1-5-9-15 by 64/45 bihexany

A 5-limit bihexany. This creates a scale of 1 16/15 9/8 6/5 32/25 4/3 64/45 3/2 8/5 27/16 9/5 15/8 2/1, with steps of 16/15 135/128 16/15 16/15 25/24 16/15 135/128 16/15 135/128 16/15 25/24 16/15. This may seem like a complex interval to offset the base hexany by, but many of the factors cancel out, leaving a quite even (1.58:1) 12 note scale with only three different step sizes that maps unambiguously to a standard keyboard, with the main oddity being the 32/25 above the root note instead of a 5/4. 8 of the notes have perfect fifths above them, 2 are sharp by 2048/2025, 1 is flat by 81/80 and 1 is flat by 128/125.

Circle diagram.

! 1-5-9-15_by_64/45_Bihexany.scl
!
1 5 9 15 by 64/45 2-combination Bihexany
12
!
111.731
203.910
315.641
427.372
498.044
609.776
701.955
813.686
905.865
1017.596
1088.268
1200