Another question regarding Well Temperament

[Clark]

Hi Ric,

> The only notible coincidence arithmeticaly I could find is that
> 13.327/5.549=  2.401693998919  while 7.778/5.549= 1.401693998919  an EXACT
> difference of 1 !.   Such an exactness to the 13th place is too signifigant
> to be ignored, yet what does it mean??

No coincidence at all. Think of it this way - you're describing

b/(b-a) - a/(b-a)=1

Ok?


I thought Ed wrote a very clear description of the effects of WT's
mentioned in Jorgensen's passage. Beats are, well, beats.

Without adjusting for inharmonicity, beat proportions within 12tET
triads all stay the same. For instance a major triad:

5/4:6/5 ~ 1.7
5/4:3/2 ~ 11.7
6/5:3/2 ~ 20.1	
8/5:3/2 ~ 23.4

Here are the same for 22tET. See if you think it qualifies proportional
beats or rhythmic harmoniousness:

5/4:3/2 ~ 1.05
8/5:3/2 ~ 2.1
5/4:6/5 ~ 3.9
6/5:3/2 ~ 4.1

Of course, tuned properly it affords no tonal distinction save through
enharmonic substitutions of ±~54.5 cents.

Regards,


Clark