1-3-5-7-11-13-15 enaeikosany

Circle diagram.

Circle diagram. (rotated)

A 15-odd-limit enaeikosany. This creates a scale of 1 65/64 13/12 35/32 55/48 7/6 5/4 65/48 11/8 35/24 143/96 25/16 77/48 13/8 5/3 55/32 7/4 11/6 15/8 91/48 2/1, with steps of 65/64 16/15 105/104 22/21 56/55 15/14 13/12 66/65 35/33 143/140 150/143 77/75 78/77 40/39 33/32 56/55 22/21 45/44 91/90 96/91. (5/4 appears twice, reducing this to a 20 note scale.) As the simplest enaeikosany that lacks a factor of 9, this has fewer perfect fifths than any of its predecessors and they do not appear in chains apart from 5/3-5/4-15/8, which is connected through the duplicated note. It does still have 8 perfect fifths, plus additional diatonic ones flat by 225/224, 144/143 and 105/104, which gives you more than enough simple chords to produce consonant music, but modulation becomes more challenging when they are only connected by more xenharmonic intervals.

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