Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Posting-Version: version B 2.10 5/3/83; site watdaisy.UUCP
Path: utzoo!watmath!watdaisy!cbostrum
From: cbostrum@watdaisy.UUCP (Calvin Bruce Ostrum)
Newsgroups: net.music
Subject: Scales Again
Message-ID: <240@watdaisy.UUCP>
Date: Sat, 30-Jul-83 03:30:43 EDT
Article-I.D.: watdaisy.240
Posted: Sat Jul 30 03:30:43 1983
Date-Received: Sat, 30-Jul-83 04:53:16 EDT
Organization: U of Waterloo, Ontario
Lines: 36

I am getting confused about this alternate scale stuff. Can we have some
expert commentary? Particularly hazy points include the following:

It is a little off the mark to come down upon the "western system" as
"limited". It is not so ad hoc as some may think. Here is how we get it:
First we decide to have a discrete scale. Seems sensible to me but perhaps 
the most arbitrary of all the assumptions this is based on.
Now, once we note that human hearing works to produce a
metric on tones that is a logarithmic function of frequency (does it?) we
get a scale where each note's frequency is a multiple of the previous ones.
(how many "nonwestern" scales actually fall outside this category essentially?)
This decision also produces the nice logical feature that the tone metrics
are not essentially related to the starting tone of the piece (ie it can
be transposed without losing any of the metric structure, although it may
lose qualities associated with absolute frequencies).
Next, if we agree that small integer ratios 2, 3/2, etc are very nice, we find
that the 12 tone scale is the very best scale with a manageable number of 
tones. So it doesnt seem that ad hoc at all.

The argument above is based upon a lot of assumptions that I and probably
others would appreciate expert commentary on. The one I am particularly
interested in is the assumption that there is something intrinsically
aesthetic, from a sonic point of view, about octaves, fifths, etc. If so,
how is it related to the physical property that such waves have? I have
always been somewhat skeptical of this claim, because it seems to me that
only exact multiples would have special phsyical properties, whereas most of
us still fully appreciate the out of tuneness of a tempered scale, and many
of us still appreciate much worse.

		Calvin Bruce Ostrum, Computer Science, University of Waterloo
		...{decvax,allegra,utzoo}!watmath!watdaisy!cbostrum

ps: i posted this to net.music although it is a response to something
in net.math. what does this have to do with math? surely we computer types
know enough math that simple applied math problems can go in the group for
the area to which our math is being applied?