Received 23 May 1966 6.9 Synthesis of Wind-Instrument Tones WILLIAM STRONG PhysicsDepartment, Brigham Young University,Provo, Utah 84601 MELVILLE CLARK Melville Clark Associates,Cochituate, Massachusetts 01763 Clarinet, oboe,bassoon, tuba, flute, trumpet, trombone,French horn, and English horn toneshave been synthesizedwith partials controlledby one spectralenvelope (fixed for each instrumentregardless of note frequency) and three temporal envelopes.Musically literate auditorsidentified natural toneswith 85% accuracyand our synthesizedtones with 66% accuracy;a numberof the confusionswere intrafamily. With intrafamily confusionstolerated in the scoring,the auditors identified natural tones with 94% accuracyand our syntheticones with 77% accuracy. INTRODUCTION may enablethe creationof new types of musicalinstru- ments having greater artistic capabilities than those YNTHESISniques for andfindinganalysis an areaurallycomplementary complete, tech-non- presently available. Such an ability will probablybring redundant, and easily implemented representationof some systematizationand rationality to the creation the tones producedby musicalinstruments. The aural and physicalcharacterization of new soundsartistically identification of a musical instrument from its tones usefulin music--or will, at least, openavenues to such is independent,or nearly independent,of many variables a systematization. of performance:the particular exampleused of a given The use of the tones of conventional musical instru- instrument, the intensity with which the tone is ments, rather than arbitrarily generated signals, is produced,the note played, the acousticalenvironment, advantageous,since such tones are easily generated, and so on. To the perceptualinvariant of identification, can be readily reproducedat will, and provide a there must correspondone or more physicalinvariants standard, reasonably well-quantized and well-estab- that characterizethe soundsproduced by an instrument lished set of timbres known to be musically useful, that serve to identify and distinguishit aurally from familiar to, identifiable by, and capable of being other instruments.The aural significanceof the physical uniquely labeledby, a large body of musicallyliterate invariants found in analysis can be assessedby the auditors. Thus, we are provided with a means for accuracy of identification of synthetic tones with testing the accuracyof any particular synthesis;the systematicperturbations of the invariants.Because of articulation score of musically literate subjects in the enormous number and range of the variables identifying the instrumentsthought to produce the required, synthesis,to be fruitful, must be guided by tones,or in distinguishingthe artificial tonesfrom those analysis.Before examining the effectsof perturbations, producedby natural means,provides a good measure it is necessaryto get reasonablyclose auditory approxi- of the accuracy of synthesisor the sensitivity of a mations to the tonesproduced by musicalinstruments, parameter to perturbation. and this is the subject of this paper for wind instru- There has been some analysis of the steady states, ments.The matter of perturbationswill be treated in a rather less of transients of instrumental tones, and a subsequentpaper. little synthesis.Fletcher •,•' and his associatesat Brigham Ability to characterizethe tones of familiar instru- ments in a simple and aurally satisfactory manner • H. Fletcher, E. D. Blackham, and R. Stratton, "Quality of enables the invention of more controllable and flexible Piano Tones,"J. Acoust.Soc. Am. 34, 749-761 (1962). 2 H. Fletcher,E. D. Backham,and D. A. Christensen,"Quality meansfor producingthe tonesof theseinstruments and of Organ Tones," J. Acoust.Soc. Am. 35, 314-325 (1963). The Journal of the AcousticalSociety of America Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 128.187.97.20 On: Sat, 26 Apr 2014 20:43:57 STRONG AND CLARK Young University have synthesizedorgan and piano transient appears to be of little importance to this tones.As regardspiano tones,the choraleffects arising identification.7-n Again, in speech,consonants, which from the presenceof several strings at each note had are of much shorter duration than vowels, contribute to be reflectedin the synthesis2Since we are concerned more significantlyto the intelligibility22The harmonic only with the tones produced by single structures, content of a tone becomes richer with increasing no attempt is made here at examiningthe questionof intensity; yet, the timbre is only weakly intensity- choral tones--which is itself regarded as a separate, dependent.•a Complex instrumental tones can be massivesubject. Fletcher et al. found the partials of identifiedfrom only a few partials.•4 organ tonesto be harmonicfor solo tones (excluding mixtures).2 Risset, at Bell Laboratories,and his co- I. MATHEMATICAL REPRESENTATION workers have synthesized trumpet tones with due Ideally, the mathematicalrepresentation of the pres- regardto economyof specificationand objectivity, and sure wave producedby a musical instrument should have found no evidencefor inharmonicpartials? Their be complete enough so that pressurewaves created system was such that they limited their synthesisto from the representationand producedby the musicalin- partials below 4000 cps, a fact that leads to a rather strument are indistinguishablevia the auditory process. muffled, nonbrilliant character for their sounds. It Distinguishabilityby measuringmethods other than the appears that only the signals of high quality were auditoryprocess is regardedas irrelevant for our present presentedto auditors.Freedman, at the University of purposes.Second, the representationshould contain Illinois, has describedan analysis-synthesisscheme and only elementshaving auditory significancein charac- has synthesizedone tone for each of the following terizing the tone. Though not necessary,it is highly instruments' clarinet, trumpet, saxophone,bassoon, desirablethat the representationbe readily generated and violin) Freedman started from the wave equation in the laboratory to enhance its utility--with the and heuristically generalized his resulting represen- principle of parsimony as a collorary. The selection tation, essentiallyto accountfor the propertiesof the of sucha representationrequires knowledge and insight sound sourcethat are largely unknown. He then used far beyond thosepresently available. time-limited Fourier transforms4.5 to computevarious However, certain facts served to narrow our choice parameters,at the expenseof very great amounts of of representations.It was observed that the signals computertime. He did find inharmonicpartials for the created by an important classof musicalinstruments saxophone. have a middle section (pseudosteadystate) during The Fourier analysesø of Luce and Clark on the which the signalis approximatelycyclically repetitive, temporal dependencesof the partials of 14 nonper- althoughthe waveformsare, in general,very complex. cussive orchestral instruments is the basis of the Instruments producing such signals are called non- presentwork. Theseauthors found that, within a given percussive.Although a frequencyis quite precisely tone, the durationsof the attack transientsfor different definedfor thesesignals, the use of a Fourier seriesof partials will differ. Also, there may be some "Zitter- trigonometricfunctions with constant coefficientsis bewegung"in the tone of an instrument,in that the barredby theknown significance of the attack transient, fundamental frequency may fluctuate in a fast and during which the amplitude of the wave and usually quasirandommanner. Waveform modulationmay be its shape are changingmarkedly. A Fourier-integral quite pronouncedduring the steady state, especially representation,though complete,is obviouslyaurally in flute tones. The less intense partials may display redundant as regards characteristicsthat distinguish short-term amplitude variations during the steady state, while the more intense partials are of nearly 7 M. Clark, D. Luce, R. Abrams, H. Schlossberg,and J. Rome, "Preliminary Experiments on the Aural Significanceof Parts of constant amplitude from one cycle to the next. The Tones of OrchestralInstruments and on Choral Tones," J. Audio spectral envelopedetermines the relative amplitudes Eng. Soc. 11, No. 1, 45-54 (1963). of the harmonicswith considerableaccuracy for the 8 K. W. Berger, "Some Factors in the Recognitionof Timbre," J. Acoust.Soc. Am. 36, 1888-1891 (1964). steady state.ø 0 E. L. Saldanha and j. F. Corso, "Timbre Cues and the Work other than that in analysisalso served to guide Identification of Musical Instruments," j. Acoust. Soc. Am. 36, our synthesis.The attack transient appearsto be of 2021-2026 (1964). •0H. V. Eagleson and O. W. Eagelson, "Identification of preponderantimportance for identifying the tones of Musical Instruments When Heard Directly and over a Public nonpercussivemusical instruments, and the decay AddressSystem," j. Acoust.Soc. Am. 19, 338-342 (1947). n W. H. George,"A Sound Reversal Technique Applied to the a j. C. Risset, "Computer Study of Trumpet Tones," J. Acoust. Study of Tone Quality," Acustica4, 224-225 (1954). Soc. Am. 38, 912(A) (1965). •' J. C. R. Licklider and G. A. Miller, Handbookof Experimental 4 M.D. Freedman, "A Technique for the Analysis of Musical Psychology,S.S. Stevens,Ed. (John Wiley & Sons, Inc., New Instrument Tones," Tech. Rept. No. 6 (Elec. Eng. Res. Lab., York, 1951). Univ. I11.,