Path: utzoo!utgpu!watserv1!watmath!att!rutgers!njin!princeton!pucc!ROGER
From: ROGER@pucc.Princeton.EDU (Roger Lustig)
Newsgroups: comp.music
Subject: Re: theory behind the scales
Message-ID: <11274@pucc.Princeton.EDU>
Date: 10 Jul 90 19:40:28 GMT
References: <8547@uhccux.uhcc.Hawaii.Edu> <1307@fs1.ee.ubc.ca>
Reply-To: ROGER@pucc.Princeton.EDU
Organization: Princeton University, NJ
Lines: 39
Disclaimer: Author bears full responsibility for contents of this article

In article <1307@fs1.ee.ubc.ca>, jthornto@fs1.ee.ubc.ca (THORNTON JOHAN A) writes:

>The major scale is indeed based on harmonics.  In the key of C (what else?) :

>    Note   Decimal frequency fraction

>     C       1                 1
>     D       1.125             9/8
>     E       1.25              5/4
>     F       1.333333...       4/3
>     G       1.5               3/2
>     A       1.666666...       5/3
>     B       1.875             15/8
>     C       2                 2

>This is of course the true tempered scale.

This is, in fact, one tuning that sounds like what we think of as the
major scale.  It is not, however, what the major scale is 'based'
on in any historical or practical sense.  Nowadays, in any music that
uses more than one pitch at once, the above is utterly useless because
the interval d:f is nasty.  (27:32; try it!)

Reconciling the harmonic series with the practice of harmony is
well-nigh impossible; check out things like Rameau's _Generation
Harmonique_ for an example that trips over itself in all kinds of
ways.

So, since intervals and their physical ratios have been known for
much longer than there's been a major scale as such in use, and
since the various diatonic modes were all considered to be pretty
much equal in value, I can't see how the major scale is 'based'
on the overtone series.  Most music using the major scale requires
great deviations from pure intonation to sound at all nice.

Roger
Roger Lustig (ROGER@PUCC.BITNET roger@pucc.princeton.edu)

Disclaimer: I thought it was a costume party!