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