3-5-13-15 by 19/17 bihexany
A 19-limit bihexany. This creates a scale of 1 13/12 19/17 247/204 5/4 13/10 95/68 247/170 3/2 13/8 57/34 247/136 2/1, with steps of 13/12 228/221 13/12 255/247 26/25 475/442 26/25 255/247 13/12 228/221 13/12 272/247. Unlike many good bihexanies, this does not use the offset interval to cancel out composite ratios and achieve simpler ones. Instead, the interval is picked to maximise the size of the smallest step and make the scale as melodically effective as possible. However, in this case it also has the effect of splitting the major third almost precisely in two and adding 4 fifths that are approximately 10 cents flat along with the 4 perfect ones, making this a detemper of the aureusmic temperament that sounds far more consonant than it would appear merely from looking at the numbers.
! 3-5-13-15_by_19/17_Bihexany.scl ! 3 5 13 15 by 19/17 2-combination Bihexany 12 ! 138.572 192.557 331.130 386.313 454.213 578.871 646.771 701.955 840.572 894.512 1033.085 1200