keynote of
the lyre) is out of tune everything is out of tune; yet when any other
string is out of tune it affects only the particular string which is
not correctly adjusted. One of his most instructive, but also, as it
turned out, most misleading questions was why they did not magadize
(sing in) fourths and fifths as well as in octaves, since the
consonances of the fourth and the fifth are almost as well sounding as
those of the octave. This question appears to have led to the practice
of what Hucbald called "diaphony." This question, it may be remarked
incidentally, is conclusive that they did _not_ use the third as a
consonance in Aristotle's time, nor sing together in fourths, fifths,
or any other intervals than the octave.

In spite of the talk about music by the Greek writers, musical theory,
in an exact form, occupies but a small place in the volume of their
works. The earliest theorist of whom we have any account was
Pythagoras, who lived about 580 B.C. He was one of the first of the
Greek wise men to avail himself of the opening of Egypt to foreigners,
which took place by Psammeticus I in the year 600 B.C. Pythagoras
lived there twenty years in connection with one of the temples, where
he seems to have gained the confidence of the priesthood and learned
much of his philosophy and so-called musical science. He defined the
mathematical relation of the octave as produced by half of a given
string, the fifth produced by two-thirds and the fourth by
three-fourths. He also found the ratio of the major step by
subtracting the fourth from the fifth. This was the ratio 9:8. With
this as a measure he attempted to place the tones of the tetrachord,
or Greek scale of four tones, which was the unit of their tonal
system. This gave him two major steps, and a half step somewhat too
small, being equal to the ratio of 256:243.

The most important part of Pythagoras' influence upon the art of music
was of a sentimental character. From Egypt he acquired many ideas of a
musical nature, such as that certain tones represented the planets,
and that time was the essence of all things. It was one of the laws of
his religion that before retiring at night his disciples should sing a
hymn in order to compose their spirits and prepare them for rest. The
verses selected for this use were probably of a devotional character,
like what are now known as the Orphic hymns, of which the lines upon
the next page may be taken as a specimen. Ambros