Re: Explain the Circle of 5ths

"Alain Naigeon" <anaigeon@[EMAIL PROTECTED]
> wrote in message 
news:47feae51$0$2694$426a74cc@[EMAIL PROTECTED]
> "David Webber" <dave@[EMAIL PROTECTED]
> a écrit dans le
message 
> de
> news: ftkfs7$8iq$1$830fa79d@[EMAIL PROTECTED]
>> Sorry if I missed this is in another answer.     Apart from
mathematical
>> reasons, the strongest musical reason is the V-I cadence.    For
example
>> chord-of-G -> chord-of-C.   If you're in the key of C this sounds like
a
>> particularly good "finish" (so good that it is known as a "perfect
>> cadence") and has been around for hundreds of years.
>
> Well, it was, IMHO, not as frequent as it became later, and nevertheless

> the
> "circle" of fifths was used to build the Pythagorean scale used in these
> times.

Except that Pythagoras found it was a spiral of 5ths <g>- it was only with

tempered scales that it became a circle - one of the reasons I prefer
"cycle 
of fifths".       (Another being that you don't have to draw them in a 
circle.  I shall copyright the term "dodecagon of fifths".)

But building a scale from frequency ratios 3^m/2^n is what I regard as a 
"mathematical" exercise.    It does underlie music, but it is buried so
deep 
that I don't tend to think of it as a "musical" exercise  (whereas 
composing/arranging a piece of music *is*).

Dave
-- 
David Webber
Author of 'Mozart the Music Processor'
http://www.mozart.co.uk
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