rt. Its
doctrine is Pythagorean. The first book is divided into thirty-four
chapters. In the first he develops the thought of Aristotle, that
music is inherent in human nature. He there renders the text of a
decree which the Ephori of Sparta rendered against Timotheus of
Miletus, but which better critics have regarded as fictitious. The
second chapter establishes that there are three sorts of music: the
worldly, which is universal harmony; the human, which has its source
in the intelligence, which reunites and co-ordinates the elements;
finally, the third kind is artificial, made by instruments of
different sorts. The chapters following treat of the voice as the
source of music; of consonances and their proportions; of the division
of the voice and its compass; of the perception of sounds by the ear;
of the correspondence of the semitones; of the division of the octave;
of tetrachords; of the three genera--enharmonic, chromatic and
diatonic; of intervals of sounds compared to those of the stars; of
the musical and different faculties.

All the second book, divided into thirty chapters, is speculative, and
devotes itself to the different kinds and relations of intervals,
according to the different systems of theoreticians. The third book,
in seven chapters, is a continuation of the subject of the second. It
is particularly employed in refuting the errors of Aristoxenus. The
fourth book, in eighteen chapters, is entirely relative to the
practice of the art, particularly to the notation. It is in this book
that Boethius makes known the Latin notation of the first fifteen
letters of the alphabet without preparation, without the slightest
explanation, and as if he had done something which any one concerned
with music at Rome would readily understand, as a matter of course.
There is not one word to show that it was new, or that he claimed the
invention. It was undoubtedly the usual notation.

The fifth book of this treatise has for its object the determination
of intervals by the divisions of a monochord, and a refutation of the
systems of Ptolemy and Archytas. We here find this proposition,
remarkable if we recall the time when the author lived, that: "If the
ear did not count the vibrations, and did not seize the inequalities
of movement of two sounds resonating by percussion, the intelligence
would not be able to render account of them by the science of
numbers." After Boethius there is nothing in Roman literature
conce