SOUND GENERATION WINDS STRINGS COMPUTERS Papers by Benade, Chowning, Hutchins, Jansson, Alonso Moral given at seminars of The Committee for the Acoustics of Music Publications issued by the Royal Swedish Academy of Music No. 29 - 2 - CONTENTS Page Preface J .M. Chowning Computer synthesis of the singing voice Wind instruments and music acoustics A.H. Benade Introduction 15 Sound production in wind 17 instruments Sound radiation from 47 instruments Instrument sound in a room 76 Re£erences 99 Bowed instruments and music acoustics C.M. Hutchins History of violin research 102 How to make a violin 130 How the violin works 151 Tuning of violin plates 165 The new violin family 182 References 201 E.V. Jansson Function and factors deter- mining quality of the violin E .V. Jansson- Recent violin research at KTH 229 J. Alonso Moral Sound examples ISBN 91-85428-13-3 @ 1980 by Kungl. Musikaliska Akademien, Stockholm Eken2is Tryckeri AB, Ekenzs, Finland PREFACE On ?lay 19 and November 10 1979, the Committee for Music Acoustics of the Royal Swedish Academy of Music arranged two full day seminars at the Royal Institute of Technology (KTH). The seminars were devoted to wind and bowed instrument acous- tics with A.H. Benade and C.M. Hutchins as the main talkers. They were arranged in cooperation with the Center for Speech Communication Research and Music Acoustics, KTH. All contri- butions presented at the seminars are now published in this book except for the final panel discussion at the wind instru- ment seminar with A.H. Benade, J.M. Chowning, E. Jansson, S. Berger and C. Carp as participants. This book is the fourth seminar proceedings published by the Committee. As previously, the sound illustrations are collected in a grammophone record. A practical result of the bowed instrument seminar might be mentioned. A full setup of Hutchins' new violin family instru- ments was purchased by and are kept for musical use at the Stockholm Music Museum. The editing work has been done by Erik Jansson and myself. The examples of music played on the new violin family was edited by Semmy Lazaroff and the grammophone record was pro- duced by Lennart Fahl6n. Printable copies of all Dapers except Benade's were pre~aredby Marianne Beskow of the Music Academy, and Sven Wilson of the same Academy is responsible for the layout. KTH, September 1980 Johan Sundberg President of the Committee for Music Acoustics COMPUTER SYNTHESIS OF THE SINGING VOICE by John M. Chowning Center for Computer Research in Music and Acoustics Department of Music Stanford University Stanford, California Introduction The work represented here demonstrates above all that accept- able synthesis of a sung tone demands careful attention to rather simple characteristic details of the real target tone which are Largely -independent of the synthesis technique. While the particular spectral content of a wave may be achieved by a variety of synthesis techniques, "naturalness" depends upon the temporal characteristics of very basic de- scriptors such as pitch and loudness, and spectral changes during the attack-decay portions of the tone. Although fre- quency modulation (FM) synthesis has been used to simulate some orchestral instrument tones (Schottstaedt 1977, Morrill 1977), the singing voice seems to remain the province of synthesis models borrowed from speech research (Sundberg 1978, Moorer 1979). The purpose of this paper is to show a strategy for the use of FM in the synthesis of two cases of the singing voice 1) a soprano, and 3) an un-naturally low male voice we might call basso profodissimo! In as much as the basis concepts underlying FM synthesis are by now well-known (Chowning 1973) and the synthesis pro- gram which was used, MUSIC 10, is not unlike many others in general use (Mathews 1970), detailed descriptions will not be presented here. Frequency Modulation Tone Synthesis The fundamental FM algorithm is based upon the output of a modulating oscillator which adds to the frequency term of a carrier oscillator thereby producing a complex waveform. This is expressed in the equation e = A sin ( 27~f t + Isin 27Tfmt1 eq. 1 C where e = the instantaneous amplitude of the carrier A = the peak amplitude of the carrier f c = the carrier frequency f,= the modulating frequency I = the modulation index The ratio of the carrier and modulating frequencies, fc/fm, determines the relative interval of the component frequen- cies in the modulated carrier signal while the modulation index determines the amplitudes of the components and the overall bandwidth of the signal. The modulation index is the ratio of the depth of modulation or peak deviation to the modulating frequency. Of particular interest in the app- lication of FM to voice synthesis presented below are ratios of frequencies where f = Nf, and 1 $ N and where N is an integer. C The spectra resulting fron this class of ratios are such that the frequency components form the harmonic series with f as the fundamental. m There are a number of useful extensions of this basic al- gorithm, l) summing the outputs of two or more of the basic algorithm in parallel, 2) one carrier oscillator and two or more modulating oscillator in parallel, 3) one carrier oscil- lator and two ormore modulating oscillators in series and 4) two or more carrier oscillators and one modulating oscil- lator, to name some of the basic types of extensions. It is the last of these which is appropriate to voice synthesis. General Characteristics of Natural Soprano Tones Spectral representations of the attack, quasi steady-state, and decay portions of recorded soprano tones show that for most vowel timbres and through the greater part of the range 1) there is a weighting of the spectral energy around the low order harmonics with the fundamental as the strongest harmonic, thus supporting the theory that in female sing- ing the lowest formant tracks the pitch period (Sundberg 1978), 2) there are one or more secondary peaks in the spectrum, depending on the vowel and fundamental pitch, which cor- respond to resonances of the vocal tract or upper formants. 3) the formants are not necessarily at constant frequen- cies independent of the fundamental pitch, but rather follow formant trajectories which may either ascend or de- scend, depending on the vowel, as a function of the fun- damental frequency (Sundberg, 1978), 4) the upper formants decrease in energy more rapidly than does the lowest formant when a tone is sung at de- creasing loudnessess, 5) only the lowest formant is prominent at the amplitude threshholds of the attack and decay protions, while the upper f ormants only become pronounced as the overall amplitude of the signal approaches the quasi steady-state, 6) there is a small but discernable fluctuation of the pitch period even in the singing condition without vibrato. .FM Model for Synthesized Singing Voice - Soprano- For the simplest FM model of sung soprano tones two formants are included, the lowest formant and the vost dominant of the upper formants. Therefore, one oscillator can be used to modulate two carrier oscillators. The frequencies of the modulating oscillator and the first carrier are always set to the frequency of the pitch of the tone, while the fre- quency of the second carrier oscillator is set at that har- monic frequency closest to the 2nd formant frequency. In this model the various parameters, or terms, of the FM equation are computed from the basic musical descriptors of overall amplitude and fundamental pitch frequency and from a set of tables which form the data base for the terms at selected pitches through the soprano range. In this sense, then, it is an adaptive algorithm since all of the computa- tion is based upon the following two "performance" variables. Amp = overall amplitude of the signal, where 05.AmpF1.0, Pitc 4 =fundamental pitch frequency, , HZ) G~(1568 Hz). where G 3 (195.9 5 .Pitch<-- The modulating signal is defined to be M = sin2 * fmt eq. 2 where M = the instantaneous frequency deviation of the modulating signal f = the modulating frequency 4 Pitch m The signal resulting from the sum of the two modulated carriers is e = Alt sin(2~f t + I~M) + cl eq.3 + ~mp'W Apt sin(2n f t + 12M) where c 2 , e = the instantaneous amplitude of the sum of the two modulated carrier signals A = the relative amplitude of the second carrier, 2 0.0 L. A,L 1.0, L A = the relative amplitude of the first carrier = 1.0-A 1 2 fcl= the first carrier frequency = Pitch = the second carrier frequency = Nf , where N is an £c2 m integer I1 = the modulation index for the first carrier I2 = the modulation index for the second carrier The data base used for the computation of the amplitudes, indices of modulation, and the second carrier frequency is in the form of tables, where there is a set of four tables for each vowel as represented in Tables 1-4. The data is stored for the frequencies of pitches. and the data for the intervening pitches is computed by linear interpolation. Thus, for the frequency of the second carrier, fc2 - Nfm, the integer N is determined by taking the integer part of the following division'after rounding (upper formant frequency) Pitch + 0.5 where the upper formant frequency is computed from Table 1. as a function of Pitch. The values for the amplitude and indices of modulation are computed directly from the tables Upper formant frequency (from which f c 2 is computed) A, (contribution of second carrier) I, (Modulation index for first carrier) I, (Modulation index for second carrier) Tables 1.