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Violin acoustics

Violin acoustics is an area of study within musical acoustics concerned with how the sound of a violin is created as the result of interactions between its many parts. These acoustic qualities are similar to those of other members of the violin family, such as the viola.

The energy of a vibrating string is transmitted through the bridge to the body of the violin, which allows the sound to radiate into the surrounding air. Both ends of a violin string are effectively stationary, allowing for the creation of standing waves. A range of simultaneously produced harmonics each affect the timbre, but only the fundamental frequency is heard. The frequency of a note can be raised by the increasing the string's tension, or decreasing its length or mass. The number of harmonics present in the tone can be reduced, for instance by the using the left hand to shorten the string length. The loudness and timbre of each of the strings is not the same, and the material used affects sound quality and ease of articulation. Violin strings were originally made from catgut but are now usually made of steel or a synthetic material. Most strings are wound with metal to increase their mass while avoiding excess thickness.


During a bow stroke, the string is pulled until the string's tension causes it to return, after which it receives energy again from the bow. Violin players can control bow speed, the force used, the position of the bow on the string, and the amount of hair in contact with the string. The static forces acting on the bridge, which supports one end of the strings' playing length, are large: dynamic forces acting on the bridge force it to rock back and forth, which causes the vibrations from the strings to be transmitted. A violin's body is strong enough to resist the tension from the strings, but also light enough to vibrate properly. It is made of two arched wooden plates with ribs around the sides and has two f-holes on either side of the bridge. It acts as a sound box to couple the vibration of strings to the surrounding air, with the different parts of the body all respond differently to the notes that are played, and every part (including the bass bar concealed inside) contributing to the violin's characteristic sound. In comparison to when a string is bowed, a plucked string dampens more quickly.


The other members of the violin family have different, but similar timbres. The viola and the double bass’s characteristics contribute to them being used less in the orchestra as solo instruments, in contrast to the cello (violoncello), which is not adversely affected by having the optimum dimensions to correspond with the pitch of its open strings.

Historical background[edit]

The nature of vibrating strings was studied by the ancient Ionian Greek philosopher Pythagoras, who is thought to have been the first to observe the relationship between the lengths of vibrating strings and the consonant sounds they make.[1][2] In the sixteenth century, the Italian lutenist and composer Vincenzo Galilei pioneered the systematic testing and measurement of stretched strings, using lute strings. He discovered that while the ratio of an interval is proportional to the length of the string, it was directly proportional to the square root of the tension. His son Galileo Galilei published the relationship between frequency, length, tension and diameter in Two New Sciences (1638).[3][4] The earliest violin makers, though highly skilled, did not advance any scientific knowledge of the acoustics of stringed instruments.[5]


During the nineteenth century, the multi-harmonic sound from a bowed string was first studied in detail by the French physicist Félix Savart.[1][6] The German physicist Hermann von Helmholtz investigated the physics of the plucked string,[7] and showed that the bowed string travelled in a triangular shape with the apex moving at a constant speed.[8]


The violin's modes of vibration were researched in Germany during the 1930s by Hermann Backhaus and his student Hermann Meinel, whose work included the investigation of frequency responses of violins. Understanding of the acoustical properties of violins was developed by F.A. Saunders in the 1930s and 40s, work that was continued over the following decades by Saunders and his assistant Carleen Hutchins, and also Werner Lottermoser, Jürgen Meyer, and Simone Sacconi.[9] Hutchins' work dominated the field of violin acoustics for twenty years from the 1960s onwards, until it was superseded by the use of modal analysis, a technique that was, according to the acoustician George Bissinger, "of enormous importance for understanding [the] acoustics of the violin".[10]

The bridge[edit]

The bridge, which is placed on the top of the body of the violin where the soundboard is highest,[34] supports one end of the strings' playing length. The static forces acting on the bridge are large, and dependent on the tension in the strings:[35] 20 lbf (89 N) passes down through the bridge as a result of a tension in the strings of 50 lbf (220 N).[36] The string 'break' angle made by the string across the bridge affects the downward force, and is typically 13 to 15° to the horizontal.[37]


The bridge transfers energy from the strings to the body of the violin.[35] As a first approximation, it is considered to act as a node, as otherwise the fundamental frequencies and their related harmonics would not be sustained when a note is played, but its motion is critical in determining how energy is transmitted from the strings to the body, and the behaviour of the strings themselves.[13] One component of its motion is side-to-side rocking as it moves with the string.[38] It may be usefully viewed as a mechanical filter, or an arrangement of masses and "springs" that filters and shapes the timbre of the sound.[39] The bridge is shaped to emphasize a singer's formant at about 3000 Hz.[40]


Since the early 1980s it has been known that high quality violins have vibrated better at frequencies around 2–3 kHz because of an effect attributed to the resonance properties of the bridge, and now referred as the 'bridge-hill' effect.[39]


Muting is achieved by fitting a clip onto the bridge, which absorbs a proportion of the energy transmitted to the body of the instrument. Both a reduction in sound intensity and a different timbre are produced, so that using a mute is not seen by musicians as the main method to use when wanting to play more quietly.[41]

(1997). The Violin Explained: Components, Mechanism, and Sound. Oxford, New York: Oxford University Press. ISBN 978-0-19-816739-6.

Beament, James

Bucur, Voichita (2018). . AG Switzerland: Cham Springer International Publishing. ISBN 978-3-319-81191-8.

Handbook of Materials for String Musical Instruments

, ed. (1886). "Double bass" . Dictionary of National Biography. Vol. 8. London: Smith, Elder & Co.

Chisholm, Hugh

Farga, Franz (1969). . New York: F. A. Praeger. OCLC 68030679.

Violins and Violinists

(1914) [1638]. Dialogues Concerning Two New Sciences. Translated by Crew, Henry; de Salvio, Alfonso. New York: Dover Publications Inc. OCLC 708455337.

Galilei, Galileo

(1978). The Physics of Music. San Francisco: W.H. Fremman and Company. ISBN 978-0-7167-0095-1. (registration required)

Hutchins, Carleen Maley

(1895). Ellis, Alexander J. (ed.). On the Sensations of Tone as a Physiological basis for the Theory of Music (translation of the 1877 German edition) (3rd ed.). London, New York: Longmans, Green and Co. OCLC 1453852.

Helmholtz, Hermann L. F. von

The Acoustics of Violin Plates. Scientific American, vol 245, No. 4. Oct 1981

Hutchins, Carleen Maley

(1967). Music, physics and engineering. New York: Dover Publications. ISBN 978-0-486-31702-1. (registration required)

Olson, Harry F.

(1976). Orchestration (7th ed.). London: Victor Gollancz Ltd. OCLC 1016330383.

Piston, Walter

(1977). Physics and the sound of music. New York: Wiley. ISBN 978-0-471-87412-6.

Rigden, John S

Siminoff, Roger H. (2002). The Luthier's Handbook: A Guide to Building Great Tone in Acoustic Stringed Instruments. Milwaukee: Hal Leonard Corp.  978-0-634-01468-0.

ISBN

Rossing, Thomas, ed. (2014). . New York: Springer. ISBN 978-0-387-30446-5.

Springer Handbook of Acoustics

Wishart, Trevor (1996). Emmerson, Simon (ed.). On Sonic Art. Amsterdam: OPA.  978-3-7186-5847-3.

ISBN

(1944). The Physics of Music. London: Methuen & Co. Ltd. OCLC 640010938.

Wood, Alexander

Woodhouse, J.; Galluzzo, P.M. (2004). (PDF). Acta Acustica. 90: 579–589. Retrieved 11 May 2020.

"The Bowed String As We Know It Today"

Askenfelt, A. (1995). (PDF). STL-QPSR. 36 (2–3): 23–42. S2CID 17812511. Archived from the original (PDF) on 2019-03-07.

"Observations on the violin bow and the interaction with the string"

Bissinger, George (2006). . The Journal of the Acoustical Society of America. 120 (1): 482–491. Bibcode:2006ASAJ..120..482B. doi:10.1121/1.2207576. PMID 16875244.

"The violin bridge as filter"

Cremer, Lothar (1984). Physics of the Violin (translation of Physik der Geige by John S. Allen). Cambridge, Massachusetts: MIT Press.  978-0-262-03102-8.

ISBN

(1918). "On the mechanical theory of vibrations of bowed strings and of musical instruments of the violin family". Indian Association of the Cultivation of Science.

Raman, C.V.

published by the University of New South Wales

How does a violin work? An introduction to violin acoustics

The use of computer aided tomography (CT Scanning) to examine great Italian instruments in order to replicate their acoustics in modern instruments.

Path Through the Woods - The Use of Medical Imaging in Examining Historical Instruments

- animations of violins showing how the plates vibrate at various frequencies, from Borman Violins.

Modal Animations

Wire-frame animation of a 1712 Stradivari violin at various eigenmode frequencies

a YouTube video of the patterns produced on a violin-shaped Chladni plate, uploaded by the University of Milan Physics Department (text in Italian).

Piastra di Chladni: violino