Beats on fundamental (was :Tuning Curves)

[Isaac OLEG SIMANOT]

Dear colleagues ,

I just had a fine explanation on why we hear beats on the fundamental while
tuning a tempered or almost pure fifth.
The same process apply to other intervals so that well may be the
explanation of the "global hearing" vs. / one partial match hearing that had
been discussed yet.

When we play, say a fifth : A = 100 Hz & E = 149 HZ.

The coincidence of the partials at the 300 hz level are producing a beat
between E 300 hz and E 298 hz ( second partial of E 149 Hz) = a 2 Hz beat (2
beats/second).
at the same time E 298 is interacting with the second partial of A100, which
is actually 200 hz on a string without iH.
The relation 298 Hz -200 Hz is simply producing a 2 hz beat at A100 Hz level
because there is a 98Hz vibration present in the spectra.

the same happens at the E (150 hz)level  ( E300 hz - E 149 hz = E 151 hz,
which beats against the E149 of our fifth : - 2 Hz)

What is fun is that there is even a E higher than pure in the show (and
these are computed without iH)

That explain me why, on pianos with a strong iH, I could hear a tuning with
very even progressive thirds, that where somewhat irregular if tested only
at the 5:4 ratio level.

And this is why your tuner is ....too simple

With all my best, I hope I am not too much unclear.


Regards.

Isaac OLEG