source file: m1367.txt
Date: Sat, 28 Mar 1998 03:54:29 -0600 (CST)

Subject: Re: "Numbers Separated by Colons" Notation

From: mr88cet@texas.net (Gary Morrison)

>>Maybe it's my lack of formal music training, but I don't understand the
>>"4:5:6" reference.
>I don't think you'd learn this stuff in "formal music training".  I think
>it's more of a "higher math" kind of thing.

   Uhmmm...  Well, it's not especially high math really.  (But perhaps you
were joking there.  Whatever...)

   Let me go to an even lower level than Mark did, just to make sure that
we have the basics covered.

   As I'm sure you know, sound is the vibration of pressure waves in the
air.  Those numbers are ratios, or "proportions", of the sound frequencies
of pitches sounding simultaneously in a chord.  As an aside, they're
somewhat like the proportions of a rectangle a 2:1-ratio rectangle is twice
the size on one side than it is on the other.

   Notice, by the way, that it doesn't really matter whether you say 2:1 or
1:2, because you can turn rectangles on their sides without changing their
shapes.

   A 4:5:6 chord has vibrational frequencies in that ratio, such as an A
major chord of frequencies 440Hz, 550Hz, and 660Hz.  As you can see, you
can divide all three of those numbers by 110Hz to get 4:5:6.

   And notice that, as with rectangles, the order of the numbers don't
matter.  It doesn't matter whether you state the ratio of the upper note to
the lower note, or the lower note to the upper note;  it's still the same
chord.

   That particular 4:5:6 relationship is that of the usual Just Intonation
major chord (in root position, closest voicing).  So, in short, every such
set of numbers concisely defines an essential harmony relative to whatever
the root pitch may be.