5-7-9-15 by 29/18 bihexany

A 29-limit Bihexany. This creates a scale of 1 29/28 15/14 29/24 9/7 29/20 3/2 87/56 29/18 9/5 27/14 2/1, with steps of 29/28 30/29 203/180 218/203 203/180 30/29 29/28 28/27 15/14 756/725 15/14 28/27. This expands the base hexany out in a way that maximises the size of the smallest step and cancels out many of the factors, turning the steps around the root into a neat 27:28:29:30, a fragment of the harmonic sequence. It has 4 perfect fifths, 2 that are sharp by 406/405 and 2 that are flat by 145/144, which are all still within the diatonic tuning range. It does not have any true 5-limit major thirds, but as 29/24 and 36/29 are only 145/144 cents out from just, they can still pass as ordinary minors and majors to most ears in the same way that 22edo and 48edo thirds do.

Circle diagram.

! 5-7-9-15_by_29/18_Bihexany.scl
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5 7 9 15 by 29/18 2-combination Bihexany
12
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60.751
119.442
327.622
435.084
643.263
701.955
762.706
825.667
945.110
1017.596
1137.039
1200