Another question regarding Well Temperament

[Richard Moody]

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?

Ha I figured something like this was in number teory.



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 I don't know how you got your figures.  Do you mean the beat rate of
5/4  divided by the beat rate of 6/5? Of course the 5/4 ratio does not exist
in ET, only the coincident frequencies.  The actual "3/2 ratio" or 1.5 is
actually 1.49830......

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

I am not sure what you mean by proportional beats or what rhythmic
harmoniousness is.  If the beats of the interval are proportional to either
of the frequencies then you get a kind of resultant tone.  Whether this is
"reinforced" because it is proportional I don't know. But I hear these in ET
3rds quite often in certain ranges and these beats are not proportional that
I know of.   Not all the time so I think "conditions" must be
nvolved.  ---ric