1-7-13-15 hexany

A 13-limit Hexany. This creates a scale of 1 15/14 13/8 195/112 13/7 15/8, with steps of 15/14 91/60 15/14 16/15 105/104 16/15. This is an extremely lopsided hexany with a gap of more than 700 cents on one side. It is of interest though, as it very precisely approximates half of 10edo with one of the notes detempered into two notes a small comma apart. This is explained by the fact that 10edo tempers out 43904/43875, turning the fragment of the harmonic series 13:14:15:16 into equidistant steps quite accurately. This means that offsetting by any interval near 600 cents will create a bihexany that approximates all intervals in 10edo within less than 10 cents while allowing for beating effects by exploiting the microtones that an equal temperament does not.

! 1-7-13-15_Hexany.scl
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1 7 13 15 2-combination Hexany
6
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119.442
840.527
959.970
1071.701
1088.268
1200

Suggested keyboard mapping: C Db G# A Bb B C