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Re: Top D

Tuning is actually more problematic even than that, arising from the
fundamental physics behind it. If you figure out the "correct" pitches
of all the notes from a cycle of fifths, you can't get back to where you
started. This is why, long ago, E flat was a note different from D
sharp. To "fix" the problem, keyboards went to the well-tempered system
in Bach's time, and have been there ever since.

But we in the brass world can never have well-tempered instruments,
because we're constrained by the fundamental physics that define the
harmonics of our instruments. So if you tune your B flat horn's C to a
well-tempered piano's B flat, that's the *only* note that's going to be
bang in tune with the piano. Everything else is close, but not exact.
Even your 3rd-harmonic G is 0.01955 semitones (um, that's a
well-tempered semitone) sharper than the piano. (And while we're on the
subject, what exactly *is* a semitone if a brass instrument is the
reference?)

Okay, forget pianos for a minute. What does this mean for the brass
band? Specifically what does it mean for B flat instruments playing with
E flat instruments? Well, if you tune the sop's G to the cornet's C,
then any notes derived (i.e. by valve combinations) from those notes
will be bang in tune with each other (though in general different from
any objective reference, but we'll leave out that complication for now).
After that it gets iffy, but let's cut straight to the major problem:
the 5th harmonic (open) E. That E, on the cycle-of-fifths plan, should
be 81/64 times the frequency of the C. This is 0.07820 semitones sharper
than its well-tempered counterpart (yeah I know I said we'd forget
pianos, but I had a little relapse), but it gets worse. The note you
actually get with an open E is 5/4 times the frequency of the C. That's
a whacking 0.215 semitones flat, compared with the E derived from the
cycle-of-fifths! No wonder it sounds such a dog.

Yes, yes, we can adjust the pitch with our lips (though *always* at the
expense of tone, but that's a subject for another rant), and instruments
have their vagaries, but basic physics causes us severe problems before
we even get into those subjects.

Bill Buffam

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