fact, to effect a
transposition for each part upon principles peculiar to itself.

The progress of classification is distinctly seen in the use of seven
letters instead of fifteen, affording a tacit recognition of the most
essential underlying facts of harmony--_the equivalence of octaves_.
The staff, however, affords the eye no assistance at this point, since
the octaves of notes occupy relatively entirely different positions
upon it, the octave of a space being invariably a line, and the octave
of a line a space. Moreover, the octave of a bass line is always very
differently located when it falls upon the treble staff, and, _vice
versa_, the octave of a treble note falling in the bass is very
differently placed. If a notation had to be made anew it would no
doubt facilitate matters to make use of a staff so planned as to bring
out the equivalence of octaves more perfectly. A recent American
designer, Mrs. Wheeler, has proposed a double staff of six lines,
divided into two groups of three, for the treble and bass, thus
presenting for the piano score four groups of three lines each,
separated by smaller or larger intervals. Upon such a staff every tone
would fall in the same place upon the three lines in every octave, the
octave of the first line of the lower three would be the first line of
the second three, and so on.

This, however, is to anticipate. The smaller rhythmic divisions of the
measure were very little used in the old music which, if not sung in
slow time, was at least written in long notes, and the smaller
varieties of notes are the invention of a period perhaps rather later
than that at which we have now arrived. They belong to the elaborate
rhythmic construction of the music of Haendel, Bach, Scarlatti and
Haydn.

CHAPTER XVI.

MUSICAL INSTRUMENTS. THE VIOLIN, ORGAN, ETC.

I.

During the entire period covered by the division of the story with
which we have been now for some time dealing, the influences operating
upon the tonal sense in the direction of harmonic perception had also
been highly stimulative to the sense of melody. All the devices of
counterpoint, with their two, three and four tones of the moving voice
against one of the _cantus fermus_, were so many incitations in the
direction of melodic cleverness. This influence was still further
strengthened by the constant effort of the composer to impart to each
voice as characteristic an individuality of movement as possible.
Hence