para-inharmonicity and tuning curves

[Richard Brekne]

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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

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