Chapter 21 Musical Sound

1
Chapter 21 Musical Sound
2
Musical Instruments
Now that we understand more about the physics of
sound, lets analyze how it is produced by
different types of musical instruments.
3
Musical Notes

• A musical note has four characteristics
• Duration
• Loudness
• Pitch (e.g., soprano versus alto)
• Timbre or Quality (e.g, piano versus violin)
• Lets investigate the physical properties
  underlying these four characteristics.

4
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 notes duration.
Traditional metronome is a wind-up pendulum clock.
5
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.
Drumhead
Same is true for a plucking guitar string,
banging a drum, or blowing on a horn, etc.
6
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.
7
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.

8
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
Sing Some-where over the rainbow
9
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
Sing Twin-kle, twin-kle little star
10
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

12
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
13
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

Modern piano has many long, massive steel strings
under high tension (hundreds of pounds) on a
large sounding board.

• Loudness depends on
• Amplitude of oscillation
• Mass of the string
• Frequency

15
Evolution of the Piano
Dulcimer
Clavichord
Piano Hammer
Harpsichord
Visit the Beethoven Center on the fifth floor of
MLK library.
16
Musical Pipe Instruments
17
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.

18
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
  pipes length.

FLAME
19
Demo Whirly Tube

• Whirl a corrugated tube to produce a pure tone at
  the tubes natural frequency.
• Bernoulli principle creates low pressure at the
  moving end, drawing air through the tube.

L
A
20
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 its compact.
21
Brass Woodwind Vibrations

• Vibrations in a pipe instrument created by
• Vibrating ones lips (e.g., trumpet)
• Blowing past an opening (e.g., flute)
• Blowing vibrating a reed (e.g., clarinet)

22
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)?
23
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
25
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
Similar to using a crook but easy to open close
27
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
28
Percussion Instruments

• Create oscillations by striking an object, such
  as
• Stretched drumhead
• Metal rod or disk
• Wooden object

29
Drum Heads

• Drum heads are stretched membranes that vibrate
  at different frequencies depending on the
  membranes oscillation pattern.

Note These animations are not accurate because
complex patterns should oscillate faster.
30
Timbre or Quality

• A musical instrument playing a single note
  produces not just that notes 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).

Playing this note (196 Hz)
32
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.

Same effect seen with two combs with different
tooth spacing.
33
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
In phase
34
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