[chuck-users] Diatonic tuning system

Hans Aberg haberg at math.su.se
Sun May 3 13:14:17 EDT 2009

This code now allows defining diatonic tuning systems, which once  
defined, selects the intervals. It is very easy to add a new tuning  
system: just one line. Plus adding its name were you want to have it  
on the keyboard.

A tuning system is defined by giving intervals, which can be given in  
different units (ratio, log, cents), and their diatonic coordinates,  
plus an octave which needs not be the interval ratio 2 or be equal to  
2m+5M. Intermediate pitches are supported (but at most one for the  
moment). Also a function that computes all ETs, plus some other  
illustrating tuning systems.

In order to illustrate that the octave needs not the interval ratio 2,  
Georgian style tunings have been added, which divides the perfect  
fifth into four equal steps, so that m = M and the octave is slightly  
sharp. Plus Bohlen-Pierce scales, dividing the ratio 3 into 13 steps,  
with the octave 5m+4M.

And the intermediate pitches are illustrated by Just intonation  
relative Pythagorean (might also be used for Turkish music  
description), Turkish E53, and Persian style tunings. So with just one  
neutral second added, one can cover a lot.

Details: see the file. Stay tuned!


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