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

Grey’s axes

overtones arise and decay together or not

Timbre space based on

nearness ratings by people

Psychology experiment

From McAdams, S. et al. Psychological Research, 58, 177-192 (1995)

Broad band vs Tonal

“Beat That” by Beat Kaufmann

The Syrinx

Hz

Filtered Broad Band

• ASA demo 5

• A Low pass filter cuts off all high frequencies

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

What are the characteristics of sounds used for music?

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?

Terms Introduced

• Timbre space and popular choices for their dimensions

Reading:

• Butler chapter 8

• Hopkins chap 1