1-3-5-7-9-15 eikosany

The simplest possible 15-odd-limit eikosany. This creates a scale of 1 21/20 35/32 9/8 7/6 5/4 21/16 7/5 45/32 3/2 63/40 27/16 7/4 9/5 15/8 63/32 2/1, with steps of 21/20 25/24 36/35 28/27 15/14 21/20 16/15 225/224 16/15 21/20 15/14 28/27 36/35 25/24 21/20 64/63. As with hexanies, dekanies and pentadekanies, the 15-odd-limit is where you start seeing combination product sets with repeated notes, in this case reducing it all the way from a 20 note scale to a 16 note one. On top of the 4 direct repeats, there are also two comma steps that blur into their neighbours, making this more of a 14-tone scale for melodic purposes. There are still more than enough notes in good positions to compose music both familiar and xenharmonic with this, but it is definitely not optimal for its size.

Circle diagram.

! 1-3-5-7-9-15_Eikosany.scl
!
1 3 5 7 9 15 3-combination Eikosany
16
!
84.467
155.139
203.910
266.871
386.313
470.781
582.512
590.223
701.955
786.422
905.865
968.825
1017.596
1088.268
1172.735
1200