3-5-7-15 hexany

A 7-limit Hexany. This creates a scale of 1 7/6 5/4 7/5 3/2 7/4 2/1, with steps of 7/6 15/14 28/25 15/14 7/6 8/7. This is highly notable because it contains both the harmonic sequence 4:5:6:7 and the subharmonic sequence 7/7 7/6 7/5 7/4 above the root, and at least one copy of every interval in the 7-odd-limit tonality diamond somewhere in the scale. This means it is the optimal configuration for maximising the number and variety of simple harmonies available in a hexatonic scale. Melodically it is fairly strong as well, with every step larger than a 12edo semitone and a ratio of approximately 2.2 between the largest and smallest step. However, expanding it out to a bihexany without including any repeated notes or intervals too small to be melodically useful is significantly more challenging than many seemingly more complex hexanies.

Circle diagram.

! 3-5-7-15_Hexany.scl
!
3 5 7 15 2-combination Hexany
6
!
266.871
386.313
582.512
701.955
968.825
1200

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