The Origin and Development of Musical Scales [pp. 324-343]

THE ORIGIN AND DEVELOPMENT OF MUSICAL SCALES. 327
is known as the Scale of Even Temperament, and consists of
1v2
twelve equal semitones whose length is -. Number 7 in the
I
above table gives the ratios and vibration-numbers thus obtained.
Comparison with the preceding theoretical scales, and with
some others not given, reveals the remarkable fact that the tempered scale coincides at but tkree points with its theoretical companions; namely, at its two extremities-C and C'-and at its
middle point-the F# or Gb that bisects the interval between F
and G. At other points its departures from them range from
3 to 6~ vibrations per second.
To these scales might be added a large number that are
known to be used by peoples whose music has not attained the
complexity of ours. For our present purpose we need mention
but a few, all of which recognize the fundamentalness of the
octave.
The popular melodies of the Scotch and Irish, so long as they
remain uncontaminated by foreign influences, employ a scale of
five tones. The Chinese, also, altho attempting a theoretical
division similar to that of our tempered scale, are confined in
practice to but five of the notes thus obtained. They content
themselves, so to speak, with playing upon the black keys of
their theoretical gamut. The fancy for similar scales of five
tones prevails among many semi-civilized peoples.
The Indo-Germanic family in general carry this subdivision
of the octave much further, our own systems being surpassed in
this particular by thocse of our oriental cousins. The Arabs, for
examnple, count sixteen or seventeen notes to the octave. The
traditional scale of India contains twenty-two theoretical degrees, which practice combines in various ways into modes of
seven. And the Persians are just twice as minute as we, extending their subdivision to quarter-tones, and thus obtaining
twenty-four notes to the octave.
I From a musical system recognizing small intervals in some
sueh way as this it is supposed that the earliest music of the
Greeks was derived; for Olympos, the first Greek theoretical
musician of whom we have record, is said to have used a scale
with extremely small intervals. Exactly what was the nature
of the system of Olympos, however, is difficult to determine.
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