I will begin with some remarks on musical notation. Musical
notation represents musical units of several different types:
units of pitch, of meter, of duration ,of loudness, of timbre, etc.,
as well as directions to performers on how to produce the desired
musical units. The units of pitch represented in traditional
western notation are not absolute pitches (identifiable as
such-and-such number of vibrations per second) but rather
pitches that are identified in terms of intervals that have
special melodic and harmonic significance. Physically,
an interval corresponds to the ratio f the frequency of the upper note
to that of the lower note, e.g. a pure fifth has a frequency ratio of
3/2 = 1.5. However, an interval does not have to have exactly
that frequency ration in order to be heard as a fifth: an interval
with a frequency ratio significantly larger or smaller than 1.5 still
can be heard as a fifth (an out-of-tune fifth, perhaps, but still a fifth),
and similarly with regard to all of the other musical intervals.