SCALES
76. A _scale_ (from _scala_, a Latin word meaning _ladder_; Ger.
_Ton-leiter_) is an ascending or descending series of tones, progressing
according to some definite system, and all bearing (in the case of
tonality scales at least) a very intimate relation to the first
tone--the _key-tone_ or _tonic_. (See p. 28, Sec. 78; also note 1 at
bottom of p. 38.)
Many different kinds of scales have existed in various musical
eras, the point of resemblance among them all being the fact
that they have all more or less recognized the _octave_ as the
natural limit of the series. The difference among the various
scales has been in the selection of intervals between the
scale-tones, and, consequently, in the number of tones within
the octave. Thus _e.g._, in our major scale the intervals
between the tones are all whole-steps except two (which are
half-steps), and the result is a scale of _eight_ tones
(including in this number both the key-tone and its octave):
but in the so-called _pentatonic_ scale of the Chinese and
other older civilizations we find larger intervals (_e.g._,
the step-and-a-half), and consequently a smaller number of
tones within the octave. Thus in the scale upon which many of
the older Scotch folk songs are based the intervals are
arranged as follows:
1 whole 2 whole 3 step-and- 4 whole 5 step-and- 6
step step a-half step a-half
The result is a scale of six tones, corresponding
approximately with C--D--E--G--A--C in our modern system.
The term _pentatonic_ is thus seen to be a misnomer since the
sixth tone is necessary for the completion of the series, just
as the eighth tone is essential in our diatonic scales.
The following Chinese tune (called "Jasmine") is based on the
pentatonic scale.
[Illustration]
77. In studying the theory of the scale the student should bear in mind
the fact that a scale is not an arbitrary series of tones which some one
has invented, and which others are required to make use of. It is rather
the result of accustoming the ear to certain melodic combinations (which
were originally hit upon by accident), and finally analyzing and
systematizing these combinations into a certain definite order or
arrangement. The application of this idea may be verified when it is
recalled that most primitive peoples have invented melodies of some
sort, but that only in modern times, and particularly since the
development of instrumental music, have these melodies been analyzed,
and the scale upon which they have been based, discovered, the inventors
of the melodies being themselves wholly ignorant of the existence of
such scales.
78. A _key_ is a number of tones grouping themselves naturally (both
melodically and harmonically) about a central tone--the key tone. The
word _tonality_ is often used synonymously with _key_ in this sense.
The difference between _key_ and _scale_ is therefore this,
that while both _key_ and _scale_ employ the same tone
material, by _key_ we mean the material in general, without
any particular order or arrangement in mind, while by _scale_
we mean the same tones, but now arranged into a regular
ascending or descending series. It should be noted in this
connection also that not all scales present an equally good
opportunity of having their tones used as a basis for tonality
or key-feeling: neither the chromatic nor the whole-step scale
possess the necessary characteristics for being used as
tonality scales in the same sense that our major and minor
scales are so used.
79. There are _three general classes of scales_ extant at the present
time, viz.: (1) Diatonic; (2) Chromatic; (3) Whole-tone.[13]
[Footnote 13: If strictly logical terminology is to be insisted upon the
whole-tone scale should be called the "whole-step" scale.]
80. The word _diatonic_ means "through the tones" (_i.e._, through the
tones of the key), and is applied to both major and minor scales of our
modern tonality system. In general a diatonic scale may be defined as
one which proceeds by half-steps and whole-steps. There is, however, one
exception to this principle, viz., in the progression six to seven in
the harmonic minor scale, which is of course a step-and-a-half. (See p.
33, Sec. 86.)
81. A _major diatonic scale_ is one in which the intervals between the
tones are arranged as follows:
1 whole 2 whole 3 half 4 whole 5 whole 6 whole 7 half 8
step step step step step step step
In other words, a major diatonic scale is one in which the intervals
between three and four, and between seven and eight are half-steps, all
the others being whole-steps. A composition based on this scale is said
to be written in the major mode, or in a major key. The major diatonic
scale may begin on any one of the twelve pitches C, C[sharp] or D[flat],
D, D[sharp] or E[flat], E, F, F[sharp] or G[flat], G, G[sharp] or
A[flat], A, A[sharp] or B[flat], B, but in each case it is the same
scale because the intervals between its tones are the same. We have then
one major scale only, but this scale may be written in many different
positions, and may be sung or played beginning on any one of a number of
different pitches.
82. It is interesting to note that the major scale consists of two
identical series of four tones each; _i.e._, the first four tones of the
scale are separated from one another by exactly the same intervals and
these intervals appear in exactly the same order as in the case of the
last four tones of the scale. Fig. 53 will make this clear. The first
four tones of any diatonic scale (major or minor) are often referred to
as the _lower tetrachord_[14] and the upper four tones as the _upper
tetrachord_.
[Footnote 14: The word _tetrachord_ means literally "four strings" and
refers to the primitive instrument, the four strings of which were so
tuned that the lowest and the highest tones produced were a perfect
fourth apart. With the Greeks the tetrachord was the unit of analysis as
the octave is with us to-day, and all Greek scales are capable of
division into two tetrachords, the arrangement of the intervals between
the tones in each tetrachord differentiating one scale from another, but
the tetrachords themselves always consisting of groups of four tones,
the highest being a perfect fourth above the lowest.]
[Illustration: Fig. 53.]
It is interesting further to note that the upper tetrachord of any
_sharp_ scale is always used without change as the lower tetrachord of
the next major scale involving sharps, while the lower tetrachord of any
_flat_ scale is used as the upper tetrachord of the next flat scale. See
Figs. 54 and 55.
[Illustration: Fig. 54.]
[Illustration: Fig. 55.]
83. From the standpoint of staff notation the major scale may be written
in fifteen different positions, as follows:
[Illustration]
It will be observed that in the above series of scales those beginning
on F[sharp] and G[flat] call for the same keys on the piano, _i.e._,
while the notation is different, the actual tones of the scale are the
same. The scales of C[sharp] and D[flat] likewise employ the same tones.
When two scales thus employ the same tones but differ in notation they
are said to be _enharmonic_, (cf. p. 38, Sec. 93.)
_Note_.--The student is advised to adopt some uniform method
of writing scales, preferably the one followed in those given
above, the necessary sharps and flats appearing before the
notes in the scale and then repeated collectively at the end
as a signature. He is also advised to repeat these scales and
signatures over and over until absolute familiarity is
attained. _E.g._, E--F[sharp]--G[sharp]--A--B--C[sharp]--D[sharp]--E;
signature, four sharps, F, C, G, and D.