Grove's dictionary of music and musicians

—
—
SCALE SCALE 237
C to G,
,
Perfect Fifth,
, A, Major sixth,
,, B, Major seventh,
,, C, Octave.
In has been stated, however, that for modem
European music we have the power of adding,
to the seven sounds of the diatonic scale,
certain other intermediate chromatic notes.
Thus between C and D we may add two notes
called Cjt and D|>. Between G and A we may
add Gjt and Al>, and so on. In order to determine
what the exact pitch of these notes
should be, it is necessary to consider that they
may be used for two quite distinct purposes,
i.e. either to embellish melody without change
of key, or to introduce new diatonic scales by
modulation. In the former case the pitch of
the chromatic notes is indeterminate, and
depends on the taste of the performer ; but for
the second use it is obvious that the new note
must be given its correct hannonic position
according to the scale it belongs to : in fact
it loses its chromatic character, and becomes
strictly diatonic. For example, if an Fi[ be
introduced, determining the new diatonic scale
of G, it must be a true major third above D,
in the same way that in the scale of C, B is a
major third above G. In this manner any
other chromatic notes may be located, always
adhering to the same general principle that
they must bear concordant harmonic relations
to other notes in the diatonic scale of which
they form part.
Proceeding in this way we should obtain a
number of chromatic notes forming a considerable
addition to the diatonic scale. For example,
in order to provide for eleven keys, all in
common use, we should get ten chromatic notes
in addition to the seven diatonic ones, making
seventeen in all, within the compass of a single
octave. This multiplication of notes would
produce such a troublesome complication in
practical music, that in order to get rid of it
there has been adopted an ingenious process of
compromising, which simplifies enormously the
construction of the scale, particularly in its
chromatic parts. In the first place it is found
that the distance between the diatonic notes
nearly half
E and F, and between B and C is
that between C and D, or G and A ; and
secondly, it is known that the adjacent chromatic
notes Cit and Dl>, Gj[ and A[>, etc., are not
very different from each other. Putting all
these things together, it follows that if the
octave be divided into twelve egual parts, a set
of notes will be produced not much differing
in pitch from the true ones, and with the
property of being applicable to all keys alike.
Hence has arisen the modem chromatic scale,
according to what is called equal temperament,
and as represented on the key -board
of the ordinary pianoforte. According to
this, the musical scale consists of twelve semitones,
each equal to a twelfth part of an
octave ;
two of these are taken for the tone
of the diatonic scale, being a very little less
in value than the original major tone of the
Greek divisions.
This duodecimal division of the octave was
known to the Greeks, but its modern revival,
which dates about the 16th century, has been
one of the happiest and most ingenious simplifications
ever known in the history of music,
and has had the effect of advancing the art to
an incalculable extent. Its defect is that certain
harmonic combinations produced by its notes
are slightly imperfect, and lose the satisfactory
effect produced by harmonies perfectly in tune.
The nature and extent of this defect, and the
means adopted to remedy it, will be more properly
explained under the article Tempekament,
which see.
Minor Scale.—It is a peculiarity of the minor
scale adopted in modern music, that its form
is frequently varied by accidental chromatic
alterations, to satisfy what are assumed to be
the requirements of the ear ; and as these
alterations most commonly take place in ascending
passages, it is usual, in elementary works,
to give different forms of the minor scale, for
ascending and descending.
For example, the normal form of the scale of
A minor is
and in descending, as here shown, the progressions
seem natural and proper.
But if the motion take place m the reverse
direction, thus :
'
No. 1.
it is said that the succession of the upper notes
in approaching the key note A, do not give the
idea which ought to correspond to our modern
tonality. It is argued that the penultimate
note, or seventh, being the leading or sensible
note of the key, ought to be only a semitone
distant from it, as is customary in all welldefined
keys ;
and that, in fact, unless this is
done, the tonality is not properly determined.
This reason has led to the accidental sharpening
of the seventh in ascending, thus :
No. 2.
But here there is another thing objected to ;
namely, the wide interval of three semitones
(an augmented second) between the sixth and
the seventh, Fl) and Git, which it is said is
abrupt and unnatural, and this has led to the
sharpening of the sixth also, thus