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Quality of Violin, Viola, 'Cello, and Bass-Viol Tones. I

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Quality of Violin, Viola, 'Cello, and Bass-Viol Tones. I THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA VOLUME 37, NUMBER 5 MAY 1965 Quality of Violin, Viola, 'Cello, and Bass-Viol Tones. I HARVEYFLETCHER, E. DONNELLBLACKHAM, AND O. NORMANGEERTSEN Brigham Young University,Provo, Utah 84601 (Received 9 November 1964) The elementsthat are important in the identificationof the violin, viola, 'cello,and bass-violtones were analyzed.These elementswere found to be the harmonicstructure of the middle portion of the tone; the harmonicstructure of the endingportion of the tone (certainpartials decayed rapidly leavingan afterring); the attack and decayof the tones;the vibrato (whenpresent) of the tones;and the noisesinherent in the mechanicsof producingthe tones.With the exceptionof vibrato, the importantelements were determined and successfulsynthesis was accomplished. By the useof a jury of observers,identification tests were made. A successfuldescription was arrived at when and only when synthetictones could not be identifiedfrom real tones. It was found that there is a vibrato both in frequencyand relative intensity. INTRODUCTION whim of the personproducing the tone. The frequency, the intensity,the vibrato, and the attack and decayare HISsearchpaper study reports on thethat qualitypart of of our musicalgeneral tonesre- produced with the guidanceof the player's ear rather which is concernedwith the violin, viola, 'cello, and than by any mechanicalmeans. For this reason, it is bassviol. The generalprocedure used in thisstudy is the difficult for a player to produce two or more tones sameas that describedin our two previouspapers2 ,2 that are alike. It will be seenthat, evenwhen the player The tonesare recordedon magnetictape. They then thinks that the tonesare alike, an analysisshows very definite differences. are reproducedfrom the tape and elementsthat are importantin identificationof themare analyzed. These The tonesfor this studywere produced by studentsof analysesenable one to constructsynthetic tones. Such musicwho were consideredgood musicians. They were synthetic tones are then comparedto the real tones askedto producefour successivetones that were alike, by an identificationtest, using a jury of observers. then to switchto anothernote and producefour other When suchsynthetic tonescannot be identifiedfrom tonesuntil they had coveredthe range of the instru- the real tones,then, and then only, can one be sure ment. Sometones were producedwith and somewith- out vibrato. The duration of the tones was between 1 that the analysisis correctand that all the elements such as frequency,intensity, partial-tone structure, and 3 sec. For discussion,the duration time has been attack and decay,underlying noise, and the variation divided into three parts; the beginningor attack, the of thesewith time for the durationof the tone, have central period, and the ending or decay. During all beengiven proper attention. It is well known that when thesephases, the amplitude and the frequencyof each suchmusical tones are recordedon the usualmagnetic- harmonic varied with time. It was found that during tape machinesthe phasesare changed,and conse- the centralportion the harmonicstructure changes were quentlythe waveformis changed.It is alsoknown that small, however,and could be imitated by a synthetic thesechanges do not change the quality of tonesas heard tone having constantharmonic structure. The attack is so fast that the harmonic structure by the ear, exceptin extremecases. The tonesfrom the violin,viola, 'cello,and bassviol during this beginningperiod was made the sameas for are somewhat like those from the human voice in that the central period. For some tones from stringedin- thereis a widevariation in qualitydepending upon the struments, the harmonic structure for the ending period is very different from that during the central • H. Fletcher,E. D. Blackham,and R. Stratton,"Quality of portion. The tone continuesafter the bow is removed, PianoTones," J. Acoust.Soc. Am. 34, 749-761(1962). • H. Fletcher,E. D. Blackham,and D. A. Christensen,"Quality and this part of the tone is referredto as the afterring. of OrganTones," J. Acoust.Soc. Am. 35, 314--325(1963). During the central period, there may be a vibrato 851 Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 128.187.97.22 On: Fri, 14 Mar 2014 23:04:15 852 FLETCHER, BLACKHAM, AND GEERTSEN sw 1 sw 2A TAPE REC ORDER ANPLIFER s•• 1 HIGH-SPEED LEVEL REFERENCE RECORDER OSCILLATOR VARIABLE SCHMITT A•PLIFIER TRICKIER DISCRININATOR STROBOCONN To measure, set • 2 to Overall lewel 1 Partial level 2 Partial frequency 3 Fro. 1. Block diagramof the systemused to measurethe relative intensity and frequencyfluctuations. that is a periodicvariation of both the frequencyand of our measurements. The tone with all its harmonics intensitylevel of the tone. The vibrato is an important is called the total tone. aspect of the quality of the tone. The frequenciesof Frequencylevel as used in this paper refers to the the partials of these central-periodtones were meas- readingof the Stroboconn,which givesthe interval in ured and found to be harmonic within the accuracy centssharp or flat from oneof the notesof the chromatic TONE 1 STNTItETIC TONE D o 1O 0 i 2 o 1 2 o 1 2 TIHE - •o$m8 Fro. 2. Frequencyand intensity level vs time for violin G'. Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 128.187.97.22 On: Fri, 14 Mar 2014 23:04:15 VIOLIN, VIOLA, 'CELLO, AND BASS VIOL 853 scale.It readsfrom C"', correspondingto a frequency type 2305). Sincethis level recordermeasures the true of 32.7 cps,to Ba-t-50cents, corresponding to a fre- root-mean-squarevalue of the input signal, the plot quencyof 4066.8cps. is independentof the waveshapeof the tone. To record the level versus time of a particular I. ANALYSIS OF VIOLIN TONES partial of a tone, the signal was first filtered by a The tonesselected for thesetests were G'-196, variable-frequency,variable-width, bandpass filter (HP G-392, G1-784, and G2-1568. These tones were con- model 302A). The filter is centeredon the average sideredto be typicalof thoseusually produced in a frequencyof the toneand the bandwidthis adjustedso as to includeall of the significantsidebands of the FM goodorchestra. The playerwas asked to producefour spectrumaccording to the expecteddeviation ratio. toneson each note that wereas nearly alike as possible. Eachof thesetones was analyzed to find (1) theinterval To recordthe frequencyversus time of any partial, in centsversus the time in seconds;(2) the intensity the filteredsignal was passed into a Schmitttrigger to level in decibels versus the time in seconds for the producea squarewave of the samefrequency as the filtered partial. Since the squarewave is rich in odd harmonic(usually the fundamental)used for deter- miningthe pitch; (3) the intensitylevel in decibels harmonicsthat changein frequencyin synchronism versus the time in seconds for the total tone. with the fundamental component, the variable- frequency FM discriminator could be set to detect the frequencyof oneof the higherharmonics of the square II. MEASUREMENT OF FREQUENCY AND INTENSITY LEVEL wave. By doing this, a small time constantin the dis- criminator is achieved and unwanted transients in the A blockdiagram of the systemused to measurethe output are avoided. With the discriminatorthus set, relativeintensity level fluctuations is shownin Fig. 1. its output was amplifiedand fed to the input of the In orderto plot theover-all level of theparticular tone, high-speedlevel recorder, which then plotted the the signalfrom the taperecorder was passed directly instantaneousrelative frequencyof the partial being to the high-speed(1000-dB/sec) level recorder (B&K analyzed.A static calibrationof this systemwas made TONE3 SYNTHETIC TONE I I I,t !,l lJ i / ^ ß • klv v v u U II •'Y'u o 10 nAAAA ' k • o o•10 o X 2 0 1 2 0 1 2 FIc. 3. Frequencyand intensitylevel vs time for violin G. Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 128.187.97.22 On: Fri, 14 Mar 2014 23:04:15 854 FLETCHER, BLACKHAM, AND GEERTSEN by useof a referenceoscillator and a Stroboconn,which In Fig. 3, the resultsfor G are given.It is seenhere measuresfrequency level to an accuracyof ! cent. that there is a strongvibrato both in frequencyand With theexception of theSchmitt trigger, the system intensitylevel. The strongintensity vibrato may be just describedwas composed of apparatusalready at due to the body resonanceof the violin. As the fre- hand.Consequently, it was not possible to designthe quencyof the tonemoves toward and away from reso- systemfor optimum performanceand the amount of nancefrequency, there are large changes in theamplitude usabledata obtained was limited. Some difficulty was of the fundamental.It will be noticedthat suchlarge causedby the slight hysteresiseffect in the Schmitt changesdid not occurin the synthetictone. No device triggercircuit. A newsystem is nowbeing developed was availableto producea synthetictone having a that will allowa moreextensive investigation to be separatecontrol of vibrato amplitudeand frequency. made. This is discussedlater. For G• and G2,the vibratoof the Samplesof thesemeasurements are shownin Figs. synthetictone was approximatelythe sameas for the 2-5, correspondingto G', G, G•, andG2. In Fig. 2, the real tone. It is convenient to define the extent of the threetop curves are for thefrequency variations of the frequencyvibrato
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