LESSON X.

~THEORY OF THE TEMPERAMENT.~


The instructions given in Lessons VIII and IX cover the subject of
temperament pretty thoroughly in a way, and by them alone, the student
might learn to set a temperament satisfactorily; but the student who
is ambitious and enthusiastic is not content with a mere knowledge of
how to do a thing; he wants to know why he does it; why certain causes
produce certain effects; why this and that is necessary, etc. In the
following lessons we set forth a comprehensive demonstration of the
theory of Temperament, requirements of the correct scale and the
essentials of its mathematics.

~Equal Temperament.~--Equal temperament is one in which the twelve
fixed tones of the chromatic scale[D] are equidistant. Any chord will
be as harmonious in one key as in another.

[D] The chromatic scale is a succession of all the half steps in the
compass of one octave. Counting the octave tone, it contains
thirteen tones, but we speak of twelve, as there are only twelve
which differ in name.

~Unequal Temperament.~--Unequal temperament was practiced in olden
times when music did not wander far from a few keys which were favored
in the tuning. You will see, presently, how a temperament could be set
in such a way as to favor a certain key (family of tones) and also
those keys which are nearly related to it; but, that in favoring these