On Timbre Phy103 Physics of Music

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.

Attributes from Erickson’s Music Structure SubjectiveObjective 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 VibratoFrequency modulation TremoloAmplitude modulation

More Attributes ColorationSpectral envelope Coloration glide or formant glide Change of spectral envelope AttackPrefix Final soundSuffix Beginning/endingRise/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, (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 28 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 Demo28 In order fundamental 2rd 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 alot of broad band noise Overtones are nearly harmonic Lots of exceptions to the above rules

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

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

Changes in Timbre The singer’s formant Cook demo 42 Singing with and without the singer’s formant spectrum with singer’s format spectrum without

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

Terms Introduced Timbre space and popular choices for their dimensions