A literature review:
The acoustics of the violin
Lei Fu April, 2015 Instructor: Prof. Gary P. Scavone
Final project of Seminar MUMT 618 Schulich School of Music, McGill University
2.3 The ingredients of a full bowed-string model
Musical judgements often hinge on matters of fine detail. What is needed is a model that can be calibrated by measurements on a particular violin, with particular strings, bow, etc, and then be relied upon to predict the transient response of the string to a particular bow gesture in quantitative detail—or at least, in enough detail to match the ability of human perception to discriminate differences. This is a tall order, but if it could be achieved it would open the way to a wide range of computer-based investigations into the ‘playability’ of violins and their relatives .
2.3.1 Details of string physics
The transverse motion has already been discussed. It also needs to be kept in mind that transverse vibration of the string can occur in two polarizations: only one is directly excited by the friction force from bowing, but the other can be excited by variations of normal bow force .Less obviously, the torsional response of the string needs to be considered. The frictional force is automatically excite torsional motion. There is one more wavetype on a stretched string that may have to be considered: axial or compressional waves. In total, then, there are four types of wave on the string rather than the single type considered before.
2.3.2 Dynamics of the violin body
For the moment it is sufficient to note that interactions with the strings occur only at the contact points. Presumably the main influence comes via the notches. For the case of longitudinal waves in the string, it is far from clear that either the bridge or the fingertip acts as a very strong reflector, and it may be that dynamic interactions with the body also occur at the nut, the pegs, and the tailpiece.
2.3.3 Dynamics of the bow
So far the violin bow has been treated as a rigid object, but of course this is far from being the case, and it has its own dynamic behaviour.
One influence undoubtedly comes via such factors as the taper, camber, weight and balance point, which can have a profound influence on a player’s ability to control certain bowing gestures. Another aspect has already been mentioned, when discussing differential slipping of the string: the longitudinal elasticity of the bow-hairs can affect the details of stress concentration near the edges of the bow-hair ribbon, and thus modify the details of string slipping, possibly with directly audible effect.