On Timbre Phy103 Physics of Music

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On TimbrePhy103 Physics of Music
image by Hans-Christoph Steiner based on Grey, JM
1979, JASA, 61, 1270
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Four complex tones in which all partials have
been removed by filtering (Butler Example 2.5)

• One is a French horn, one is a violin, one is a
  pure sine, one is a piano (but out of order)
• Its hard but not impossible to identify the
  instruments. Clues remain (attack, vibrato,
  decay) and these contribute to the timbre.
  Timbre is not just due to the spectral mix.

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The importance of attack transients in sound
identification

• Listening example 4.8 (Butler) Three sustained
  tones are presented, each with the attack
  transient (initial 60 milliseconds) removed.
  Identify the instruments
• Listening example 4.9. First the sound of a
  violin (C4). Next the attack transient of that
  tone elongated to a hundred times its normal
  length through digital time expansion.
• Note this scratchiness makes it difficult for
  computer programs to transcribe music played by
  violins.

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Mixed timbres

• Butler Listening example 8.3. Starting with a
  French horn sound and ending with a clarinet
  sound. 11 short tones each shifted 10 further
  toward the clarinet tone.
• Butler Listening example 8.4. Intermediate
  between piano and violin timbre. Both spectral
  mix, and attack envelope is intermediate.

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Attributes from Ericksons Music Structure
Subjective Objective
Tonal character, usually pitched Periodic sound or sound composed of only a few frequencies
Noisy, with or without some tonal character, including rustle noise Random pulses or broad band spectrum
Vibrato Frequency modulation
Tremolo Amplitude modulation
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More Attributes
Coloration Spectral envelope
Coloration glide or formant glide Change of spectral envelope
Attack Prefix
Final sound Suffix
Beginning/ending Rise/decay time
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Schoutens Acoustic parameters

• The range between tonal and noiselike character.
• The spectral envelope.
• The time envelope in terms of rise, duration, and
  decay.
• The changes both of spectral envelope
  (formant-glide) and fundamental frequency
  (micro-intonation).
• The prefix, an onset of a sound quite dissimilar
  to the ensuing lasting vibration.
• This represents way too many free parameters for
  an engineer to cover the complexity of sounds.

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Timbre space

• Greys Timbre cube
• Is it possible to classify timbres, for example
  recognition of instrument from audio?

image by Hans-Christoph Steiner based on Grey, JM
1979, JASA, 61, 1270
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Greys axes
overtones arise and decay together or not
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Timbre space based on nearness ratings by people
Psychology experiment
From McAdams, S. et al. Psychological Research,
58, 177-192 (1995)
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Broad band vs Tonal
Beat That by Beat Kaufmann
Hz
The Syrinx
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Filtered Broad Band

• ASA demo 5
• A Low pass filter cuts off all high frequencies

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Blending of harmonics into one tone or timbre
ASA Demo 1 Cancelled Harmonics 20 harmonics of
200Hz are played together. When the relative
amplitudes of all 20 harmonics remain steady they
blend and we hear them all as one tone When one
harmonic is cancelled or given a vibrato then it
stands out and we hear it separately
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How many harmonics are needed for a tone to have
its recognizable character?

• ASA Demo 28a Adding in partials of a carillon
  bell

Hum note 251 Hz Prime or fundamental 501Hz Minor
Third and Fifth 603,750Hz Duodecime or Twelfth
1506Hz Upper Octave 2083Hz Next two partials
2421,2721Hz Remainder of partials
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Adding in partials for a guitar

• ASA Demo28b In order
• fundamental
• 2rd harmonic
• 3rd harmonic
• 4th harmonic
• 5th and 6th harmonic
• 7th and 8th harmonic
• 9th, 10th and 11th harmonic
• Remainder

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What are the characteristics of sounds used for
music?
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Properties of musical sounds

• Composed of tones, not a lot of broad band noise
• Overtones are nearly harmonic
• ---Lots of exceptions to the above rules
• A rich musical sound has a strong set of tones in
  the vocal formant region
• -- Combining instruments with different timbres

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Timbre classification in terms of spectrum only
Disordered pattern Noise wind, radio static
steady oscillation Definite pitch Tone lacking character Electronic beep, Ocharina
Fundamental plus harmonic series Definite pitch Clear tone strings woodwinds brass
Fundamental plus some harmonics Definite pitch Tone depends on which harmonics are present clarinet low register, marimba with tuned overtones
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Timbre continued
Fundamental with mistuned harmonics Fairly definite pitch but sense of pitch may depend on the fundamental strings, winds, brass, piano, digeridu
Fundamental with non-harmonic overtones Pitch and tone quality dependent on the nature of the overtones Marimbas without tuned overtones, bells, digeridu
Close non harmonic frequencies Ambiguous pitch, depending on overtones triangles, gongs, bells
Fundamental few tones plus broad band Some sense of pitch some drums
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Timbre classification and sound excitation

• Harmonic spectrum
• strings chordophones, string is vibrating
• winds areophones, column of air is vibrating
• Richer tone made by ensuring high frequency
  overtones are present in spectrum.
• Spectral envelope for guitar, piano, violin
  affected by resonating chamber
• Temporal envelope plucking vs hammer vs
  friction excitation guitar vs piano vs violin

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Timbre classification and sound excitation

• Non-harmonic spectrum
• Ideophones Solid object vibrating e.g.,
  marimba, xylophone, bells, gongs, forks
• Membranophones membrane vibrating drums
• Richer tone made by tuning overtones, ensuring
  that many overtones are present, coupling motion
  of vibrating object to resonating chamber

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Timber and Transposition

• High and low tones from a musical instrument do
  not have the same relative spectrum.
• Low notes on the piano have week fundamentals
  whereas high notes have strong ones
• ASA Demo30 shifting the spectrum of a bassoon down

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Timbre depends on frequency

• First tone has partials 1,2,3,4,5
• Second tone has partials 1,3,5,7,9
• Difference in timbre depends on frequency of
  fundamental
• Butler demo 3.5a

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The effect of Tone Envelope on Timbre

• ASA demo29
• Piano envelope is normally decaying
• but here it is reversed

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Tones and Tuning Stretched

• The scale can be stretched
• The partials can be stretched
• Here are examples of all 4 combinations
• -- pure harmonics and normal scale
• -- scale stretched
• -- partials stretched
• -- stretched harmonics and scale 1 octave2.1
• ASA demo 31

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Changes in TimbreThe singers formant
The normal 3 formants are brought close together
to form a broad spectral peak between 2500-4000Hz

• Cook demo 42 Singing with
• and without the singers formant

spectrum with singers format spectrum
without
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Changes in timbre with vocal effort

• Cook demo 78
• Successive vocal tones, amplitude only turned
  down
• Same as a) but high end of spectrum is also
  turned down, as would happen for decreasing
  effort
• Same as b) but with additional reverb that is
  held constant so voice sounds like it is getting
  quieter in a fixed location
• Same as a) but with increasing reverb so the
  voice sounds as if it is getting further away

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Discussion

• What accounts for the differences in timbre for
  oboes, clarinets, flutes and horns?
• Strings vs winds?
• Piano vs violin?
• Acoustic vs classical guitar?

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More Discussion

• Evolution of sound synthesis What properties let
  you know that the music or sounds are
  synthesized?
• How can we tell?
• Is there a body of psychoacoustic tests on how
  big a change is required before we notice a
  timbre change?
• Sound synthesis a lack of quantitative measures
  of how well timbre is matched with computerized
  sound synthesis?

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Terms Introduced

• Timbre space and popular choices for their
  dimensions
• Reading
• Butler chapter 8
• Hopkins chap 1