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. . . the ancients
[classified] music as part
of the quadrivium, that group of four sciences dealing with measurement.
Here we would find music united with geometry, which is concerned with
the measurement of nonmoving planes and bodies; with astronomy, as the
measurer of moving entities; and with arithmetic, in which measurement
is sublimated and concentrated into the operation with abstract numbers.
The science of music deals with the proportions objects assume in their
quantitative and spatial, but also in their biological and spiritual
relations. . . .
. . . . To [some opponents of the Platonic idea], it seemed quite inadmissible to couple such sober concepts as state, government, philosophy, and mathematics with music, which in its audible form seemed to be eternally elusive and irrational, and accordingly suspect.
Paul Hindemith
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