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