On 09/21/2010 04:42 PM, Han-Wen Nienhuys wrote:
> This is not the nuance implied, since by your definition,
> natural-uparrow (+1/4) and sharp-downarrow are the same, and you
> clearly want them to mean something different.
They are enharmonically the same pitch, which can be notated in two
(symbolically and semantically) different ways.
0 + 1/4 and 1/2 - 1/4 are the same if you consider only the sum, but
they're not the same if you consider the _series_. Lots of microtonal
notations work on the basis of a superposition of ever-smaller intervals
in this way.
> What is the difference between both?
Similar to the difference between C-sharp and D-flat.
C raised by a semitone is musically not the same as D lowered by a
semitone, even though in equal-tempered tuning they correspond to the
same enharmonic pitch.
Likewise, C-natural raised by a quarter-tone is musically not the same
as C-sharp lowered by a quarter-tone, even though the resulting
frequency is the same.
> The current system satisfies these constraints obviously, but it
> possibly does not represent well various nuances of scales that may
> exist.
Exactly. :-)
Best wishes,
-- Joe
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