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CH. 21 Musical Sounds

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Musical Tones have threemain characteristics

1) Pitch

2) Loudness

3) Quality

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Pitch-Relates to frequency.

In musical sounds, thesound wave is composed of

many differentfrequencies, so the pitchrefers to the lowestfrequency component.

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Slow Vibrations = LowFrequency.

Fast Vibrations = High

Frequency. Ex: Concert A = 440

vibrations per second.

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Intensity: Depends on theAmplitude.

Intensity is proportional tothe square of theamplitude.

In symbols: I A 2

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Intensity is measured inunits of Watts/m 2.

(i.e. power per unit area)

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Another closely related

quantity is the intensity level,or sound level.

Sound level is measured indecibels. (dB)

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The decibel scale is based on

the log function.# dB =10 log(I/I o)

where I o = some referenceintensity, such as thethreshold of human hearing -(I o = 10 -12 Watts/ m 2)

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Examples:

Source of Intensity SoundSound Level Jet airplane 10 2 140

Disco Music 10-1

110 Busy street

traffic 10 -5 70 Whisper 10 -10 20

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Loudness: Physiological

sensation of sound detection. The ear senses some frequencies

better than others. Ex: A 3500Hz sound at 80 dB

sounds about twice as loud as a

125-Hz sound at 80dB.

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Quality: A piano and a clarinet can bothplay the note middle C, but we candistinguish between them.Why? - Because the quality of the soundis different.

The quality is also called the Timbre. The number and relative loudness of the

partial tones determines the Quality ofthe sound.

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Musical sounds are composed of

the superposition of many toneswhich differ in frequency.

The various tones are calledpartial tones.

The partial tone with the lowest

frequency is called thefundamental frequency.

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Fundamental or 1st harmonic

2nd harmonic

3rd harmonic

NODE

Antinode

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L

L = /2

L =

L

Fundamental or 1st harmonic

2nd harmonic

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Finding the n th harmonic

(2L/2) f 2= (2L) f 1

f 2

= 2f 1 ------> f

n= nf

1

L = n /2 ----->n= 2L/n

where (n = 1,2,3,4,)

v = 1f 1 v = 2f 2

2f 2 = 1f 1

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Musical Instruments Scale&Octave

The tone an octave above hastwice the frequency as theoriginal tone.

Scale: A succession of notes offrequencies that are in simple ratiosto one another.

Octave: The eighth full tone (or 12thsuccessive note in a scale) above orbelow a given tone.

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1 2 3 4 5 6 7 8

1 2 3 4 5

WholeTones

Half Tones

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We can decompose a given

waveform into its individualpartials by Fourier Analysis.

Musical sounds are composed ofa fundamental plus variouspartials or overtones.

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Joseph Fourier, in 1822,

discovered that a complicatedperiodic wave could be

constructed by simplesinusoidal waves, and likewisedeconstructed into simplesinusoidal waves.

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The decomposition of acomplicated waveform into simpler

sinusoidal waveforms is known asFourier Analysis

The construction of a complicatedwaveform from simpler sinusoidalwaveforms is known as FourierSynthesis.

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-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 1 2 3 4 5 6 7 8

2/ p [sin( p x)+1/3sin(3 p x)+1/5sin(5 p x)]

Example of Fourier Synthesis

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COMPACT DISC

Digital Audio

Howstuffworks "How Analog-DigitalRecording Works"

http://www.howstuffworks.com/analog-digital.htmhttp://www.howstuffworks.com/analog-digital.htmhttp://www.howstuffworks.com/analog-digital.htmhttp://www.howstuffworks.com/analog-digital.htmhttp://www.howstuffworks.com/analog-digital.htmhttp://www.howstuffworks.com/analog-digital.htm

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t1 t2 t3

AnalogueSignal

Digital

Signal

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End of Chapter 20