Transcript CH. 20 Musical Sounds - Stephen F. Austin State University

CH. 21 Musical Sounds
Musical Tones have three
main characteristics
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.
2
• In symbols: I  A
• Intensity is measured in
2
units of Watts/m .
(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/Io)
where Io = some reference
intensity, such as the
threshold of human hearing (Io = 10-12 Watts/ m2)
• Examples:
• Source of
Intensity
Sound
• Jet airplane
102
• Disco Music
10-1
• Busy street
traffic
10-5
• Whisper
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=
L
2nd harmonic
Finding the
th
n
harmonic
L = n/2 -----> n= 2L/n
where (n = 1,2,3,4,…)
v = 1f1
v = 2f2
2f2 = 1f1
(2L/2) f2= (2L) f1
f2 = 2f1 ------> fn = nf1
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.
Whole
Tones
Half Tones
1
1
2
2
3
3
4
4
5
6
5
7
8
• 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
Example of Fourier Synthesis
0.8
2/p[sin(px)+1/3sin(3px)+1/5sin(5px)]
0.6
0.4
0.2
0
0
-0.2
-0.4
-0.6
-0.8
1
2
3
4
5
6
7
8
COMPACT DISC
• Digital Audio
Howstuffworks "How Analog-Digital
Recording Works"
Digital
Signal
t1 t2 t3
Analogue
Signal
End of Chapter 20