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, as is demonstrated in the following examples.
- 3-5-7-15 by 9/8 bihexany
- 3-5-7-15 by 9/5 bihexany
- 3-5-7-15 by 45/28 bihexany
- 3-5-7-15 by 27/14 bihexany
- 3-5-7-15 by 11/7 bihexany
- 3-5-7-15 by 17/14 bihexany
- 3-5-7-15 by 19/14 bihexany
- 3-5-7-15 by 23/14 bihexany
Expanding it out to a stellated hexany also has its own quirks.
! 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