On Timbre Phy 103 Physics of Music image

On Timbre Phy 103 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 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 (C 4). 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 Objective Tonal character, usually pitched Periodic sound or sound composed of only a few frequencies Noisy, with or without some Random pulses or broad tonal character, including band spectrum rustle noise 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. 2. 3. 4. 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). 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 Mc. Adams, S. et al. Psychological Research, 58, 177 -192 (1995)

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

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 200 Hz 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 28 a Adding in partials of a carillon bell Hum note 251 Hz Prime or fundamental 501 Hz Minor Third and Fifth 603, 750 Hz Duodecime or Twelfth 1506 Hz Upper Octave 2083 Hz Next two partials 2421, 2721 Hz Remainder of partials

Adding in partials for a guitar ASA Demo 28 b In order • • fundamental 2 rd harmonic 3 rd harmonic 4 th harmonic 5 th and 6 th harmonic 7 th and 8 th harmonic 9 th, 10 th and 11 th 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 rules A 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 steady oscillation Definite pitch Tone lacking character Fundamental plus Definite pitch harmonic series Clear tone Definite pitch Fundamental plus Tone depends on some harmonics which harmonics are present wind, radio static Electronic beep, Ocharina strings woodwinds brass clarinet low register, marimba with tuned overtones

Timbre continued Fairly definite Fundamental with pitch but sense of mistuned pitch may depend harmonics on the fundamental Pitch and tone Fundamental with quality dependent non-harmonic on the nature of overtones the overtones Close non Ambiguous pitch, harmonic depending on frequencies overtones Fundamental + Some sense of few tones plus pitch broad band strings, winds, brass, piano, digeridu Marimbas without tuned overtones, bells, digeridu triangles, gongs, bells some drums

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

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 Demo 30 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. 5 a

The effect of Tone Envelope on Timbre ASA demo 29 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 ASA demo 31 1 octave=2. 1

Changes in Timbre The singer’s “formant” The normal 3 formants are brought close together to form a broad spectral Cook demo 42 Singing with peak between 2500 and without the singer’s formant 4000 Hz spectrum with singer’s format spectrum without

Changes in timbre with vocal effort Cook demo #78 a) b) c) d) 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

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