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DISCUSSION Figure 2.20 displays the frequency spectrum for a clarinet playing a B-flat. The
base tone, f o is at 231 Hz, with the harmonics having frequencies of 3f o , 5f o , etc. Contrast this with
the frequency spectrum, shown in Figure 2.21, of the first few seconds of Aaron Copland’s ‘‘Fanfare
for the Common Man,’’ which is played by an ensemble of brass instruments, like French horns, and
has a fundamental frequency of approximately 700 Hz. This spectrum contains harmonics that are
2f o , 3f o , 4f o , etc.
Level (dB)
Frequency (Hz)
0
-50
-45
-40
-35
-30
-25
-20
-15
-10
-5
0
700
1400
231 Hz
693 Hz
1155 Hz
1617 Hz
Figure 2.20 Frequency spectrum for a clarinet playing the note one whole tone below middle C.
(Adapted from Campbell, D.M., Nonlinear Dynamics of Musical Reed and Brass Wind Instruments,
Contemporary Physics, 40(6) November 1999, pages 415–431.)
Level (dB)
0
-10
-20
-30
-40
-50
-60
0
700 Hz
1400 Hz
2100 Hz
2800 Hz
1400
700
2100
Frequency (Hz)
2800
3500
Figure 2.21 Frequency
spectrum for the first three
seconds of Aaron Copland’s
‘‘Fanfare for the Common
Man’’ that is played by the
brass section of the
orchestra.
70 Chapter 2 Static and Dynamic Characteristics of Signals