More on Neidhardt (was: Re: Fux's tuning )

"monz" wrote:
> i believe that the "C" in the "tenor range" is indeed
> "middle-C". that's the "C" which lies right near the center
> of the tenor clef, which is what anyone singing a
> tenor part would have been reading in Niedhardt's day.

According to my calculations, Aaron's bearing plan is correct
from small c (ASA C3, below middle C). C3 is at the *bottom* of
the traditional tenor range, hence the name. Remember the beat
ratios are from clashes of harmonics, not fundamentals:

If C3 = 128 Hz, the fifth partial of C3 is:
(5 * 128) = 640 Hz
and the E3 that is beating against this partial at 2 Hz is:
(640 + 2) / 4 = 160.5 Hz

160.5 / 128 ~= 391.7 cents

Best regards,
Robert Kelley

=====
________________
Robert T. Kelley
composer@thekeyboard.com
http://www-student.furman.edu/users/r/rkelley/
"It is no measure of health to be well-adjusted to a profoundly sick society." -Krishnamurti

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hi Robert,

--- In tuning@yahoogroups.com, "Robert T. Kelley"
<contrapunctus@y...> wrote:

> "monz" wrote:
> > i believe that the "C" in the "tenor range" is indeed
> > "middle-C". that's the "C" which lies right near the center
> > of the tenor clef, which is what anyone singing a
> > tenor part would have been reading in Niedhardt's day.
>
> According to my calculations, Aaron's bearing plan is correct
> from small c (ASA C3, below middle C). C3 is at the *bottom* of
> the traditional tenor range, hence the name. Remember the beat
> ratios are from clashes of harmonics, not fundamentals:

ah, yes ... my oversight!

> If C3 = 128 Hz, the fifth partial of C3 is:
> (5 * 128) = 640 Hz
> and the E3 that is beating against this partial at 2 Hz is:
> (640 + 2) / 4 = 160.5 Hz
>
> 160.5 / 128 ~= 391.7 cents
>
> Best regards,
> Robert Kelley

thanks for correcting that.

-monz