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From: ROGER@pucc.Princeton.EDU (Roger Lustig)
Newsgroups: comp.music
Subject: Re: theory behind the scales
Message-ID: <11290@pucc.Princeton.EDU>
Date: 11 Jul 90 20:04:57 GMT
References: <8547@uhccux.uhcc.Hawaii.Edu> <1307@fs1.ee.ubc.ca> <11274@pucc.Princeton.EDU> <8561@uhccux.uhcc.Hawaii.Edu>
Reply-To: ROGER@pucc.Princeton.EDU
Organization: Princeton University, NJ
Lines: 32
Disclaimer: Author bears full responsibility for contents of this article

In article <8561@uhccux.uhcc.Hawaii.Edu>, newsham@wiliki.eng.hawaii.edu (Timothy Newsham) writes:

>i fail to see how you arrive at a couple of those values as overtones.
>how does a value of 2/3 fit in?  division by a power of 2 is allowed
>because it represents changing the octave, but where do we get a 2/3?
>the only possible explanation i can think of is perhaps it is in the
>overtone series of one of the other prominant notes?

Well, you've just put your finger on one of the reasons why it's a bogus
explanation for the major scale.  2/3 is in fact a perfectly
pleasing-sounding ratio, but it makes the numbers imply funny things,
and it causes the wolf (27/32 or 27/40).

If you take common denominators and make everything whole notes, you
have made a scale that goes 24, 27, 30, 32, 36, 40, 45, 48.  Now, note
that the tonic is 24, which suggests that the fundamental underlying the
whole works must be -- yup, the subdominant!!!  That is, in a C scale,
the underlying fundamental that generates all the notes is an F.  See
the problem?

Now, with Lydian mode, you don't have this problem, because you have an
F
instead of an F.  But in Lydian mode, we tend to 'correct' the sharp
4th down to a perfect 4th because we don't like a tritone with the
tonic, so from experience, we know that there's nothing 'prior' about
the Lydian.  In our music, the major scale is obviously prior to others.

So much for overtone theory...

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

Disclaimer: I thought it was a costume party!