May the 4ths be with you

[Richard Brekne]

Hi RicM

I got the feeling that this was more or less what Dr Sanderson was
saying.... tho he didnt come right out and say so directly about
thirds. He did say right out that inharmonicity changes the
theoretical picture relative to 5ths and 4ths... which should also
have their contiguous relationships.  So I imagine he would agree
real quickly with what you point out below.

This goes back to what I tried to say to David Andersen about the
whole definition of ET being really quite impossible to implement on
the piano. Inharmonicity precludes that, and we are left with an ET
adjusted for inharmonicity which essentially breaks some of the rules
for what an ET is.

Cheers

RicB

Richard Moody wrote:

> The beat rates of contiguous 3rds if tuned in ET beat at the ET
> ratio, which is NOT 5/4.  Take the beat rate of C--E  and then
> E--G#   and you will see the ratio is not the EXACT ratio of 5/4.
> Actually the ratio of beat rates of  two contiguous 5/4 3rds are
> zero because those two thirds 3rds have no beat.   Dr Sanderson
> must have been giving a generalized explanation rather than a
> mathematically correct one.   The proof of the ratios of 3rds in
> ET is that ratio cubed, (or ^3)  equals 2.     1.25992105  cubed
> equals 2
>
> The ratio of the frequencies of ET 3rds is 1.25992105  ,  the
> ratio of their beat frequencies is 1.25992105  .    How can it be
> otherwise? -----ric
>