Just Intonation in Csound

John ff,

In your earlier post you mentioned the problem of setting up just intonation
in Csound. Actually, it's already easy and doesn't need anything new and
special to make it easier. Here is a little example:

A Just Major (Ptolemy's Syntonon Diatonic) Scale in Csound:

;p1 p2 p3 p4 p5 p6 p7 p8, etc.
;inst start dur amp num den oct (other parameters)
i2 1 1 10000 1 1 2
i2 2 1 10000 9 8 2
i2 3 1 10000 5 4 2
i2 4 1 10000 4 3 2
i2 5 1 10000 3 2 2
i2 6 1 10000 5 3 2
i2 7 1 10000 15 8 2
i2 8 1 10000 1 1 4

Usually I use a basic tuning frequency of G = 98 Hertz, but any frequency
will work. The numerator goes in one field, the denominator in another,
and the octave transposition in a third field. One octave above the tuning
frequency is the octave "2" and two octaves above the tuning frequency is
the octave "4," etc.

In the Csound orchestra can handle these parameters in one simple line
of code:

ifreq = 98 * p5/p6 * p7 ; tuning freq * num/den * oct

The tuning frequency can even be set using a global variable, which can be
reset during the piece, either to a specified frequency, or could even be
multiplied by another ratio, which would allow wandering tonics, as in the
following example, which multiplies the global tuning frequency by 3/2 at
10 seconds into the piece, and then by another 3/2 but drops it back down
into the same octave by using the octave transposition ".5." This is
effectively modulating to V and then to V/V.

;p1 p2 p3 p4 p5 p6
;inst start dur num den oct
i1 10 1 3 2 1
i1 10 1 3 2 .5

At the beginning of the orchestra, set the global tuning intially to 98:

gituning = 98

Within the instrument design (in this case, a special global switching
design which only changes the tuning frequency, it doesn't play any notes),
set the global tuning with the following line of code:

gituning = gituning * p4/p5 * p6

This gives a basic tuning frequency of 98 for 10 seconds, 147 for 10 seconds, and ending with 110.25 for the remainder of the piece.

Then, in the instruments that play the notes, change the code to:

ifreq = gituning * p5/p6 * p7 ; global tuning freq * num/den * oct

Happy tuning.

Lydia Ayers


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