T is possible that many who have taken an interest in the material of music have indulged at one time or another in dreams of some perfect instrument that should combine the merits and characters of all existing instruments, while avoiding all their defects. A piano capable of sustaining a tone as long as the player might desire, a horn that should possess all the notes of the chromatic scale without sacrificing its individuality, an organ that should give a faithful imitation of every orchestral instrument without loss of its characteristic "diapason" tone, a violin whose notes could be excited by an endless bow, so that no interval could be detected by the sharpest ear at the change of the bow's direction, -these are some of the ideals that have engaged the attention of so many enthusiasts, that it seems worth while to point out what value there may be in the inherent defects of the various instruments, and in how large a measure their character is due to these very shortcomings. Music has never been a perfect art; even without reference to man-made instruments, the central problem of intonation is insoluble, as the Greeks knew well. For if a circle of perfect fifths be constructed, and the intervals C-G, G-D, D-A, and so on, be tuned perfectly (or the equivalent obtained by alternately descending a perfect fourth and rising a perfect fifth), the C that will be arrived at is at a different pitch from the starting-point by a small interval known as the Pythagorean comma, amounting to about a quarter of a semitone. The history of music would be a very different thing from what it is if this tiny error could have been done away with by some miraculous agency. As it is, scientific and practical musicians in various ages have tried different expedients in order to conceal its existence, and to obtain the benefits of having all keys perfectly in tune. As every one knows, the violinist must learn to make slight compromises in many places in order to produce the effect of being in tune during changes of key; the older keyboard instruments dealt only with the simpler keys, and made these perfectly in tune, banishing the essential error of the comma into keys with many flats or