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Canon, in Music.

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1. The peculiar form of musical composition called by this name was unknown to the ancients, the earliest example extant being of the 13th century, we believe.

2. The accepted values of the several notes constituting the musical scale, expressed philosophically. Among the Greeks, followed throughout by Latin writers on music, there were two somewhat conflicting schools, the Aristoxeneans and the Pythagoreans. Pythagoras having discovered the simple ratios of i.e, 3, c, for the octave, the fifth, the fourth, and the tone (major), which last is the difference between the fourth and fifth, his disciples maintained that all sounds should be defined by determinate ratios, while Aristoxenus discarded this idea altogether, and maintained that the tetrachord, or fourth, should be divided into intervals, the values of which were to be determined by the ear only. This is probably the germ of the dispute which has lasted to the present day respecting the temperament of instruments with fixed tones; and as the true measure of an interval is a logarithm, it was, of course, impossible to reconcile completely these two opinions.

Ptolemy examined the matter, and established the truth of the Pythagorean views: Euclid seems to have endeavored to combine them, that is, if the two treatises attributed to him, the Inztroductio Harmonica and the Sectio Canonis, are both genuine. The latter of these is usually considered genuine, and it is purely Pythagorean. and rigidly exact; while the former, which is certainly Aristoxenean, and perhaps written for popular use, is considered more doubtful.

The canon of the scale, then, is the system of ratios" into which a resonant string is to be divided so as to' produce all the notes which are assumed; or, which is the same thing, the relative lengths of strings for these notes which are to be fixed in an instrument and stretched with the same tension.

The Aristoxenean system, from the Introductio Harmonica, supposes a tone to be divided into twelve equal parts, and the tetrachord therefore into thirty.

Euclid also gives the divisions of the string (which he calls also the canon) according to the diatonic system.

3. Ambrose decreed the use of the diatonic genus alone in 'church music; and it is probable that the chromatic and enharmonic genera soon fell into general desuetude, or only existed as curiosities for the learned.

The Jews are believed to have used a canon proceeding by thirds of tones, thus giving eighteen notes in the octave. It is stated that the Pythagorean canon has been developed into an Arabic scale of seventeen .sounds.;