he following beat is
represented by a rest (0). In two of the measures there are groups of
two notes. Each of the notes in these groups of course equals in time
half of an isolated note, for each occupies half the time of one beat.

The French say _dechiffrer la musique_--to puzzle it out, to decipher
it, as one would say of hieroglyphs on an Egyptian sarcophagus. The
term is well chosen. The causes of the obscurity of musical notation
are numerous, but the most prolific is undoubtedly expressing time by
the form of the symbols of sound. In slow movements, and where only
few modulations occur, this does not seem to be a serious
objection; but in the rapid movements of compound time it becomes
insupportable--at least after one has learned that there is a better
way. An example in 6/8 time--six eighth-notes to the measure--will
illustrate this:

[Illustration of 6/8 notes score]

Here each triplet fills the time of one-third of a beat; that is,
three-sixteenths equal one-eighth, according to the sublime precision
of the old notation! But then no such thing as a twenty-fourth note
is in use: three twenty-fourths would just do it! This is a part of a
vocal exercise. The learner would have to divide each beat into three
parts each, unless very familiar with such exercises; and one of these
divisions would fall on a rest, another in a prolongation, another in
the middle of an eighth note. In the new method see how the crooked
places are straightened:

--------------- ---------------
----- ----- ----- -----
1 0 2 3 4 3 2 1 . 2 3 . 4 5

It "sings itself" the moment you look at it, after a little study
of this rational notation. Note also that there is no mathematical
absurdity here: the division is logical, and yet the air is perfectly
expressed in every particular.

The mastery of time in music is at best an arduous task, yet teachers
of music, as a rule, expect their pupils to learn it incidentally
while studying intonation. They give no special drill in pure time at
every lesson; and the result is that army of mediocre singers and
players who never become able to execute any but the very simplest
music at sight. They may know the theory of time, may be able to
explain to you clearly the divisions of every measure, but this is not
sufficient for the musician: he must decipher his measures with great
readiness, precision and rapidity, or he never rises above the
mediocre. The ambition