Part 5 (2/2)

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

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