The Trombone Slide
Now
we’ll turn our attention to a real instrument: the trombone. Aside from the bugle, the trombone is the
simplest brass instrument. It’s
basically a low-pitched bugle with a variable pipe length.
A
trombone slide has seven positions, each one representing a semitone. The positions are numbered from 1 to 7. Position1 is when the slide is fully
contracted, and the pipe is the shortest.
Position 7 is when the slide is fully extended, and the pipe is the
longest. The lowest note played in
position 1 is Bb2. Position 2’s lowest
note is A2, and so on. Position 7’s
lowest note is E2, and is the lowest note that a trombone can normally play.
So
far, so good. But how do you get twelve
semitones from only seven positions? The
answer is that all notes that a trombone plays are harmonics of the pipe length.
For example, when playing Bb2 in position one, the pipe’s true
fundamental is actually Bb1, one octave lower.
These fundamentals range from Bb1 down to E1, and are called pedal tones. Although it’s possible to play them, their
sound is very weak, and little music is written for them.
Let’s
look closely at position 1. The pipe’s
fundamental is Bb1, but we’re not going to write music for that, because the
tone stinks. So the lowest note we’re
actually going to play is Bb2, the pipe’s second
harmonic. Remember from the bugle that
brass players can play higher harmonics by controlling their embouchure. Now, what’s the third harmonic of Bb1? It’s
F3, seven semitones above Bb2, the second harmonic. Seven semitones? It’s no accident that a trombone slide has
seven positions: it’s just enough to
reach down from F3 to Bb2.
Let’s
go up a little higher. The fourth harmonic of Bb1 is Bb3. Bb3 is five semitones above F3, the third
harmonic, so we need only five slide positions to reach down from Bb3 to F3.
It
turns out that those seven positions are enough, after all. Below is a chart that displays the notes in
the standard trombone range (skilled players can play higher).
|
Note |
Slide
Position |
Pipe
Fundamental |
Harmonic |
|
E2 |
7 |
E1 |
2 |
|
F2 |
6 |
F1 |
2 |
|
Gb2 |
5 |
Gb1 |
2 |
|
G2 |
4 |
G1 |
2 |
|
Ab2 |
3 |
Ab1 |
2 |
|
A2 |
2 |
A1 |
2 |
|
Bb2 |
1 |
Bb1 |
2 |
|
B2 |
7 |
E1 |
3 |
|
C3 |
6 |
F1 |
3 |
|
Db3 |
5 |
Gb1 |
3 |
|
D3 |
4 |
G1 |
3 |
|
Eb3 |
3 |
Ab1 |
3 |
|
E3 |
2 |
A1 |
3 |
|
F3 |
1 |
Bb1 |
3 |
|
Gb3 |
5 |
Gb1 |
4 |
|
G3 |
4 |
G1 |
4 |
|
Ab3 |
3 |
Ab1 |
4 |
|
A3 |
2 |
A1 |
4 |
|
Bb3 |
1 |
Bb1 |
4 |
|
B3 |
4 |
G1 |
5 |
|
C4 |
3 |
Ab1 |
5 |
|
Db4 |
2 |
A1 |
5 |
|
D4 |
1 |
Bb1 |
5 |
|
Eb4 |
3 |
Ab1 |
6 |
|
E4 |
2 |
A1 |
6 |
|
F4 |
1 |
Bb1 |
6 |
|
Gb4 |
5 |
Gb1 |
8 |
|
G4 |
4 |
G1 |
8 |
|
Ab4 |
3 |
Ab1 |
8 |
|
A4 |
2 |
A1 |
8 |
|
Bb4 |
1 |
Bb1 |
8 |
Some trombone
Q&A
- Why
doesn’t the seventh harmonic appear in the list? It’s not
in tune with the equal-tempered scale, so it’s ignored. Even the fifth harmonic is a little off,
but it’s played anyway.
- Isn’t
there a ½ octave gap between the lowest normally played tone, E2, and the
highest pedal tone, Bb1? Yes, there’s a gap. But who cares? If a composer wants low notes, he can
write for a tuba.
Finally, a patch
Let’s
use this knowledge to convert our bugle into a trombone. Below is a trombone patch.
How does it work?
The
trombone’s audio chain is almost identical to the bugle: there’s a loop made between a lip filter and
a pipe. The big difference is in the
tuning of the two sections:
- The lip filter’s frequency now tracks the
keyboard. There’s an adjustable
offset added for making squeals and falloffs, and there’s an LFO added for
making vibrato.
- The delay line is tuned to Bb1, or position 1 on
the trombone. It does not track the keyboard. Instead, we’ll use some logic modules to
map the keyboard notes to the slide positions. For example, if we want a note to play
in position 2, we need to lower the delay line’s pitch by one
semitone. If we want a note to play
in position 7, we need to lower the delay line’s pitch by six semitones.
The
G2 has a wide variety of logic modules, and there are various ways of
converting note numbers to slide positions.
This patch uses a pair of SeqCtr modules to create a 32-note range, from
E2 to B4. We’ll first add 24 to the note
number, so that E2 is zero. Multiplying
the result by 4 makes the left-most SeqCtr increase by one stage for each
note. Subtracting 16 from the note and
multiplying by 4 again makes the right-most SeqCtr address the next 16 notes. Since SeqCtrs “park” their outputs to zero
when the Ctr input is out of range, our SeqCtrs don’t interfere with each
other.
The
outputs of the SeqCtrs adjust the pitch of the delay line, in semitones. If a note should be played in position 1, the
SeqCtr output for that note is zero. If
a note should be played in position 2, the SeqCtr output for that note is -1,
lowering the pipe’s pitch from Bb1 to A1.
Position 7, E1, is achieved by setting a SeqCtr value to -6.
Glide
modules are included to smooth the tuning of both the lip filter and the pipe.