understood this quite well; to Purcell, and to composers much later than
him, the old endings were perfectly satisfactory. This, for instance,
left no sense of the unfinished:

[Illustration]

Gradually two keys swamped and swept away the modes--our major and
minor; then our modern feeling for key relationships was born. Here is
the major scale of C with a satisfactory harmonic ending:

[Illustration]

It will be noticed that the top note of the chord marked with a star,
the last note but one of the scale, is a semitone below the last note of
the scale and rises to the last note. That is a proper ending or full
close; what was called a half-close was:

[Illustration]

As a termination to a piece of music made up of the notes of the scale
of C, and therefore said to be in the key of C, this was not
satisfactory. To set the ear and the mind at ease, to get a feeling that
the music has settled down on a secure resting-place, the first chord
had to be repeated. And in these chords

[Illustration]

lies the germ of the whole of the later music. Only two more steps were
needed. By adding an F, or writing an F instead of the upper G in the
middle chord, the chord of the dominant seventh was obtained: