Re: negative scales

Sort of like, you have
positive and negative numbers, but any motion away from a point, either left
or right, is still positive distance relative to the point.

Steve

Actually I WAS thinking of the number line at that point.

In this book "Zero," the author explains how zero is another way of
saying infinity. Example: if you keep going half the distance to the
door of your house, the paradox is you never reach the door because
you must traverse half the distance before you reach it. And there
are an infinite number of steps of half the distance!

(He explains away this paradox later.)

But the point is, mathematicians figured out that fractions that keep
dividing into half (like the above example) can be finally said to
EQUAL zero, because they are approaching zero on a smaller & smaller
scale... averaging out that "infinite approach towards zero," one can
simply say it EQUALS zero!

So, rather than ALL white noise, or ZERO noise (silence) - - these are
two sides of infinity - - I am thinking that, using the above analogy
of approaching zero & fractions, Zero Musically would mean these
infinite steps between notes (that approach toward zero) or
microtones.

Yes ?

No ?

Since I'm working with complementary scales, the positive / negative
aspect would remain.

12 notes in an octave minus the 5 notes in my pentatonic scale equals
the remaining 7 notes.

But if you divide the octave into 24 notes (microtones) & subtract the
5 notes of my pentatonic scale, you now have 19 notes remaining.

So the "negative scale" corresponds to an aspect of how one divides up
the octave to begin with !

Since one can divide it up into any number of 'equal' steps, or an
infinite number of steps, this infinity is conceptually the same as
the property of zero.

But here's a question for you:

Are all infinities equal? Or can one infinity be greater than another
infinity?

The answer to that would portend something really out of this world
when related to its musical equivalent...
.

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