[Ill.u.s.tration: Fig. 51.]

[Ill.u.s.tration: Fig. 52.]

75. The _acciaccatura_ (or short appoggiatura) is written like the appoggiatura except that it has a light stroke across its stem.

[Ill.u.s.tration] It has no definite duration-value, but is sounded as quickly as possible, taking its time from that of the princ.i.p.al tone.

The appoggiatura is always accented, but the acciaccatura never is, the stress always falling on the melody tone. (See Grove, op. cit. Vol. I, p. 96.)

The use of embellishments is on the wane, and the student of to-day needs the above information only to aid him in the interpretation of music written in previous centuries. In the early days of instrumental music it was necessary to introduce graces of all sorts because the instruments in use were not capable of sustaining tone for any length of time; but with the advent of the modern piano with its comparatively great sustaining power, and also with the advent in vocal music of a new style of singing (German Lieder singing as contrasted with Italian coloratura singing), ornamental tones were used less and less, and when found now are usually written out in full in the score instead of being indicated by signs.

CHAPTER VII

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.

[Ill.u.s.tration]

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 a.n.a.lyzing 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 a.n.a.lyzed, 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 cla.s.ses 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 a.n.a.lysis 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.]

[Ill.u.s.tration: 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.

[Ill.u.s.tration: Fig. 54.]

[Ill.u.s.tration: Fig. 55.]

83. From the standpoint of staff notation the major scale may be written in fifteen different positions, as follows:

[Ill.u.s.tration]

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.

CHAPTER VIII

SCALES (_Continued_)

84. The _minor diatonic scale_ is used in several slightly different forms, but the characteristic interval between the first and third tones (which differentiates it from the major scale) remains the same in every case. This interval between the first and third tones consists of four half-steps in the major scale and of three half-steps in the minor scale and this difference in size has given rise to the designation _major_ for the scale having the larger third, and _minor_ for the scale having the smaller one.

85. _The original (or primitive) form_ of the minor scale has its tones arranged as follows.

1 whole 2 half 3 whole 4 half 5 half 6 whole 7 whole 8 step step step step step step step

As its name implies, this is the oldest of the three forms (being derived from the old Greek Aeolian scale), but because of the absence of a "leading tone" it is suitable for the simplest one-part music only, and is therefore little used at present.

86. _The harmonic minor scale_ is like the primitive form except that it subst.i.tutes a tone one half-step higher for the seventh tone of the older (_i.e._, the primitive) form. This change was made because the development of writing music in several parts (particularly _harmonic_ part-writing) made necessary a "leading tone," _i.e._, a tone with a strong tendency to move on up to the key-tone as a closing point. In order to secure a tone with such a strongly upward tendency the interval between _seven_ and _eight_ had to be reduced in size to a half-step. It should be noted that this change in the seventh tone of the scale caused an interval of a step-and-a-half between the sixth and seventh tones of the scale.

1 whole 2 half 3 whole 4 whole 5 half 6 step and 7 half 8 step step step step step a half step

87. _The melodic minor scale_ subst.i.tutes a tone one half-step higher than six as well as one a half-step higher than seven, but this change is made in the ascending scale only, the descending scale being like the primitive form. The higher sixth (commonly referred to as the "raised sixth") was used to get rid of the unmelodic interval of a step-and-a-half[15] (augmented second), while the return to the primitive form in descending is made because the ascending form is too much like the tonic major scale.

[Footnote 15: The step-and-a-half (augmented second) is "unmelodic"

because it is the same size as a _minor third_ and the mind finds it difficult to take in as a _second_ (notes representing it being on adjacent staff-degrees) an interval of the same size as a third.]

1 whole 2 half 3 whole 4 whole 5 whole 6 whole 7 half 8 step step step step step step step