[plt-scheme] Natural numbers

That could very well be the case. I am not sure about that and the only book 
I have that treats the matter well does not discuss history. The books that 
treat history of music (as far in my possession) are written by people 
afraid of numbers. Anyway, at the time the tempered scale was introduced, it 
must have been known that there are no natural number n and m such that 
(expt 3/2 n) = (expt 2 m) (where 3/2 is a quint interval and 2 an octave 
interval).This is a very fortunate fact, because it allows to put tension 
into harmony  and melody.
Jos

----- Original Message ----- 
From: "Robby Findler" <robby at eecs.northwestern.edu>
To: "Jos Koot" <jos.koot at telefonica.net>
Cc: "aditya shukla" <adityashukla1983 at gmail.com>; "PLT Scheme ML" 
<plt-scheme at list.cs.brown.edu>
Sent: Thursday, March 12, 2009 2:36 AM
Subject: Re: [plt-scheme] Natural numbers


On Wed, Mar 11, 2009 at 8:31 PM, Jos Koot <jos.koot at telefonica.net> wrote:
> (For who it concerns: I have put 'plus' between asterixes, because when
> dealing with frequencies, you must multiply ratios of frequencies, not add
> them :)

I'm not sure of the exact timing of these things myself either, but I
believe the multiplication wrinkle is around Bach's time (the
well-tempered claiver) which is significantly later than 4ths and
5ths, which seem to go way back.

Robby