Re: Lilypond's internal pitch representation and microtonal notation

[Joseph Wakeling]

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