31-tone equal temperament in Csound

Ethan Walker posted to the list about a month ago (I took a vacation and
now I'm real behind on my email):

>What I am wondering is if there is anyone out there who has
>experience with creating orchestra and score files in C-sound for the
>31-tone chromatic scale.

Several people replied, but as I didn't see an answer that gives a
simple method for direct input in Csound, I've written a belated
response.

I usually write a C program to create my scores, and the C program
calculates the frequency in Hertz. This is the simplest way to get
it in through Csound instrument designs, but C programming requires
knowing a different language from Csound. (Another advantage of
the program is that you can have it generate a lot of random numbers
in parameter fields that should vary randomly within appropriate
ranges, such as the total amount of vibrato.)

If you are not familiar with the C programming language, there are a
number of ways to input pitch directly in Csound; for an equal tempered
scale such as the 31-tone scale, you can calculate the scale in Hertz,
calculate decimal ratios and have Csound convert the ratios to Hertz,
use octave.decimal which is the same as decimal ratios but has the
octave transposition built in to the ratio, use scale degrees or use
cents. Octave.pitch class is also possible, but probably more
difficult to use for this purpose.

I wrote a chapter on this issue for an upcoming book (more about the
book at the appropriate time). The following is one way to do the
31-tone chromatic scale using scale degrees in Csound:

-----------------------------------
idur = p3 ; duration
iamp = p4 ; amplitude
idegree = p5 ; scale degree
ioct = p6 ; octave transposition
ifactor = 1.0226114 ; the factor for 31-tone et
icount = 0 ; set the counter icount to 0
iratio = 1

pow:
if icount = idgree goto powout
iratio = iratio * ifactor
icount = icount + 1
goto pow

powout:
ifreq = iratio * ifactor * ihertz * ioct
-----------------------------------
(Continue with your own instrument design; ifreq is the frequency
in Hertz.)

To calculate "ifactor":

ifactor = (interval to divide) raised to the (1/(number of divisions)) power.
Example 1: 2^(1/7) power is 1/7 of an octave.
Example 2: 3^(1/13) power is 1/13 of an octave and a perfect 5th.

Hope this works for you.

Lydia

Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Tue, 13 Feb 1996 01:52 +0100
Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI)
for id QAA13239; Mon, 12 Feb 1996 16:52:21 -0800
Date: Mon, 12 Feb 1996 16:52:21 -0800
Message-Id: <0099DCF76B66A735.A5B1@ezh.nl>
Errors-To: madole@ella.mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu