As this paper is composed from a technical point of view, some elucidation of facts, forming the basis of it, is desirable before we proceed to the chronological statement of the subject. These facts are the strings, and their strain or tension; the sound-board, which is the resonance factor; and the bridge, connecting it with the strings. The strings, sound-board, and bridge are indispensable, and common to all stringed instruments. The special fact appertaining to keyboard instruments is the mechanical action interposed between the player and the instrument itself. The strings, owing to the slender surface they present to the air, are, however powerfully excited, scarcely audible. To make them sufficiently audible, their pulsations have to be communicated to a wider elastic surface, the sound-board, which, by accumulated energy and broader contact with the air, re-enforces the strings' feeble sound. The properties of a string set in periodic vibration are the best known of the phenomena appertaining to acoustics. The molecules composing the string are disturbed in the string's vibrating length by the means used to excite the sound, and run off into sections, the comparative length and number of which depend partly upon the place in the string the excitement starts from; partly upon the force and the form of force that is employed; and partly upon the length, thickness, weight, strain, and elasticity of the string, with some small allowance for gravitation. The vibrating sections are of wave-like contour; the nodes or points of apparent rest being really knots of the greatest pressure from crossing streams of molecules. Where the pressure slackens, the sections rise into loops, the curves of which show the points of least pressure. Now, if the string be struck upon a loop, less energy is communicated to the string, and the carrying power of the sound proportionately fails. If the string be struck upon a node, greater energy ensues, and the carrying power proportionately gains. By this we recognize the importance of the place of contact, or striking-place of the hammer against the string; and the necessity, in order to obtain good fundamental tone, which shall carry, of the note being started from a node. If the hammer is hard, and impelled with force, the string breaks into shorter sections, and the discordant upper partials of the string, thus brought into prominence, make the tone harsh. If the hammer is soft, and the force employed is moderated, the harmonious partials of the longer sections strike the ear, and the tone is full and round. By the frequency of vibration, that is to say, the number of times a string runs through its complete changes one way and the other, say, for measurement, in a second of time, we determine the pitch, or relative acuteness of the tone as distinguished by the ear.