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 musi al

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.









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.]







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.







83. From the standpoint of staff notation the major scale may be written

in fifteen different positions, as follows:









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.