Attempts to understand the action of musical instruments at a level having some impact on the problem of musicians and instrument maker must face formidable unsolved problems in psychoacoustics as well as in classical physics. This review outline what is known about the physical properties of stringed instruments, with emphasis on the violin family, and tries to identify basic outstanding problem where progress may be hoped for within the next decade. One such area is assessment of the widely used simplest idealization of violin behaviour in which the driving at the bridge is assumed to be transverse, and the body is modelled as a ‘black box’ with one input and one output. Other major problem include the physical nature and psychoacoustical relevance of complex fine detail in the behaviour of the bowed string.
Get full access to this article
View all access options for this article.
References
1.
Note that some of the papers referred to below, as well as many others relating to violin acoustics, are reprinted in Musical Acoustics, Parts I and II, ed. by C. M. Hutchins (Benchmark Papers in Acoustics 5b6), Dowden, Hutchinson and Ross, distributed byWifey-Halsted, New Yorkand London (1975/1976), The relevant papers are marked * (Part I) and † (Part II) below.
2.
Much of the most recent work is as yet reported only in theCatgut Acoustical Society Newsletter. Readers having no access to this may write to: 112 Essex Avenue, Montclair, N.J. 07042, U.S.A.
3.
Boomsliter†P. C. and CreelW., Research potentials in auditory characteristics of violin tone. J. Acoust. Soc. Amer. 51, 1984–1993 (1972).
4.
Roe dererJ. C.. Introduction to the Physics and Psychophysics of Music, 2nd Edn., Springer-Verlag, New York (1975).
5.
BenadeA. H., fundamentals of Musical Acoustics, Oxford University Press, New York (1976). See alsoBenadeA. H., Musical acoustics today: a scientific crossroads in Proc. 9th Int. Congr. on Acoustics, Madrid (1977); and Musical Instruments in Encyclopaedia of Physics, ed. by R. Lerner and G. Trigg, Dowden, Hutchinson and Ross, distributed by Wiley-Halsted, New York and London (1978).
6.
Heron-AlienE., Violin Making as it Was and Is, Ward Lock, London(reprinted1976).
7.
CremerL.,*Die Geige aus der Sicht des Physikers. Nachr. Akad. Wiss. Göttingen: II Math, Physik, Kl. 12, 223–259 (1971).
8.
CremerL and LehringerF., Zur Abstrahlung geschlossener Körperoberflächen. Acustica29, 137–147 (1973); J. Meyer, Akustik und musikalische Aufführungspraxis, Verlag das Musikinstrument, Frankfurt (1972).
9.
RonanC., The music of the spheres. Interdiscip, Sci. Rev. 1, 149(1976).
10.
Hermann Hesse's novel is set in a society whose culture is founded on a supposed union of mathematics and music.
11.
LighthillM. J.M. Artificial intelligence: a paper symposium. SRC report, Science Research Council, London (1973).
12.
RissetJ. C. and MathewsM. V., Analysis of musical instrument tones. Physics Today22, 2, 23 (1969), An earlier example of analysis-synthesis work is H. Fletcher,† E. D. Slackham andGeertsenO. N., Quality of violin, viola, cello and bass viol tones t. J. Acoust. Soc. Amer. 37, 851–863 (1965).
13.
BartowH. B., NarasimhanR. and RosenfeldA., Visual pattern analysis In machines and animals. Science177, 567–675 (19721.
14.
MooreB. C. J., Frequency difference limens for short-duration tones. J. Acoust, Soc. Amer. 54, 610–619 (1973); see also p. 210 of the first reference of 3.
15.
SchumacherR. T., Some aspects of the bow. Catgut Acoustical Society Newsletter24, 5–8 (1975).
16.
SchellengJ. C.,*The bowed string and the player. J. Acoust Soc. Amer. 53, 26–41 (1973).
17.
SaundersF. A., A scientific search for the secret of Stradivari. J. Franklin Inst. 229, 1–20 (1940).
18.
RayleighJ. W. S., The Theory of Sound, § 137. Dover, New York (1945).
19.
MorseP. M. and IngardK. U., Theoretical Acoustics. McGraw-Hill, New York (1968).
20.
Minnaert*M. and VlamC. C., Vibrations of the violin bridge.Physica4, 361–372 (1937); also E. Barton and T. Ebblewhite, Vibration curves of violin bridge and strings. Philos. Mag. 20, 456 (1910).
21.
ReinickeW.,* Übertragungseigenschaften des Streich-instrumentenstegs. Catgut Acoustical Society Newsletter19, 26–34 (1973). See also Ref. 3, p. 537, and Ref. 5, p. 238.
22.
HutchinsC. M., Personal communication.
23.
RamanC. V., On the mechanical theory of vibrations of bowed strings. Indian Assoc. Cult. Sci, Bull. 15, 1–158 (1918). The beginning of this monumental work is reprinted in the first Benchmark volume*.
24.
SchellengJ. C.,* The violin as a circuit.J. Acoust. Soc. Amer. 35, 326–338 (1963). For a further explanation of certain crucial points see alsoSchellengJ. C.,† On the polarity of resonance. Catgut Acoustical Society Newsletter10, 14–18 (1968).
25.
JanssonE. and SundinH., A pilot study on coupling between top plate and air volume vibrations. Pbys. Scr. 2, 243–256 (1970).
26.
Examples of black boxes with response functions which have complex structure producing drastic audible effects but whose amplitudes, and hence response curves in the sense usually defined, are constant, may be found inStuartJ. R., An approach to audio amplifier design. Wireless World79, 387–391 (1973), and M. R. Schroeder and B. F. Logan, ‘Colourless’ artificial reverberation. IRE transactions on audio9, 209–214 (1961).
27.
MetnelH.,†Über die Beziehungen zwischen Holzdicke, Schwingungsform, Körperamplitude und Klang eines Geigenkörpers. Elek. Nachri. Tech. 14, 119–134 (1937); F. Eggers.† Untersuchung von Corpus-Schwingungen am Violoncello. Acustica 9, 453–465 11959); J. C. Luke, Measurement and analysis of body vibrations of a violin. J. Acoust. Soc. Amer. 49, 1264 (1971).
28.
AgrenC. H. and StetsonK. A.,†Measuring the resonances of treble viol plates by hologram inter-ferometry and designing an improved instrument. J. Acoust. Soc. Amer. 51, 1971(1972).
29.
JanssonE.,†MolinN. E. and SundinH., Resonances of a violin body studied by hologram interferometry and acoustical methods. Phys. Scr. 2, 243 (1970).
30.
Reinicke†W. and CremerL., Application of hologram interferometry to the vibration of bodies of stringed instruments. J. Acoust. Soc. Amer. 48, 988–992 (1970).
BetdieI. P., reported in L. Cremer, Darstellung des Geigenkörpers als ein Schwingungssystem mit vier Freiheitsgraden im tiefen Frequenzbereich. Nachr. Akad. Wiss. GöttingeniII Math. Phys. Kl. 1, 1–11 (1976). Partially summarised in I. P. Beldie, Vibration and sound radiation of the violin at low frequencies. Catgut Acoustical Society Newsletter 22, 13–14 (1974).
33.
SaundersF. A.,*The mechanical action of violins. J. Acoust. Soc. Amer. 9, 81–98 (1937); †The mechanical action of instruments of the violin family. J. Acoust. Soc. Amer. 17, 169–186 (1946); tRecent work on violins. J. Acoust. Soc. Amer. 25, 491–498 (1953).
34.
HutchinsC. M., A note on the function of the soundpost. Catgut Acoustical Society Newsletter 21, 27–28 (1974); The Helmholtz air resonance of the cello and baritone. Catgut Acoustical Society Newsletteri26i 5–6 (1976); and C. H. Ågren, Experimental findings concerning cavity-assisted resonances in stringed instruments with a soundpost. Physica Scripta 14, 179–186 (1976).
35.
CaldersmithG., Low range guitar function and design. Catgut Acoustical Society Newsletter27, 19–25 (1977); The guitar as a reflex enclosure (In press) J. Acoust. Soc. Amer. (197B).
36.
JanssonE. V.,† On higher air modes in the violin. Catgut Acoustical Society Newsletter 19, 13–15 (1973) and Acoustical properties of complex cavities. Acustica 37, 211–221 (1977).
37.
MeineH.),* Regarding the sound quality of violins and a scientific basis for violin construction. J. Acoust. Soc. Amer. 29, 817–822 (1957). Also, many more response curves may be found in previous papers by Meinett in German, cited in this reference.
38.
MeyerJ., Akustische Untersuchung zur Klangqualität von Geigen. Instrumentenbau (Musik International)29, 2–8 (1975). (Abridged English translation in Catgut Acoustical Society Newsletter23, 2–6.)
39.
A standard electroacoustic technique for driving an instrument has yet to be universally adopted. An inexpensive method of exerting an approximately constant force is that advocated by Hutchins,56 using a very light moving coil placed in a fixed magnetic field. The coil is driven at constant current (not at constant voltage as for a loudspeaker) as frequency is varied.
40.
BradleyJ. S. and StewartT. W. W., Comparison of violin response curves produced by hand bowing, machine bowing and an electromagnetic driver. J. Acoust. Soc. Amer. 48, 575 (1970).
41.
HutchinsC. M.,† Instrumentation and methods for violin testing. J. Audio Eng. Soc. 21, 563–570 (1972). The reader is cautioned that the curve in Fig. 8 labelled ‘Hutchins system'37 was in fact taken by another technique, invalidating the comparison. (This misunderstanding had not come to light when the paper was published.) See also C. M. Hutchins, Variations in violin testing. Catgut Acoustical Society Newsletter 15, 15–21 (1971).
42.
JanssonE. and SundbergJ., Long time average spectra.,. part I. Acustica34, 16 (1975).
43.
FletchertH. and SandersL. C., Quality of violin vibrato tones. J. Acoust. Soc. Amer. 41, 1534 (1967).
44.
CoxS. and FellgettP. B., Equivalent-circuit investigation of the low frequency behaviour of stringed instruments. Catgut Acoustical Society Newsletter, in press.
45.
HutchinsC. M.,† Founding a family of fiddles. Phys. Today20, 2, 23 (1967). This article describes a pioneering effort to build a full consort of instruments scaled from the violin. The musical uses of this ‘new violin family’ are now being explored at the Royal College of Music, London, and elsewhere.
46.
SchellengJ. C.,* Acoustical effects of violin varnish. J. Acoust. Soc. Amer. 44, 1175–1183 (1968). See also P. B. Fellgett, Working speculations about ‘magic varnish’. Catgut Acoustical Society Newsletter 28, 24–25 (1977).
47.
SchellengJ. C.,*The action of the soundpost. Catgut Acoustical Society Newsletter16, 11–15 (1971).
See pp. 29–30of H. Meinel.†Über Frequenzkurven von Geigen. Akust. Z. 2, 22–23 (1937).
50.
LeippE., Le Violon, Hermann, Paris (1965).
51.
MathewstM. V. and KohutJ., Electronic simulation of violin resonances, J. Acoust. Soc. Amer. 53, 1620–1626 (1973).
52.
McIntyreM. E. and WoodhouseJ., Toward a psychoacoustically realistic violin physics. Catgut Acoustical Society Newsletter22i18–19 (1974).
53.
GorrillS., A viola with electronically synthesised resonances. Catgut Acoustical Society Newsletter24, 11–13(1975).
54.
PolsL. C. W., ThL J.van derKamp and PlompR., Perceptual and physical space of vowel sounds.J. Acoust. Soc. Amer. 46, 458–467 (1969).
55.
GabrielssonA. and JanssonE. V., An analysis of long-time-average spectra of twenty-two quality rated violins. Catgut Acoustical Society Newsletter27, 13–19 (1977).
56.
HutchinsC. M., A sequence of articles inCatgut Acoustical Society Newsletters5b6b8b14b15b16 and19.
57.
McIntyreM. E. and WoodhouseJ., The influence of geometry on linear damping. Acustica39, 209–224 (1978).
58.
HutchinsC. M.,t K. A. Stetson and P. A. Taylor, Clarification of ‘free-plate tap tones’ by hologram interferometry. Catgut Acoustical Society Newsletter 16, 15–23 (1971).
59.
HearmonR. F. S., Elasticity of wood and plywood. H.iM.S.O. Forest products research special report no. 7 (1948).
60.
For example I. Barducci* andPasqualiniG., Misura dell ‘attrito interno e delle costanti elastiche del legno. II Nuovo Cimenta5, 5, 416–466 (1948).
61.
HainesD. W., HutchinsC. M., HutchinsM. and ThompsonO. A., A violin and a guitar with graphite-epoxy composite soundboards. Catgut Acoustical Society Newsletter24, 25–28 (1975).
62.
For example response curves for guitar bodies are shown inHainesD. W. and HaltiwangerM. A., A study of body resonances and their influence on the performance of a folk guitar. Catgut Acoustical Society Newsletter24, 29–34 (1975). Other studies of guitar acoustics include F. T. Dickens, Tuning of guitar plates. Catgut Acoustical Society Newsletter 26, 19–20 (1976); and H. L. Schwab and K. C. Chen, Finite element analysis of a guitar soundboard. Catgut Acoustical Society Newsletter25, (1976).
63.
HelmholtzH., On the Sensations of Tone, Dover, New York(English translation of the German edition of1877) pp. 80–88(1954).
64.
RohloffE..†Ansprache der Geigenklänge. Z. Angew. Phys. 17, 62–63 (1964). This paper reports experiments suggesting that the subjective ‘ease of speaking’ of a violin is not correlated with the steady-state tolerance at all, but rather with the player hearing enough extreme high frequency (4–8 kHz) in the starting transient. Experiments like these, attempting controlled modification of the feedback to the player's ears, deserve to be pursued further.
65.
RamanC. V.,*Experiments with mechanically played violins.Proc. Indian Assoc. Cultiv. Sci. 6, 19–36 (1920).
66.
A technicality which we gloss over here is that this is not true of the ‘air resonance’, the reason being that its effect on bridge motion is more like that of a ‘parallel’ than a ‘series’ resonance, in the electrical circuit analogy.22
67.
RamanC. V.,*On the ‘wolf-note’ in bowed stringed instruments. PhilosiMag. Ser. 6b32, 391–395 (1916).
68.
Descriptions may be found in A. H. Benade3 (p, 574), andSchellengJ. C., Adjusting the wolftone suppressor. American String Teacherp. 9, Winter1967.
69.
Firth*I. M. and BuchananJ. M., The wolf in the cello. J. Acoust. Soc. Amer. 53, 457–463 (1973); alsoI. M. Firth, The wolf tone in the cello: acoustic and holographic studies. Royal Institute of Technology (KTH), Stockholm, Speech Transmission Laboratory, Quarterly Progress and Status Report, pp. 42–56, Jan. 1975,
70.
HancockM., The mechanical impedance of violin strings, I. Catgut Acoustical Society Newsletter23, 17–26 (1975). Part II is to appear in the Catgut Acoustical Society Newsletter in 1977.
71.
FriedlanderF. G., On the oscillations of the bowed string. Proc. Cambridge Philos. Soc. 49i 3, 516 (1953).
72.
KellerJ. B., Bowing of violin strings. Commun, Pure and Appl. Math. 6, 483 (1953).
73.
CremerL. and LazarusH., 6thICA Congress, Tokyo, N.2–3 (1968).
74.
CremerL., Der Einfluss des ‘Bogendrucks’ auf die selbsterregten Schwingungen der gestrichenen Saite. Acustica30, 119–136 (1974). ‘English translation of an earlier version in Catgut Acoustical Society Newsletter 18 and19, pp. 13–19 and 21–25.
75.
Then there is no significant amplitude dependent sharpening, due simply to the increased mean tension of the string, to confuse the issue.
76.
McIntyreM. E., SchumacherR. T. and WoodhouseJ., New results on the bowed string. Catgut Acoustical Society Newsletter28 (1977).
77.
McIntyreM. E. and WoodhouseJ., On the fundamentals of bowed string dynamics. Submitted toAcustica (1977).
78.
SchumacherR. T., Self-sustained oscillations of the bowed string. Submitted toAcustica (1977).
79.
Ripple waveforms are simitar to the waveforms generated by the jew's harp, which, together with their perceptual correlates, are discussed inAdkinsC. J., Investigation of the sound-producing mechanism of the jew's harp, J. Acoust. Soc. Amer. 55, 667–670 (1974). Ripples are not to be confused with Helmholtz's ‘crumples’,61 which are described by Raman's model21 and are due to weakness of certain harmonics when the bow divides the string in a simple ratio.14,76
80.
E.g.CardozoB. C., The perception of jittered pulse trains. InFrequency analysis and periodicity detection in hearing, ed. PlompR. and SmoorenburgG. F., SijthoffA. W., Leiden (1970).
