There was in general amongst violinists an anticipation of the grand, yet simple law set forth by De Beriot in his Violin School that the human voice was the pure archetype upon which all played music should be modelled.
It was found that the violin was capable of simulating all the subtle inflexions of song, whether of passion or tenderness, and players sighed for an ideal bow that should be tongue-like in its response to the performer's emotion. A bow that should at once be flexible to "whisper soft nothings in my lady's ear"; strong—to sound a clarion-blast of defiance; and, withal, be ready for any coquetterie or badinage that might suit its owner's whim. This is what François Tourte, the starving clockmaker, gave them.
We fiddlers have to be very thankful that the master clockmakers of Paris were not more liberal to their employés!
Illiterate as he was he at once grasped all the points of art and physics involved, and commenced diligently experimenting with a view to solving the various problems that presented themselves to his consideration.
To gain facility in the manipulation of his tools, he made countless bows from old barrel staves; he could not afford to make his first attempts on anything better. When he had attained sufficient skill in the actual workmanship, and had satisfied himself as to the most suitable form, he set to work investigating the question of material. He tried all kinds of wood, and at last decided that the red wood of Pernambuco, then largely imported into Europe for dyeing purposes, was the best. To obtain this in sufficient quantities was no easy matter, for the Anglo-French wars were interfering seriously with international commerce; a circumstance that rendered this material unusually expensive. Then the nature of this wood is not by any means a bow maker's ideal. Billets and logs amounting to several tons in weight may be examined before a piece is found sufficiently free from knots and cracks, and of straight enough grain to be suitable for the purpose. However, genius and a capacity for taking infinite pains overcame all difficulties, and we now have bows worthy of the greatest masterpieces of Cremona.
How little are the workings of genius understood by the "painstaking" ones. They cannot conceive the suddenness of inspiration—the almost instantaneous grasp of essentials that precedes the plodding mechanical work necessary even to genius.
The results of "infinite pains," or of genius alone are equally unsatisfactory. It is only where these qualities are combined in perfect balance that true greatness can be achieved.
In the case of Tourte we have a remarkable example of this combination. His genius made him grasp spontaneously the qualities required, and his capacity for taking infinite pains helped him to produce the perfect bow. He it was who determined finally the length and weight of a bow, its equilibrium, the angle of the hair necessary for a good "attack," the length and breadth of the hair and sundry other points that, prior to 1775, had been quite undecided.
The mean length of a violin bow as fixed by Tourte is from 74 to 75 centimètres (29.134 to 29.528 inches English); that of a viola bow is 74 centimètres (29.134 inches), and a 'cello bow 72 to 73 centimètres (28.347 to 28.740). Many people imagine that the plates of silver or gold with which the nut of a bow is inlaid are nothing more than mere ornamentation. But their first purpose is distinctly one of utility, which is as it should be in a work of art; superfluous decoration has no beauty for an artist. It is by means of these metal "loadings" at the heel that the weight of the head is counteracted and the exact point of equilibrium determined. The centre of gravity in a violin bow should be at 19 centimètres (7.48 inches) from the nut; in a 'cello bow at 175 to 180 millimètres (6.89 to 7.087 inches) from the nut.
Concerning the geometric proportions of the Tourte bows, I cannot do better than quote Bishop's able translation of the explanation given by Fétis in his notice of A. Stradivarius.