para-inharmonicity and tuning curves

[Jim Coleman, Sr.]

Hi Richard again:

You will discover that the lower partials are not always the loudest.
Especially in the Bass, sometimes the fundamental is almost missing.
And, sometimes the 2nd partial is quite weak. Sometimes the 7th partial
sticks out like a sore thumb. Then we have the matter of longitudinal
mode vibrations which cause some very high peaks at sometimes the 25th
partial or the 31st partial, or other odd partials. This is where a
longitudinal partial is in conjunction with a transverse partial (the
ones we normally relate to), you can hear a real fast beat between the
two (mind you, this can be on a single string).

This should whet your appetite for awhile. BTW, no amount of voicing is
going to get rid of that sharp peak if it is longitudinal in nature. In
1967 we did an experiment where we clamped vise grips on the bridge pin
to eliminate the longitudinal peak, but of course that greatly modified
the tone of the note.

Jim Coleman, Sr.

On Wed, 19 May 1999, Richard Brekne wrote:

> 
> 
> Richard Moody wrote:
> 
> > And if a partial is really
> > > really weak, who cares what its frequency is?  No one will hear
> > > it.
> > >
> > > -Robert Scott
> > >  Ann Arbor, Michigan
> >
> > That is a very good question.In piano tuning we are concerned with the
> > beats caused by coincident partials. We really notice partials when they
> > beat. The question is, how weak does a partial have to be not to cause
> > beats? In terms of audible strength (decibles?) the fundamental is louder
> > than the second partial.  The second partial is louder than the third and
> > so on, or so it should seem. Yet the beatings do not sound any louder or
> > softer according to how loud or weak the partial is.
> >  Why does it seem a 5/4 third beats as loud as a 2/1 octave. One would
> > think  the first and second partials would be at least twice as loud as
> > the fourth and fifth partials. Shouldn't that affect the loudness of the
> > beats?
> > Ric
> 
> I believe this has something to do with the fact that beats from
> coincidentals are the result of two partials from two seperate partial
> series. Both would have to be more powerfull if they are to stick out more
> then expected. This sometimes is the case I suspect. The bass area
> especially. Tuning octaves you once in a while find a pairing that is just
> really loud compaired to that same pairing in adjacent octaves.
> 
> Also, Partials sound louder perhaps then we think. We train ourselves to
> listen to only a few in different situations, conciously working at not
> listening to the others. If you reverse this process and make an effort to
> listen to as many partials as you can, (in octaves for example) pick them out
> individually you might be suprised what you can hear even relatively high up
> in the  treble ( C5 - C7) area.
> 
> Richard Brekne
>