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.

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Irrational scale: Small generator is Golden Ratio, Large generator is Pi

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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