e).

The pentatonic scale is markedly primitive in character. It is known
to have been in use anterior to the time of Guido d'Arezzo, which
would give it a date prior to the beginning of the 11th century. [257]

Rowbotham ascribes the invention of scales to those primitive musicians
who, striving for greater variety in their one-toned chants, added
first one newly-discovered tone, then another, and another. [258]
The pentatonic scale might have resulted from such chanting.

Most of the primitive peoples of the present day do not seem to feel
or "hear mentally" the half step. If musicians of early days had this
same failing, it was only natural for them to avoid that interval
by eliminating from their songs one or the other of each couplet of
tones which if sung would form a half step, thus their chants would
be pentatonic.

Not only do people in the primitive state fail to sense the half step,
but also people in modern environment who have heard very infrequently
this smallest interval of modern music.

Inability to sense this interval may be better understood when we
stop to consider that most of us find it unnatural and difficult
to hear mentally the still smaller quarter-step interval or one of
the even-yet-smaller sub-divisions of the octave which some peoples
have come to recognize through cultivation, and have embodied in
their music.

This tendency to avoid the half step and develop along the line of
pentatonic character is sometimes seen in our own children when they
follow their natural bent in singing. It has been my observation
that children with some musical creative ability, but unaccustomed
to hearing modern music with its half steps, almost invariably hum
their bits of improvised melody in the pentatonic scale.

_Major Diatonic Scale_. That scale in which the constituent tones if
considered in upward sequence would show the following arrangement
of whole and half step intervals,--(whole) (whole) (half) (whole)
(whole) (whole) (half).

_Natural Minor Diatonic Scale_. That scale in which the constituent
tones, if considered in upward sequence, would show the following
arrangement of whole and half step intervals,--(whole) (half) (whole)
(whole) (half) (whole) (whole).

_Harmonic Minor Diatonic Scale_. That scale in which the
constituent tones, if considered in upward sequence, would show
the following arrangement of half, whole and whole-and-a-half step
intervals,--(whole) (half) (whole) (whole)