Re: Period vs Modern instruments?

In article <[EMAIL PROTECTED]>, Jerry Kohl
<[EMAIL PROTECTED]> writes
>Whether you have only the odd or even partials, or both, is immaterial, Matt.
>Either the overtones lie along a harmonic series, or they do not, and the more
>conicity in the bore, the further the deviation becomes.

Theory and my direct experience both contradict you.  Matt has the facts
of the matter right, though I don't use his nomenclature for the
behaviour of a close parallel tube: the way I think of it, in closed
parallel tubes (e.g. clarinet) the second overtone has (or is close to,
in practical cases) three times the frequency of the first.  Note (as
Matt has already pointed out in an earlier post) that the configuration
of nodes and antinodes in the pipe is the same as in the second overtone
of a conical pipe, but the different cross-sectional areas change their
distances and the resultant frequencies.

> Horns have such a 
>gradual
>taper that the effect is minimal, but bugles have a steeper taper and the effect
>is correspondingly more pronounced. Valved instruments introduce a further
>complication, in that you cannot add in a section of tubing without altering the
>degree of taper to the bore overall. AFAIK, the added tubing is always
>cylindrical, so the more valves you open the less conical (on average) the 
>overall
>bore becomes.

Yes, and this behaviour is detectable on the double horn in Bb and F.
Even though none of it is actually conical, the combination of the
parallel centre portion, the expanding sections (mouthpipe usually
expanding in a parabolic manner, to fair into the parallel portion, bell
expanding more and more rapidly to the mouth) and the mouthpiece
produce* acoustic characteristics very close to that of a plain cone
(overtones at all harmonic frequencies) for some intermediate length of
the parallel portion, usually close to the open F horn.  The open Bb
horn has least parallel tubing and has a compressed set of overtones and
the B basso horn (all finger levers depressed) an expanded set.  Horn
players don't think about this.  The Bb side is adjusted to match the
tuning of the F side around C space, and is close for about two octaves.
The difference is then most noticeable in the low register, where most
players avoid the Bb horn, except for any notes which are unpredictable
on the F.  All low notes can be sharpened or flattened easily; tuning
comes automatically from ear and lip, with the hand helping in difficult
cases.

*  Benade's "Fundamentals of Musical Acoustics" has two very clear
diagrams, on page 388, that show the effect of adding a bell to
cylindrical trumpet tubing, and another on page 402 showing the effect
of the mouthpiece.  The next diagram, on page 403, shows a curious
characteristic of typical brass instrument shapes: the resonant
frequencies match the harmonic series pretty well from the second
resonance upward, but the fundamental does not conform.  Pedal notes can
be played in tune however.  I think Benade explains somewhere that this
is because second and upward harmonics of the lip motion lock into
second and upward resonances of the tube.  If you bend a pedal note
downward, you may come to a stable note that is usually thought of as a
"fake", but may be the actual fundamental frequency.
 
-- 
Ken Moore
[EMAIL PROTECTED]
pg composition student, University of Reading