composer had
learned which intervals might be used without harmonic offense, and
which not.

Before proceeding to the story of this chapter, the definition of a
few terms may be advisable, in the interests of clearness. By
"imitation," then, we mean the exact repetition of the melody of one
part by another part, at the same or a different pitch. Such an
imitation may be "strict," as when the intervals and progressions are
exactly repeated; or "free," as when certain changes are made here and
there in order to lead the imitation around better to the principal
key. Canonic imitation is one in which the imitation is strict, the
repeating voice exactly repeating the melody of the principal. By
"counterpoint" we mean a second voice added to a melody already
existing, the counterpoint having a strict relation to the leading
melody, but a wholly independent movement. This conception had its
origin in the art of extemporaneous descant, in which, while the choir
and congregation repeated the melody of the plain song, a few talented
singers performed variations to it, guided solely by ear and
tradition, returning to the tone of the plain song at all the points
of repose. We do not know when extemporaneous descant gave place to
written composition, but it was probably early in the twelfth century.
By "double counterpoint" is meant a counterpoint which, although
written to be sung an octave lower than the principal song, can be
transposed an octave and sung higher than the principal song without
giving rise to forbidden progressions. This will be the case only when
the original relations of the two voices have been restricted to
certain prescribed intervals. By "fugue" is meant a form of
composition in which every voice in turn enters with the leading
melody of the piece, the same given out by the leading voice at first,
called the "subject," responding alternately in tonic and dominant.
This form comes later than the period we are now about to consider,
but it grew out of the devices of polyphony, and accordingly is always
to be kept in mind as the goal toward which all this progress was
tending.

The art of polyphony is to be understood as an effort toward variety
and unity combined. The unity consisted in all the voices following
with the same melodic idea; variety, in the different combinations
resulting in the course of the progress. The limitations of polyphony
were reached when the true expression of melodic intervals wa