1-5-11-15 by 6/5 bihexany
An 11-limit Bihexany. This creates a scale of 1 33/32 11/10 9/8 6/5 99/80 33/25 11/8 3/2 33/20 9/5 15/8 2/1, with steps of 33/32 16/15 45/44 16/15 33/32 16/15 25/24 12/11 11/10 12/11 25/24 16/15. This is the simplest interval you can offset the base hexany by to produce a full 12 note scale, and so produces the greatest number of simple ratios overall, including 6 perfect 5ths, but is not quite melodically optimal as it introduces a smallest step of 45/44 on top of the already existing 33/32, nor does it have a 5/4 above the root note. Raising the offset interval by a small comma like 385/384 or 225/224 will make the smallest step more melodically functional and compromise between the purity of the major & minor thirds better, or you could raise the minor third by a full 100/99 to give an offset interval of 40/33 and a pure 5th harmonic.
! 1-5-11-15_by_6/5_BiHexany.scl ! 1 5 11 15 by 6/5 2-combination Hexany 12 ! 53.272 165.004 203.910 315.641 368.914 480.645 551.317 701.955 866.959 1017.596 1088.268 1200