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There is a distinction to be drawn between making
use of a new overtone in harmony, and fully assimilating that tone into
older harmonic material. For example, two tones used together in a new
interval may be justified both mathematically, as related tones of the
overtone series, and to the ear, as a not inacceptable [sic]
dissonance. But
the new interval, if combined freely with several other tones in the series,
may give an effect markedly dissonant, if not discordant. What is called
the “spacing” of tones, or the choice of octaves in which
given tones are
used, has also its effect upon the acceptability of a given combination,
since it changes the ratio between the tones in question. Thus, the interval
of a major seventh within the octave has a ratio of 8:15, whereas if it
were spaced three octaves and a seventh apart, the ratio would be 1:15.
Since this ratio contains no beats, but, on the contrary, the vibrations
are periodically even, it is questionable whether the interval of a major
seventh can be called dissonant when in this spacing. . . .
Henry Cowell
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