a whole note; a short stem affixed to this note
doubled its value. It was then called the _longa_. A note head twice
as long represented a still longer duration, called the _maxima_ or
longest. There was also a _semibreve_, a diamond-shaped note which was
used when two or more tones were sung to one syllable. There were no
bars for indicating the place of the strong pulse in the measure, but
a bar was used to show the end of the musical phrase belonging to a
line of verse. The notation was made still more uncertain by the
license of the breve in triple time being equal to three semibreves,
and so in general each long note in triple measure being equal to
three of the next class shorter. In short, the time notation was of
the most crude and imperfect description, but it was at least a
beginning, and all the theoretical writers upon music for the next two
centuries rest in the precepts of Franco of Cologne, as a sure
stronghold, where no false doctrine can find admission. Franco
remarks, concerning the dissonances, that the imperfect dissonances,
the thirds and sixths, go very well between two consonances, showing
that in his time the third and sixth were still regarded as licenses
in harmony to be explained or excused. The general principle that any
dissonance is admissible when smoothly placed between two consonances
is a fundamental law of modern counterpoint.

There was another Franco whose work has often been confounded with
that of the celebrated master at Cologne. Franco of Paris was
connected with the Sorbonne or with Notre Dame, and his writing had
mostly to do with harmonic music. He classifies the consonances
as--complete, the unison and octave; the incomplete, the major and
minor thirds; the middle, the fourth and fifth. This is the first
instance in musical theory where the third has been recognized as a
consonance. Among the dissonances he classes the major and minor
sixth as incomplete, and says concerning these two only that
immediately before a consonance any incomplete dissonance goes very
well. From the superior celebrity of the Cologne Franco the work of
the Parisian master was overlooked for many years, and it is only
through the investigation of Coussemaker that his real standing and
importance have been ascertained.

[Illustration]

CHAPTER XII.

THE RISE OF POLYPHONY. OLD FRENCH AND GALLO-BELGIC SCHOOLS.

I.

We here enter upon one of the most interesting and important chapters
in