Transcript Slide 1

Chapter 21
Musical Sound
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Musical Instruments
Now that we understand more about the physics of
sound, let’s analyze how it is produced by different
types of musical instruments.
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Musical Notes
A musical note has four characteristics:
• Duration
• Loudness
• Pitch (e.g., soprano versus alto)
• Timbre or Quality (e.g, piano versus violin)
Let’s investigate the physical properties
underlying these four characteristics.
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Duration of a Note
Duration is the amount of time from the
beginning to the end of the note.
The tempo set by the
composer establishes the
conversion between the
measure of a note (whole
note, half note, etc.) and the
number of milliseconds of time
for that note’s duration.
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Traditional metronome is a
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wind-up pendulum clock.
Loudness & Amplitude
The loudness of a note is an indication
of the amplitude of the sound.
The harder you strike a tuning fork, the larger the
amplitude of the oscillation and the louder the
sound made by the tuning fork.
Same is true for a plucking
guitar string, banging a drum, or
blowing on a horn, etc.
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Drumhead
Pitch & Frequency
The faster the vibrations (shorter the
period), the higher the pitch of the
musical note produced.
There is a direct
relationship between
the pitch of a note
and the frequency of
the sound wave.
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Pythagoras & Music
Pythagoras discovered
that different musical
notes were related by
mathematical ratios,
such as the ratios of
lengths or sizes in
musical instruments or
even in simple objects.
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Octave
The note produced by two strings, one half
the length of the other, sounded similar.
In Western music these two notes are said
to be an octave apart.
Men and women
typically sing an
octave apart.
C5
C4
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SJSU the rainbow…”
Sing “Some-where
over
Perfect Fifth
If the second string is 2/3rd the length then
the two notes are said to be “a fifth apart.”
Typical separation
between tenor and
bass or soprano
and alto.
G4
C4
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Sing “Twin-kle,
twin-kle
little star…”
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Fundamental & Overtones
The Fundamental is the lowest frequency standing wave.
The Overtones are twice, three times, etc., the frequency of
the Fundamental.
110 Hz (A2)
One Octave
220 Hz (A3)
Perfect Fifth
330 Hz (E4)
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Notes and Powers of Two
An octave has 12 steps and going up an
octave doubles the frequency.
The frequency of “Concert A” is 440 Hz.
The frequency of other notes is
(Frequency) = 2(steps)/12 x (440 Hz)
counting number of steps from Concert A
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Notes & Frequencies
Middle C
C (Do) C#
D (Re) D#
E (Mi)
F (Fa)
262 Hz 277 Hz 294 Hz 311 Hz 330 Hz 349 Hz
Concert A
F#
G (So) G#
A (La)
A#
B (Ti)
370 Hz 392 Hz 415 Hz 440 Hz 466 Hz 494 Hz
For example, Middle C is 9 steps below Concert A so it is
(Frequency) = 2(-9)/12 x (440) = 2(-0.75) x (440) = 262 Hz
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Piano Keyboard (Upper Half)
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String Instruments
Standing wave on the vibrating string causes
forced oscillation of the sounding board.
Frequency for a string depends on:
• Length of string
• Thickness and composition
• Tension in the string
Loudness depends on:
• Amplitude of oscillation
• Mass of the string
• Frequency
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Modern piano
has many long,
massive steel
strings under
high tension
(hundreds of
pounds) on a
large sounding
board.
Evolution of the Piano
Dulcimer
Clavichord
Piano
Hammer
Harpsichord
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Visit the Beethoven Center on the fifth floor of MLK library.
Musical Pipe Instruments
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Demo: Hoot Tubes
Large tube has a metal screen near
one end.
Heat screen with a flame.
Remove tube from the flame and it
plays like an organ pipe.
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Hoot Tubes, Analyzed
Remove the flame and
hot air rises from the
screen, drawing in air
from the bottom.
Hot air rising through the
pipe produces pressure
vibrations with a
frequency determined
by the pipe’s length.
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FLAME
Demo: Whirly Tube
Whirl a corrugated tube
to produce a pure
tone at the tube’s
natural frequency.
Bernoulli principle
creates low pressure
at the moving end,
drawing air through
the tube.
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L
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A
Playing Simple Horns
Standing waves of different frequencies (different notes) are
produced, depending on how musician blows into the horn.
Simple bugle is just a
long pipe wrapped in a
coil so it’s compact.
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Brass & Woodwind Vibrations
Vibrations in a pipe instrument created by:
• Vibrating one’s lips (e.g., trumpet)
• Blowing past an opening (e.g., flute)
• Blowing & vibrating a reed (e.g., clarinet)
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Demo: Playing a Straw
Can make a simple reed by cutting a straw,
as shown, lightly placing it between your
lips, and blowing hard.
What happens if you
shorten the straw (e.g.,
cut it in half)?
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Harmonic Series
Music for natural horns and bugles is limited
by harmonic series, the frequencies of the
fundamental and overtones.
Fundamental
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Changing the Length
To play notes beyond the harmonic series
requires changing the frequency of the
fundamental by changing the length of tube.
Crooks
Finger-holes
Cornett
Disadvantage: Reduced amplitude
Disadvantage: Clumsy
Changing the Length
Trombone uses a continuous slide to vary its length
Cornett
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Changing the Length
Valves used in trumpet, tuba, and French horn
Cornett
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Similar to using a crook but easy to open & close
Woodwind Instruments
Resonant standing waves also produced in a pipe but the
pipe length varied by air holes (finger-holes, keys, or pads).
Flute
Oboe
Cor anglais
Saxophone
Clarinet
Bassoon
Meter stick
Using air holes reduces amplitude of the sound
Percussion Instruments
Create oscillations by
striking an object,
such as:
• Stretched drumhead
• Metal rod or disk
• Wooden object
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Drum Heads
Drum heads are stretched
membranes that vibrate at
different frequencies
depending on the membrane’s
oscillation pattern.
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Note:
These animations are not accurate
complex patterns should oscillate faster.
Timbre or Quality
A musical instrument playing a single note
produces not just that note’s frequency but
others as well, mostly overtones.
The frequencies produced by
a flute playing an A (slightly
flat) show that the
fundamental (436 Hz) and the
harmonic (872 Hz) have
almost the same amplitude.
The spectrum of a tuning fork
would have only a single peak
at the fundamental.
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Why Instruments Differ
The unique spectrum
of frequencies for
an instrument gives
that instrument a
unique signature,
called the timbre (or
quality).
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Playing this
note (196 Hz)
Adding Different Frequencies
Two waves of different frequencies will
alternate between constructive and
destructive interference, as they alternate
between in phase and out of phase.
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Same effect seen with two combs
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with different tooth spacing.
Beats
When the two frequencies are almost the same, the
sum is about the same frequency but periodically
varying amplitude. This is called a beat.
Wave A
Wave B
Sum of
A+B
Out of phase
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In phase
Dissonance & The Ear
Different tones stimulate different spots on the basilar
membrane in the cochlea.
When two tones are close together, the stimulation of two
nearby spots is unpleasant and heard as dissonant.
Cochlea “unrolled”
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