1-3-5-7 hexany

The simplest possible Hexany, comprised of two-combination sum products of the first four odd numbers. This creates a scale of 1 7/6 5/4 35/24 5/3 7/4 2/1, with steps of 7/6 15/14 7/6 8/7 21/20 8/7. Despite having simpler factors, it's most complex number (the 35/24) is more complex than that of its immediate neighbour 1-3-5-9, the smallest step is also smaller and the overall sound is more xenharmonic as it involves 7-limit intervals. It has two 5-limit chords that can be used to provide stable roots, a major one rooted on the 7/6 and a minor one rooted on the 5/3.

! 1-3-5-7_Hexany.scl
!
1 3 5 7 2-combination Hexany
6
!
7/6
5/4
35/24
5/3
7/4
2/1

Suggested keyboard mapping: C D# E G A Bb C

Expansions

As it has 1 as a factor, turning this from a standard hexany into a stellated hexany only adds two notes to your options rather than a full 14 due to the large number of repeated notes, which still leaves plenty of gaps on a standard keyboard.

1-3-5-7 stellated hexany

There are 6 ways of expanding this out to a bihexany that will put a 3/2 above the root, expanding your options in a way that gives you a stable 5-limit chord to centre your scale upon and plenty of other consonant chords. 3 of them produce a full 12 note scale.

Another 3 have overlapping notes and so only produce 10 note scales, but may still be useful nonetheless.

Other bihexanies derived from this that produce a 10 note scale are: (using the rotation that produces the more consonant mode overall where possible)

Other bihexanies derived from this that produce a 11 note scale are:

All other offset intervals will produce a 12 note scale with at least 4 perfect fifths, although they may not be positioned in a way that provides familiar chord sequences. Ones that have five or more perfect fifths include: