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

THE ORIGIN AND DE VELOPMENT OF MUSICAL SCALES. 331
Through a train of reasoning like the foregoing, Helmholtz
reaches the following conclusion: "We have seen, then, that
melody has to express a motion in such a manner that the hearer
can easily, clearly, and certainly appreciate the character of that
motion by immediateperception. This is only possible when the
steps of this motion, their rapidity and extent, are also exactly
measurable by immediate perception. Melodic motion is change
of pitch in time. To measure it perfectly, the length of time
elapsed, and the distance between the pitches, must be measurable. This is possible for immediate audition only on condition
that the alterations both in time and pitch should proceed by
regular and determinate degrees."
"It may be objected," he adds, "that architecture in its arabesques... constantly employs curved lines and not lines
broken into determinate lengths. But... the eye which contemplates arabesques can take in and compare all parts of the
curved lines at once, and glance to and fro and return to its first
contemplation. Hence, notwithstanding the continuous curvature of such lines, their paths are perfectly comprehensible....
The individual parts of a melody reach the ear in succession.
We cannot perceive them all at once. We cannot observe
backwards and forwards at pleasure. Hence for a clear and
sure measurement of the change of pitch no means is left but
progression by determinate degrees.... When the wind howls
and its pitch rises and falls in insensible gradations... the
whole phenomenon produces a confused, unpleasant impression.
The musical scale is, as it were, the divided rod by which we
measure progression in pitch as rhythm measures progression
in time....
"We consequently find the most complete agreement among
all nations that use music at all... as to the separation of
certain determinate degrees of tone from the possible mass of
continuous gradations of sound.... But in selecting the particular degrees of pitch deviations of national taste become
immediately apparent."
It would seem that throughout this discussion our author
has exerted himself more to show why, even when we have
learnt that it is not strictly necessary, we still cling to a determinate scale as a prerequisite for melody, than to discover howr