Re: Undertones, overtones and equaltones

Hi Paul

I've had a thought.

Suppose you played the bassoon partials on piano voice, and got the volumes and
pitches all exactly right.

Then there would be no way of telling from the partials if what you heard were
several bassoons playing a piano timbre, or several pianos playing a bassoon timbre.
Both in theory should sound identical.

To see that (except perhaps you do anyway on just mentioning the idea)
make an array with the first row giving the bassoon partials, the first column the piano
partials, and each entry is result of multiplying the volumes of the corr. bassoon and
piano partials together. The entries are all the partials you hear. Then, interchanging
rows and columns gives the same entries in the array.

One might be able to tell from non partial components, such as the clatter of piano
keys (or bassoon keys for that matter), and I imagine there are other non partial
components too.

However, I imagine it could be hard to tell even then, once all the non partial components
are added together, with varying volumes for each transposition of them.

(and if you had something more flexible than midi, you could do fourier
analysis of both timbres, and then multiply the non partials as well in
the same way, and you then _really_ would have no chance of telling
which it was)

If someone tells you that what you heard is a bassoon, then one will probably
then be able to pick it out.

But suppose nobody said what it was, and you thought it was a piano. Maybe
you'd be able to pick that out instead?

Also, another point is that one can pick out apparent component instruments in
genuine timbres too.

Some timbres fall apart easily in that way, if you listen closely, like the
Rhodes piano, or the glockenspiel for that matter (perhaps why it
seemed a good match with the "fuzzy instruments").

Robert

Hi Robert.

The bassoon has perfect integer harmonics.
The piano has partials which are slightly stretched.

However, if you were to resynthesize a piano with perfect integer partials,
and a bassoon with piano partials, the piano would still sound like a piano,
and the bassoon like a bassoon. A little less realistic, but still
identifiable.

Why? Because the realtive loudnesses of the partials, the amplitude
envelopes for the various partials over time, and the additional noise
contained in the tone, are very different for the two instruments.

Putting that aside,

>Suppose you played the bassoon partials on piano voice, and got the volumes
and
>pitches all exactly right.

>Then there would be no way of telling from the partials if what you heard
were
>several bassoons playing a piano timbre, or several pianos playing a
bassoon timbre.
>Both in theory should sound identical.

>To see that (except perhaps you do anyway on just mentioning the idea)
>make an array with the first row giving the bassoon partials, the first
column the piano
>partials, and each entry is result of multiplying the volumes of the corr.
bassoon and
>piano partials together. The entries are all the partials you hear. Then,
interchanging
>rows and columns gives the same entries in the array.

A real piano's partials are stretched more in the high register and the
ultra-low register than in the middle register. Also a realistic bassoon
timbre has "formants" -- absolute frequencies at which partials tend to be
reinforced or attenuated. Your matrix method would ignore these features in
making the assumption that the timbre in one register is an exact
transposition of the timbre in another register.

Anyway, in your matrix method you are going to have the set of bassoons or
the set of pianos playing one big otonal chord. Since both timbres are
essentially harmonic, as I mentioned before the big chord will sound like
one big timbre -- in this case with a little beating due to the
inharmonicity of the piano. So rather than sounding like a chord of bassoons
or a chord of pianos, I expect this to sound like one big low note in a
timbre that is richer than either bassoon or piano.

--- In tuning@y..., "Paul H. Erlich" <PERLICH@A...> wrote:

/tuning/topicId_18405.html#18407

>
> Anyway, in your matrix method you are going to have the set of
bassoons or the set of pianos playing one big otonal chord. Since
both
timbres are essentially harmonic, as I mentioned before the big chord
will sound like one big timbre -- in this case with a little beating
due to the inharmonicity of the piano. So rather than sounding like a
chord of bassoons or a chord of pianos, I expect this to sound like
one big low note in a timbre that is richer than either bassoon or
piano.

Oh, by the way... is this actually possible to construct and HEAR, or
is it too difficult to practically put together??
______ ____ ____ ___
Joseph Pehrson