1-3-5-9 by 7/5 bihexany

The second simplest possible bihexany that produces a full 12 note scale, comprised of two-combination sum products of the first four 5-limit odd numbers offset by the simple septimal tritone. This creates a scale of 1 21/20 9/8 7/6 5/4 21/16 7/5 3/2 63/40 5/3 7/4 15/8 2/1, with steps of 21/20 15/14 28/27 15/14 21/20 16/15 15/14 21/20 200/189 21/20 15/14 16/15. This is particularly notable because it extends the near complete diatonic scale created by the basic 1-3-5-9 hexany neatly to a 12 note scale that is an unambiguous detemper of septimal meantone. No note deviates by more than 33 cents from 12edo and it maps neatly to a standard keyboard with many highly consonant chords available. 8 notes have a perfect fifth above them, 2 have ones that are flat by a syntonic comma, 1 is flat by a marvel comma and still entirely usable as a regular fifth, and the final one is sharp by a septimal comma.

Circle diagram.

! 1-3-5-9_by_7/5_Hexany.scl
!
1 3 5 9 by 7/5 2-combination Hexany
12
!
21/20
9/8
7/6
5/4
21/16
7/5
3/2
63/40
5/3
7/4
15/8
2/1