source file: m1399.txt
Date: Tue, 28 Apr 1998 21:38:55 -0500 (CDT)

Subject: Brass Spectra

From: mr88cet@texas.net (Gary Morrison)

Somebody, in the course of the discussion on the possible
not-completely-harmonic nature of orchestral instruments, suggested that
brass instruments have more-detuned partials than average.

   I don't personally have much information on that question, although I do
generally remember them to be more consistent than woodwinds from one cycle
to the next, which seems to suggest that that would not be the case.

   Buuuuut, I do have very direct information on another interesting aspect
of brass instruments in general:  Their amplitude spectra - almost always -
have a shape that might be described as a "truncated bell-curve" -
truncated at the fundamental.  Something like this:
         ___
        /   \
Amp   /       ` _
     /            ` ________
                            \
     -------------------------------
     123456789...
     harmonic#

   That in contrast to woodwinds, which frequently have lumpy, jagged spectra.

   And there are some general patterns to how this spectrum changes with
pitch and volume.  What I drew above is more or less what a loud,
low-pitched tone would look like.  A quiet tone at the same pitch has only
moderately lower energies in the lower harmonics, but that high-harmonic
shelf toward the right of the spectrum goes away.

   Also, as you move toward higher notated pitches, that bell-curve narrows
(as if it represented a bell-curve with a lower standard deviation), and
also moves toward the left.  So the spectrum of a higher note typically
looks somewhat like this:
      __
     /  \
Amp      `_
           `___
                \
     -------------------------------
     123456789...
     harmonic#

   These are all only broad generalizations of course, and obviously the
details vary a lot between trumpets vs. F.horns, vs. trombones, etc., and
of course by different players and manufacturers of the instrument.