inharmonicity/beats

[John Meulendijks]

Question: why should you hear a difference tone? There is only root, second
partial, third etc. How could the string be resonating at 1602 minus 800? I
am not really sure about the following, but maybe it helps thinking about
it: In the tone-wheel there is a root, an octave, a quint(fifth) etc. All
these extra wheels happen to function as a root at some time. So the tuning
must be well-tempered, which means the quint is to low, the third is to
high, (i.e. the 5th partial). This should produce the meanest tones ever
possible because of the unevenes of the partials. It does. But not, repeat
not, because of beats. Instead it does because of a total lack of beats. It
sounds terrible fixed concrete. I believe that is the deeper reason for
having the Leslie on it. Any interval is comparatively beatless because the
partials are piced from well tempered half tones.

Please let me know if and why this reasoning is incorrect. Maybe already my
understanding of the Tone-wheel system is......

Apart from this I've experienced many times the feeling (not sure about
actual hearing) of two low bass notes playing a fifth and a fourth under the
note I'm tuning in the 5th and 6th octave. I think they are related to each
other as a a lower octave of the fifth and an even more lower octave of the
tuning note.  Let's assume it happens on c''', then there is a feeling of a
root F on the fifth f''-c''', and a feeling of C' on g''-c'''. A
fysicist-teacher said it was in my head  (but in a polite way: we tend to
complete a sequence of upper partials without having the basic tone (the
first partial) actually sounding). Any other explanations?

John Meulendijks
Tilburg
the Netherlands

----- Original Message -----
From: Howard S. Rosen <hsrosen@gate.net>
To: Pianotech <pianotech@ptg.org>
Sent: Saturday, February 17, 2001 4:57 PM
Subject: inharmonicity/beats


> Tom,
>
> I was going to write the same thing to Kevin as you did, but just as I was
> about to hit the send button, a thought came to mind and I erased my
letter.
> Theoretically inharmonicity *should* cause beats but you and I know that
we
> don't hear beats on a single string resulting from inharmonicity. Here is
my
> thinking: Remember Helmholtz and his work with "difference tones"? Well,
> using a string with a fundamental of 800Hz, if inharmonicity causes the
2nd
> partial to be 1602 instead of a textbook 1600, then there would be a
> difference tone of 802 Hz. This 802 would be coincidental with the
> fundamental of 800 and thereby cause 2 beats per second. So you see,
> theoretically it happens, but we just don't hear it. I can't explain why
nor
> am I certain that my scenario is correct. What do you think?
>
> Howard S. Rosen, RPT
> 7262 Angel Falls Ct.
> Boynton Beach, Fl  33437
>
> hsrosen@gate.net
>
>
>
> <!--StartFragment-->
> Date: Fri, 16 Feb 2001 18:25:09 -0800
> From: Tom Cole <tcole@cruzio.com>
> Subject: Re: Virgil's beatless octaves.
>
> Kevin,
>
> A single string will not beat because it doesn't have any coincident
> partials. The partials of a single string are far enough away from each
> other that you don't hear any beats.
>
> Tom Cole
>
> "Kevin S. Riggs" wrote:
> >
> > Hi folks,
> >  I've been reading this thread for a while and must be a little confused
> > (relative newbie).
> > If a single strings' partials have inharmonicity, theoretically it seems
> > like it should
> > beat on its' own. Unless something is astray I only hear one beatless
> > tone. So something,
> > maybe the phase relationship, cancels out the beats. Why should it be
> > hard to believe that
> > the same thing can be accomplished when tuning an octave? When my
> > octaves are tuned so that
> > I hear no beat, none of the coincident partials are necessarily pure.
> > But it sounds better
> > to myself and my customers tuned in that fashion. May be a bit
> > simplistic but I would
> > greatly appreciate any attempt to enlighten me. Any takers?
> >
> > Thanks, and have a great day!
> > Kevin S. Riggs
> > NC associate
>
>
>
>