Physics 371 April 9, 2002

1
Physics 371 April 9, 2002
Acoustics for Musicians

• Brass Instruments
• lip-driven oscillations (feedback)
• adjustment of natural modes
• mouthpiece and bell
• playing a chromatic scale
• slides and valves

2
pressure distribution for different modes
3
adjusting the natural modes of a brass instrument
f
(a)
(b)
(c)
(a) natural mode frequencies of a cylindrical
tube closed at one end (b) upper shift of
frequencies of the lower modes caused by
replacing part of the tube by a bell (c)
downward shift of the higher modes caused by
adding a mouth piece.
its a misconception to think of it as an open
pipe!
4
for a periodic excitation, the partials are
by necessity exact multiples of the fundamental
x
x
x
but misconception brass intruments play in JUST
tuning table on p. 267of Backus shows that e.g.
8th resonance is as much as 54 cent off
5
Tuba players have a sense of humor about their
instrument......
note Tuba has a long conical section
6
a home-built tuba
reminder conical horn has same modes as OPEN pipe
Tuba
f0, 2f0, 3f0,4f0,
for trumpet, pedestal note is out of tune, but
tuba has a larger conical section than a trumpet
or French horn so that pedestal note (lowest
mode) is more nearly in tune
7
note if the conical section is nearly 50 of the
horn length, the pedestal tone is in tune (Tuba)
8
Playing a chromatic scale (sequence of
half-steps)
one method the slide (trombone)
to bridge the gap from mode 2 to mode 3 (a
fifth) requires 7 slide positions
Bb-A-Ab-G-Gb-F-E
how long should I make the trombone if I can
extend arm by 0.5 m? Answ no longer than 3 m
when slide is extended -gt 2m for pos 1
9
another method valves to add length of tubing
entire scale with only three valves - how?
Trumpet
French Horn
10
example of a piston valve valve depressed adds
more length (lowers pitch)
11
need to bridge the gaps in the natural scale
if first mode is not used - biggest gap is FIFTH
(1) 2 3 4 5 6
7 8 9 10
fifth fourth major minor
third third
semitones 7 5 4 3
lower pitch 1 semitone by adding length l1 to
original length lo
2
l2 3
l3
4
l1 l3
5 l2
l3 6
l1 l2 l3

12
problem the lengths do not add up properly!
example take trumpet of length 137 cm
lower pitch by added cm new
length (cm) needed 1 137x1.059...
145.1 8.1 2 137x(1.059..)2 153.8 16.8
3 137x(1.059..)3 162.9 25.9
4 137x(1.059..)4 172.6 35.7 but 8.125.9
34.0 off 1.7cm/172cm 1 5
137x(1.059..)5 182.9 6 137x(1.059..)6
7
solution thumb slide or add more valves
13
Schematic airflow through a French horn F horn
on top, Bb horn on the bottom. Each numbered
valve pair is operated by a single lever