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

THE ORIGIN AND DEVELOPMENT OF MUSICAL SCALES. 343
be welcome of the exclusion of the latter by the former. It is
also true that Prof. Helmholtz seems to push too far his theory
that we have no harmonic influences whatever to account for in
the very early development of a scale, such as, for instance, a
rude tuning of instruments by the simultaneous production of
two notes. The Greeks knew of binary and ternary chords even
if they were unable to employ them practically; several barbarous tribes of to-day not only know of such chords but have
developed an elaborate polyphonic system of music; and it is
in general probable that every people possessing any musical
instruments have some notion of combining their tones in pairs
and triads and even of tuning them by the resultant harmonies.
The difficulty in this matter is of course that the simpler workings of harmonic influence and the influence of tone-relation as
we have described it give precisely the same results, and it is
absolutely impossible to say from mere inspection whether a
given scale was moulded by the one or the other agency or by
both. As soon as harmony becomes elaborate it begins to make
a marked impression upon scales. To this influence are justly
ascribed many of the later steps in the crystallization of modern
scales out of the church modes, the whole of which process we
were forced to compress into a single paragraph. Helmholtz
will not admit any harmonic factor in the problem until that
comparatively late period.
After making whatever small deductions are demanded by
these seeming deficiencies, however, there remains a remarkable
body of combined observation and speculation which challenges
our heartiest admiration for its amount, its logical solidity, and
its exceeding interest. To one who appreciates the care and
ingenuity displayed throughout the whole treatment, it is surprising that Prof. Helmholtz's brilliant and triumphant grappling with an extraordinarily difficult problem has not been
more widely published and recognized.
WALDO S. PRATT.