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 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 second part, either above or below a given melodic phrase.  This will be the foundation of later work in formal counterpoint.

The class is now ready for the treatment of modulations on the piano.  If the preliminary work in cadences, dominant sevenths, &c. has been conscientiously done in all keys there will be no difficulty in extemporizing a sung melody, which modulates, and adding a simple accompaniment at the piano.

Other chords can now be added, and the children will be ready to extemporize short tunes, entirely at the piano, without the aid of the voice.  To some people this may seem an easier thing to do than to accompany the voice, but experience has proved the contrary.  The child is so accustomed to use the voice that it will at first be inclined to think of all melody as vocal, and will be a little troubled when told not to think about vocal pitch.

The discipline of these early restrictions is obvious, and cannot be over-estimated.  It quite does away with the ‘hymn-tune’ style of early composition, which is such a trap to many amateurs.