erfection of clearness in the sound of their strings by
means of bronze plates or horn [Greek: echeia], so the ancients devised
methods of increasing the power of the voice in theatres through the
application of harmonics.

CHAPTER IV

HARMONICS

1. Harmonics is an obscure and difficult branch of musical science,
especially for those who do not know Greek. If we desire to treat of it,
we must use Greek words, because some of them have no Latin equivalents.
Hence, I will explain it as clearly as I can from the writings of
Aristoxenus, append his scheme, and define the boundaries of the notes,
so that with somewhat careful attention anybody may be able to
understand it pretty easily.

2. The voice, in its changes of position when shifting pitch, becomes
sometimes high, sometimes low, and its movements are of two kinds, in
one of which its progress is continuous, in the other by intervals. The
continuous voice does not become stationary at the "boundaries" or at
any definite place, and so the extremities of its progress are not
apparent, but the fact that there are differences of pitch is apparent,
as in our ordinary speech in _sol_, _lux_, _flos_, _vox_; for in these
cases we cannot tell at what pitch the voice begins, nor at what pitch
it leaves off, but the fact that it becomes low from high and high from
low is apparent to the ear. In its progress by intervals the opposite is
the case. For here, when the pitch shifts, the voice, by change of
position, stations itself on one pitch, then on another, and, as it
frequently repeats this alternating process, it appears to the senses to
become stationary, as happens in singing when we produce a variation of
the mode by changing the pitch of the voice. And so, since it moves by
intervals, the points at which it begins and where it leaves off are
obviously apparent in the boundaries of the notes, but the intermediate
points escape notice and are obscure, owing to the intervals.

3. There are three classes of modes: first, that which the Greeks term
the enharmonic; second, the chromatic; third, the diatonic. The
enharmonic mode is an artistic conception, and therefore execution in it
has a specially severe dignity and distinction. The chromatic, with its
delicate subtlety and with the "crowding" of its notes, gives a sweeter
kind of pleasure. In the diatonic, the distance between the intervals is
easier to understand, because it is natural. These three classes diffe