The harpsichords and the clavichords were what one might call the domestic substitutes for the organ. Of these the clavichord was perhaps slightly the older instrument. Its origin is somewhat obscure, though it is easy to see in it the union of the organ keyboard with strings, on the principle of that ancient darling of the theorists, the monochord, the great and undisputed ruler over intervals of musical pitch, from the days of Pythagoras down throughout the Middle Ages. This monochord was hardly an instrument. It was a single string stretched over a movable bridge. By shifting the bridge the string could be stopped off into different lengths, which gave out, when plucked, different pitches of sound. The relative lengths of the stopped string offered a simple mathematical basis for the classification of musical intervals. The clavichord worked on the same principle. At the back end of each key lever was an upright tangent, at first of wood, later of metal, which, when the key was depressed, sprang up against the wire string stretched above it. The blow of this tangent caused the wire to vibrate and produce sound; and at the same time the tangent determined the length of the string which was to vibrate, just as the finger determines the length of a violin string by stopping it at some point on the fingerboard. The strings of the clavichord were so stretched that of the two lengths into which the tangent might divide them, the longer lay to the left. It was this longer length which was allowed to vibrate, giving the desired pitch; the shorter length to the right being muffled or silenced by strips of felt laid or woven across the strings. Thus the little tangents at the back end of the keys performed the double function of sounding the string by hitting it and determining its pitch by stopping it. Thus, too, one string served several keys. By the middle of the sixteenth century the normal range was four full octaves, from C to c^3. There were many more keys than strings, which was a serious restriction upon music for the instrument; for notes which lay as closely together as, let us say, C-sharp and E could not be sounded at once, since both must be played upon the same string. Not until practically the beginning of the eighteenth century were clavichords made with a string for each key. They were then called _bundfrei_, in distinction from the older clavichords, which had been called _gebunden_.