modulation

It might be useful to think of modulation not as selecting a different subset
of notes out of a scale, but as selecting a different scale. Then we wouldn't
be looking for symmetry from a scale, but rather from a set of possible
scales. But just as a single piece of music usually only uses a small subset of
the key signatures available in 12TET, the space of scale signatures
available could really be quite abstract, because a given piece of music will
only pick out a few to use. Just as the notes in a given key are not at all
interchangable, but each has a unique function, so once we open up to
modulation between scales, then it becomes quite acceptable for the various
notes in a scale to have a unique set of available intervals.

Jim

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