Violin acoustics - Knowledge (XXG)

1478:

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.

260:, 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 3465: 1112: 987:, 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 1121: 33: 1470: 1458:, 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. 753: 462: 1323: 4365: 3752: 1177:(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 1240: 1017: 1346:. 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. 520:, 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. 249:. 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 1338:

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

1255:

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

1193:

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

1001:

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

1208:

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

1477:

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

1213:, based on the complex relationship behaviour of the bow's velocity and the frictional forces that were present. The model was a success in simulating Helmholtz motion (including the 'flattening' effect of the motion caused by larger forces), and was later extended to take into account the string's 1247:

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

1365:

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

1080:

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

962:

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

1028:

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

1274:

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

1449:

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

1256:

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

1081:

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.

950:, 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 677:, 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 333:

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

1181:

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.

590:), 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 1314:, 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. 994:

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.

971:

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:

1278:

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

1465:

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.

1135:"...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 481:. 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 1096:—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. 1283:. 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 391:

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

1221:

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

868: 1298:, 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 732: 1366:

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.

1450:

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

668: 1264:. 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 744:. 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). 1056:. 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 811: 567: 268:

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

1361:

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

932: 414: 3269: 943:

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.

1129:

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

549:

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

3104: 1342:

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

4028: 1052:

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

741: 566: 508:

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

3232: 3226: 1173:

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

980:(220 N). The string 'break' angle made by the string across the bridge affects the downward force, and is typically 13 to 15° to the horizontal. 3220: 253:

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.

3347:

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

413: 3788: 3674: 1252:

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

1217:, its twisting motion, and the effect on the string of body vibrations and the distortion of the bow hair. However, the model assumed that the 1414:

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.

3195: 3036: 3017: 2996: 2977: 2926: 2863: 2778: 2757: 1398: 403:, a technique that was, according to the acoustician George Bissinger, "of enormous importance for understanding acoustics of the violin". 1294:, which enables analysis of the motion of the violin surface to be measured, a method first developed by scientists in the 1960s, and the 387:

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

3401: 565: 399:. Hutchins' work dominated the field of violin acoustics for twenty years from the 1960s onwards, until it was superseded by the use of 1382: 49: 3356: 1399: 3953: 1225:

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.

195: 121: 2747: 1381: 2799: 170: 1339:

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

983:

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

3344: 412: 827: 4340: 4267: 3825: 3339: 1234: 687: 516:

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

129: 3350: 4272: 1307: 1045:

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

3781: 3007: 1210: 3513: 1092:

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

1024:

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

318:, who is thought to have been the first to observe the relationship between the lengths of vibrating strings and the 3208:(1918). "On the mechanical theory of vibrations of bowed strings and of musical instruments of the violin family". 3046: 2886:

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

1291: 380:

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

312: 3320: 3256: 2935: 2872: 3634: 3242: 627: 319: 3127: 2146:

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

1469: 492:

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

272:

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

3689: 1299: 1275:

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

1111: 4003: 3569: 3426: 3394: 1997: 1796: 781: 451: 435: 396: 605:

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

4369: 4063: 3774: 3508: 3418: 2768: 1195: 2967: 2884: 2831: 963:

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

469:

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

4345: 4293: 3929: 3649: 3547: 3464: 3451: 2880: 1295: 678: 470: 373: 343: 238: 100: 93: 32: 3050: 2613: 1120: 899: 295:(violoncello), which is not adversely affected by having the optimum dimensions to correspond with the 3246: 2809: 2020: 757: 40:

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

4196: 3301: 3151: 2793: 2202: 2155: 1042: 351: 163: 2254: 1041:

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

4105: 3978: 3669: 3579: 3373: 3353:- animations of violins showing how the plates vibrate at various frequencies, from Borman Violins. 2905: 1350: 513: 493: 431: 388: 242: 214: 72: 3069: 2045: 4391: 3830: 3755: 3601: 3552: 3387: 3119: 2171: 1076:

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

3591: 976:(89 N) passes down through the bridge as a result of a tension in the strings of 50 lb 674: 1565: 4100: 3725: 3557: 3275: 3191: 3167: 3056: 3032: 3013: 2992: 2973: 2951: 2922: 2890: 2859: 2837: 2815: 2774: 2753: 1280: 1214: 1178: 1053: 737:

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

595: 524: 283:

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

187: 139: 1349:

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

477:, which cause the sound to have a quality that is individual to the instrument, known as the 4396: 4313: 4242: 4176: 4038: 3840: 3654: 3618: 3586: 3537: 3446: 3309: 3159: 2901: 2849: 2210: 2163: 1265: 1257: 1011: 955: 584: 528: 392: 330: 210: 107: 86: 57: 1745: 17: 4252: 4181: 4090: 3901: 3896: 3835: 3820: 3730: 3684: 3525: 3483: 2827: 1174: 1057: 752: 443: 335: 156: 3265: 1310:

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

762: 369: 3305: 3155: 2206: 2159: 1964: 4303: 4216: 4191: 4186: 4171: 4156: 4146: 4128: 4008: 3911: 3863: 3679: 3664: 3611: 3345:

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

2989:

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

2963: 2916: 2912: 1455: 1417:

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

1311: 1261: 1199: 1061: 1049: 1029:

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

984: 447: 427: 419: 400: 300: 226: 222: 3139: 1938: 1248:

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

873:

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

512:, but in some cases a string lightly touched with the fingertip is enough, causing an 461: 4385: 4201: 4161: 4013: 3868: 3797: 3644: 3606: 3574: 3529: 3491: 3441: 3436: 3369: 2943: 2853: 2788: 2743: 1432: 1284: 1202: 1089: 1077: 501: 439: 296: 277: 199: 146: 3123: 2175: 1322: 531:

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

4350: 4330: 4211: 4206: 4166: 3873: 3845: 3639: 2836:. Translated by Crew, Henry; de Salvio, Alfonso. New York: Dover Publications Inc. 998: 532: 37: 3289: 2574: 2046:"String Tech. Everything you wanted to know about strings, but were afraid to ask" 3357:

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

3335: 2792: 1397: 1380: 1060:

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

681:

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

4320: 4262: 4247: 4151: 4095: 4046: 3998: 3966: 3921: 3891: 3659: 3471: 3205: 1696: 1239: 1190: 1030: 1025: 558: 554: 509: 384: 292: 284: 241:

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

4232: 4122: 4051: 4018: 3993: 3720: 3710: 3496: 3361: 2955: 1461:

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

1335: 1038: 1016: 890: 486: 455: 362: 338:

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

315: 261: 257: 3060: 2841: 2280: 1033:, used because of its particular elastic properties. The hair is coated with 4298: 4117: 4110: 4057: 4023: 3501: 3431: 3410: 3279: 2819: 1451: 1362: 1249: 818: 772: 606: 576: 505: 482: 474: 377: 366: 347: 288: 273: 265: 230: 48: 3171: 2894: 1198:

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

446:

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

442:

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

4308: 4085: 4073: 3983: 3971: 3961: 3939: 3596: 3564: 1331: 1306:

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

1222: 1218: 358: 346:, though highly skilled, did not advance any scientific knowledge of the 327: 323: 269: 198:. These acoustic qualities are similar to those of other members of the 4237: 4078: 4068: 3934: 3906: 3542: 3365: 1065: 988: 951: 602: 572: 3313: 3163: 2400: 2398: 2215: 2190: 2167: 771:

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

4257: 3988: 3812: 1462: 947: 478: 250: 234: 191: 79: 65: 3105:"Observations on the violin bow and the interaction with the string" 4325: 3883: 3855: 3715: 1468: 1343: 1303: 1186: 1034: 1015: 959: 751: 610: 563: 550: 460: 410: 218: 203: 31: 485:—is heard. The violin is unusual in that it produces frequencies 4335: 3766: 3705: 3271:

Mémoire sur la construction des instrumens à cordes et à archets

1143:

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

517: 497: 465:

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

246: 3770: 3383: 1088:) produces what the 20th century American composer and author 1803:. Center for Computer Research in Music and Acoustics (CCRMA) 287:’s characteristics contribute to them being used less in the 3379: 598:

higher harmonics diminish more quickly than the lower ones.

221:

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

3336:

How does a violin work? An introduction to violin acoustics

1260:

through a metal string when it is placed in an oscillating

2889:(3rd ed.). London, New York: Longmans, Green and Co. 2773:. AG Switzerland: Cham Springer International Publishing. 1585: 1583: 1454:

as a solo instrument. According to the American physicist

1290:

Modern research has used sophisticated techniques such as

2102: 2100: 2098: 2096: 2094: 1671: 1669: 1667: 1665: 1663: 225:

are effectively stationary, allowing for the creation of

2081: 2079: 1882: 1880: 1878: 1494: 1492: 1490: 2711: 2709: 2696: 2694: 2749:

The Violin Explained: Components, Mechanism, and Sound

1897: 1895: 863:{\displaystyle f={\frac {1}{T}}={\frac {v}{\lambda }}} 1650: 1648: 1646: 1302:, the American acoustician George Bissinger has used 902: 830: 784: 690: 630: 613:

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

2770:

Handbook of Materials for String Musical Instruments

1523: 1521: 1519: 727:{\displaystyle f={1 \over 2}{\sqrt {\frac {T}{LM}}}} 4281: 4225: 4137: 4037: 3952: 3920: 3882: 3854: 3811: 3804: 3698: 3627: 3524: 3482: 3417: 1287:, who first developed this experimental technique. 740:The strings of a violin are attached to adjustable 311:The nature of vibrating strings was studied by the 3368:video of the patterns produced on a violin-shaped 1370:Comparison with other members of the violin family 1209:developed during the 1970s and 1980s to produce a 926: 862: 805: 726: 662: 621:The tension (T) in a stretched string is given by 583:When the violinist is directed to pluck a string ( 2476: 2440: 2428: 2416: 2404: 2389: 2305: 395:, and also Werner Lottermoser, Jürgen Meyer, and 365:string was first studied in detail by the French 322:they make. In the sixteenth century, the Italian 194:is created as the result of interactions between 3294:The Journal of the Acoustical Society of America 3251:The Journal of the Acoustical Society of America 3210:Indian Association of the Cultivation of Science 3144:The Journal of the Acoustical Society of America 2195:The Journal of the Acoustical Society of America 742:tuning pegs and (with some strings) finer tuners 3027:Wishart, Trevor (1996). Emmerson, Simon (ed.). 1194:lost energy when the wave was reflected with a 1104: 1998:"A Guide to Choosing the Right Violin Strings" 609:. A typical vibrato has a frequency of 6 418:The sound of the open strings (G, D, A and E) 3782: 3395: 2950:(7th ed.). London: Victor Gollancz Ltd. 2803:. Vol. 8. London: Smith, Elder & Co. 2752:. Oxford, New York: Oxford University Press. 2191:"An electronic violin with a singing formant" 1084:Bowing directly above the fingerboard (Ital. 954:. Violin strings (with the exception of most 164: 8: 3274:. Paris: Librairie Encyclopédique de Roret. 2148:Journal of the Acoustical Society of America 1435:lower than a violin (with a length of about 1431:inches (69.2 cm), with strings tuned a 430:of a violin are of the same length from the 217:to the body of the violin, which allows the 2858:. San Francisco: W.H. Fremman and Company. 663:{\displaystyle T=ES{\frac {{\Delta }L}{L}}} 264:on either side of the bridge. It acts as a 3808: 3789: 3775: 3767: 3402: 3388: 3380: 171: 157: 43: 2614:"How to Tame Annoying Howling Wolf Tones" 2214: 1740: 1738: 1736: 1734: 1732: 1730: 1589: 946:Violin strings were originally made from 909: 901: 850: 837: 829: 793: 791: 783: 707: 697: 689: 646: 643: 629: 487:beyond the upper audible limit for humans 2700: 2524: 2512: 2500: 2118: 2106: 1721: 1564:O'Connor, J.J.; Robertson, E.F. (2007). 1551: 1498: 1321: 1238: 291:as solo instruments, in contrast to the 3190:. Cambridge, Massachusetts: MIT Press. 2560: 2353: 2274: 2272: 2130: 2085: 1925: 1886: 1697:"Strings, standing waves and harmonics" 1675: 1539: 1510: 1486: 64: 3070:"The Bowed String As We Know It Today" 3068:Woodhouse, J.; Galluzzo, P.M. (2004). 2727: 2715: 2685: 2673: 2661: 2649: 2377: 2365: 2341: 2317: 2229: 2141: 2139: 1991: 1989: 1987: 1985: 1901: 1869: 1857: 1845: 1833: 1797:"Modeling the stiffness of the string" 1770: 1690: 1688: 1686: 1684: 1637: 806:{\displaystyle v={{\lambda } \over T}} 27:Area of study within musical acoustics 3376:Physics Department (text in Italian). 2833:Dialogues Concerning Two New Sciences 2637: 2536: 2464: 2452: 2070: 1821: 1625: 1613: 229:. A range of simultaneously produced 7: 2599: 2548: 2488: 2329: 2241: 1913: 1782: 1654: 1601: 1527: 535:interval on an open string is about 2883:(1895). Ellis, Alexander J. (ed.). 2019:Pociask, Stefan (31 October 2018). 357:During the nineteenth century, the 3288:Schelleng, John C (January 1973). 1064:of the instrument is from 25 to 30 647: 190:concerned with how the sound of a 25: 3290:"The bowed string and the player" 3253:, Vol. 9, No. 2, pp. 81–98. 3055:. London: Methuen & Co. Ltd. 1752:. American Physical Society. 2020 927:{\displaystyle f={\frac {v}{2L}}} 4364: 4363: 3751: 3750: 3463: 3247:The mechanical action of violins 2921:. New York: Dover Publications. 2904:The Acoustics of Violin Plates. 2800:Dictionary of National Biography 1996:Ward, Richard (22 August 2012). 1395: 1378: 1119: 1110: 376:investigated the physics of the 313:ancient Ionian Greek philosopher 47: 2991:. Milwaukee: Hal Leonard Corp. 2612:Freiberg, Sarah (12 May 2005). 2581:. University of New South Wales 2287:. University of New South Wales 2255:"Basic Parts of the Violin Bow" 1703:. University of New South Wales 1318:The bass bar and the sound post 3009:Springer Handbook of Acoustics 2969:Physics and the sound of music 2918:Music, physics and engineering 245:, or decreasing its length or 1: 3340:University of New South Wales 3140:"The violin bridge as filter" 3006:Rossing, Thomas, ed. (2014). 2477:Woodhouse & Galluzzo 2004 2441:Woodhouse & Galluzzo 2004 2429:Woodhouse & Galluzzo 2004 2417:Woodhouse & Galluzzo 2004 2405:Woodhouse & Galluzzo 2004 2390:Woodhouse & Galluzzo 2004 2306:Woodhouse & Galluzzo 2004 1235:Violin making and maintenance 889:λ, where λ is the associated 2881:Helmholtz, Hermann L. F. von 458:travelling past each other. 450:(eigenmodes), caused by the 3362:Piastra di Chladni: violino 2987:Siminoff, Roger H. (2002). 2814:. New York: F. A. Praeger. 2021:"What Is Catgut Made From?" 1568:. University of St. Andrews 1408:The open strings of a cello 1388:The open strings of a viola 1223:energy supplied by friction 527:positions for a particular 438:of the violin, but vary in 213:is transmitted through the 186:is an area of study within 18:Basic physics of the violin 4413: 3138:Bissinger, George (2006). 2908:, vol 245, No. 4. Oct 1981 1292:holographic interferometry 1232: 1009: 4359: 3746: 3458: 1795:Smith, Julius O. (2019). 1166:On the Sensations of Tone 1037:to provide a controlled ' 767:, shown stopping a string 4125:(changing string tuning) 2767:Bucur, Voichita (2018). 1939:"How to Tune the Violin" 1300:East Carolina University 1048:The length, weight, and 3427:Architectural acoustics 3179:Cremer, Lothar (1984). 2902:Hutchins, Carleen Maley 2850:Hutchins, Carleen Maley 2257:. Benning Violins. 2020 2121:, String "break" angle. 1219:coefficient of friction 1211:digital waveguide model 1164:Hermann von Helmholtz, 991:at about 3000 Hz. 372:. The German physicist 3514:Fletcher–Munson curves 3509:Equal-loudness contour 3419:Acoustical engineering 3181:Physics of the Violin 3103:Askenfelt, A. (1995). 3012:. New York: Springer. 2811:Violins and Violinists 2189:Mathews, M.V. (1982). 1969:ViolinStringReview.com 1965:"String Tension Guide" 1474: 1353:modes as it vibrates. 1327: 1244: 1205:and F.G. Friedlander. 1196:reflection coefficient 1161: 1021: 928: 864: 807: 768: 728: 664: 580: 466: 423: 344:earliest violin makers 41: 4346:Violin musical styles 4294:History of the violin 3930:Electric upright bass 3650:Hermann von Helmholtz 3548:Fundamental frequency 3452:Sympathetic resonance 3321:registration required 3257:registration required 2936:registration required 2873:registration required 2808:Farga, Franz (1969). 2575:"Helmholtz Resonance" 1472: 1325: 1296:finite element method 1243:Structure of a violin 1242: 1062:sound pressure levels 1019: 1010:Further information: 929: 865: 808: 755: 729: 679:directly proportional 665: 570: 471:fundamental frequency 464: 417: 374:Hermann von Helmholtz 307:Historical background 239:fundamental frequency 35: 4197:Double bass concerto 3052:The Physics of Music 2855:The Physics of Music 1326:Interior of a violin 1043:Cambridge University 900: 828: 782: 688: 628: 557:(violoncello) and a 352:stringed instruments 4226:Related instruments 4140:and genres of music 4106:Finger substitution 3670:Werner Meyer-Eppler 3580:Missing fundamental 3374:University of Milan 3306:1973ASAJ...53...26S 3156:2006ASAJ..120..482B 2972:. New York: Wiley. 2906:Scientific American 2794:"Double bass" 2332:, pp. 34, 102. 2207:1982ASAJ...71...43M 2160:2008ASAJ..123.3656B 1351:Helmholtz resonance 514:artificial harmonic 389:frequency responses 3831:Five-string violin 3553:Frequency spectrum 3372:, uploaded by the 3031:. Amsterdam: OPA. 2407:, pp. 579–80. 2281:"Bows and strings" 1616:, pp. 6, 931. 1475: 1473:Double bass tuning 1328: 1245: 1022: 924: 860: 803: 769: 724: 660: 581: 467: 424: 385:modes of vibration 42: 4379: 4378: 3948: 3947: 3764: 3763: 3726:Musical acoustics 3558:harmonic spectrum 3338:published by the 3314:10.1121/1.1913322 3245:(October 1937). " 3197:978-0-262-03102-8 3187:by John S. Allen) 3164:10.1121/1.2207576 3038:978-3-7186-5847-3 3019:978-0-387-30446-5 2998:978-0-634-01468-0 2979:978-0-471-87412-6 2928:978-0-486-31702-1 2865:978-0-7167-0095-1 2780:978-3-319-81191-8 2759:978-0-19-816739-6 2652:, pp. 65–69. 2640:, pp. 120–1. 2602:, pp. 100–1. 2551:, pp. 97–98. 2503:, pp. 61–62. 2443:, pp. 583–4. 2431:, pp. 581–2. 2216:10.1121/1.2019392 2168:10.1121/1.2934961 1872:, pp. 23–24. 1773:, pp. 29–30. 1628:, pp. 930–1. 1400: 1383: 1215:bending stiffness 1179:plane of rotation 1072:Physics of bowing 1054:moment of inertia 922: 858: 845: 801: 722: 721: 705: 658: 568: 415: 188:musical acoustics 181: 180: 16:(Redirected from 4404: 4367: 4366: 4289:Violin acoustics 4243:Hardanger fiddle 4177:String orchestra 3841:Alexander violin 3809: 3791: 3784: 3777: 3768: 3754: 3753: 3655:Carleen Hutchins 3587:Combination tone 3474: 3467: 3447:String vibration 3404: 3397: 3390: 3381: 3351:Modal Animations 3324: 3317: 3283: 3260: 3213: 3201: 3185:Physik der Geige 3183:(translation of 3175: 3134: 3132: 3126:. Archived from 3109: 3092: 3090: 3088: 3074: 3064: 3042: 3023: 3002: 2983: 2959: 2939: 2932: 2898: 2876: 2869: 2845: 2828:Galilei, Galileo 2823: 2804: 2796: 2784: 2763: 2731: 2725: 2719: 2713: 2704: 2698: 2689: 2683: 2677: 2671: 2665: 2659: 2653: 2647: 2641: 2635: 2629: 2628: 2626: 2624: 2609: 2603: 2597: 2591: 2590: 2588: 2586: 2570: 2564: 2558: 2552: 2546: 2540: 2534: 2528: 2522: 2516: 2510: 2504: 2498: 2492: 2486: 2480: 2474: 2468: 2462: 2456: 2450: 2444: 2438: 2432: 2426: 2420: 2414: 2408: 2402: 2393: 2387: 2381: 2375: 2369: 2363: 2357: 2351: 2345: 2339: 2333: 2327: 2321: 2315: 2309: 2303: 2297: 2296: 2294: 2292: 2276: 2267: 2266: 2264: 2262: 2251: 2245: 2239: 2233: 2227: 2221: 2220: 2218: 2186: 2180: 2179: 2143: 2134: 2128: 2122: 2116: 2110: 2104: 2089: 2083: 2074: 2068: 2062: 2061: 2059: 2057: 2042: 2036: 2035: 2033: 2031: 2016: 2010: 2009: 2007: 2005: 1993: 1980: 1979: 1977: 1975: 1961: 1955: 1954: 1952: 1950: 1935: 1929: 1923: 1917: 1911: 1905: 1899: 1890: 1884: 1873: 1867: 1861: 1855: 1849: 1843: 1837: 1831: 1825: 1819: 1813: 1812: 1810: 1808: 1792: 1786: 1780: 1774: 1768: 1762: 1761: 1759: 1757: 1746:"Fiddle Physics" 1742: 1725: 1719: 1713: 1712: 1710: 1708: 1692: 1679: 1673: 1658: 1652: 1641: 1635: 1629: 1623: 1617: 1611: 1605: 1599: 1593: 1587: 1578: 1577: 1575: 1573: 1561: 1555: 1549: 1543: 1537: 1531: 1525: 1514: 1508: 1502: 1496: 1448: 1447: 1443: 1440: 1430: 1429: 1425: 1422: 1402: 1401: 1385: 1384: 1304:laser technology 1169: 1123: 1114: 1100:Helmholtz motion 1012:Violin technique 933: 931: 930: 925: 923: 921: 910: 888: 886: 885: 882: 879: 869: 867: 866: 861: 859: 851: 846: 838: 812: 810: 809: 804: 802: 797: 792: 766: 758:Erich Donnerhack 733: 731: 730: 725: 723: 720: 709: 708: 706: 698: 669: 667: 666: 661: 659: 654: 650: 644: 569: 548: 547: 543: 540: 504:effects and the 416: 393:Carleen Hutchins 340:Two New Sciences 331:Vincenzo Galilei 320:consonant sounds 233:each affect the 211:vibrating string 209:The energy of a 184:Violin acoustics 173: 166: 159: 51: 44: 21: 4412: 4411: 4407: 4406: 4405: 4403: 4402: 4401: 4382: 4381: 4380: 4375: 4355: 4341:Violin lutherie 4277: 4253:Lira da braccio 4221: 4182:Violin concerto 4139: 4133: 4033: 3944: 3916: 3902:Cello da spalla 3897:Baritone violin 3878: 3850: 3836:Violino piccolo 3821:Electric violin 3800: 3795: 3765: 3760: 3742: 3694: 3685:D. Van Holliday 3623: 3592:Mersenne's laws 3526:Audio frequency 3520: 3484:Psychoacoustics 3478: 3477: 3470: 3456: 3413: 3408: 3332: 3318: 3287: 3264: 3254: 3204: 3198: 3178: 3137: 3130: 3107: 3102: 3099: 3097:Further reading 3086: 3084: 3072: 3067: 3047:Wood, Alexander 3045: 3039: 3026: 3020: 3005: 2999: 2986: 2980: 2962: 2942: 2933: 2929: 2913:Olson, Harry F. 2911: 2879: 2870: 2866: 2848: 2826: 2807: 2787: 2781: 2766: 2760: 2742: 2739: 2734: 2726: 2722: 2714: 2707: 2699: 2692: 2684: 2680: 2672: 2668: 2660: 2656: 2648: 2644: 2636: 2632: 2622: 2620: 2611: 2610: 2606: 2598: 2594: 2584: 2582: 2579:Music Acoustics 2572: 2571: 2567: 2559: 2555: 2547: 2543: 2535: 2531: 2523: 2519: 2511: 2507: 2499: 2495: 2487: 2483: 2475: 2471: 2463: 2459: 2451: 2447: 2439: 2435: 2427: 2423: 2415: 2411: 2403: 2396: 2388: 2384: 2376: 2372: 2364: 2360: 2352: 2348: 2340: 2336: 2328: 2324: 2316: 2312: 2304: 2300: 2290: 2288: 2285:Music Acoustics 2278: 2277: 2270: 2260: 2258: 2253: 2252: 2248: 2240: 2236: 2228: 2224: 2188: 2187: 2183: 2145: 2144: 2137: 2129: 2125: 2117: 2113: 2105: 2092: 2084: 2077: 2069: 2065: 2055: 2053: 2044: 2043: 2039: 2029: 2027: 2025:mentalfloss.com 2018: 2017: 2013: 2003: 2001: 1995: 1994: 1983: 1973: 1971: 1963: 1962: 1958: 1948: 1946: 1937: 1936: 1932: 1924: 1920: 1912: 1908: 1900: 1893: 1885: 1876: 1868: 1864: 1856: 1852: 1844: 1840: 1832: 1828: 1820: 1816: 1806: 1804: 1794: 1793: 1789: 1781: 1777: 1769: 1765: 1755: 1753: 1750:Physics Central 1744: 1743: 1728: 1720: 1716: 1706: 1704: 1701:Music Acoustics 1694: 1693: 1682: 1674: 1661: 1653: 1644: 1636: 1632: 1624: 1620: 1612: 1608: 1600: 1596: 1588: 1581: 1571: 1569: 1563: 1562: 1558: 1550: 1546: 1538: 1534: 1526: 1517: 1509: 1505: 1497: 1488: 1484: 1445: 1441: 1438: 1436: 1427: 1423: 1420: 1418: 1412: 1411: 1410: 1409: 1405: 1404: 1403: 1396: 1391: 1390: 1389: 1386: 1379: 1372: 1359: 1320: 1269: 1237: 1231: 1171: 1163: 1158: 1154: 1150: 1146: 1142: 1138: 1133: 1132: 1131: 1130: 1126: 1125: 1124: 1116: 1115: 1102: 1074: 1031:Pernambuco wood 1014: 1008: 979: 975: 969: 941: 914: 898: 897: 883: 880: 877: 876: 874: 826: 825: 780: 779: 760: 750: 713: 686: 685: 675:Young's modulus 673:where E is the 645: 626: 625: 619: 564: 545: 541: 538: 536: 411: 409: 336:Galileo Galilei 309: 237:, but only the 177: 134: 131: 28: 23: 22: 15: 12: 11: 5: 4410: 4408: 4400: 4399: 4394: 4384: 4383: 4377: 4376: 4374: 4373: 4360: 4357: 4356: 4354: 4353: 4348: 4343: 4338: 4333: 4328: 4323: 4318: 4317: 4316: 4311: 4306: 4304:Bass amplifier 4296: 4291: 4285: 4283: 4279: 4278: 4276: 4275: 4270: 4265: 4260: 4255: 4250: 4245: 4240: 4235: 4229: 4227: 4223: 4222: 4220: 4219: 4217:Carnatic music 4214: 4209: 4204: 4199: 4194: 4192:Cello concerto 4189: 4187:Viola concerto 4184: 4179: 4174: 4172:String section 4169: 4164: 4159: 4157:String quintet 4154: 4149: 4147:String quartet 4143: 4141: 4135: 4134: 4132: 4131: 4126: 4120: 4115: 4114: 4113: 4103: 4098: 4093: 4088: 4083: 4082: 4081: 4076: 4071: 4066: 4061: 4054: 4043: 4041: 4035: 4034: 4032: 4031: 4026: 4021: 4016: 4011: 4006: 4001: 3996: 3991: 3986: 3981: 3976: 3975: 3974: 3964: 3958: 3956: 3950: 3949: 3946: 3945: 3943: 3942: 3937: 3932: 3926: 3924: 3918: 3917: 3915: 3914: 3912:Electric cello 3909: 3904: 3899: 3894: 3888: 3886: 3880: 3879: 3877: 3876: 3871: 3866: 3864:Vertical viola 3860: 3858: 3852: 3851: 3849: 3848: 3843: 3838: 3833: 3828: 3823: 3817: 3815: 3806: 3802: 3801: 3796: 3794: 3793: 3786: 3779: 3771: 3762: 3761: 3759: 3758: 3747: 3744: 3743: 3741: 3740: 3739: 3738: 3733: 3723: 3718: 3713: 3708: 3702: 3700: 3699:Related topics 3696: 3695: 3693: 3692: 3687: 3682: 3680:Joseph Sauveur 3677: 3672: 3667: 3665:Marin Mersenne 3662: 3657: 3652: 3647: 3642: 3637: 3631: 3629: 3625: 3624: 3622: 3621: 3616: 3615: 3614: 3604: 3599: 3594: 3589: 3584: 3583: 3582: 3577: 3572: 3562: 3561: 3560: 3550: 3545: 3540: 3534: 3532: 3522: 3521: 3519: 3518: 3517: 3516: 3506: 3505: 3504: 3499: 3488: 3486: 3480: 3479: 3476: 3475: 3468: 3460: 3459: 3457: 3455: 3454: 3449: 3444: 3439: 3434: 3429: 3423: 3421: 3415: 3414: 3409: 3407: 3406: 3399: 3392: 3384: 3378: 3377: 3359: 3354: 3348: 3342: 3331: 3330:External links 3328: 3327: 3326: 3285: 3262: 3243:Saunders, F.A. 3239: 3238: 3237: 3236: 3235:(pp. 332-389). 3230: 3229:(pp. 277-331). 3224: 3215: 3214: 3202: 3196: 3176: 3150:(1): 482–491. 3135: 3133:on 2019-03-07. 3118:(2–3): 23–42. 3098: 3095: 3094: 3093: 3065: 3043: 3037: 3024: 3018: 3003: 2997: 2984: 2978: 2964:Rigden, John S 2960: 2944:Piston, Walter 2940: 2927: 2909: 2899: 2877: 2864: 2846: 2824: 2805: 2791:, ed. (1886). 2789:Chisholm, Hugh 2785: 2779: 2764: 2758: 2744:Beament, James 2738: 2735: 2733: 2732: 2730:, p. 143. 2720: 2705: 2690: 2678: 2676:, p. 142. 2666: 2654: 2642: 2630: 2604: 2592: 2565: 2553: 2541: 2539:, p. 931. 2529: 2517: 2505: 2493: 2491:, p. 100. 2481: 2479:, p. 587. 2469: 2467:, p. 198. 2457: 2445: 2433: 2421: 2419:, p. 580. 2409: 2394: 2392:, p. 579. 2382: 2370: 2358: 2346: 2334: 2322: 2310: 2308:, p. 588. 2298: 2268: 2246: 2234: 2222: 2181: 2135: 2123: 2111: 2090: 2075: 2063: 2037: 2011: 1981: 1956: 1930: 1928:, p. 588. 1918: 1906: 1891: 1874: 1862: 1850: 1838: 1826: 1824:, p. 118. 1814: 1787: 1775: 1763: 1726: 1714: 1680: 1678:, p. 591. 1659: 1642: 1630: 1618: 1606: 1594: 1592:, p. 374. 1590:Helmholtz 1895 1579: 1566:"Félix Savart" 1556: 1544: 1542:, p. 100. 1532: 1515: 1503: 1485: 1483: 1480: 1407: 1406: 1394: 1393: 1392: 1387: 1377: 1376: 1375: 1374: 1373: 1371: 1368: 1358: 1355: 1319: 1316: 1312:modal analysis 1267: 1262:magnetic field 1230: 1227: 1200:mathematicians 1156: 1152: 1148: 1144: 1140: 1136: 1128: 1127: 1118: 1117: 1109: 1108: 1107: 1106: 1105: 1103: 1101: 1098: 1094:Sul ponticello 1086:sulla tastiera 1073: 1070: 1020:Violin and bow 1007: 1004: 977: 973: 968: 965: 940: 937: 936: 935: 920: 917: 913: 908: 905: 871: 870: 857: 854: 849: 844: 841: 836: 833: 815: 814: 800: 796: 790: 787: 756:The violinist 749: 746: 735: 734: 719: 716: 712: 704: 701: 696: 693: 671: 670: 657: 653: 649: 642: 639: 636: 633: 618: 615: 496:, length, and 448:standing waves 408: 405: 401:modal analysis 397:Simone Sacconi 359:multi-harmonic 308: 305: 280:more quickly. 227:standing waves 202:, such as the 196:its many parts 179: 178: 176: 175: 168: 161: 153: 150: 149: 143: 142: 136: 135: 128: 125: 124: 118: 117: 111: 110: 104: 103: 101:Musical styles 97: 96: 90: 89: 83: 82: 76: 75: 69: 68: 62: 61: 53: 52: 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 4409: 4398: 4395: 4393: 4390: 4389: 4387: 4372: 4371: 4362: 4361: 4358: 4352: 4349: 4347: 4344: 4342: 4339: 4337: 4334: 4332: 4329: 4327: 4324: 4322: 4319: 4315: 4312: 4310: 4307: 4305: 4302: 4301: 4300: 4297: 4295: 4292: 4290: 4287: 4286: 4284: 4280: 4274: 4271: 4269: 4266: 4264: 4261: 4259: 4256: 4254: 4251: 4249: 4246: 4244: 4241: 4239: 4236: 4234: 4231: 4230: 4228: 4224: 4218: 4215: 4213: 4210: 4208: 4205: 4203: 4202:Violin sonata 4200: 4198: 4195: 4193: 4190: 4188: 4185: 4183: 4180: 4178: 4175: 4173: 4170: 4168: 4165: 4163: 4162:String sextet 4160: 4158: 4155: 4153: 4150: 4148: 4145: 4144: 4142: 4136: 4130: 4127: 4124: 4121: 4119: 4116: 4112: 4109: 4108: 4107: 4104: 4102: 4099: 4097: 4094: 4092: 4089: 4087: 4084: 4080: 4077: 4075: 4072: 4070: 4067: 4065: 4062: 4060: 4059: 4055: 4053: 4050: 4049: 4048: 4045: 4044: 4042: 4040: 4036: 4030: 4027: 4025: 4022: 4020: 4017: 4015: 4014:Shoulder rest 4012: 4010: 4007: 4005: 4002: 4000: 3997: 3995: 3992: 3990: 3987: 3985: 3982: 3980: 3977: 3973: 3970: 3969: 3968: 3965: 3963: 3960: 3959: 3957: 3955: 3951: 3941: 3938: 3936: 3933: 3931: 3928: 3927: 3925: 3923: 3919: 3913: 3910: 3908: 3905: 3903: 3900: 3898: 3895: 3893: 3890: 3889: 3887: 3885: 3881: 3875: 3872: 3870: 3869:Viola pomposa 3867: 3865: 3862: 3861: 3859: 3857: 3853: 3847: 3844: 3842: 3839: 3837: 3834: 3832: 3829: 3827: 3824: 3822: 3819: 3818: 3816: 3814: 3810: 3807: 3803: 3799: 3798:Violin family 3792: 3787: 3785: 3780: 3778: 3773: 3772: 3769: 3757: 3749: 3748: 3745: 3737: 3734: 3732: 3729: 3728: 3727: 3724: 3722: 3719: 3717: 3714: 3712: 3709: 3707: 3704: 3703: 3701: 3697: 3691: 3688: 3686: 3683: 3681: 3678: 3676: 3675:Lord Rayleigh 3673: 3671: 3668: 3666: 3663: 3661: 3658: 3656: 3653: 3651: 3648: 3646: 3645:Ernst Chladni 3643: 3641: 3638: 3636: 3633: 3632: 3630: 3626: 3620: 3617: 3613: 3610: 3609: 3608: 3607:Standing wave 3605: 3603: 3600: 3598: 3595: 3593: 3590: 3588: 3585: 3581: 3578: 3576: 3575:Inharmonicity 3573: 3571: 3568: 3567: 3566: 3563: 3559: 3556: 3555: 3554: 3551: 3549: 3546: 3544: 3541: 3539: 3536: 3535: 3533: 3531: 3527: 3523: 3515: 3512: 3511: 3510: 3507: 3503: 3500: 3498: 3495: 3494: 3493: 3490: 3489: 3487: 3485: 3481: 3473: 3469: 3466: 3462: 3461: 3453: 3450: 3448: 3445: 3443: 3442:Soundproofing 3440: 3438: 3437:Reverberation 3435: 3433: 3430: 3428: 3425: 3424: 3422: 3420: 3416: 3412: 3405: 3400: 3398: 3393: 3391: 3386: 3385: 3382: 3375: 3371: 3370:Chladni plate 3367: 3363: 3360: 3358: 3355: 3352: 3349: 3346: 3343: 3341: 3337: 3334: 3333: 3329: 3322: 3315: 3311: 3307: 3303: 3299: 3295: 3291: 3286: 3281: 3277: 3273: 3272: 3267: 3266:Savart, Félix 3263: 3258: 3252: 3248: 3244: 3241: 3240: 3234: 3231: 3228: 3225: 3222: 3219: 3218: 3217: 3216: 3211: 3207: 3203: 3199: 3193: 3189: 3186: 3182: 3177: 3173: 3169: 3165: 3161: 3157: 3153: 3149: 3145: 3141: 3136: 3129: 3125: 3121: 3117: 3113: 3106: 3101: 3100: 3096: 3082: 3078: 3077:Acta Acustica 3071: 3066: 3062: 3058: 3054: 3053: 3048: 3044: 3040: 3034: 3030: 3025: 3021: 3015: 3011: 3010: 3004: 3000: 2994: 2990: 2985: 2981: 2975: 2971: 2970: 2965: 2961: 2957: 2953: 2949: 2948:Orchestration 2945: 2941: 2937: 2930: 2924: 2920: 2919: 2914: 2910: 2907: 2903: 2900: 2896: 2892: 2888: 2887: 2882: 2878: 2874: 2867: 2861: 2857: 2856: 2851: 2847: 2843: 2839: 2835: 2834: 2829: 2825: 2821: 2817: 2813: 2812: 2806: 2802: 2801: 2795: 2790: 2786: 2782: 2776: 2772: 2771: 2765: 2761: 2755: 2751: 2750: 2745: 2741: 2740: 2736: 2729: 2724: 2721: 2718:, p. 98. 2717: 2712: 2710: 2706: 2702: 2701:Chisholm 1886 2697: 2695: 2691: 2688:, p. 80. 2687: 2682: 2679: 2675: 2670: 2667: 2664:, p. 77. 2663: 2658: 2655: 2651: 2646: 2643: 2639: 2634: 2631: 2619: 2615: 2608: 2605: 2601: 2596: 2593: 2580: 2576: 2569: 2566: 2563:, p. 33. 2562: 2557: 2554: 2550: 2545: 2542: 2538: 2533: 2530: 2527:, p. 62. 2526: 2525:Hutchins 1978 2521: 2518: 2515:, p. 58. 2514: 2513:Hutchins 1978 2509: 2506: 2502: 2501:Hutchins 1978 2497: 2494: 2490: 2485: 2482: 2478: 2473: 2470: 2466: 2461: 2458: 2455:, p. 10. 2454: 2449: 2446: 2442: 2437: 2434: 2430: 2425: 2422: 2418: 2413: 2410: 2406: 2401: 2399: 2395: 2391: 2386: 2383: 2380:, p. 21. 2379: 2374: 2371: 2368:, p. 20. 2367: 2362: 2359: 2356:, p. 29. 2355: 2350: 2347: 2343: 2338: 2335: 2331: 2326: 2323: 2320:, p. 10. 2319: 2314: 2311: 2307: 2302: 2299: 2286: 2282: 2275: 2273: 2269: 2256: 2250: 2247: 2244:, p. 98. 2243: 2238: 2235: 2232:, p. 35. 2231: 2226: 2223: 2217: 2212: 2208: 2204: 2200: 2196: 2192: 2185: 2182: 2177: 2173: 2169: 2165: 2161: 2157: 2153: 2149: 2142: 2140: 2136: 2133:, p. 28. 2132: 2127: 2124: 2120: 2119:Siminoff 2002 2115: 2112: 2109:, p. 59. 2108: 2107:Hutchins 1978 2103: 2101: 2099: 2097: 2095: 2091: 2088:, p. 35. 2087: 2082: 2080: 2076: 2073:, p. 11. 2072: 2067: 2064: 2051: 2050:Quinn Violins 2047: 2041: 2038: 2026: 2022: 2015: 2012: 1999: 1992: 1990: 1988: 1986: 1982: 1970: 1966: 1960: 1957: 1944: 1943:Get-Tuned.com 1940: 1934: 1931: 1927: 1922: 1919: 1916:, p. 58. 1915: 1910: 1907: 1903: 1898: 1896: 1892: 1889:, p. 30. 1888: 1883: 1881: 1879: 1875: 1871: 1866: 1863: 1859: 1854: 1851: 1848:, p. 52. 1847: 1842: 1839: 1836:, p. 40. 1835: 1830: 1827: 1823: 1818: 1815: 1802: 1798: 1791: 1788: 1785:, p. 55. 1784: 1779: 1776: 1772: 1767: 1764: 1751: 1747: 1741: 1739: 1737: 1735: 1733: 1731: 1727: 1724:, p. 12. 1723: 1722:Hutchins 1978 1718: 1715: 1702: 1698: 1691: 1689: 1687: 1685: 1681: 1677: 1672: 1670: 1668: 1666: 1664: 1660: 1657:, p. 97. 1656: 1651: 1649: 1647: 1643: 1639: 1634: 1631: 1627: 1622: 1619: 1615: 1610: 1607: 1604:, p. 99. 1603: 1598: 1595: 1591: 1586: 1584: 1580: 1567: 1560: 1557: 1554:, p. 57. 1553: 1552:Hutchins 1978 1548: 1545: 1541: 1536: 1533: 1530:, p. 90. 1529: 1524: 1522: 1520: 1516: 1512: 1507: 1504: 1501:, p. 61. 1500: 1499:Hutchins 1978 1495: 1493: 1491: 1487: 1481: 1479: 1471: 1467: 1464: 1459: 1457: 1453: 1434: 1415: 1369: 1367: 1364: 1356: 1354: 1352: 1347: 1345: 1340: 1337: 1333: 1324: 1317: 1315: 1313: 1309: 1305: 1301: 1297: 1293: 1288: 1286: 1285:Ernst Chladni 1282: 1276: 1272: 1270: 1263: 1259: 1253: 1251: 1241: 1236: 1228: 1226: 1224: 1220: 1216: 1212: 1206: 1204: 1203:Joseph Keller 1201: 1197: 1192: 1188: 1183: 1180: 1176: 1170: 1167: 1160: 1122: 1113: 1099: 1097: 1095: 1091: 1090:Walter Piston 1087: 1082: 1079: 1078:perpendicular 1071: 1069: 1067: 1063: 1059: 1055: 1051: 1050:balance point 1046: 1044: 1040: 1036: 1032: 1027: 1018: 1013: 1005: 1003: 1000: 996: 992: 990: 986: 981: 966: 964: 961: 958:strings) are 957: 953: 949: 944: 938: 918: 915: 911: 906: 903: 896: 895: 894: 892: 855: 852: 847: 842: 839: 834: 831: 824: 823: 822: 820: 798: 794: 788: 785: 778: 777: 776: 774: 764: 759: 754: 747: 745: 743: 738: 717: 714: 710: 702: 699: 694: 691: 684: 683: 682: 680: 676: 655: 651: 640: 637: 634: 631: 624: 623: 622: 616: 614: 612: 608: 604: 599: 597: 593: 589: 586: 578: 574: 573:G major scale 562: 560: 556: 552: 534: 530: 526: 521: 519: 515: 511: 507: 503: 500:, as well as 499: 495: 490: 488: 484: 480: 476: 472: 463: 459: 457: 453: 452:superposition 449: 445: 441: 437: 433: 429: 421: 406: 404: 402: 398: 394: 390: 386: 383:The violin's 381: 379: 375: 371: 368: 364: 361:sound from a 360: 355: 353: 349: 345: 341: 337: 332: 329: 325: 321: 317: 314: 306: 304: 302: 298: 294: 290: 286: 281: 279: 275: 271: 267: 263: 259: 254: 252: 248: 244: 240: 236: 232: 228: 224: 220: 216: 212: 207: 205: 201: 200:violin family 197: 193: 189: 185: 174: 169: 167: 162: 160: 155: 154: 152: 151: 148: 145: 144: 141: 138: 137: 133: 127: 126: 123: 120: 119: 116: 113: 112: 109: 106: 105: 102: 99: 98: 95: 92: 91: 88: 85: 84: 81: 78: 77: 74: 71: 70: 67: 63: 59: 55: 54: 50: 46: 45: 39: 34: 30: 19: 4368: 4351:Violin octet 4331:Stradivarius 4288: 4212:Cello sonata 4207:Viola sonata 4167:String octet 4056: 3874:Tenor violin 3846:Stroh violin 3735: 3690:Thomas Young 3640:Jens Blauert 3628:Acousticians 3300:(1): 26–41. 3297: 3293: 3270: 3250: 3223:(pp. 1-276). 3209: 3188: 3184: 3180: 3147: 3143: 3128:the original 3115: 3111: 3085:. Retrieved 3080: 3076: 3051: 3029:On Sonic Art 3028: 3008: 2988: 2968: 2947: 2917: 2885: 2854: 2832: 2810: 2798: 2769: 2748: 2737:Bibliography 2723: 2681: 2669: 2657: 2645: 2633: 2621:. Retrieved 2617: 2607: 2595: 2583:. Retrieved 2578: 2573:Wolfe, Joe. 2568: 2561:Beament 1997 2556: 2544: 2532: 2520: 2508: 2496: 2484: 2472: 2460: 2448: 2436: 2424: 2412: 2385: 2373: 2361: 2354:Beament 1997 2349: 2344:, p. 8. 2337: 2325: 2313: 2301: 2289:. Retrieved 2284: 2279:Wolfe, Joe. 2259:. Retrieved 2249: 2237: 2225: 2198: 2194: 2184: 2151: 2147: 2131:Beament 1997 2126: 2114: 2086:Beament 1997 2066: 2054:. Retrieved 2049: 2040: 2028:. Retrieved 2024: 2014: 2002:. Retrieved 1972:. Retrieved 1968: 1959: 1947:. Retrieved 1942: 1933: 1926:Rossing 2014 1921: 1909: 1904:, p. 7. 1887:Beament 1997 1865: 1860:, p. 5. 1853: 1841: 1829: 1817: 1805:. Retrieved 1800: 1790: 1778: 1766: 1754:. Retrieved 1749: 1717: 1705:. Retrieved 1700: 1695:Wolfe, Joe. 1676:Rossing 2014 1640:, p. 4. 1633: 1621: 1609: 1597: 1570:. Retrieved 1559: 1547: 1540:Galilei 1914 1535: 1513:, Chapter 3. 1511:Wishart 1996 1506: 1476: 1460: 1416: 1413: 1360: 1348: 1341: 1329: 1289: 1277: 1273: 1254: 1246: 1207: 1184: 1172: 1165: 1162: 1134: 1093: 1085: 1083: 1075: 1047: 1023: 997: 993: 982: 970: 945: 942: 872: 816: 770: 739: 736: 672: 620: 600: 591: 587: 582: 522: 491: 468: 428:open strings 425: 382: 370:Félix Savart 356: 342:(1638). The 339: 310: 301:open strings 282: 255: 208: 183: 182: 122:Construction 114: 38:Andrea Amati 29: 4321:Jazz violin 4263:Nyckelharpa 4248:Hurdy-gurdy 4152:String trio 4096:Double stop 3999:Fingerboard 3922:Double bass 3892:Bass violin 3805:Instruments 3660:Franz Melde 3635:John Backus 3619:Subharmonic 3472:Spectrogram 3284:(in French) 3206:Raman, C.V. 2728:Rigden 1977 2716:Piston 1976 2686:Piston 1976 2674:Rigden 1977 2662:Piston 1976 2650:Piston 1976 2378:Piston 1976 2366:Piston 1976 2342:Piston 1976 2318:Piston 1976 2230:Piston 1976 2201:(S1): S43. 2154:(5): 7248. 1902:Piston 1976 1870:Piston 1976 1858:Piston 1976 1846:Piston 1976 1834:Piston 1976 1771:Piston 1976 1638:Piston 1976 1456:John Rigden 1191:C. V. Raman 761: [ 559:double bass 510:fingerboard 422:on a violin 285:double bass 132:maintenance 4386:Categories 4233:Arpeggione 4123:Scordatura 4052:Bow stroke 4039:Techniques 4029:Tuning peg 4019:Sound post 3721:Ultrasound 3711:Infrasound 3497:Bark scale 3325:(May 2020) 3261:(May 2020) 2956:1016330383 2638:Olson 1967 2537:Bucur 2018 2465:Olson 1967 2453:Farga 1969 2071:Farga 1969 1822:Olson 1967 1626:Bucur 2018 1614:Bucur 2018 1357:Wolf tones 1336:sound post 1308:efficiency 1233:See also: 1189:physicist 1039:stick-slip 972:20 lb 967:The bridge 891:wavelength 594:note, the 575:played by 533:whole tone 456:sine waves 316:Pythagoras 258:bow stroke 130:Making and 73:Violinists 4392:Acoustics 4314:Slap bass 4299:Jazz bass 4138:Ensembles 4118:Pizzicato 4111:Bariolage 4101:Fingering 4091:Harmonics 4058:Col legno 4024:Tailpiece 3602:Resonance 3502:Mel scale 3432:Monochord 3411:Acoustics 3083:: 579–589 3061:640010938 2842:708455337 2830:(1914) . 2600:Wood 1944 2549:Wood 1944 2489:Wood 1944 2330:Wood 1944 2242:Wood 1944 2000:. Strings 1914:Wood 1944 1783:Wood 1944 1655:Wood 1944 1602:Wood 1944 1528:Wood 1944 1452:orchestra 1363:wolf tone 1250:sound box 1002:quietly. 960:helically 939:Materials 856:λ 819:frequency 795:λ 648:Δ 607:oscillate 592:pizzicato 588:pizzicato 525:fingering 518:unfretted 506:stiffness 483:amplitude 475:overtones 367:physicist 348:acoustics 289:orchestra 266:sound box 256:During a 231:harmonics 115:Acoustics 108:Technique 4370:Category 4309:Big band 4268:Pochette 4086:Arpeggio 4074:Spiccato 3984:Chinrest 3962:Bass bar 3940:Octobass 3826:Pochette 3756:Category 3597:Overtone 3565:Harmonic 3280:24148967 3268:(1819). 3172:16875244 3124:17812511 3112:STL-QPSR 3049:(1944). 2966:(1977). 2946:(1976). 2915:(1967). 2852:(1978). 2820:68030679 2746:(1997). 2176:55533227 1344:leverage 1332:bass bar 1229:The body 1139:b and bc 596:decaying 579:a violin 577:plucking 529:interval 473:and its 328:composer 324:lutenist 270:bass bar 140:Luthiers 87:Fiddlers 58:a series 56:Part of 4397:Violins 4273:Quinton 4238:Baryton 4129:Vibrato 4079:Tremolo 4069:Portato 4064:Martelé 3935:Violone 3907:Cellone 3543:Formant 3366:YouTube 3302:Bibcode 3152:Bibcode 2895:1453852 2618:Strings 2203:Bibcode 2156:Bibcode 1444:⁄ 1426:⁄ 1258:current 1168:(1865). 1006:The bow 989:formant 887:⁠ 875:⁠ 617:Tension 603:vibrato 544:⁄ 502:damping 494:tension 454:of two 434:to the 407:Strings 378:plucked 299:of its 278:dampens 276:string 274:plucked 262:f-holes 243:tension 94:History 4258:Lirone 4047:Bowing 4009:Scroll 3994:F-hole 3989:Endpin 3979:Bridge 3813:Violin 3736:Violin 3570:Series 3278: 3249:", in 3233:Part 3 3227:Part 2 3221:Part 1 3194: 3170: 3122: 3087:11 May 3059: 3035: 3016: 2995: 2976: 2954: 2925: 2893: 2862: 2840: 2818: 2777: 2756: 2623:11 May 2291:15 May 2174: 2052:. 2020 1945:. 2020 1463:octave 1334:and a 1187:Indian 1155:and bc 1147:and bc 999:Muting 952:Perlon 948:catgut 893:, so 817:For a 773:period 748:Length 479:timbre 444:string 432:bridge 251:catgut 235:timbre 223:string 215:bridge 192:violin 147:Family 80:Fiddle 66:Violin 4326:Rosin 4282:Other 3954:Parts 3884:Cello 3856:Viola 3731:Piano 3716:Sound 3530:pitch 3492:Pitch 3131:(PDF) 3120:S2CID 3108:(PDF) 3073:(PDF) 2585:7 May 2261:6 May 2172:S2CID 2056:6 May 2030:6 May 2004:6 May 1974:6 May 1949:6 May 1807:6 May 1756:6 May 1707:6 May 1572:8 May 1482:Notes 1433:fifth 1281:plate 1151:or ac 1058:power 1035:rosin 775:T, 765:] 585:Ital. 555:cello 551:viola 440:pitch 420:bowed 363:bowed 297:pitch 293:cello 219:sound 204:viola 4336:Viol 3972:Frog 3706:Echo 3612:Node 3538:Beat 3528:and 3276:OCLC 3192:ISBN 3168:PMID 3089:2020 3057:OCLC 3033:ISBN 3014:ISBN 2993:ISBN 2974:ISBN 2952:OCLC 2923:ISBN 2891:OCLC 2860:ISBN 2838:OCLC 2816:OCLC 2775:ISBN 2754:ISBN 2625:2020 2587:2020 2293:2020 2263:2020 2058:2020 2032:2020 2006:2020 1976:2020 1951:2020 1809:2020 1758:2020 1709:2020 1574:2020 1185:The 1175:apex 985:node 601:The 553:, a 523:The 498:mass 426:The 326:and 247:mass 4004:Nut 3967:Bow 3310:doi 3160:doi 3148:120 2211:doi 2164:doi 2152:123 1801:JOS 1159:." 1026:bow 821:f 436:nut 350:of 36:An 4388:: 3364:a 3308:. 3298:53 3296:. 3292:. 3166:. 3158:. 3146:. 3142:. 3116:36 3114:. 3110:. 3081:90 3079:. 3075:. 2797:. 2708:^ 2693:^ 2616:. 2577:. 2397:^ 2283:. 2271:^ 2209:. 2199:71 2197:. 2193:. 2170:. 2162:. 2150:. 2138:^ 2093:^ 2078:^ 2048:. 2023:. 1984:^ 1967:. 1941:. 1894:^ 1877:^ 1799:. 1748:. 1729:^ 1699:. 1683:^ 1662:^ 1645:^ 1582:^ 1518:^ 1489:^ 1437:23 1419:27 1330:A 1271:. 1068:. 1066:dB 763:de 611:Hz 571:A 561:. 489:. 354:. 303:. 206:. 60:on 3790:e 3783:t 3776:v 3403:e 3396:t 3389:v 3323:) 3319:( 3316:. 3312:: 3304:: 3282:. 3259:) 3255:( 3212:. 3200:. 3174:. 3162:: 3154:: 3091:. 3063:. 3041:. 3022:. 3001:. 2982:. 2958:. 2938:) 2934:( 2931:. 2897:. 2875:) 2871:( 2868:. 2844:. 2822:. 2783:. 2762:. 2703:. 2627:. 2589:. 2295:. 2265:. 2219:. 2213:: 2205:: 2178:. 2166:: 2158:: 2060:. 2034:. 2008:. 1978:. 1953:. 1811:. 1760:. 1711:. 1576:. 1446:8 1442:3 1439:+ 1428:4 1424:1 1421:+ 1268:4 1266:A 1157:2 1153:2 1149:1 1145:1 1141:2 1137:1 978:f 974:f 956:E 934:. 919:L 916:2 912:v 907:= 904:f 884:2 881:/ 878:1 853:v 848:= 843:T 840:1 835:= 832:f 813:. 799:T 789:= 786:v 718:M 715:L 711:T 703:2 700:1 695:= 692:f 656:L 652:L 641:S 638:E 635:= 632:T 546:4 542:1 539:+ 537:1 172:e 165:t 158:v 20:)

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.

Index