65	9.1
91	2641.9	23/5	-0.025	-0.1
96	2787.1	5/1	0.783	2.7
116	3367.7	7/1	-1.084	-3.7
124	3600.0	8/1	0.0	0.0
131	3803.2	9/1	-0.684	-2.4
143	4151.6	11/1	0.295	1.0
153	4441.9	13/1	1.408	4.8
169	4906.5	17/1	1.496	5.2
187	5429.0	23/1	0.758	2.6
192	5574.2	25/1	1.566	5.4