1-7-13-15 stellated hexany
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A 15-odd-limit stellated Hexany. This creates a scale of 1 1365/1024 91/64 195/128 13/8 105/64 7/4 15/8 2/1, with steps of 1365/1024 16/15 15/14 16/15 105/104 16/15 15/14 16/15. This only adds two steps to the base hexany, which do somewhat reduce the size of the largest step, but still leave a gap of nearly 500 cents on one side, making conventional songwriting impossible using it. While it has no perfect fifths, it does have one that is only out by 4096/4095, which is more than close enough to provide a stable rooting point, but your chord options remain quite xenharmonic, with only neutral thirds or slendric style wide seconds and fourths to add to it.
! 1-7-13-15_Stellated_Hexany.scl ! 1 7 13 15 1-3-combination Hexany 8 ! 497.622 609.353 728.796 840.527 857.094 968.825 1088.268 1200
Suggested keyboard mapping: C F F# G G# A A# B C.