Path: utzoo!attcan!uunet!samsung!usc!wuarchive!udel!princeton!pucc!ROGER
From: ROGER@pucc.Princeton.EDU (Roger Lustig)
Newsgroups: comp.music
Subject: Re: theory behind scales
Message-ID: <11376@pucc.Princeton.EDU>
Date: 20 Jul 90 15:17:20 GMT
References: <8667@uhccux.uhcc.Hawaii.Edu>
Reply-To: ROGER@pucc.Princeton.EDU
Organization: Princeton University, NJ
Lines: 48
Disclaimer: Author bears full responsibility for contents of this article

In article <8667@uhccux.uhcc.Hawaii.Edu>, newsham@wiliki.eng.hawaii.edu (Timothy Newsham) writes:

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

>okay, some more stupid questions (hey, i'm gettting good at this)
>i did find out what 4/3 came from (inversion of 3/4 or 3/2, the perfect
>fifth, so its a fifth below the tonic, i hope i got that right), but i am
>still baffled about the 5/3. inverting it u get 3/5. either way u dont
>get a power of 2 on the top or bottom.  how do u get this note?
>also, if u are accepting 4/3 what about 8/5?  ...etc?  anyone ever
>exerimented with those?

Think of these as ratios or operations.  The approach given above is
based on 3 operations: doubling, tripling, quintupling.  (x4 is twice
x2, so it's not necessary to mention it.)  What we're tupling is
the frequency of a fundamental.    What we've done here is to take
the three operations, apply them to the fundamental, and get a bunch
of intervals.  Starting with low F, x3 is a 12th above: c.  x5 is
a 17th: a'.  The interval c-a' is a major 6th.

As I pointed out before, the C major scale above is based on a
fundamental F, which is one of the sticky bits in the theory.   Since
all notes are calculated wrt C, you'd expect a common denominator
that gives C primacy.

Ratios above have also been reduced to lowest terms.  But to get the
ones you see here all over a common denominator, you need an F at the
bottom.

8/5 is a minor 6th, such as e' to c".

And 9/8, the major whole tone, is simply a fifth on top of a fifth.
(The minor whole-tone is 10/9.)
Roger Lustig (ROGER@PUCC.BITNET roger@pucc.princeton.edu)

Disclaimer: I thought it was a costume party!