From: milo@cbnews.cb.att.com (guy.f.klose)
Subject: Re: Trumpets
Organization: AT&T
Date: Wed, 12 Aug 1992 22:10:21 GMT

In article <9208101918.AA03958@morgana.pubserv.com>, jmh@morgana.pubserv.com (Jeff Helgesen) writes:
> (a good description of the harmonic series, as applied to trumpet or
>  trombone).

As a trombonist, I wanted to add just a couple of comments about the
harmonic series, as applied to us brass players.

> For the trumpet, the
> intervals work like this, starting on low C (fingered open):
> 
> C   G   C   E    G    Bb   C   D   E   F#    G ...

On trombone, and I think also trumpet, there is a "pedal tone" that sits
one octave below the first C.  Also, there are certain spots in the harmonic
series that are naturally out of tune.  For example, in the above list,
the Bb is slightly flat...in fact, flat enough to make it a poor choice
in that position.  On trombone, it's pretty common to adjust for these
notes that are out of tune, by moving the slide.  Trumpeters sometimes
have spring actions on their tuning slides to make small adjustments while
they're playing.

For trombone, one moves the slide out, increasing the length of tubing,
to flatten the notes in the harmonic series.  There are seven virtual
stops that the slide can make (actually, since it is an "analog" system,
there are all sorts of adjustments to make to those seven positions, for
the sake of intonation) that lower the fundamental by a half step.

For example, if one is playing a C, moving the slide out one position will
lower the pitch by a half step.  All together then, the trombone has seven
sets of harmonic series.

A trumpet works exactly the same way, as others pointed out, its just that
trumpets have a "digital" system.  Instead of seven positions, there are
seven possible sets of valve combinations.  The second valve of a trumpet,
when depressed, lowers the pitch by a half step.  The first valve, a whole
step, and the third valve, a step and a half.  Trumpets, also, tend to have
spots that are naturally out of tune...best exemplified by playing a note
with all three valves depressed...those notes tend to be sharp.  The
trumpeter adjusts for it by extending the third valve tuning slide.

In the following chart, I'll notate trombone position, trumpet valve
combination, and the corresponding harmonic series.  All will be in concert
key, assuming a Bb trumpet...

tbn   tpt   series:
 1   (open)  Bb  Bb  F   Bb  D   F   Ab  Bb  C   D  ...
 2     2     A   A   E   A   Db  E   G   A   B   Db ...
 3    1      Ab  Ab  Eb  Ab  C   Eb  Gb  Ab  Bb  C  ...
 4    12     G   G   D   G   B   D   F   G   A   B  ...
 5     23    Gb  Gb  Db  Gb  Bb  Db  E   Gb  Ab  Bb ...
 6    1 3    F   F   C   F   A   C   Eb  F   G   A  ...
 7    123    E   E   B   E   Ab  B   D   E   Gb  Ab ...

Trumpeters have an alternate fingering with the 12 valve combination...it can
also be fingered with the third valve.

Now for an application:  a concert C scale on trombone and trumpet...by 
at "nearest neighbors" on the chart above, you can see how the scales are
played.

tbn:  6    4    2    1    4    2    4    3

tpt:  13   12   2   open  12   2    12   1

the trumpet scale an octave higher (look at the next higher spot in the chart):
tpt:  1  open   2  open   12   2    2   open

There are opportunities in both scales for alternate fingerings...the
combinations listed above are just one possibility.  Also, valve trombones
operate exactly as trumpets, they are just pitched an octave lower.

Study of trumpet or trombone always includes lots of work with alternate
fingerings or alternate positions.  If a musician has several ways of
playing notes, they can make choices according to speed of fingering
changes.  Bop trumpeters, for example, relied heavily on alternate
and false fingerings to play fast scales and arpeggios.  Trombonists had
other techiniques as well, such as "fretting", which is a techinique where
one can use the changes in harmonic series as the slide lengthens or shortens
to help with the note articulation.  Trombonists such as Frank Rosolino and
Bill Watrous have used it extensively.

Guy
-- 
Guy Klose
milo@mvuxi.att.com
Newsgroups: rec.music.bluenote