writers with many others which he did not himself
originate, but which grew out of some of his suggestions. He is
generally credited with having invented the art of solmization, the
introduction of the staff, the use of the hand for teaching intervals,
and the introduction of notes. He was not the first who introduced the
staff. Hucbald, as we have already seen, employed the spaces between
the lines for designating pitch. Between his time and that of Guido,
one or more lines were introduced in connection with the neumae, as
will be more particularly illustrated in chapter XV. Guido, however,
employed both the lines and the spaces, but instead of notes he wrote
the Roman letters upon the lines and spaces according to their pitch.
The notes were invented shortly after his time. For determining the
correct pitch of the notes of the scale he explains the manner of
demonstrating them upon the monochord. He mentions organum and
diaphony, and remarks that he finds the succession of fifths and
fourths very tiresome. The last treatise of the thirteenth century was
written by John Cotton, an English monk, whose entire theory of music
is made up from the Greek works.

[Illustration: Fig. 29.

GUIDO OF AREZZO.]

This summary of the didactic writers between Boethius and Franco at
Cologne fully confirms the justice of the remark, in the chapter
previous, concerning the influence of the Church upon music. At the
very time when a well marked beginning was being made in counterpoint
by the old French school at Paris, and when the English, Welsh and
Scandinavian musicians were in possession of an art of expressive
melody resting upon a simple harmonic foundation, these writers can
find nothing to say but to repeat over and over again their tedious
calculations concerning the intonations of _nete hypate_ and the other
Aristoxinean notes in the enharmonic and chromatic genera, which had
been dead names in the art of music for more than ten centuries.

With the appearance of Franco at Cologne, there is something new in
music. Late in the twelfth century he wrote a treatise upon measured
music, the first one in all the history of the art, so far as we know,
in which musical measure is treated independently of verse, and a
notation given for representing it. He recognizes two kinds of
measure--triple or perfect, and duple or imperfect. He gives four
kinds of notes--the shortest being the _brevis_, an oblong note having
twice the value of