1) Pitch
2) Loudness
3) Quality

•
Pitch-Relates to frequency.
In musical sounds, the sound wave is composed of many different frequencies, so the pitch refers to the lowest frequency component.

•
Slow Vibrations = Low
Frequency.
•
Fast Vibrations = High
Frequency.
•
Ex: Concert A = 440 vibrations per second.

•
Intensity: Depends on the
Amplitude.
•
Intensity is proportional to the square of the amplitude.
•
In symbols: I

A 2

•
Intensity is measured in units of Watts/m 2 .
(i.e. power per unit area)

•
Another closely related quantity is the intensity level, or sound level.
•
Sound level is measured in decibels. (dB)

•
The decibel scale is based on the log function.
# dB =10 log(I/I o
) where I o
= some reference intensity, such as the threshold of human hearing -
(I o
= 10 -12 Watts/ m 2 )

• Examples:
•
Source of Intensity
Sound
•
Jet airplane
•
Disco Music
10
10
2
-1
•
Busy street traffic
•
Whisper
10 -5
10 -10
Sound
Level
140
110
70
20

• 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.

• Quality: A piano and a clarinet can both play the note “middle C”, but we can distinguish between them.
Why? - Because the quality of the sound is different.
• The quality is also called the “Timbre”.
The number and relative loudness of the partial tones determines the “Quality” of the sound.

Musical sounds are composed of the superposition of many tones which differ in frequency.
• The various tones are called partial tones.
• The partial tone with the lowest frequency is called the fundamental frequency.

Fundamental or 1st harmonic
NODE
3rd harmonic
2nd harmonic
Antinode

Fundamental or 1st harmonic
L =

/2
L
L =
 2nd harmonic
L

Finding the n th harmonic
L = n

/2 ----->
 n
= 2L/n where (n = 1,2,3,4,…) v =

1 f
1

2 f
2
=

1 f
1 v =

2 f
2
(2L/2) f
2
= (2L) f
1 f
2
= 2f
1
------> f n
= nf
1

Musical Instruments Scale&Octave
Scale: A succession of notes of frequencies that are in simple ratios to one another.
•
Octave: The eighth full tone (or 12th successive note in a scale) above or below a given tone.
•
The tone an octave above has twice the frequency as the original tone.

Half Tones
1 2 3 4 5
1 2 3 4 5 6 7 8
Whole
Tones

•
We can decompose a given waveform into its individual partials by Fourier Analysis.
•
Musical sounds are composed of a fundamental plus various partials or overtones.

•
Joseph Fourier, in 1822, discovered that a complicated periodic wave could be constructed by simple sinusoidal waves, and likewise deconstructed into simple sinusoidal waves.

• The construction of a complicated waveform from simpler sinusoidal waveforms is known as Fourier
Synthesis.
•
The decomposition of a complicated waveform into simpler sinusoidal waveforms is known as
Fourier Analysis

0.2
-0.6
-0.8
0
0
-0.2
-0.4
0.4
0.6
0.8
Example of Fourier Synthesis
2/ p
[sin( p x)+1/3sin(3 p x)+1/5sin(5 p x)]
1 2 3 4 5 6 7 8

COMPACT DISC
• Digital Audio
Howstuffworks "How Analog-Digital
Recording Works"

t1 t2 t3
Digital
Signal
Analogue
Signal

End of Chapter 20