Complex tones: mixtures of simple tones of various amplitudes and frequencies, partials

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• Complex tones mixtures of simple tones of
  various amplitudes and frequencies, partials
• Combination of harmonics (partials)
• Musical instruments produce complex tones rather
  than pure tones.

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How do we make square waves?
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How do we make sawtooth waves?
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Frequency Range of Musical Sounds
? Working range of tones produced by musical
instruments 27 4200 Hz
? Beyond 10000 Hz, little sound produced by
musical instruments
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Harmonic Series
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Analysis of Musical Instrument Tones
??No characteristic spectrum, somewhat the same
from note to note associated with a given musical
instrument ??
Ex.) Oboe does not show a certain pattern of
harmonic amplitudes that characterize its sound
over the playing range.
? A few general trends ?
? Low tones of a clarinet are deficient in the
even harmonics
?Tones with many high frequency harmonics sound
brighter. ? Tones with fewer high frequency
harmonics sound darker.
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Why Is It Hard to Know the Details of the
Harmonic Structure of a Tone?
The structure of a tone depends on various
factors.
? Loudness
? Where it is heard
? How the player produces it
? Acoustics of a room
? The frequency separation in higher harmonics
will be within the range of critical bands.
Luckily,
Experiments reveal that for musical instruments,
the harmonics above about the seventh are rather
unimportant.
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However, we identify an instrument when we hear
music...
How?
?? Initial transient of the tone of the instrument
?? Decay transient of the tone
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Formants
?An instrument has a certain fixed frequency
regions in which harmonics of a tone are
emphasized.
? the frequency region Formants
? The formants seem to characterize the
instrument.
Instrument
Formant I
Formant II
3000 2300 3700-4300 1220-1280 2500
800 1400 930 1500-1700 440-500 1200-1400 600-800 2
00-400 400-500
Flute Oboe English horn Clarinet Basson Trumpet Tr
ombone Tuba French Horn
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Formants
Frequency
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Timbre

• Characteristic of a tone that can distinguish it
  from others of the same frequency and loudness