on timbre phy103 physics of music image by hans-christoph steiner based on grey, jm 1979, jasa, 61,...
TRANSCRIPT
On TimbrePhy103 Physics
of Music
image by Hans-Christoph Steiner based on Grey, JM 1979, JASA, 61, 1270
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)
It’s 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.
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.
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.
Attributes from Erickson’s Music Structure
Subjective ObjectiveTonal 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
More Attributes
Coloration Spectral envelope
Coloration glide or formant glide
Change of spectral envelope
Attack Prefix
Final sound Suffix
Beginning/ending Rise/decay time
Schouten’s “Acoustic parameters”
1. The range between tonal and noiselike character.
2. The spectral envelope.
3. The time envelope in terms of rise, duration, and decay.
4. The changes both of spectral envelope (formant-glide) and fundamental frequency (micro-intonation).
5. 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.
Timbre space
• Grey’s 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
Timbre space based on
nearness ratings by people
Psychology experiment
From McAdams, S. et al. Psychological Research, 58, 177-192 (1995)
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
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
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
Properties of musical sounds
• Composed of tones, not a lot of broad band noise
• Overtones are nearly harmonic---Lots of exceptions to the above rulesA rich musical sound has a strong set of tones
in the vocal formant region-- Combining instruments with different
timbres
Timbre classification in terms of spectrum only
Disordered pattern Noise wind,
radio static
steady oscillationDefinite pitchTone lacking character
Electronic beep,Ocharina
Fundamental plus harmonic series
Definite pitchClear tone
stringswoodwindsbrass
Fundamental plus some harmonics
Definite pitchTone depends on which harmonics are present
clarinet low register,marimba with tuned overtones
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
Timbre classification and sound excitation
Harmonic spectrum:strings – chordophones, string is vibrating winds – areophones, column of air is vibratingRicher tone made by ensuring high frequency
overtones are present in spectrum.Spectral envelope for guitar, piano, violin affected
by resonating chamberTemporal envelope: plucking vs hammer vs friction
excitation: guitar vs piano vs violin
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
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
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
The effect of Tone Envelope on Timbre
ASA demo29 Piano envelope is normally decaying
but here it is reversed
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 octave=2.1
ASA demo 31
Changes in TimbreThe singer’s “formant”
Cook demo 42 Singing with
and without the singer’s formantspectrum with singer’s format spectrum without
The normal 3 formants are brought close together to form a broad spectral peak between 2500-4000Hz
Changes in timbre with vocal effort
Cook demo #78a) Successive vocal tones, amplitude only turned down
b) Same as a) but high end of spectrum is also turned down, as would happen for decreasing effort
c) Same as b) but with additional reverb that is held constant so voice sounds like it is getting quieter in a fixed location
d) Same as a) but with increasing reverb so the voice sounds as if it is getting further away
Discussion
• What accounts for the differences in timbre for oboes, clarinets, flutes and horns?
• Strings vs winds?• Piano vs violin?• Acoustic vs classical guitar?
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?