181edo and stretched hemififths

Normal Hemififths

181edo supports normal Hemififths (MOS 3L 4s) with the mode 31 22 31 22 31 22 22

Hemififths

#\181	Cents	Approximated Ratios
31	205.525	9/8
53	351.381	11/9, 16/13
84	556.906	11/8, 18/13
106	702.762	3/2
137	908.287	22/13
159	1054.144	11/6
181	1200.000	2/1

Stretched Hemififths

This mode can be improved in 181edo by adding 1 more step on the fifth, and 1 more step on the octave: 31 22 31 23 31 22 23

With this stretched mode, various simple Just Intonation ratios are approximated thoughout the octaves.

Stretched Hemififths (octave-reduced )

#\181	Cents	Approximated Ratios
31	205.525	9/8
53	351.381	11/9, 16/13
84	556.906	11/8, 18/13
107	709.392	3/2
138	914.917	22/13
160	1060.773	24/13
2	13.260	2/1
33	218.785	9/8, 8/7
55	364.641	16/13
86	570.166	18/13
109	722.652
140	928.177	12/7
162	1074.033	13/7
4	26.519
35	232.044	8/7
57	377.901	5/4
88	583.425	7/5
111	735.912	20/13
142	941.436	12/7
164	1087.293	15/8
6	39.779
37	245.304	15/13
59	391.160	5/4
90	596.685	7/5
113	749.171	20/13
144	954.696	26/15
166	1100.552	15/8
8	53.039

! 181edo_stretched-hemififths.scl
!
181edo stretched hemififths
7
!
205.524862
351.381215
556.906077
709.392265
914.917127
1060.773481
1213.259669

See Also

• 93edo and stretched hemififths