3-9-13-15 by 27/26 bihexany

A 13-limit bihexany. This creates a scale of 1 27/26 13/12 9/8 5/4 135/104 13/9 3/2 5/3 45/26 65/36 15/8 2/1, with steps of 27/26 169/162 27/26 10/9 27/26 1352/1215 27/26 10/9 27/26 169/162 27/26 16/15. This degree of offset divides the smallest steps in the base hexany near equally in two, while also cancelling out many factors to produce strings of simple ratios that are near the optimal size for melody. 6 notes have perfect fifths above them, although not all are mapped to 7 steps above their roots, and it can still be mapped to a standard 12 tone keyboard without any note deviating from 12edo by more than 100 cents, although the need to map 9/8 to Eb and 5/3 to Ab may be unintuitive to some players.

Circle diagram.

! 3-9-13-15_by_27/26_Bihexany.scl
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3 9 13 15 by 27/26 2-combination Bihexany
12
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65.337
138.572
204.910
386.313
451.651
636.617
701.955
884.358
949.696
1022.931
1088.268
1200