e [6/4] [5/3] cadence.

2. Four bars to the principal modulation.

3. Repeat the first four bars.

4. Four bars to the end.

Three children can be used for this, in the following way:

The first child sings the first four bars, the second goes on to the end
of the eighth bar, then the first child repeats what she sang, and a
third child finishes. This affords excellent practice, particularly for
the first child, who soon learns to confine herself to a simple opening,
as this must be remembered and repeated later.

Memory plays a much larger part in the power to extemporize than many
people realize, and if this step in the preliminary work be
conscientiously taken there will be abundant results later.

We now come to the important stage of extemporizing on the piano. It
must be remembered that a very thorough foundation of the knowledge of
chords has been laid by the ear-training work, leading up to the power
to write down chords from dictation, and to sing them in arpeggio.

The first exercise will consist in playing a very simple tonic and
dominant accompaniment on the piano, while a melody is extemporized with
the voice. There is far more variety possible in this than appears at
first sight. For instance, the sequence of the chords may run in any of
the following ways, among others:

I V I V I I V I }
}
I I V I I I V I }
}
I I I V I I V I }
}
I V V I I I V I }

Those who have studied elementary algebra will recognize a simple
application of the theory of permutations!

It is interesting to note the ease with which children will do this
exercise, if they have been carefully trained in all the preceding work.
Grown-up students are usually very much slower than children at it,
partly because they are inclined to be self-conscious, and to worry
about the sound of their voice, &c. But the child who has been
accustomed to sing at sight and to extemporize with the voice in front
of a class is not in the least embarrassed at being told to go to the
piano and combine a sung melody with a simple piano accompaniment. At
first there will be a tendency to restrict the melodies to the actual
notes of the tonic and dominant chords, but with a little practice
passing notes, &c. are soon added, and graceful little tunes will
result.

The next exercise consists in the use of three chords, tonic, dominant,
and subdominant; the melody, as before, being sung. At this stage