NumerologicalNontemperament: Difference between revisions
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Numerological Nontemperament is a scale developed by Rozencrantz the sane in a fit of irrationality. After reading about irrational ratios and [[Charles_Lucy|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 | Numerological Nontemperament is a scale developed by Rozencrantz the sane in a fit of irrationality. After reading about irrational ratios and [[Charles_Lucy|Charles Lucy]]'s use of pi, I wondered what a truly irrational scale would sound like. A rank-2 temperament, the [[Period|large generator]] (formal-octave) is [[Wikipedia:Pi|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. | 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. | ||
<pre> | |||
! | ! | ||
Irrational scale: Small generator is Golden Ratio, Large generator is Pi | |||
Irrational scale: Small generator is | |||
19 | 19 | ||
! | ! | ||
88.10600 | 88.10600 | ||
201.86100 | 201.86100 | ||
315.61500 | 315.61500 | ||
403.72100 | 403.72100 | ||
517.47500 | 517.47500 | ||
605.58200 | 605.58200 | ||
719.33600 | 719.33600 | ||
833.09000 | 833.09000 | ||
921.19600 | 921.19600 | ||
1034.95100 | 1034.95100 | ||
1148.70500 | 1148.70500 | ||
1236.81100 | 1236.81100 | ||
1350.56600 | 1350.56600 | ||
1464.32000 | 1464.32000 | ||
1552.42600 | 1552.42600 | ||
1666.18100 | 1666.18100 | ||
1754.28700 | 1754.28700 | ||
1868.04100 | 1868.04100 | ||
1981.79600</pre> | |||
[[Category:19-note scales]] | |||
[[Category: | [[Category:Tempered scales]] | ||
[[Category: | [[Category:Golden]] | ||
[[Category: | [[Category:Pi]] | ||
[[Category:Transcendental]] | |||
[[Category:Pages with Scala files]] | [[Category:Pages with Scala files]] | ||
Revision as of 16:14, 9 August 2021
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