}
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 it is
wise to let the dictation work in the class take the form of phrases
which can be harmonized with these chords, so as to accustom the
children to use them. This gives invaluable practice in the first
principles of harmonizing melodies, and should precede all formal
treatment of the subject.

Another useful exercise at this stage is to let the children add a