1. On Timbre Phy103 Physics of Music
image by Hans-Christoph Steiner based on Grey, JM 1979, JASA, 61, 1270

2. 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.

3. 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.

4. Mixed timbres
Butler Listening example 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 Intermediate between piano and violin timbre. Both spectral mix, and attack envelope is intermediate.

5. Attributes from Erickson’s 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

6. More Attributes Coloration Spectral envelope
Coloration glide or formant glide
Change of spectral envelope
Attack
Prefix
Final sound
Suffix
Beginning/ending
Rise/decay time

7. Schouten’s “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.

8. 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

9. Grey’s axes
overtones arise and decay together or not

10. Timbre space based on nearness ratings by people Psychology experiment
From McAdams, S. et al. Psychological Research, 58, (1995)

11. Broad band vs Tonal
“Beat That” by Beat Kaufmann Hz
The Syrinx

12. Filtered Broad Band ASA demo 5
A Low pass filter cuts off all high frequencies

13. 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

14. 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

15. 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

16. What are the characteristics of sounds used for music?

17. 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

18. 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
Clear tone
strings
woodwinds
brass
Fundamental plus some harmonics
Tone depends on which harmonics are present
clarinet low register,
marimba with tuned overtones

19. 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

20. 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

21. 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

22. 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

23. 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

24. The effect of Tone Envelope on Timbre
ASA demo29
Piano envelope is normally decaying
but here it is reversed

25. 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

26. Changes in Timbre The singer’s “formant”
The normal 3 formants are brought close together to form a broad spectral peak between Hz
Cook demo 42 Singing with
and without the singer’s formant
spectrum with singer’s format spectrum without

27. 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

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

29. 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?

30. Terms Introduced Timbre space and popular choices for their dimensions
Reading:
Butler chapter 8
Hopkins chap 1