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112 THE PIANOFORTE. [ V. § 56.
of 3 to 2, and so forth. The relations existing between these lengths and the vibration-numbers of the notes produced by them were, however, entirely unknown to Pythagoras and his contemporaries; indeed it was not until the seventeenth century that they were discovered by Galileo.
In instruments of the violin class, the pitch of the notes varies according to the position of the finger on the vibrating string. The length of string intercepted between the fixed bridge and the finger admits of being altered at pleasure, and thus every shade of pitch can be produced from such instruments. The resined bow maintains the vibration of the string by alternately dragging it out of its position of rest, letting it fly back again, catching it once more, and so on. The hollow cavity of the instrument reinforces the string-sound by resonance. The quality of instruments of the violin class is vivacious and piercing. The first eight partial-tones are well represented in their sounds.
56. In this instrument each wire is stretched between two pegs, which are fixed into a flat plate of wood called the sound-board. The string is fastened to one peg, and coiled round the other which admits of being turned about its own axis by means