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.
! 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