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From: jgk@osc.COM (Joe Keane)
Newsgroups: sci.math,comp.music
Subject: Re: A Mathematical Theory of Music
Summary: Equal temperament sucks.
Message-ID: <3022@osc.COM>
Date: 10 Jul 90 20:45:53 GMT
References: <1268.268f84e0@gp.govt.nz> <25556@unix.cis.pitt.edu> <1269.26909383@gp.govt.nz> <1990Jul4.114930.29133@sbcs.sunysb.edu> <1278.2694ccd9@gp.govt.nz>
Reply-To: jgk@osc.COM (Joe Keane)
Followup-To: comp.music
Organization: Object Sciences Corp., Menlo Park, CA
Lines: 32

In article <1278.2694ccd9@gp.govt.nz> philip@gp.govt.nz (Philip Dorrell)
writes:
>A rather popular chord sequence is -
>
>C major --------------> G major --------------> D major ------------> C major
>                                                                      (again)
>C  ----(* 3/2)--------> G --( * 3/4)------> D (*3/2) --->A (*3/5)---> C
>
>total - 
>
>  C -----------------------------( * 81/80)------------------------->  C

The A in the key of C major is defined to be a major sixth (5/3) above C.  The
A in the key of D major is defined to be a perfect fifth (3/2) above D.  If we
say D is a major tone (9/8) higher than C, the first A is lower than the
second one by the ratio 81/80.  The interval 81/80 is called a comma and pops
up all over the place.

This kind thing of thing has been studied since Pythagoras.  There is actually
a rich theory dealing with somewhat subtle differences, where you talk about
different kinds of commas, chromatic versus diatonic semitones, major versus
minor tones, and so on.  One conclusion is that the second note in a major
scale is somewhat flexible.

Unfortunately, the result of equal temperament has been to pave over this
theory.  If you ask a piano player what is the difference between G# and Ab,
he will say there is none.  This ignores the fact that some organs had keys
for each, or that modern electronic instruments can easily play them as
different notes.  Also, if you ask people what are CX or Ebb (excuse my ASCII)
you're likely to get blank looks.

This is interesting, but not math; followups are directed to `comp.music'.