Dr. Liljencrants, thanks for your excellent article.  Reeds are
a complex subject.  I now understand them much better.

I was looking at some spectrum envelopes of instruments on my analyzer
tonight when it suddenly dawned on me how we can tell instrument
sounds apart.  I was looking at an oboe WAV file and noticed that there
wasn't much consistency of which harmonic (1st, 2nd, 3rd, etc.) was the
strongest across pitches.  But what was constant was the frequencies of
the peaks and valleys in the spectrum as a whole.  Of course that makes
sense.  Those are the natural resonances of the tube!

Then I looked at the write-up of my experimental reed pipes on Dr.
Liljencrants' page.  Sure enough!  There were those spectrum envelopes
based on the natural resonance frequencies of the pipes.  And they
certainly didn't look like the oboe or saxophone envelopes.

Does this explain why an orchestral trumpet is so much nicer than an
organ reed trumpet?  Perhaps the fact that an orchestral trumpet must
be in tune with so many pitches gives it a more even envelope compared
to am organ reed whose resonator only needs to be tuned to the pitch
being produced?

This has important implications for my quest to create realistic
imitations of (reed) instrument sounds completely with small sets of
flue pipes.

Dave Goggin