flats in the signature) would therefore sound out of
tune. There would be many other disadvantages in such a system, notably
the inability to modulate freely to other keys, and since modulation is
one of the predominant and most striking characteristics of modern
music, this would constitute a serious barrier to advances in
composition. To obviate these disadvantages a system of _equal
temperament_ was invented and has been in universal use since the time
of Bach (1685-1750) who was the first prominent composer to use it
extensively. _Equal temperament_ means simply dividing the octave into
twelve equal parts, thus causing all scales (as played on keyboard
instruments at least) to sound exactly alike.

To show the practicability of equal temperament Bach wrote a
series of 48 _preludes and fugues_, two in each major and two
in each minor key. He called the collection "The Well-tempered
Clavichord."

13. Various _standards of pitch_ have existed at different times in the
last two centuries, and even now there is no absolute uniformity
although conditions are much better than they were even twenty-five
years ago. Scientists use what is known as the "scientific standard"
(sometimes called the "philosophic standard"), viz., 256 double
vibrations for "middle C." This pitch is not in actual use for musical
purposes, but is retained for theoretical purposes because of its
convenience of computation (being a power of 2). In 1885 a conference of
musicians at Vienna ratified the pitch giving Middle C 261 vibrations,
this having been adopted by the French as their official pitch some 26
years before. In 1891 a convention of piano manufacturers at
Philadelphia adopted this same pitch for the United States, and it has
been in practically universal use ever since. This pitch (giving Middle
C 261 vibrations) is known as "International Pitch."

_Concert pitch_ is slightly higher than _International_, the difference
between the two varying somewhat, but being almost always less than
one-half step. This higher pitch is still often used by bands and
sometimes by orchestras to give greater brilliancy to the wind
instruments.

REFERENCES

Lavignac--Music and Musicians, pp. 1-66.

Broadhouse--The Student's Helmholz.

Helmholtz--Sensations of Tone.

Hamilton--Sound and its Relation to Music.

NOTE:--For a simple and illuminating treatment of the subject
from the standpoint of