NumerologicalNontemperament

Numerological Nontemperament is a scale developed by Rozencrantz the sane in a fit of irrationality. After reading about irrational ratios and Charles Lucy's use of pi, I wondered what a truly irrational scale would sound like. A rank-2 temperament, the large generator (formal-octave) is pi (approximately 355/113, a wide 12th) and the small generator is the golden ratio (around 830 cents)

The scale lies on top of the halberstadt keyboard quite nicely, though it lacks the key orientation that would make raised accidentals at all meaningful.

!
Irrational scale: Small generator is Golden Ratio, Large generator is Pi
19
!
88.10600
201.86100
315.61500
403.72100
517.47500
605.58200
719.33600
833.09000
921.19600
1034.95100
1148.70500
1236.81100
1350.56600
1464.32000
1552.42600
1666.18100
1754.28700
1868.04100
1981.79600