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This use of consecutive changes of tempo is of
course no new thing; it is the mathematical ratio between tempi that has
not been systematized. It can be observed in current practice that when
the relations between successive tempi do not follow a simple ratio, but
are accidental and arbitrary, the result is felt to be rhythmically rough.
Conversely, I am convinced that further investigation would confirm my
own experiments, which show that when successive tempi, as chosen by the
best conductors, give an impression of smoothness, the conductors have
actually, though probably unconsciously, chosen a ratio that is demonstrably
simple.
Henry Cowell
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