1-3-5-7-9-11-13-15 octaeikosany

The simplest possible octaeikosany, comprised of two-combination sum products of the first 8 odd numbers. This creates a scale of 1 65/64 33/32 13/12 35/32 9/8 55/48 7/6 39/32 5/4 21/16 65/48 11/8 45/32 35/24 143/96 3/2 25/16 77/48 13/8 5/3 55/32 7/4 11/6 15/8 91/48 2/1, with steps of 65/64 66/65 104/99 105/104 36/35 55/54 56/55 117/112 40/39 21/20 65/63 66/65 45/44 28/27 143/140 144/143 25/24 77/75 78/77 40/39 33/32 56/55 22/21 45/44 91/90 96/91. (5/4 and 15/8 appear twice, reducing it to a 26 note scale.) This contains all the smaller 15-odd-limit hexanies and dekanies, although some will require rotation to see in the mode they originally appear in. It has 14 perfect fifths and covers the whole harmonic sequence from 8-16 above the root, as well as the familiar diatonic scale in the lydian mode, making it more than capable of playing all kinds of music both familiar and xenharmonic.

Circle diagram.

! 1-3-5-7-9-11-13-15_Octaeikosany.scl
!
1 3 5 7 9 11 13 15 2-combination Octaeikosany
26
!
26.841
53.272
138.572
155.139
203.910
235.676
266.871
342.482
386.313
470.781
524.886
551.317
590.223
653.184
689.890
701.955
772.627
818.188
840.527
884.358
937.631
968.825
1049.362
1088.268
1107.398
1200