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

THE PRINCE TON RE VIE W.
the octave, but is so rarely practicable that it has produced notendency to subdivide our scale of possible tones into similar
sections of more than eight notes in length.
Imitation at the next nearest intervals, the fifth and fourth,
gives quite satisfactory results, but differs from that at the octave
in introducing new partials. Notwithstanding this, the fifth and
the fourth have sometimes played the role of the octave. For
example, the Greek diazeutic tetrachords divided the whole
range of possible notes into similar fifths; and in the early part
of the middle ages it is said that melodies were sung by two
voices in parallel fifths and fourths as now tenors and sopranos
frequently sing together in parallel octaves. Imitation at the
fifth and fourth still survives in the fugue and the sonata.
(d) Having pointed out the pre-eminence of the octave and
the position of the fifth and fourth, let us now endeavor to trace
the process of scale-formation according to the principle of tonerelationship. Beginning with any given note, and proceeding
to add one by one its nearest kindred, we soon obtain a scale
some of whose notes lie inconveniently near together and some
inconveniently far apart. To avoid the crowding together of
some of its notes, and at the same time to obtain a greater evenness in their distribution, we are then obliged to replace some of
them by others more remotely related to the tonic. This is the
practical effect of the first limitation-that of smallest tolerable
interval.
The Mongols, the Malays, certain Polynesian, American,
and African tribes, the Celts of Scotland and Ireland, together
with perhaps the ancient Assyrians and Egyptians, avoid intervals
less than V, which is between one sixth and one seventh of an octave. The Greeks ultimately agreed on A, or about one twelfth
of an octave, as their limit; and modern music has. gone but
little further. The Arabs, Hindus, and Persians tolerate much
shorter intervals than these.
It is obvious that the smaller the intervals tolerated the
longer will the process of adding new relatives go on, and the
more notes will there be to the octave. Thus the Chinese and
Scotch may have five notes exclusive of the octave of the tonic;
we may have twelve; and some Asiatics even as many as twenty-four.
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