31edo is very close to quarter-comma meantone; that, and a 19 note scale, were used in Renaissance times. But here I am exploiting intervals that approximate just tuned intervals involving the prime number 7. For example, 8:7 is very close to 6 steps of 31edo. This 19 note scale includes many 6 step intervals.
This diagram shows the primary intervals available in this 19 note scale. Green arrows are perfect fifth, blue arrows are major thirds, and red arrows are 7:4 intervals that don't fit well into conventional terminology. Rather than arranging the notes into a circle of fifth, I used a spiral of fifths that prioritizes chains of major thirds. The conventional diatonic scale can be arranged this way, too:
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