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Temperament calculation in Scala

🔗Manuel Op de Coul <manuel.op.de.coul@eon-benelux.com>

1/19/2008 10:56:35 AM

Here's an overview of Scala's routines to calculate optimal
temperaments, in the current version 2.24z:

Equal temperament, TOP: EQUALTEMP/DATA
Equal temperament, TOP-RMS: EQUALTEMP/DATA
(This uses the standard mapping for a given equal temperament. So it's
possible to get adjacent mappings by specifying a smaller or larger
step size or period.)
Go to Tools:Equal temperament data.

Linear temperament, optimal generator, fixed period, minimax:
CALCULATE/MINIMAX
Linear temperament, optimal generator, fixed period, least-squares:
CALCULATE/LEASTSQUARE
Linear temperament, optimal generator and period, minimax and TOP:
CALCULATE/TOP
Linear temperament, optimal generator and period, least-squares and
TOP-RMS:
CALCULATE/RMS_TOP
(Given are a set of intervals to be approximated plus their mapping in
terms of generator steps. See lintemp.par for a list of the best
linear temperaments.) No GUI dialog.

Tempered primes, minimax: PROJECT/TEMPER/MINIMAX
Tempered primes, least-squares (smallest Frobenius norm):
PROJECT/TEMPER/FROBENIUS
Tempered primes, TOP: PROJECT/TEMPER/TOP
Tempered primes, TOP-RMS: PROJECT/TEMPER/RMS_TOP
(Given are a set of comma's that will vanish.)
Go to Modify:Temper.

The temperament list lintemp.par has been updated with Herman's recent
posting. Additions are welcome.

Manuel