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.

• In symbols: I A2

• Intensity is measured in units of Watts/m2.

(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

SoundLevel

• Jet airplane 102 140

• Disco Music 10-1 110

• Busy street

traffic 10-5 70

• Whisper 10-10 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

2nd harmonic

3rd harmonic

NODE

Antinode

L

L = /2

L = L

Fundamental or 1st harmonic

2nd harmonic

Finding the nth harmonic

(2L/2) f2= (2L) f1

f2 = 2f1 ------> fn = nf1

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

where (n = 1,2,3,4,…)

v = 1f1 v = 2f2

2f2 = 1f1

Musical Instruments Scale&Octave

• The tone an octave above has twice the frequency as the original tone.

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.

1 2 3 4 5 6 7 8

1 2 3 4 5

Whole Tones

Half 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 decomposition of a complicated waveform into simpler sinusoidal waveforms is known as Fourier Analysis

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

-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/[sin(x)+1/3sin(3x)+1/5sin(5x)]

Example of Fourier Synthesis

COMPACT DISC

• Digital Audio

Howstuffworks "How Analog-Digital Recording Works"

t1 t2 t3

Analogue Signal

Digital Signal

End of Chapter 20