Abstract
The use of vibrating strings in musical instruments was certainly known to the ancient Greeks. However, bowed string instruments probably originated in Asia. One author suggests that the invention of the bow on that continent may be traced to the fact that Asiatic peoples were among the first to use horses as domestic animals—horse hair being the most suitable material for stringing a bow. The southern Slavs actually used horsehair for the bow and the string in a primitive instrument called the gusle. The earliest instruments had crude sound boxes consisting of a drum or hollow wooden tube. The two-stringed Chinese erhu, which used two silken strings with the bow hair passing between them, is still in use today and may even be heard in the New York subways.
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- 1.
See Yilu Zhao, “Asian Music Accompanied by the A Train,” New York Times, July 6, 2004, p. B1. The sound may be heard on a CD recorded by erhu virtuoso YU Hon-mei (Wind Records SMCD-1010, 1998).
- 2.
According to Heron-Allen (1885), the rebab was in use in Spain for centuries before 1200 AD and still exists in the Basque districts of the Pyrenees under the names “rabel” and “arrabel.” He adds that it was seldom mentioned because of its “rudeness.”
- 3.
- 4.
An 8-ft “viola pomposa” stop was found on some pipe organs of Bach’s time.
- 5.
Apel (1972, p. 907) asserts the attribution of this invention to J.S. Bach is unfounded and based on unreliable sources dating from 32 to 42 years after Bach’s death in 1750.
- 6.
Letter from C.P.E. Bach to his father’s biographer Johan Nicolaus Forkel in 1774 (quoted by Allan Kozinn in the New York Times, 7/16/2003, page AR 24).
- 7.
Silverman (1957, p. 244) has “before” and “after” photographs of San Domenico.
- 8.
Lawrence Witten is more widely known as the person who sold the Vinland Map to Yale University.
- 9.
Faber (2005, p. 25) suggested that Stradivari never was apprenticed to Nicolo Amati. The usual assumption is based on one violin (the oldest known) made by Stradivari in 1666 in which the label was inscribed “Antonius Stradivarius Cremonensis Alumnus Nicolaii Amati”. However, the word Alumnus (meaning “pupil of”) was dropped from his labels by the time his next violin was made in 1667 and never appeared on any of his later violins. Faber suggests the wording may have been used to help sell his first violin by using Nicolo Amati’s name and that Amati himself may have objected to that practice. Faber goes on to note that Stradivari was already an expert wood carver and inlayer at the age of 13, before coming under the influence of Amati and that the few examples of fancy inlaid work on Amati instruments may actually have been done by Stradivari. Faber suggests that Francesco Ruggieri was a more probable teacher of Stradivari in the art of violin making.
- 10.
- 11.
Galileo Galilei is thought to have bought a violin by Nicolò Amati for his nephew. In a letter dated May 28, 1638, Father Micanzio regretted than he had not been able to get it for less than 15 ducats! [One ducat contained ≈ 3.49 g of gold, hence 15 ducats would be worth about $72 in the fall of 2004.] Galileo had been advised by the Musical Director at St. Marks in Venice that the Cremona instruments were incomparably better and much cheaper than those made in Brescia (Hill et al. 1902, pp. 240–243) It has also been suggested that the Cremona violin purchased by Thomas Jefferson for £5 in 1768 was made by Nicolò Amati Salgo (2000, p. 17). Salgo (Salgo 2000, p. 18) went on to suggest that Jefferson probably acquired a Tourte-style bow while serving as a diplomat in Paris, despite his (by then) almost crippled right wrist.
- 12.
Sacconi’s book The Secrets of Stradivari had as a main thesis that there actually were no secrets and that everything Stradivari knew was well-known to other luthiers of the period.
- 13.
The most recent, record-breaking sale of a Stradivari violin (the 1707 “Christian Hammer”) was for $3.5 million on May 16, 2006. However, Sherlock Holmes only paid 55 shillings for a Strad worth 500 guineas (see Conan-Doyle 1981). Faber (2005, pp. 214–216) gave a careful summary of the sale prices of various instruments by Stradivari; Faber converted the currency used to dollars and corrected the values for inflation as of 2003.
- 14.
Some claim that terpenoid resin can rejuvenate the spruce in a sound board.
- 15.
Those who have seen the 1998 movie Hilary and Jackie might suspect that leaving it out in a snow storm overnight was the trouble.
- 16.
The Hill et al. (1931) note that the quality of Del Gesu’s workmanship deteriorated toward the end of his life. One luthier suggested to me that the unusual brilliance and harmonic content found in the later del Gesu instruments arose because he used extreme quantities of varnish to cover up his mistakes in wood carving.
- 17.
The Hill et al. (1931) note that J.B. Guadagnini spent a short time in Cremona in 1758, but he was hardly a permanent resident.
- 18.
The Heberlein-Taylor violin was recently donated by Hugh Taylor to the San Francisco Symphony. The Concert Master of that orchestra also has the use of the 1742 Guarneri del Gesu previously owned by Jascha Heifetz. In contrast, Jack Benny bequeathed his 1729 Strad to the Los Angeles Philharmonic.
- 19.
However, power can be a liability. The recent legal feud between members of the Audubon Quartet may have come about in part because the first violinist acquired a 1735 Carlo Bergonzi instrument capable of drowning out the rest of the quartet. (See Daniel J. Wakin, “The Broken Chord”, in the New York Times, December 11, 2005, p. AR 1.) They solved the problem by firing the first violinist.
- 20.
According to Silverman (1957, pp. 196–198), Vuillaume was such an expert that (working with physicist Felix Savart) he secretly made a copy of Paganini’s Guarneri del Gesu (“The Cannon”) while the instrument was on loan for repair that Paganini himself couldn’t tell from the original. (However, a later attempt to repeat that experiment failed, probably due to poorer quality wood.) Faber (2005, p. 116) presents a more prosaic version of this story: The color of the varnish was quite different, as was the tone quality. But Paganini still liked it.
- 21.
Silverman’s account of the life of Luigi Tariso is very engaging, even if you don’t play the violin. (His 1957 book also contains numerous color photographs of instruments from the Golden Age of Cremona.)
- 22.
Skeptics note that Alard’s father-in-law (who bought and sold the Messiah several times) was a master at building fake violins and might have been good at concocting fake stories to go with them. At one point, suspicion of the Messiah’s authenticity arose from a tree ring analysis suggesting the wood was cut after Stradivari died. However, a recent more thorough study by Grissino-Mayer et al. (2004) implied that the tree rings dated between 1577–1687, well before the completion of the Messiah in 1716. In the account by Silverman (1957, p. 45), Sister Francesca supposedly told Tarisio of her grandfather’s “most perfect violin called Le Messie” on her death bed in 1809—long before Tarisio met Vuillaume (1827) and still longer before Alard could have christened it “The Messiah.” Another doubter, violinist Joseph Gold (private communication) thought that the purfling on the instrument did not look up to par with the other work of Stradivari.
- 23.
One wag commented that of the original 1116 Stradivari instruments made by the great master, over 4000 still exist. According to the Hills, the Italians themselves began the habit of putting false labels on these instruments, a tradition carried on by Vuillaume. According to Faber, the Messiah is the most-copied violin in the world. In case you want to make one yourself, the Heinrich Dick Company of Metten, Germany sells a kit with precut wood.
- 24.
Helmholtz obtained an equivalent result in a somewhat different manner.
- 25.
A more rigorous solution for that case was given by Raman (1918).
- 26.
Pickering notes that the word chorde in Greek originally meant the intestines of animals, just as the word gut means today.
- 27.
In contrast to harpsichord and piano strings, a large damping factor is desirable for the strings on bowed instruments. Here, in contradistinction to the keyboard instruments, one does not want the tone to persist long after the excitation process has stopped.
- 28.
See Jansson et al. (1997).
- 29.
Another kind of “sound post” was invented by the Belgian cello virtuoso Adrien-François Servais (1807–1866) who became so fat that he could no longer support the instrument between his knees (the traditional method used since the time of the viola da gamba.) He designed an end-pin to support the instrument on the floor, an innovation that has since been adopted by most modern cellists. Faber (2005, p. 131) suggests that vibrations from the cello may be enhanced by coupling through the end pin to resonances in the wooden floor of a stage.
- 30.
Because the main body of the violin is symmetric about the long dimension, it is relatively easy to adapt the instrument to left-handed players merely by interchanging the bass bar and sound post locations and reversing the bridge. Thus, for example, the left-handed Austrian violinist Rudolph Kolisch (1896–1978), founder of the Kolisch Quartet, and Charlie Chaplin could easily be accommodated. (Accommodating left-handed pianists would be much more of a problem.)
- 31.
Although modern bridges are generally made of hard maple, they sometimes contain a V-shaped insert of still-harder ebony at the location of the E string to minimize the danger of that thin wire cutting into the bridge.
- 32.
Acoustic data for some twenty-one different modern violin bridges was given by Atwood (1997).
- 33.
Cremer (1981), p. 206) suggested that the 2 ft of the bridge transmitted sound very differently and that the bridge acts like an electric circuit with four input terminals and two output terminals.
- 34.
Model SH SV2 made in Erlangen, Germany and distributed by Shadow Electronics. These elements are said to have nearly constant response within the audio band up to 20 kHz.
- 35.
Paul Arnold, private communication.
- 36.
After an initial apprenticeship in Tokyo during the 1970s, Hiroshi Iizuka spent some 4 years as an apprentice to a well-known Yugoslavian expert named Josef Kantuscher, who had settled in Germany. After his years as an apprentice, Iizuka moved to Narberth, PA where he set up his shop. He brought with him a lifetime supply of Balkan maple and Dolomite spruce and has made some 265 instruments over the past 25 years. Michael Tree told me that he thought Iizuka’s violas were just as good as any of the famous Italian instruments. He feels that young musicians make a bad mistake by going into debt to buy over-priced old instruments when much cheaper and equally good ones are being made by contemporary craftsmen.
- 37.
Plans of the Savart violin are given by Heron-Allen (1855), pp. 117–120. The instrument looks more like a balakaika than a violin. Savart’s reasoning was that a flat top-plate would radiate sound more efficiently than a curved one. Further, with the flat geometry, the “f-holes” no longer need to be curved and could be made without cutting the long fibers in the wood that he thought tended to vibrate more efficiently at low frequencies. The violin was also cheaper and easier to make. Although a panel of “experts” (including Savart’s colleague Biot) thought it compared favorably with a Cremona masterpiece, most audiences disagreed.
- 38.
- 39.
Illustrations of grain patterns obtained by numerous different saw cuts are given by Berlyn and Richardson (2001).
- 40.
This interpretation, given by William Huggins in his 1883 paper (see Helmholtz 1885, p. 86 footnote), is a slight oversimplification. As shown by Savart, a major role of the sound post is in defining the nodes for top plate resonances. (See later discussion of top-plate modes.).
- 41.
I am indebted to botanist Dr. Frone Eisenstadt for a helpful discussion of the properties of “horsetail.”
- 42.
Other measurements for an enormous number of Stradivari instruments are contained in Appendices III–V of the Hill brothers (1902) biography.
- 43.
- 44.
See Carolyn Wilson Field, “Tuning the B0 Mode in Four New Violins,” in the Journal of the Catgut Acoustical Society Retrospective Issue (Op. Cit., 2001), pp. 60–61. In that same issue (pp. 57–58), Carleen Hutchins describes the advantage of adjusting the A 0 air and B 0 wood modes to the same frequency.
- 45.
He added that you wouldn’t believe how dirty the inside of a violin can sometimes be. If you’re a good detective, you can tell the lifestyle of the owner, or even tell where the musician has traveled. Upon taking old instruments apart, you sometimes find large balls of fuzz that have rolled around inside the instrument gathering dust and dirt.
- 46.
Using the method of phase shift analysis discussed in Chap. 1 and noting that “hard reflections” are present at both ends of the doubly-closed pipe, it is seen that the resonance in this case is of exactly the same form as that for an open pipe of the same length.
- 47.
See, for example, “A Retrospective on Air and Wood Modes,” edited by Jeffrey S. Loen, Catgut Acoustical Society Journal, vol. 4, No. 3 (Series II), May, 2001.
- 48.
See the reproduction of Janson’s article “ On Higher Air Modes in the Violin” in the Catgut Journal retrospective issue, May, 2001 (op. cit.)
- 49.
According to the 1989 Oxford English Dictionary vol. II, p. 449, 5. A “bout” is the inward curve of a rib in a violin or similar instrument, by which the waist is formed. From the 1893 Fiddler’s Handbook, 4. Bouts are the sides of the fiddle, divided into the lower, middle, and upper bouts. The term apparently comes from the obsolete word “bought” for “bending.” In German, the word for “bout” is “bogen” meaning “arch,” “vault,” or “bow.”
- 50.
See Bennett (1977, pp. 21–32).
- 51.
Effective values for a 1700 Stradivarius of L x ≈ 7.59 in. and L y ≈ 14 in. were used for the equivalent cigar box calculation. See Appendix III of Hill brothers (1902).
- 52.
- 53.
Paul Arnold, private communication.
- 54.
For a review of the properties of vibrational modes that are controllable by the violin maker, see Woodhouse (2002).
- 55.
The interference patterns were computed by the author using a Monte Carlo calculation in which sums were evaluated of the type
$$\displaystyle \begin{aligned} \left[\sum_i{A_i \frac{\sin{}( 2\pi R_i / \lambda)}{R_i}}\right]^2 \end{aligned} $$where R i is the distance from the ith source to the point of observation, A i is the source amplitude (proportional to the area of the source), and λ is the wavelength of the sound in air. The white versus black color was determined by the sign of the total amplitude at each observation point, while the intensity was computed from the square of the total amplitude. The intensity was displayed as a “probability cloud” using random fluctuations in the vicinity of each observation point. (See Bennett 1976, Chapter 3.)
- 56.
For a review of measurements of sound radiation patterns from the violin, see Weinreich (2002).
- 57.
- 58.
A mathematical derivation of this effect for a string resonance in strong coupling with another resonance has also been given by Gough (1981; see Fig. 10).
- 59.
David Oistrakh’s advice: “I do three things to avoid a wolf. I press my left shoulder tightly against the violin, I vibrate more, and I pray.” (Steinhardt 2006, p. 78.).
- 60.
See Hector Berlioz’s report “Of the Great Exhibition in London (1851) to the French Commission of the International Jury” and his Traité d’Orchestration et d’Instrumentation Modernes; also see, Millant (1972, p. 116).
- 61.
P.J. Kindlmann, private communication.
- 62.
Atkins and Newman (1978, p. 20).
- 63.
Sacconi (2000, Chapter XII) gives numerous prescriptions for varnish that may or may not have been used by Stradivari.
- 64.
In attempts to understand why the old Italian instruments sounded so great, all kinds of suggestions have arisen: floating the logs down the Po river from the Alps, soaking them in salt water [no doubt mixed with sewage] in the canals of Venice, and coating the wood with volcanic ash before applying the varnish. The most bizarre suggestion was provided by the movie industry in which varnish for The Red Violin (supposedly inspired by 1720 Red Mendelssohn Strad) was mixed with human blood.
- 65.
This microphone (Serial No. 19689) was the same one used to study the spectra from different bows and had a frequency response curve provided by the manufacturer that was flat within about ± 1 dB over the range from 50 to 20,000 Hz. (Two similar microphones were used to make stereo recordings, the second placed about 1-m laterally on the right side. But the spectra shown here were taken from the microphone on the left side facing the instrument—i.e., in the usual direction of an audience.)
- 66.
Heron-Allen (1885, Chapter IV) gives an exhaustive discussion of the history of the violin bow.
- 67.
Steinhardt (2006, p. 227) notes that the “chaconne” derives from a dance form known as the chacona—an invention frequently attributed to the devil and outlawed in Spain in 1615. He also implies it might have originated with the natives of South America and brought to Europe by the Spanish conquistadors.
- 68.
Jeremy Eichler, “The Bow of Bach’s Dreams? Not Quite.” The New York Times, August 10, 2003, p. AR22.
- 69.
See Paul Griffiths, “Bringing a Reclusive Composer to Light,” The New York Times, Art Section, February 16, 1997.
- 70.
Still another method of bowing the cello was discovered by Piatigorsky. While rehearsing with Stravinsky, he was so nervous that the bow jumped out of his hand and slid behind the bridge producing a strange whistling sound. “Marvelous!” said Stravinsky. “How did you do it?” (Milstein and Volkov, 1990, p. 143.)
- 71.
See discussion in Faber (2005, p. 75).
- 72.
The author is indebted to cellist Frances-Marie Uitti and her bow maker, Andreas Gruter, for helpful comments on the art of bow making.
- 73.
A experimental study of the bouncing bow has been given by Askenfelt and Guettler in the CAS Journal, vol. 3, No. 6 (November 1998), pp. 3–8. Also see the second article in that same journal by these authors on spiccato and ricochet bowing; Askenfelt and Guettler, CAS Journal, pp. 9–15, and the earlier study by George Bissinger of bounce tests and modal analysis of the violin bow in the CAS Journal, vol. 2, No. 5 (1995), pp. 17–22.
- 74.
It is said that manikara kauki wood grown in Asia is similar to pernambuco and is suitable for making good bows (Dick 2003, p. 14). However, the violinists I’ve talked to who tried it remain unconvinced.
- 75.
The Violin Society of America Newsletter, March 2004, p. 6.
- 76.
The author is much indebted to the Heinrich Dick Company of Metten, Germany for supplying these samples. He is also indebted to Dr. Jean Bennett Maguire for taking the photomicrographs shown.
- 77.
Dominique Peccatte (1810–1874) worked for J.B. Vuillaume and was an acquaintance of François Tourte. He is generally regarded as the second best maker after Tourte and apparently started in making bows where Tourte left off. (Beare 1980a). He was probably a great disappointment to his father, who intended him to be a barber. (Millant 1972, p. 112.)
- 78.
Eugène Sartory (1871–1946) studied bow making with Charles Peccatte (son of Dominique Peccatte) and made several bows for the famous violinist Ysaÿe. (Beare 1980b).
- 79.
Aging tends to reduce the upper limit of hearing in people by about 300 Hz per year after the age of 20—hence, often leading to near-total deafness by the age of 100.
- 80.
For example, instead of playing his well-known first concerto as originally written in E-flat major, he tuned all his strings a semitone higher so that he could read it off in D-major. He never tuned in front of an audience and did not even let the conductor see the part he played from. (His first concerto is generally played in D major currently.)
- 81.
Joseph Gold (private communication) learned much about Paganini’s technique from discussions with a person who actually knew H. W. Ernst, the famous nineteenth century violinist and friend of Paganini’s.
- 82.
As demonstrated to me by Syoko Aki, some violinists are able to sustain the harmonic after removing the finger from the node merely by bowing in the right position.
- 83.
Knut Guettler (2002) has discussed the mechanics of exciting such harmonics in more detail.
- 84.
The word “tastiera” means “keyboard” in Italian. Bowing over the keyboard is often described by that same term in the world of violinists.
- 85.
Meyer and Wit in the CAS Journal vol. 3, No. 5, (May 1998), pp. 22, 23 claim to have detected the emission of difference tones produced by a violin. However, their resultant tones were at least 70 dB lower than the primary tones and it is not obvious that they were not produced by nonlinearities in their instrumentation. The psychoacoustic tones heard in the violinist’s ear are extremely loud.
- 86.
Published as Trattato di Musica Secondo la Vera Scienza Dell’ Armonia in Padova in 1754. This treatise contains a table of intervals such as fifths, fourths, thirds, and their difference-frequency subtones.
- 87.
This logarithmic nonlinearity is known as “Fechtner’s Law” in psychology. The actual nonlinearity in the ear is a good deal more complex than the example used in the text to illustrate the generation of difference-frequency tones by a nonlinearity.
- 88.
The trigonometric identities, which are among the most useful things taught in high school, are \(2ab\sin A\sin B ab\cos {}(A-B)-ab \cos {}(A B)\,,\) \( a^2 \sin ^2 A = \frac {a^2}{2} - \frac {a^2}{2}\cos 2A \text{ and } \ b^2\sin ^2 = \frac {b^2}{2} - \frac {b^2}{2}\cos 2B\).
- 89.
When Kimura demonstrated that she could play an entire scale below open G for a master class at Juilliard, one of the students exclaimed, “HOLY SHIT!”.
- 90.
Gold’s source of information about Paganini was in private discussion with a friend who actually knew Mme H.W. Ernst—wife of the famous nineteenth-century violinist who was also a close friend of Paganini.
- 91.
See Neuwirth (1994) for a more extended background discussion.
- 92.
Measurements by the author showed that twisting the string counterclockwise in Kimura’s sense slightly increases the torsion constant (K), presumably by tightening the metal winding on the string. Typically K ≈ 1135 ergs/radian when a cylindrical weight is suspended by the 33 cm string and adjusted to produce the normal tension (10.4 lbs).
- 93.
Mari Kimura, http://pages.nyu.edu/~mk4.
- 94.
Six Caprices for Subharmonics (1997); Gemini for Solo Violin (1995); ALT in Three Movements (1992) produced by Mari Kimura (private publication) and available from her privately by Email: mari.kimura@nyu.edu.
- 95.
The subharmonics described by McIntyre et al. (1982) were incoherent. The difference between a coherent audio signal and an incoherent one is similar to that between the filtered output from a light bulb and the output amplitude from a laser. In the former case, the amplitude fluctuates wildly at low intensities, as well as the phase. In the latter case, both the amplitude and phase are constant within normal statistical fluctuation limits. (e.g., fluctuations in the photon count over a prescribed time vary as the square root of the number of photons detected.)
- 96.
- 97.
M.A. Cornu, Journal de Physique vol. 3, p. 5.1 (1896).
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Bennett Jr., W.R. (2018). Violins and Bowed Strings. In: Morrison, A. (eds) The Science of Musical Sound. Springer, Cham. https://doi.org/10.1007/978-3-319-92796-1_5
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