Temperament Setting Question

[Jim Coleman, Sr.]

Hi Bob:

Here is a little known bit of minutae. The 5:4 ratio which we use for
contiguous M3rd beat rates is also just a round number for the number 
2 raised to the 1/3 power which is 1.259952.

               1.259952                1.25      5
The fraction   -------- rounds off to  ----- or ---
               1.000000                 1        4

Then if we wanted to get real persnickety, we could say
that the number 2 in the original formula isn't quite
right either since due to inharmonicity our octaves are
not exactly 2:1

Hey, for all practical purposes the 5/4 ratio works just
fine.

Jim Coleman, Sr.

On Thu, 16 Dec 1999 BobDavis88@AOL.COM wrote:

> A440A@AOL.COM writes:
> 
> >  A third which has a 5:4 
> >  ratio is a Just third and doesn't beat at all. 
> 
> Ed,
> You are right, of course, but the 5:4 mentioned here doesn't refer to the 
> ratio of FREQUENCIES within the third, but the ratio of beat RATES of 
> contiguous thirds - A3-C#4 beats 5/4 as fast (or mighty close to it) as 
> F3-A3. Sorry for the confusion. 
> Bob Davis
>