Daniel F Heiman wrote:

>The point is that on brass instruments, pitch is in large part determined by
the tension of the >lip muscles.

>Let's say that we are talking about playing an 'a" above the staff in modern
treble clef.  This is >at least a moderately high note on either a modern or
a Baroque valveless trumpet.  To >produce that note in the Tief-Kammerton
environment, the player has to generate frequency >of about 800 Hz.  To
produce that note in the Cornett-Ton environment, the player has to >produce
a frequency of around 940 Hz.  The difference in terms of muscular effort
required is >quite substantial.

But why would it be? In either case, he's playing the 11th harmonic on
whatever horn he's playing.  He should be doing the same thing with his
embouchure (which is buzzing with his lips, not producing the frequency that
comes out the bell) and the only thing that would change is the length of
the horn he's blowing.   The same buzz that produces the A above the staff
on a trumpet in C will produce a written A on a trumpet in E flat, but it
will sound the C a third higher.  This is the same pitch difference, more or
less, as there would be between tief kammerton and chorton.

(Time out for those who may not know what Dan and I are talking about: The
valveless trumpet for which Bach--and Beethoven and Mendelssohn--wrote
always read a part written in C, and used longer or shorter lengths of
inserted tubing to adjust the trumpet's length, and thus pitch, to whatever
key it was playing in.  The longest was in nominal B flat, the shortest in
F.)

If high notes were harder on a shorter horn, some composers would surely
have written lower for the trumpet in F than for the trumpet in C.  But I
don't see that: I think Bach's trumpet parts, for example, always top out at
written D above high C regardless of the actual pitch.

Perhaps we've strayed a bit off topic?  Let me try to reel it in.  Trumpet
parts were written in a sort of tablature, with the notes representing not
pitch per se, but what the player needed to do.  And the notation lent
itself to transposing by picking up a bigger or smaller instrument, just as
a lutenist might transpose a lute song tablature by playing it on a D or A
lute instead of a G lute.  

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