Violin acoustics - Knowledge

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74 inches (188.0 cm). The back can be arched or flat. The bassist's fingers have to stretch twice as far as a cellist's, and greater force is required to press them against the finger-board. The pizzicato tone, which is 'rich' sounding due to the slow speed of vibrations, is changeable according to which of the associated harmonies are more dominant. The technical capabilities of the double bass are limited. Quick passages are seldom written for it; they lack clarity because of the time required for the strings to vibrate. The double bass is the foundation of the whole orchestra and therefore musically of great importance. According to John Rigden, a double bass would need to be twice as large as its present size for its bowed notes to sound powerful enough to be heard over an orchestra.

249:, 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 3454: 1101: 1110: 22: 976:, 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. One component of its motion is side-to-side rocking as it moves with the string. 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. The bridge is shaped to emphasize a singer's 1459: 742: 451: 1447:, the lower notes of the viola (along with the cello and the double bass) suffer from strength and quality. This is because typical resonant frequencies for a viola lie between the natural frequencies of the middle open strings, and are too high to reinforce the frequencies of the lower strings. To correct this problem, Rigden calculated that a viola would need strings that were half as long again as on a violin, which would making the instrument inconvenient to play. 1312: 4354: 3741: 1229: 1006: 1166:(known as the 'Helmholtz corner') that moves along the main part of the string at a constant speed. Here, the nature of the friction between bow and string changes, and slipping or sticking occurs, depending on the direction the corner is moving. The wave produced rotates as the Helmholtz corner moves along a plucked string, which caused a reduced amount of energy to be transmitted to the bridge when the 1335:. This behaviour enhances the violin tone quality: if the sound post's position is adjusted, or if the forces acting on it are changed, the sound produced by the violin can be adversely affected. Together they make the shape of the violin body asymmetrical, which allows different vibrations to occur, which causing the timbre to become more complex. 509:, any frequency on the length of the string is possible. There is a difference in timbre between notes made on an 'open' string and those produced by placing the left hand fingers on the string, as the finger acts to reduce the number of harmonics present. Additionally, the loudness and timbre of the four strings is not the same. 238:. 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 1327:

concealed inside the body both help transmit sound to the back of the violin, with the sound post also serving to support the structure. The bass bar is glued to the underside of the top, whilst the sound post is held in place by friction. The bass bar was invented to strengthen the structure, and is

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The existence of expensive violins is dependent on small differences in their physical behaviour in comparison with cheaper ones. Their construction, and especially the arching of the belly and the backplate, has a profound effect on the overall sound quality of the instrument, and its many different

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was the first to obtain an accurate model for describing the mechanics of the bowed string, publishing his research in 1918. His model was able to predict the motion described by Helmholtz (known nowadays as Helmholtz motion), but he had to assume that the vibrating string was perfectly flexible, and

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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

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Helmholtz and Raman produced models that included sharp cornered waves: the study of smoother corners was undertaken by Cremer and Lazarus in 1968, who showed that significant smoothing occurs (i.e. there are fewer harmonics present) only when normal bowing forces are applied. The theory was further

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The double bass, in comparison with the other members of the family, is more pointed where the belly is joined by the neck, possibly to compensate for the strain caused by the tension of the strings, and is fitted with cogs for tuning the strings. The average overall length of an orchestral bass is

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The body of a violin is oval and hollow, and has two f-shaped holes, called sound holes, located on either side of the bridge. The body must be strong enough to support the tension from the strings, but also light and thin enough to vibrate properly. It is made of two arched wooden plates known as

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is produced when small changes in the fundamental frequency—caused by the motion of the bridge—become too great, and the note becomes unstable. A sharp resonance response from the body of a cello (and occasionally a viola or a violin) produces a wolf tone, an unsatisfactory sound that repeatedly

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to the string. In bowing, the three most prominent factors under the player's immediate control are bow speed, force, and the place where the hair crosses the string (known as the 'sounding point'): a vibrating string with a shorter length causes the sounding point to be positioned closer to the

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wound with metal chosen for its density and cost. The winding on a string increases the mass of the string, alters the tone (quality of sound produced) to make it sound brighter or warmer, and affects the response. A plucked steel string sounds duller than one made of gut, as the action does not

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until an opposing force caused by the string's tension becomes great enough to cause the string to slip back. The string returns to its equilibrium position and then moves sideways past this position, after which it receives energy again from the moving bow. The bow consists of a flat ribbon of

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The ribs are reinforced at their edges with lining strips, which provide extra gluing surface where the plates are attached. The wooden structure is filled, glued and varnished using materials which all contribute to a violin's characteristic sound. The air in the body also acts to enhance the

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inches (59.4 cm)). The viola's larger size is not proportionally great enough to correspond to the strings being pitched as they are, which contributes to its different timbre. Violists need to have hands large enough to be able to accomplish fingering comfortably. The C string has been

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resonant frequencies are caused by the nature of the wooden structure. The different parts all respond differently to the notes that are played, displaying what Carleen Hutchins described as 'wood resonances'. The response of the string can be tested by detecting the motion produced by the

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bridge. The player may also vary the amount of hair in contact with the string, by tilting the bow stick more or less away from the bridge. The string twists as it is bowed, which adds a 'ripple' to the waveform: this effect is increased if the string is more massive.

939:, which is still available and used by some professional musicians, although strings made of other materials are less expensive to make and are not as sensitive to temperature. Modern strings are made of steel-core, stranded steel-core, or a synthetic material such as 666:, S is the cross-sectional area, ΔL is the extension, and L is the string length. For vibrations with a large amplitude, the tension is not constant. Increasing the tension on a string results in a higher frequency note: the frequency of the vibrating string, which is 322:

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

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is not parallel to the fingerboard. Less energy still is supplied when the string is bowed, as a bow tends to dampen any oscillations that are at an angle to the bow hair, an effect enhanced if an uneven bow pressure is applied, e.g. by a novice player.

554: 579:), the sound produced dies away, or dampens, quickly: the dampening is more striking for a violin compared with the other members of the violin family because of its smaller dimensions, and the effect is greater if an open string is plucked. During a 1303:, involves the use of 'tonal copies' of old instruments to compare a new instrument with an older one. The effects of changing the new violin in the smallest way can be identified, with the aim of replicating the tonal response of the older model. 983:

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.

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The bridge, which is placed on the top of the body of the violin where the soundboard is highest, 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:

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The belly and the backplate can display modes of vibration when they are forced to vibrate at particular frequencies. The many modes that exist can be found using fine dust or sand, sprinkled on the surface of a violin-shaped

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below the viola. The proportionally greater thickness of its body means that its timbre is not adversely affected by having dimensions that do not correspond to its pitch of its open strings, as is the case with the viola.

403: 1124:"...The foot d of the ordinate of its highest point moves backwards and forwards with a constant velocity on the horizontal line ab, while the highest point of the string describes in succession the two parabolic arcs ac 470:. The timbre is affected by the number and comparative strength of the overtones (harmonics) present in a tone. Even though they are produced at the same time, only the fundamental frequency—which has the greatest 1085:—when the bow is played close to the bridge—is the opposite technique, and produces what Piston described as a "glassy and metallic" sound, due to normally unheard harmonics becoming able to affect the timbre. 1272:. When a mode is found, the dust accumulates at the (stationary) nodes: elsewhere on the plate, where it is oscillating, the dust fails to appear. The patterns produced are named after the German physicist 380:

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

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due to the rosin was solely determined by the bow's speed, and ignored the possibility that the coefficient could depend on other variables. By the early 2000s, the importance of variables such the

857: 1287:, where discrete parts of the violin are studied with the aim of constructing an accurate simulation. The British physicist Bernard Richardson has built virtual violins using these techniques. At 1387: 721: 1355:

appears and disappears. A correctly positioned suppressor can remove the tone by reducing the resonance at that frequency, without dampening the sound of the instrument at other frequencies.

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described by Piston as having a timbre that is "powerful and distinctive", but perhaps in part because the sound it produces is easily covered, the viola is not so frequently used in the

657: 555: 1253:. Such tests have shown that the optimum 'main wood resonance' (the wood resonance with the lowest frequency) occurs between 392 and 494 Hz, equivalent to a tone below and above 733:. Tuning each string is done by loosening or tightening it until the desired pitch is reached. The tension of a violin string ranges from 8.7 to 18.7 pounds-force (39 to 83 N). 1045:. A violinist or violist would naturally tend to play louder when pushing the bow across the string (an 'up-bow'), as the leverage is greater. At its quietest, the instrument has a 800: 257:

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

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Bowing is an example of resonance where maximum amplification occurs at the natural frequency of the system, and not the forcing frequency, as the bow has no periodic force. A

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String material influences the overtone mix and affects the quality of the sound. Response and ease of articulation are also affected by choice of string materials.

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Helmholtz motion for a bowed violin string: an illustration of Helmholz's diagram of the motion; and a clip showing the 'Helmholtz corner' travelling back and forth

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inches (31.8 mm)—at the other end of the string, the same interval is less than a third of this size. The equivalent numbers are successively larger for a

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When the bridge receives energy from the strings, it rocks, with the sound post acting as a pivot and the bass bar moving with the plate as the result of

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of modern bows are standardized. Players may notice variations in sound and handling from bow to bow, based on these parameters as well as stiffness and

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of the string. Violinists stop a string with a left-hand fingertip, shortening its playing length. Most often the string is stopped against the violin's

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Modern research on the physics of violins began with Helmholtz, who showed that the shape of the string as it is bowed is in the form of a 'V', with an

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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.

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

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to couple the vibration of strings to the surrounding air, making it audible. In comparison, the strings, which move almost no air, are silent.

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The physics of the viola are the same as that of the violin, and the construction and acoustics of the cello and the double bass are similar.

392:, a technique that was, according to the acoustician George Bissinger, "of enormous importance for understanding acoustics of the violin". 1283:, which enables analysis of the motion of the violin surface to be measured, a method first developed by scientists in the 1960s, and the 376:

were researched in Germany during the 1930s by Hermann Backhaus and his student Hermann Meinel, whose work included the investigation of

388:. Hutchins' work dominated the field of violin acoustics for twenty years from the 1960s onwards, until it was superseded by the use of 4017: 730: 3345: 1214:

to the rosin on the bow, and the player's input into the action of the bow were recognised, showing the need for an improved model.

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positioned directly below one of the bridge's feet. Near the foot of the bridge, but not directly below it, is the sound post.

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The bridge transfers energy from the strings to the body of the violin. As a first approximation, it is considered to act as a

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to be produced. Stopping the string at a shorter length has the effect of raising its pitch, and since the fingerboard is

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described the motion of a bowed string as being "the only stick-slip oscillation which is reasonably well understood".

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described as a "very soft, floating quality", caused by the string being forced to vibrate with a greater amplitude.

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A violin can sustain its tone by the process of bowing, when friction causes the string to be pulled sideways by the

307:, who is thought to have been the first to observe the relationship between the lengths of vibrating strings and the 184: 110: 3309: 3245: 3197:(1918). "On the mechanical theory of vibrations of bowed strings and of musical instruments of the violin family". 2924: 2875:

On the Sensations of Tone as a Physiological basis for the Theory of Music (translation of the 1877 German edition)

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string, and showed that the bowed string travelled in a triangular shape with the apex moving at a constant speed.

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Boutin, Henri; Besnainou, Charles (2008). "Physical parameters of the violin bridge changed by active control".

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The fundamental frequency and overtones of the resulting sound depend on the material properties of the string:

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concealed inside) contributing to the violin's characteristic sound. In comparison to when a string is bowed, a

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violin's resonating properties, which are affected by the volume of enclosed air and the size of the f-holes.

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effect on a violin is achieved when muscles in the arm, hand and wrist act to cause the pitch of a note to

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deform steel into a pointed shape as easily, and so does not produce as many higher frequency harmonics.

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A vibrating string does not produce a single frequency. The sound may be described as a combination of a

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violin, which may have been made as early as 1558, making it one of the earliest violins in existence

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oscillation' as it moves at right angles to the string. In 2004, Jim Woodhouse and Paul Galluzzo of

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Violinists generally bow between the bridge and the fingerboard, and are trained to keep the bow

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where f is the fundamental frequency of the string, T is the tension force and M is the mass.

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The other members of the violin family have different, but similar timbres. The viola and the

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In addition to the normal modes of the body structure, the enclosed air in the body exhibits

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and damping of the violin's vibrations depend on frequency. Another technique, known as

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

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The Luthier's Handbook: A Guide to Building Great Tone in Acoustic Stringed Instruments

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The viola is a larger version of the violin, and has on average a total body length of

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parallel horse hairs stretched between the ends of a stick, which is generally made of

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the belly and the backplate, whose sides are formed by thin curved ribs. It acts as a

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For the fundamental frequency of a vibrating string on a violin, the string length is

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vary according to the length of the vibrating part of the string. For a violin, the

4385: 4302: 4231: 4165: 4027: 3829: 3643: 3607: 3575: 3526: 3435: 3298: 3148: 2890: 2838: 2825:. Translated by Crew, Henry; de Salvio, Alfonso. New York: Dover Publications Inc. 2199: 2152: 1254: 1246: 1000: 944: 573: 517: 381: 319: 199: 96: 75: 46: 3278: 2563: 2101: 2035:"String Tech. Everything you wanted to know about strings, but were afraid to ask" 4241: 4170: 4079: 3890: 3885: 3824: 3809: 3719: 3673: 3514: 3472: 3346:

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

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of 0.0000038 watts, compared with 0.09 watts for a small orchestra: the range of

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to the square root of the tension, can be represented by the following equation:

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is heard. The frequency of a note can be raised by the increasing the string's

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The cello, with an overall length of 48 inches (121.9 cm), is pitched an

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published the relationship between frequency, length, tension and diameter in

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that depended upon the bow speed. Raman's model was later developed by the

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are essentially stationary when it vibrates, allowing for the creation of

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because they have different masses per unit length. Both ends of a violin

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to produce frequency responses that have helped him to determine how the

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For any wave travelling at a speed v, travelling a distance λ in one

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Mémoire sur la construction des instrumens à cordes et à archets

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a, and the string itself is always stretched in the two lines ac

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Waveform for a violin, the result of combining many simple waves

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higher harmonics diminish more quickly than the lower ones.

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to radiate into the surrounding air. Both ends of a violin

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How does a violin work? An introduction to violin acoustics

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through a metal string when it is placed in an oscillating

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as a solo instrument. According to the American physicist

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Modern research has used sophisticated techniques such as

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are effectively stationary, allowing for the creation of

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The Violin Explained: Components, Mechanism, and Sound

2620: 2507: 2495: 2080: 1908: 1886: 1884: 1704: 1649: 1608: 1596: 852:{\displaystyle f={\frac {1}{T}}={\frac {v}{\lambda }}} 2710: 2656: 2582: 2543: 2531: 2336: 2113: 2065: 1864: 1639: 1637: 1635: 1552: 1534: 1522: 1476: 1291:, the American acoustician George Bissinger has used 891: 819: 773: 679: 619: 602:

and causes the pitch to vary by a quarter of a tone.

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Handbook of Materials for String Musical Instruments

2695: 2680: 2668: 2644: 2519: 2447: 2360: 2348: 2300: 2212: 1828: 1816: 1804: 1512: 1510: 1508: 716:{\displaystyle f={1 \over 2}{\sqrt {\frac {T}{LM}}}} 2471: 2435: 2324: 2053: 1881: 1840: 1620: 1276:, who first developed this experimental technique. 729:The strings of a violin are attached to adjustable 300:The nature of vibrating strings was studied by the 3357:video of the patterns produced on a violin-shaped 2224: 1896: 1765: 1632: 1359:Comparison with other members of the violin family 1306: 1198:developed during the 1970s and 1980s to produce a 915: 851: 794: 715: 651: 610:The tension (T) in a stretched string is given by 572:When the violinist is directed to pluck a string ( 3056: 2465: 2429: 2417: 2405: 2393: 2378: 2294: 1584: 1505: 384:, and also Werner Lottermoser, Jürgen Meyer, and 354:string was first studied in detail by the French 311:they make. In the sixteenth century, the Italian 183:is created as the result of interactions between 4372: 3283:The Journal of the Acoustical Society of America 3240:The Journal of the Acoustical Society of America 3199:Indian Association of the Cultivation of Science 3133:The Journal of the Acoustical Society of America 2184:The Journal of the Acoustical Society of America 731:tuning pegs and (with some strings) finer tuners 3016:Wishart, Trevor (1996). Emmerson, Simon (ed.). 2134: 1183:lost energy when the wave was reflected with a 1987:"A Guide to Choosing the Right Violin Strings" 598:. A typical vibrato has a frequency of 6 407:The sound of the open strings (G, D, A and E) 3771: 3384: 2939:(7th ed.). London: Victor Gollancz Ltd. 2792:. Vol. 8. London: Smith, Elder & Co. 2741:. Oxford, New York: Oxford University Press. 2180:"An electronic violin with a singing formant" 1073:Bowing directly above the fingerboard (Ital. 943:. Violin strings (with the exception of most 153: 3263:. Paris: Librairie Encyclopédique de Roret. 2137:Journal of the Acoustical Society of America 1424:lower than a violin (with a length of about 1420:inches (69.2 cm), with strings tuned a 419:of a violin are of the same length from the 206:to the body of the violin, which allows the 2847:. San Francisco: W.H. Fremman and Company. 652:{\displaystyle T=ES{\frac {{\Delta }L}{L}}} 253:on either side of the bridge. It acts as a 3778: 3764: 3391: 3377: 160: 146: 2868: 2603:"How to Tame Annoying Howling Wolf Tones" 2203: 1729: 1727: 1725: 1723: 1721: 1719: 1578: 935:Violin strings were originally made from 476:beyond the upper audible limit for humans 2975: 2837: 2776: 2689: 2600: 2513: 2501: 2489: 2107: 2095: 1710: 1553:O'Connor, J.J.; Robertson, E.F. (2007). 1540: 1487: 1457: 1310: 1227: 1004: 740: 552: 449: 399: 295: 280:as solo instruments, in contrast to the 20: 3179:. Cambridge, Massachusetts: MIT Press. 3015: 2994: 2815: 2731: 2549: 2342: 2263: 2261: 2177: 2119: 2074: 2007: 1914: 1875: 1686:"Strings, standing waves and harmonics" 1664: 1528: 1499: 4373: 3059:"The Bowed String As We Know It Today" 3057:Woodhouse, J.; Galluzzo, P.M. (2004). 2951: 2931: 2716: 2704: 2674: 2662: 2650: 2638: 2366: 2354: 2330: 2306: 2218: 2130: 2128: 1980: 1978: 1976: 1974: 1890: 1858: 1846: 1834: 1822: 1786:"Modeling the stiffness of the string" 1759: 1716: 1679: 1677: 1675: 1673: 1626: 795:{\displaystyle v={{\lambda } \over T}} 16:Area of study within musical acoustics 3759: 3372: 3365:Physics Department (text in Italian). 2900: 2822:Dialogues Concerning Two New Sciences 2796: 2755: 2626: 2525: 2453: 2441: 2059: 1810: 1783: 1614: 1602: 218:. A range of simultaneously produced 3034: 2588: 2537: 2477: 2318: 2258: 2230: 1984: 1902: 1771: 1643: 1590: 1516: 1060: 524:interval on an open string is about 2872:(1895). Ellis, Alexander J. (ed.). 2125: 2008:Pociask, Stefan (31 October 2018). 1971: 1777: 1670: 1088: 346:During the nineteenth century, the 13: 3277:Schelleng, John C (January 1973). 3085: 1053:of the instrument is from 25 to 30 636: 179:concerned with how the sound of a 14: 4397: 3785: 3318: 3279:"The bowed string and the player" 3242:, Vol. 9, No. 2, pp. 81–98. 3044:. London: Methuen & Co. Ltd. 2561: 2267: 1741:. American Physical Society. 2020 1683: 916:{\displaystyle f={\frac {v}{2L}}} 4353: 4352: 3740: 3739: 3452: 3236:The mechanical action of violins 2910:. New York: Dover Publications. 2893:The Acoustics of Violin Plates. 2789:Dictionary of National Biography 1985:Ward, Richard (22 August 2012). 1384: 1367: 1108: 1099: 365:investigated the physics of the 302:ancient Ionian Greek philosopher 36: 2980:. Milwaukee: Hal Leonard Corp. 2725: 2601:Freiberg, Sarah (12 May 2005). 2594: 2570:. University of New South Wales 2555: 2276:. University of New South Wales 2244:"Basic Parts of the Violin Bow" 2236: 2171: 2027: 2001: 1946: 1920: 1692:. University of New South Wales 1307:The bass bar and the sound post 2998:Springer Handbook of Acoustics 2958:Physics and the sound of music 2907:Music, physics and engineering 1546: 234:, or decreasing its length or 1: 3398: 3329:University of New South Wales 3129:"The violin bridge as filter" 2995:Rossing, Thomas, ed. (2014). 2466:Woodhouse & Galluzzo 2004 2430:Woodhouse & Galluzzo 2004 2418:Woodhouse & Galluzzo 2004 2406:Woodhouse & Galluzzo 2004 2394:Woodhouse & Galluzzo 2004 2379:Woodhouse & Galluzzo 2004 2295:Woodhouse & Galluzzo 2004 1345: 1224:Violin making and maintenance 955: 878:λ, where λ is the associated 2870:Helmholtz, Hermann L. F. von 927: 447:travelling past each other. 439:(eigenmodes), caused by the 7: 3351:Piastra di Chladni: violino 2976:Siminoff, Roger H. (2002). 2803:. New York: F. A. Praeger. 2010:"What Is Catgut Made From?" 1557:. University of St. Andrews 1397:The open strings of a cello 1377:The open strings of a viola 1217: 1212:energy supplied by friction 516:positions for a particular 427:of the violin, but vary in 202:is transmitted through the 175:is an area of study within 10: 4402: 3127:Bissinger, George (2006). 2897:, vol 245, No. 4. Oct 1981 1281:holographic interferometry 1221: 998: 994: 605: 395: 4348: 4270: 4214: 4126: 4026: 3941: 3909: 3871: 3843: 3800: 3793: 3735: 3687: 3616: 3513: 3471: 3447: 3406: 1784:Smith, Julius O. (2019). 1155:On the Sensations of Tone 1026:to provide a controlled ' 756:, shown stopping a string 736: 4114:(changing string tuning) 2756:Bucur, Voichita (2018). 1928:"How to Tune the Violin" 1470: 1289:East Carolina University 1037:The length, weight, and 3416:Architectural acoustics 3168:Cremer, Lothar (1984). 2891:Hutchins, Carleen Maley 2839:Hutchins, Carleen Maley 2246:. Benning Violins. 2020 2110:, String "break" angle. 1208:coefficient of friction 1200:digital waveguide model 1153:Hermann von Helmholtz, 980:at about 3000 Hz. 361:. The German physicist 3503:Fletcher–Munson curves 3498:Equal-loudness contour 3408:Acoustical engineering 3170:Physics of the Violin 3092:Askenfelt, A. (1995). 3001:. New York: Springer. 2800:Violins and Violinists 2178:Mathews, M.V. (1982). 1958:ViolinStringReview.com 1954:"String Tension Guide" 1463: 1342:modes as it vibrates. 1316: 1233: 1194:and F.G. Friedlander. 1185:reflection coefficient 1150: 1010: 917: 853: 796: 757: 717: 653: 569: 455: 412: 333:earliest violin makers 30: 4335:Violin musical styles 4283:History of the violin 3919:Electric upright bass 3639:Hermann von Helmholtz 3537:Fundamental frequency 3441:Sympathetic resonance 3310:registration required 3246:registration required 2925:registration required 2862:registration required 2797:Farga, Franz (1969). 2564:"Helmholtz Resonance" 1461: 1314: 1285:finite element method 1232:Structure of a violin 1231: 1093: 1051:sound pressure levels 1008: 999:Further information: 918: 854: 797: 744: 718: 668:directly proportional 654: 559: 460:fundamental frequency 453: 406: 363:Hermann von Helmholtz 296:Historical background 228:fundamental frequency 24: 4186:Double bass concerto 3041:The Physics of Music 2844:The Physics of Music 1315:Interior of a violin 1032:Cambridge University 889: 817: 771: 677: 617: 546:(violoncello) and a 341:stringed instruments 4215:Related instruments 4129:and genres of music 4095:Finger substitution 3659:Werner Meyer-Eppler 3569:Missing fundamental 3363:University of Milan 3295:1973ASAJ...53...26S 3145:2006ASAJ..120..482B 2961:. New York: Wiley. 2895:Scientific American 2783:"Double bass" 2321:, pp. 34, 102. 2196:1982ASAJ...71...43M 2149:2008ASAJ..123.3656B 1340:Helmholtz resonance 503:artificial harmonic 378:frequency responses 3820:Five-string violin 3542:Frequency spectrum 3361:, uploaded by the 3020:. Amsterdam: OPA. 2396:, pp. 579–80. 2270:"Bows and strings" 1605:, pp. 6, 931. 1464: 1462:Double bass tuning 1317: 1234: 1011: 913: 849: 792: 758: 713: 649: 570: 456: 413: 374:modes of vibration 31: 4368: 4367: 3937: 3936: 3753: 3752: 3715:Musical acoustics 3547:harmonic spectrum 3327:published by the 3303:10.1121/1.1913322 3234:(October 1937). " 3186:978-0-262-03102-8 3176:by John S. Allen) 3153:10.1121/1.2207576 3027:978-3-7186-5847-3 3008:978-0-387-30446-5 2987:978-0-634-01468-0 2968:978-0-471-87412-6 2917:978-0-486-31702-1 2854:978-0-7167-0095-1 2769:978-3-319-81191-8 2748:978-0-19-816739-6 2641:, pp. 65–69. 2629:, pp. 120–1. 2591:, pp. 100–1. 2540:, pp. 97–98. 2492:, pp. 61–62. 2432:, pp. 583–4. 2420:, pp. 581–2. 2205:10.1121/1.2019392 2157:10.1121/1.2934961 1861:, pp. 23–24. 1762:, pp. 29–30. 1617:, pp. 930–1. 1389: 1372: 1204:bending stiffness 1168:plane of rotation 1061:Physics of bowing 1043:moment of inertia 911: 847: 834: 790: 711: 710: 694: 647: 557: 404: 177:musical acoustics 170: 169: 4393: 4356: 4355: 4278:Violin acoustics 4232:Hardanger fiddle 4166:String orchestra 3830:Alexander violin 3798: 3797: 3780: 3773: 3766: 3757: 3756: 3743: 3742: 3644:Carleen Hutchins 3576:Combination tone 3463: 3456: 3436:String vibration 3393: 3386: 3379: 3370: 3369: 3340:Modal Animations 3313: 3306: 3272: 3249: 3202: 3190: 3174:Physik der Geige 3172:(translation of 3164: 3123: 3121: 3115:. Archived from 3098: 3081: 3079: 3077: 3063: 3053: 3031: 3012: 2991: 2972: 2948: 2928: 2921: 2887: 2865: 2858: 2834: 2817:Galilei, Galileo 2812: 2793: 2785: 2773: 2752: 2720: 2714: 2708: 2702: 2693: 2687: 2678: 2672: 2666: 2660: 2654: 2648: 2642: 2636: 2630: 2624: 2618: 2617: 2615: 2613: 2598: 2592: 2586: 2580: 2579: 2577: 2575: 2559: 2553: 2547: 2541: 2535: 2529: 2523: 2517: 2511: 2505: 2499: 2493: 2487: 2481: 2475: 2469: 2463: 2457: 2451: 2445: 2439: 2433: 2427: 2421: 2415: 2409: 2403: 2397: 2391: 2382: 2376: 2370: 2364: 2358: 2352: 2346: 2340: 2334: 2328: 2322: 2316: 2310: 2304: 2298: 2292: 2286: 2285: 2283: 2281: 2265: 2256: 2255: 2253: 2251: 2240: 2234: 2228: 2222: 2216: 2210: 2209: 2207: 2175: 2169: 2168: 2132: 2123: 2117: 2111: 2105: 2099: 2093: 2078: 2072: 2063: 2057: 2051: 2050: 2048: 2046: 2031: 2025: 2024: 2022: 2020: 2005: 1999: 1998: 1996: 1994: 1982: 1969: 1968: 1966: 1964: 1950: 1944: 1943: 1941: 1939: 1924: 1918: 1912: 1906: 1900: 1894: 1888: 1879: 1873: 1862: 1856: 1850: 1844: 1838: 1832: 1826: 1820: 1814: 1808: 1802: 1801: 1799: 1797: 1781: 1775: 1769: 1763: 1757: 1751: 1750: 1748: 1746: 1735:"Fiddle Physics" 1731: 1714: 1708: 1702: 1701: 1699: 1697: 1681: 1668: 1662: 1647: 1641: 1630: 1624: 1618: 1612: 1606: 1600: 1594: 1588: 1582: 1576: 1567: 1566: 1564: 1562: 1550: 1544: 1538: 1532: 1526: 1520: 1514: 1503: 1497: 1491: 1485: 1437: 1436: 1432: 1429: 1419: 1418: 1414: 1411: 1391: 1390: 1374: 1373: 1293:laser technology 1158: 1112: 1103: 1089:Helmholtz motion 1001:Violin technique 922: 920: 919: 914: 912: 910: 899: 877: 875: 874: 871: 868: 858: 856: 855: 850: 848: 840: 835: 827: 801: 799: 798: 793: 791: 786: 781: 755: 747:Erich Donnerhack 722: 720: 719: 714: 712: 709: 698: 697: 695: 687: 658: 656: 655: 650: 648: 643: 639: 633: 558: 537: 536: 532: 529: 493:effects and the 405: 382:Carleen Hutchins 329:Two New Sciences 320:Vincenzo Galilei 309:consonant sounds 222:each affect the 200:vibrating string 198:The energy of a 173:Violin acoustics 162: 155: 148: 40: 33: 32: 4401: 4400: 4396: 4395: 4394: 4392: 4391: 4390: 4371: 4370: 4369: 4364: 4344: 4330:Violin lutherie 4266: 4242:Lira da braccio 4210: 4171:Violin concerto 4128: 4122: 4022: 3933: 3905: 3891:Cello da spalla 3886:Baritone violin 3867: 3839: 3825:Violino piccolo 3810:Electric violin 3789: 3784: 3754: 3749: 3731: 3683: 3674:D. Van Holliday 3612: 3581:Mersenne's laws 3515:Audio frequency 3509: 3473:Psychoacoustics 3467: 3466: 3459: 3445: 3402: 3397: 3321: 3307: 3276: 3253: 3243: 3193: 3187: 3167: 3126: 3119: 3096: 3091: 3088: 3086:Further reading 3075: 3073: 3061: 3036:Wood, Alexander 3028: 3009: 2988: 2969: 2922: 2918: 2902:Olson, Harry F. 2859: 2855: 2770: 2749: 2728: 2723: 2715: 2711: 2703: 2696: 2688: 2681: 2673: 2669: 2661: 2657: 2649: 2645: 2637: 2633: 2625: 2621: 2611: 2609: 2599: 2595: 2587: 2583: 2573: 2571: 2568:Music Acoustics 2560: 2556: 2548: 2544: 2536: 2532: 2524: 2520: 2512: 2508: 2500: 2496: 2488: 2484: 2476: 2472: 2464: 2460: 2452: 2448: 2440: 2436: 2428: 2424: 2416: 2412: 2404: 2400: 2392: 2385: 2377: 2373: 2365: 2361: 2353: 2349: 2341: 2337: 2329: 2325: 2317: 2313: 2305: 2301: 2293: 2289: 2279: 2277: 2274:Music Acoustics 2266: 2259: 2249: 2247: 2242: 2241: 2237: 2229: 2225: 2217: 2213: 2176: 2172: 2133: 2126: 2118: 2114: 2106: 2102: 2094: 2081: 2073: 2066: 2058: 2054: 2044: 2042: 2033: 2032: 2028: 2018: 2016: 2014:mentalfloss.com 2006: 2002: 1992: 1990: 1983: 1972: 1962: 1960: 1952: 1951: 1947: 1937: 1935: 1926: 1925: 1921: 1913: 1909: 1901: 1897: 1889: 1882: 1874: 1865: 1857: 1853: 1845: 1841: 1833: 1829: 1821: 1817: 1809: 1805: 1795: 1793: 1782: 1778: 1770: 1766: 1758: 1754: 1744: 1742: 1739:Physics Central 1733: 1732: 1717: 1709: 1705: 1695: 1693: 1690:Music Acoustics 1682: 1671: 1663: 1650: 1642: 1633: 1625: 1621: 1613: 1609: 1601: 1597: 1589: 1585: 1577: 1570: 1560: 1558: 1551: 1547: 1539: 1535: 1527: 1523: 1515: 1506: 1498: 1494: 1486: 1477: 1473: 1434: 1430: 1427: 1425: 1416: 1412: 1409: 1407: 1401: 1400: 1399: 1398: 1394: 1393: 1392: 1385: 1380: 1379: 1378: 1375: 1368: 1361: 1348: 1309: 1258: 1226: 1220: 1160: 1152: 1147: 1143: 1139: 1135: 1131: 1127: 1122: 1121: 1120: 1119: 1115: 1114: 1113: 1105: 1104: 1091: 1063: 1020:Pernambuco wood 1003: 997: 968: 964: 958: 930: 903: 898: 890: 887: 886: 872: 869: 866: 865: 863: 839: 826: 818: 815: 814: 782: 780: 772: 769: 768: 749: 739: 702: 696: 686: 678: 675: 674: 664:Young's modulus 662:where E is the 635: 634: 632: 618: 615: 614: 608: 553: 534: 530: 527: 525: 400: 398: 325:Galileo Galilei 298: 226:, but only the 166: 123: 120: 17: 12: 11: 5: 4399: 4389: 4388: 4383: 4366: 4365: 4363: 4362: 4349: 4346: 4345: 4343: 4342: 4337: 4332: 4327: 4322: 4317: 4312: 4307: 4306: 4305: 4300: 4295: 4293:Bass amplifier 4285: 4280: 4274: 4272: 4268: 4267: 4265: 4264: 4259: 4254: 4249: 4244: 4239: 4234: 4229: 4224: 4218: 4216: 4212: 4211: 4209: 4208: 4206:Carnatic music 4203: 4198: 4193: 4188: 4183: 4181:Cello concerto 4178: 4176:Viola concerto 4173: 4168: 4163: 4161:String section 4158: 4153: 4148: 4146:String quintet 4143: 4138: 4136:String quartet 4132: 4130: 4124: 4123: 4121: 4120: 4115: 4109: 4104: 4103: 4102: 4092: 4087: 4082: 4077: 4072: 4071: 4070: 4065: 4060: 4055: 4050: 4043: 4032: 4030: 4024: 4023: 4021: 4020: 4015: 4010: 4005: 4000: 3995: 3990: 3985: 3980: 3975: 3970: 3965: 3964: 3963: 3953: 3947: 3945: 3939: 3938: 3935: 3934: 3932: 3931: 3926: 3921: 3915: 3913: 3907: 3906: 3904: 3903: 3901:Electric cello 3898: 3893: 3888: 3883: 3877: 3875: 3869: 3868: 3866: 3865: 3860: 3855: 3853:Vertical viola 3849: 3847: 3841: 3840: 3838: 3837: 3832: 3827: 3822: 3817: 3812: 3806: 3804: 3795: 3791: 3790: 3783: 3782: 3775: 3768: 3760: 3751: 3750: 3748: 3747: 3736: 3733: 3732: 3730: 3729: 3728: 3727: 3722: 3712: 3707: 3702: 3697: 3691: 3689: 3688:Related topics 3685: 3684: 3682: 3681: 3676: 3671: 3669:Joseph Sauveur 3666: 3661: 3656: 3654:Marin Mersenne 3651: 3646: 3641: 3636: 3631: 3626: 3620: 3618: 3614: 3613: 3611: 3610: 3605: 3604: 3603: 3593: 3588: 3583: 3578: 3573: 3572: 3571: 3566: 3561: 3551: 3550: 3549: 3539: 3534: 3529: 3523: 3521: 3511: 3510: 3508: 3507: 3506: 3505: 3495: 3494: 3493: 3488: 3477: 3475: 3469: 3468: 3465: 3464: 3457: 3449: 3448: 3446: 3444: 3443: 3438: 3433: 3428: 3423: 3418: 3412: 3410: 3404: 3403: 3396: 3395: 3388: 3381: 3373: 3367: 3366: 3348: 3343: 3337: 3331: 3320: 3319:External links 3317: 3316: 3315: 3274: 3251: 3232:Saunders, F.A. 3228: 3227: 3226: 3225: 3224:(pp. 332-389). 3219: 3218:(pp. 277-331). 3213: 3204: 3203: 3191: 3185: 3165: 3139:(1): 482–491. 3124: 3122:on 2019-03-07. 3107:(2–3): 23–42. 3087: 3084: 3083: 3082: 3054: 3032: 3026: 3013: 3007: 2992: 2986: 2973: 2967: 2953:Rigden, John S 2949: 2933:Piston, Walter 2929: 2916: 2898: 2888: 2866: 2853: 2835: 2813: 2794: 2780:, ed. (1886). 2778:Chisholm, Hugh 2774: 2768: 2753: 2747: 2733:Beament, James 2727: 2724: 2722: 2721: 2719:, p. 143. 2709: 2694: 2679: 2667: 2665:, p. 142. 2655: 2643: 2631: 2619: 2593: 2581: 2554: 2542: 2530: 2528:, p. 931. 2518: 2506: 2494: 2482: 2480:, p. 100. 2470: 2468:, p. 587. 2458: 2456:, p. 198. 2446: 2434: 2422: 2410: 2408:, p. 580. 2398: 2383: 2381:, p. 579. 2371: 2359: 2347: 2335: 2323: 2311: 2299: 2297:, p. 588. 2287: 2257: 2235: 2223: 2211: 2170: 2124: 2112: 2100: 2079: 2064: 2052: 2026: 2000: 1970: 1945: 1919: 1917:, p. 588. 1907: 1895: 1880: 1863: 1851: 1839: 1827: 1815: 1813:, p. 118. 1803: 1776: 1764: 1752: 1715: 1703: 1669: 1667:, p. 591. 1648: 1631: 1619: 1607: 1595: 1583: 1581:, p. 374. 1579:Helmholtz 1895 1568: 1555:"Félix Savart" 1545: 1533: 1531:, p. 100. 1521: 1504: 1492: 1474: 1472: 1469: 1396: 1395: 1383: 1382: 1381: 1376: 1366: 1365: 1364: 1363: 1362: 1360: 1357: 1347: 1344: 1308: 1305: 1301:modal analysis 1256: 1251:magnetic field 1219: 1216: 1189:mathematicians 1145: 1141: 1137: 1133: 1129: 1125: 1117: 1116: 1107: 1106: 1098: 1097: 1096: 1095: 1094: 1092: 1090: 1087: 1083:Sul ponticello 1075:sulla tastiera 1062: 1059: 1009:Violin and bow 996: 993: 966: 962: 957: 954: 929: 926: 925: 924: 909: 906: 902: 897: 894: 860: 859: 846: 843: 838: 833: 830: 825: 822: 804: 803: 789: 785: 779: 776: 745:The violinist 738: 735: 724: 723: 708: 705: 701: 693: 690: 685: 682: 660: 659: 646: 642: 638: 631: 628: 625: 622: 607: 604: 485:, length, and 437:standing waves 397: 394: 390:modal analysis 386:Simone Sacconi 348:multi-harmonic 297: 294: 269:more quickly. 216:standing waves 191:, such as the 185:its many parts 168: 167: 165: 164: 157: 150: 142: 139: 138: 132: 131: 125: 124: 117: 114: 113: 107: 106: 100: 99: 93: 92: 90:Musical styles 86: 85: 79: 78: 72: 71: 65: 64: 58: 57: 51: 50: 42: 41: 15: 9: 6: 4: 3: 2: 4398: 4387: 4384: 4382: 4379: 4378: 4376: 4361: 4360: 4351: 4350: 4347: 4341: 4338: 4336: 4333: 4331: 4328: 4326: 4323: 4321: 4318: 4316: 4313: 4311: 4308: 4304: 4301: 4299: 4296: 4294: 4291: 4290: 4289: 4286: 4284: 4281: 4279: 4276: 4275: 4273: 4269: 4263: 4260: 4258: 4255: 4253: 4250: 4248: 4245: 4243: 4240: 4238: 4235: 4233: 4230: 4228: 4225: 4223: 4220: 4219: 4217: 4213: 4207: 4204: 4202: 4199: 4197: 4194: 4192: 4191:Violin sonata 4189: 4187: 4184: 4182: 4179: 4177: 4174: 4172: 4169: 4167: 4164: 4162: 4159: 4157: 4154: 4152: 4151:String sextet 4149: 4147: 4144: 4142: 4139: 4137: 4134: 4133: 4131: 4125: 4119: 4116: 4113: 4110: 4108: 4105: 4101: 4098: 4097: 4096: 4093: 4091: 4088: 4086: 4083: 4081: 4078: 4076: 4073: 4069: 4066: 4064: 4061: 4059: 4056: 4054: 4051: 4049: 4048: 4044: 4042: 4039: 4038: 4037: 4034: 4033: 4031: 4029: 4025: 4019: 4016: 4014: 4011: 4009: 4006: 4004: 4003:Shoulder rest 4001: 3999: 3996: 3994: 3991: 3989: 3986: 3984: 3981: 3979: 3976: 3974: 3971: 3969: 3966: 3962: 3959: 3958: 3957: 3954: 3952: 3949: 3948: 3946: 3944: 3940: 3930: 3927: 3925: 3922: 3920: 3917: 3916: 3914: 3912: 3908: 3902: 3899: 3897: 3894: 3892: 3889: 3887: 3884: 3882: 3879: 3878: 3876: 3874: 3870: 3864: 3861: 3859: 3858:Viola pomposa 3856: 3854: 3851: 3850: 3848: 3846: 3842: 3836: 3833: 3831: 3828: 3826: 3823: 3821: 3818: 3816: 3813: 3811: 3808: 3807: 3805: 3803: 3799: 3796: 3792: 3788: 3787:Violin family 3781: 3776: 3774: 3769: 3767: 3762: 3761: 3758: 3746: 3738: 3737: 3734: 3726: 3723: 3721: 3718: 3717: 3716: 3713: 3711: 3708: 3706: 3703: 3701: 3698: 3696: 3693: 3692: 3690: 3686: 3680: 3677: 3675: 3672: 3670: 3667: 3665: 3664:Lord Rayleigh 3662: 3660: 3657: 3655: 3652: 3650: 3647: 3645: 3642: 3640: 3637: 3635: 3634:Ernst Chladni 3632: 3630: 3627: 3625: 3622: 3621: 3619: 3615: 3609: 3606: 3602: 3599: 3598: 3597: 3596:Standing wave 3594: 3592: 3589: 3587: 3584: 3582: 3579: 3577: 3574: 3570: 3567: 3565: 3564:Inharmonicity 3562: 3560: 3557: 3556: 3555: 3552: 3548: 3545: 3544: 3543: 3540: 3538: 3535: 3533: 3530: 3528: 3525: 3524: 3522: 3520: 3516: 3512: 3504: 3501: 3500: 3499: 3496: 3492: 3489: 3487: 3484: 3483: 3482: 3479: 3478: 3476: 3474: 3470: 3462: 3458: 3455: 3451: 3450: 3442: 3439: 3437: 3434: 3432: 3431:Soundproofing 3429: 3427: 3426:Reverberation 3424: 3422: 3419: 3417: 3414: 3413: 3411: 3409: 3405: 3401: 3394: 3389: 3387: 3382: 3380: 3375: 3374: 3371: 3364: 3360: 3359:Chladni plate 3356: 3352: 3349: 3347: 3344: 3341: 3338: 3335: 3332: 3330: 3326: 3323: 3322: 3311: 3304: 3300: 3296: 3292: 3288: 3284: 3280: 3275: 3270: 3266: 3262: 3261: 3256: 3255:Savart, Félix 3252: 3247: 3241: 3237: 3233: 3230: 3229: 3223: 3220: 3217: 3214: 3211: 3208: 3207: 3206: 3205: 3200: 3196: 3192: 3188: 3182: 3178: 3175: 3171: 3166: 3162: 3158: 3154: 3150: 3146: 3142: 3138: 3134: 3130: 3125: 3118: 3114: 3110: 3106: 3102: 3095: 3090: 3089: 3071: 3067: 3066:Acta Acustica 3060: 3055: 3051: 3047: 3043: 3042: 3037: 3033: 3029: 3023: 3019: 3014: 3010: 3004: 3000: 2999: 2993: 2989: 2983: 2979: 2974: 2970: 2964: 2960: 2959: 2954: 2950: 2946: 2942: 2938: 2937:Orchestration 2934: 2930: 2926: 2919: 2913: 2909: 2908: 2903: 2899: 2896: 2892: 2889: 2885: 2881: 2877: 2876: 2871: 2867: 2863: 2856: 2850: 2846: 2845: 2840: 2836: 2832: 2828: 2824: 2823: 2818: 2814: 2810: 2806: 2802: 2801: 2795: 2791: 2790: 2784: 2779: 2775: 2771: 2765: 2761: 2760: 2754: 2750: 2744: 2740: 2739: 2734: 2730: 2729: 2718: 2713: 2707:, p. 98. 2706: 2701: 2699: 2691: 2690:Chisholm 1886 2686: 2684: 2677:, p. 80. 2676: 2671: 2664: 2659: 2653:, p. 77. 2652: 2647: 2640: 2635: 2628: 2623: 2608: 2604: 2597: 2590: 2585: 2569: 2565: 2558: 2552:, p. 33. 2551: 2546: 2539: 2534: 2527: 2522: 2516:, p. 62. 2515: 2514:Hutchins 1978 2510: 2504:, p. 58. 2503: 2502:Hutchins 1978 2498: 2491: 2490:Hutchins 1978 2486: 2479: 2474: 2467: 2462: 2455: 2450: 2444:, p. 10. 2443: 2438: 2431: 2426: 2419: 2414: 2407: 2402: 2395: 2390: 2388: 2380: 2375: 2369:, p. 21. 2368: 2363: 2357:, p. 20. 2356: 2351: 2345:, p. 29. 2344: 2339: 2332: 2327: 2320: 2315: 2309:, p. 10. 2308: 2303: 2296: 2291: 2275: 2271: 2264: 2262: 2245: 2239: 2233:, p. 98. 2232: 2227: 2221:, p. 35. 2220: 2215: 2206: 2201: 2197: 2193: 2189: 2185: 2181: 2174: 2166: 2162: 2158: 2154: 2150: 2146: 2142: 2138: 2131: 2129: 2122:, p. 28. 2121: 2116: 2109: 2108:Siminoff 2002 2104: 2098:, p. 59. 2097: 2096:Hutchins 1978 2092: 2090: 2088: 2086: 2084: 2077:, p. 35. 2076: 2071: 2069: 2062:, p. 11. 2061: 2056: 2040: 2039:Quinn Violins 2036: 2030: 2015: 2011: 2004: 1988: 1981: 1979: 1977: 1975: 1959: 1955: 1949: 1933: 1932:Get-Tuned.com 1929: 1923: 1916: 1911: 1905:, p. 58. 1904: 1899: 1892: 1887: 1885: 1878:, p. 30. 1877: 1872: 1870: 1868: 1860: 1855: 1848: 1843: 1837:, p. 52. 1836: 1831: 1825:, p. 40. 1824: 1819: 1812: 1807: 1791: 1787: 1780: 1774:, p. 55. 1773: 1768: 1761: 1756: 1740: 1736: 1730: 1728: 1726: 1724: 1722: 1720: 1713:, p. 12. 1712: 1711:Hutchins 1978 1707: 1691: 1687: 1680: 1678: 1676: 1674: 1666: 1661: 1659: 1657: 1655: 1653: 1646:, p. 97. 1645: 1640: 1638: 1636: 1628: 1623: 1616: 1611: 1604: 1599: 1593:, p. 99. 1592: 1587: 1580: 1575: 1573: 1556: 1549: 1543:, p. 57. 1542: 1541:Hutchins 1978 1537: 1530: 1525: 1519:, p. 90. 1518: 1513: 1511: 1509: 1501: 1496: 1490:, p. 61. 1489: 1488:Hutchins 1978 1484: 1482: 1480: 1475: 1468: 1460: 1456: 1453: 1448: 1446: 1442: 1423: 1404: 1356: 1353: 1343: 1341: 1336: 1334: 1329: 1326: 1322: 1313: 1304: 1302: 1298: 1294: 1290: 1286: 1282: 1277: 1275: 1274:Ernst Chladni 1271: 1265: 1261: 1259: 1252: 1248: 1242: 1240: 1230: 1225: 1215: 1213: 1209: 1205: 1201: 1195: 1193: 1192:Joseph Keller 1190: 1186: 1181: 1177: 1172: 1169: 1165: 1159: 1156: 1149: 1111: 1102: 1086: 1084: 1080: 1079:Walter Piston 1076: 1071: 1068: 1067:perpendicular 1058: 1056: 1052: 1048: 1044: 1040: 1039:balance point 1035: 1033: 1029: 1025: 1021: 1016: 1007: 1002: 992: 989: 985: 981: 979: 975: 970: 953: 950: 947:strings) are 946: 942: 938: 933: 907: 904: 900: 895: 892: 885: 884: 883: 881: 844: 841: 836: 831: 828: 823: 820: 813: 812: 811: 809: 787: 783: 777: 774: 767: 766: 765: 763: 753: 748: 743: 734: 732: 727: 706: 703: 699: 691: 688: 683: 680: 673: 672: 671: 669: 665: 644: 640: 629: 626: 623: 620: 613: 612: 611: 603: 601: 597: 593: 588: 586: 582: 578: 575: 567: 563: 562:G major scale 551: 549: 545: 541: 523: 519: 515: 510: 508: 504: 500: 496: 492: 489:, as well as 488: 484: 479: 477: 473: 469: 465: 461: 452: 448: 446: 442: 441:superposition 438: 434: 430: 426: 422: 418: 410: 393: 391: 387: 383: 379: 375: 372:The violin's 370: 368: 364: 360: 357: 353: 350:sound from a 349: 344: 342: 338: 334: 330: 326: 321: 318: 314: 310: 306: 303: 293: 291: 287: 283: 279: 275: 270: 268: 264: 260: 256: 252: 248: 243: 241: 237: 233: 229: 225: 221: 217: 213: 209: 205: 201: 196: 194: 190: 189:violin family 186: 182: 178: 174: 163: 158: 156: 151: 149: 144: 143: 141: 140: 137: 134: 133: 130: 127: 126: 122: 116: 115: 112: 109: 108: 105: 102: 101: 98: 95: 94: 91: 88: 87: 84: 81: 80: 77: 74: 73: 70: 67: 66: 63: 60: 59: 56: 53: 52: 48: 44: 43: 39: 35: 34: 28: 23: 19: 4357: 4340:Violin octet 4320:Stradivarius 4277: 4201:Cello sonata 4196:Viola sonata 4156:String octet 4045: 3863:Tenor violin 3835:Stroh violin 3724: 3679:Thomas Young 3629:Jens Blauert 3617:Acousticians 3289:(1): 26–41. 3286: 3282: 3259: 3239: 3212:(pp. 1-276). 3198: 3177: 3173: 3169: 3136: 3132: 3117:the original 3104: 3100: 3074:. Retrieved 3069: 3065: 3040: 3018:On Sonic Art 3017: 2997: 2977: 2957: 2936: 2906: 2874: 2843: 2821: 2799: 2787: 2758: 2737: 2726:Bibliography 2712: 2670: 2658: 2646: 2634: 2622: 2610:. Retrieved 2606: 2596: 2584: 2572:. Retrieved 2567: 2562:Wolfe, Joe. 2557: 2550:Beament 1997 2545: 2533: 2521: 2509: 2497: 2485: 2473: 2461: 2449: 2437: 2425: 2413: 2401: 2374: 2362: 2350: 2343:Beament 1997 2338: 2333:, p. 8. 2326: 2314: 2302: 2290: 2278:. Retrieved 2273: 2268:Wolfe, Joe. 2248:. Retrieved 2238: 2226: 2214: 2187: 2183: 2173: 2140: 2136: 2120:Beament 1997 2115: 2103: 2075:Beament 1997 2055: 2043:. Retrieved 2038: 2029: 2017:. Retrieved 2013: 2003: 1991:. Retrieved 1961:. Retrieved 1957: 1948: 1936:. Retrieved 1931: 1922: 1915:Rossing 2014 1910: 1898: 1893:, p. 7. 1876:Beament 1997 1854: 1849:, p. 5. 1842: 1830: 1818: 1806: 1794:. Retrieved 1789: 1779: 1767: 1755: 1743:. Retrieved 1738: 1706: 1694:. Retrieved 1689: 1684:Wolfe, Joe. 1665:Rossing 2014 1629:, p. 4. 1622: 1610: 1598: 1586: 1559:. Retrieved 1548: 1536: 1529:Galilei 1914 1524: 1502:, Chapter 3. 1500:Wishart 1996 1495: 1465: 1449: 1405: 1402: 1349: 1337: 1330: 1318: 1278: 1266: 1262: 1243: 1235: 1196: 1173: 1161: 1154: 1151: 1123: 1082: 1074: 1072: 1064: 1036: 1012: 986: 982: 971: 959: 934: 931: 861: 805: 759: 728: 725: 661: 609: 589: 580: 576: 571: 511: 480: 457: 417:open strings 414: 371: 359:Félix Savart 345: 331:(1638). The 328: 299: 290:open strings 271: 244: 197: 172: 171: 111:Construction 103: 27:Andrea Amati 18: 4310:Jazz violin 4252:Nyckelharpa 4237:Hurdy-gurdy 4141:String trio 4085:Double stop 3988:Fingerboard 3911:Double bass 3881:Bass violin 3794:Instruments 3649:Franz Melde 3624:John Backus 3608:Subharmonic 3461:Spectrogram 3273:(in French) 3195:Raman, C.V. 2717:Rigden 1977 2705:Piston 1976 2675:Piston 1976 2663:Rigden 1977 2651:Piston 1976 2639:Piston 1976 2367:Piston 1976 2355:Piston 1976 2331:Piston 1976 2307:Piston 1976 2219:Piston 1976 2190:(S1): S43. 2143:(5): 7248. 1891:Piston 1976 1859:Piston 1976 1847:Piston 1976 1835:Piston 1976 1823:Piston 1976 1760:Piston 1976 1627:Piston 1976 1445:John Rigden 1180:C. V. Raman 750: [ 548:double bass 499:fingerboard 411:on a violin 274:double bass 121:maintenance 4375:Categories 4222:Arpeggione 4112:Scordatura 4041:Bow stroke 4028:Techniques 4018:Tuning peg 4008:Sound post 3710:Ultrasound 3700:Infrasound 3486:Bark scale 3314:(May 2020) 3250:(May 2020) 2945:1016330383 2627:Olson 1967 2526:Bucur 2018 2454:Olson 1967 2442:Farga 1969 2060:Farga 1969 1811:Olson 1967 1615:Bucur 2018 1603:Bucur 2018 1346:Wolf tones 1325:sound post 1297:efficiency 1222:See also: 1178:physicist 1028:stick-slip 961:20 lb 956:The bridge 880:wavelength 583:note, the 564:played by 522:whole tone 445:sine waves 305:Pythagoras 247:bow stroke 119:Making and 62:Violinists 4381:Acoustics 4303:Slap bass 4288:Jazz bass 4127:Ensembles 4107:Pizzicato 4100:Bariolage 4090:Fingering 4080:Harmonics 4047:Col legno 4013:Tailpiece 3591:Resonance 3491:Mel scale 3421:Monochord 3400:Acoustics 3072:: 579–589 3050:640010938 2831:708455337 2819:(1914) . 2589:Wood 1944 2538:Wood 1944 2478:Wood 1944 2319:Wood 1944 2231:Wood 1944 1989:. Strings 1903:Wood 1944 1772:Wood 1944 1644:Wood 1944 1591:Wood 1944 1517:Wood 1944 1441:orchestra 1352:wolf tone 1239:sound box 991:quietly. 949:helically 928:Materials 845:λ 808:frequency 784:λ 637:Δ 596:oscillate 581:pizzicato 577:pizzicato 514:fingering 507:unfretted 495:stiffness 472:amplitude 464:overtones 356:physicist 337:acoustics 278:orchestra 255:sound box 245:During a 220:harmonics 104:Acoustics 97:Technique 4359:Category 4298:Big band 4257:Pochette 4075:Arpeggio 4063:Spiccato 3973:Chinrest 3951:Bass bar 3929:Octobass 3815:Pochette 3745:Category 3586:Overtone 3554:Harmonic 3269:24148967 3257:(1819). 3161:16875244 3113:17812511 3101:STL-QPSR 3038:(1944). 2955:(1977). 2935:(1976). 2904:(1967). 2841:(1978). 2809:68030679 2735:(1997). 2165:55533227 1333:leverage 1321:bass bar 1218:The body 1128:b and bc 585:decaying 568:a violin 566:plucking 518:interval 462:and its 317:composer 313:lutenist 259:bass bar 129:Luthiers 76:Fiddlers 47:a series 45:Part of 4386:Violins 4262:Quinton 4227:Baryton 4118:Vibrato 4068:Tremolo 4058:Portato 4053:Martelé 3924:Violone 3896:Cellone 3532:Formant 3355:YouTube 3291:Bibcode 3141:Bibcode 2884:1453852 2607:Strings 2192:Bibcode 2145:Bibcode 1433:⁄ 1415:⁄ 1247:current 1157:(1865). 995:The bow 978:formant 876:⁠ 864:⁠ 606:Tension 592:vibrato 533:⁄ 491:damping 483:tension 443:of two 423:to the 396:Strings 367:plucked 288:of its 267:dampens 265:string 263:plucked 251:f-holes 232:tension 83:History 4247:Lirone 4036:Bowing 3998:Scroll 3983:F-hole 3978:Endpin 3968:Bridge 3802:Violin 3725:Violin 3559:Series 3267: 3238:", in 3222:Part 3 3216:Part 2 3210:Part 1 3183: 3159: 3111: 3076:11 May 3048: 3024: 3005: 2984: 2965: 2943: 2914: 2882: 2851: 2829: 2807: 2766: 2745: 2612:11 May 2280:15 May 2163: 2041:. 2020 1934:. 2020 1452:octave 1323:and a 1176:Indian 1144:and bc 1136:and bc 988:Muting 941:Perlon 937:catgut 882:, so 806:For a 762:period 737:Length 468:timbre 433:string 421:bridge 240:catgut 224:timbre 212:string 204:bridge 181:violin 136:Family 69:Fiddle 55:Violin 4315:Rosin 4271:Other 3943:Parts 3873:Cello 3845:Viola 3720:Piano 3705:Sound 3519:pitch 3481:Pitch 3120:(PDF) 3109:S2CID 3097:(PDF) 3062:(PDF) 2574:7 May 2250:6 May 2161:S2CID 2045:6 May 2019:6 May 1993:6 May 1963:6 May 1938:6 May 1796:6 May 1745:6 May 1696:6 May 1561:8 May 1471:Notes 1422:fifth 1270:plate 1140:or ac 1047:power 1024:rosin 764:T, 754:] 574:Ital. 544:cello 540:viola 429:pitch 409:bowed 352:bowed 286:pitch 282:cello 208:sound 193:viola 4325:Viol 3961:Frog 3695:Echo 3601:Node 3527:Beat 3517:and 3265:OCLC 3181:ISBN 3157:PMID 3078:2020 3046:OCLC 3022:ISBN 3003:ISBN 2982:ISBN 2963:ISBN 2941:OCLC 2912:ISBN 2880:OCLC 2849:ISBN 2827:OCLC 2805:OCLC 2764:ISBN 2743:ISBN 2614:2020 2576:2020 2282:2020 2252:2020 2047:2020 2021:2020 1995:2020 1965:2020 1940:2020 1798:2020 1747:2020 1698:2020 1563:2020 1174:The 1164:apex 974:node 590:The 542:, a 512:The 487:mass 415:The 315:and 236:mass 3993:Nut 3956:Bow 3299:doi 3149:doi 3137:120 2200:doi 2153:doi 2141:123 1790:JOS 1148:." 1015:bow 810:f 425:nut 339:of 25:An 4377:: 3353:a 3297:. 3287:53 3285:. 3281:. 3155:. 3147:. 3135:. 3131:. 3105:36 3103:. 3099:. 3070:90 3068:. 3064:. 2786:. 2697:^ 2682:^ 2605:. 2566:. 2386:^ 2272:. 2260:^ 2198:. 2188:71 2186:. 2182:. 2159:. 2151:. 2139:. 2127:^ 2082:^ 2067:^ 2037:. 2012:. 1973:^ 1956:. 1930:. 1883:^ 1866:^ 1788:. 1737:. 1718:^ 1688:. 1672:^ 1651:^ 1634:^ 1571:^ 1507:^ 1478:^ 1426:23 1408:27 1319:A 1260:. 1057:. 1055:dB 752:de 600:Hz 560:A 550:. 478:. 343:. 292:. 195:. 49:on 3779:e 3772:t 3765:v 3392:e 3385:t 3378:v 3312:) 3308:( 3305:. 3301:: 3293:: 3271:. 3248:) 3244:( 3201:. 3189:. 3163:. 3151:: 3143:: 3080:. 3052:. 3030:. 3011:. 2990:. 2971:. 2947:. 2927:) 2923:( 2920:. 2886:. 2864:) 2860:( 2857:. 2833:. 2811:. 2772:. 2751:. 2692:. 2616:. 2578:. 2284:. 2254:. 2208:. 2202:: 2194:: 2167:. 2155:: 2147:: 2049:. 2023:. 1997:. 1967:. 1942:. 1800:. 1749:. 1700:. 1565:. 1435:8 1431:3 1428:+ 1417:4 1413:1 1410:+ 1257:4 1255:A 1146:2 1142:2 1138:1 1134:1 1130:2 1126:1 967:f 963:f 945:E 923:. 908:L 905:2 901:v 896:= 893:f 873:2 870:/ 867:1 842:v 837:= 832:T 829:1 824:= 821:f 802:. 788:T 778:= 775:v 707:M 704:L 700:T 692:2 689:1 684:= 681:f 645:L 641:L 630:S 627:E 624:= 621:T 535:4 531:1 528:+ 526:1 161:e 154:t 147:v

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Index