Re: Lilypond's internal pitch representation and microtonal notation

[Han-Wen Nienhuys]

On Sun, Sep 19, 2010 at 7:50 PM, Joseph Wakeling
<address@hidden> wrote:
> >From a notational perspective, the first two numbers are used to
> calculate the vertical staff position of the notehead, while the value
> of the alteration is used to determine the accidental: e.g. (1,1,-1/2)
> corresponds to the D-flat a semitone above middle C.
>
> *A key assumption of this approach is that there is a one-to-one
> correspondence between accidental and alteration value.*  This clearly
> holds for conventional Western 12-tone notation.  However, it does _not_
> hold for many _microtonal_ notations.
>
> For example, if we are using the very common 'arrow' notation for
> quarter-tones, there are two distinct accidentals that can be used to
> represent the alteration +1/4 (i.e. quarter-tone-sharp): the first is a
> natural sign with an up arrow, the second is a sharp sign with a down
> arrow.  There is currently no effective, well-defined way to indicate
> which of the two is desired at any given moment.
>
> The arrow quarter-tone notation is just one of a whole variety of
> microtonal notations which operate not on the basis of single symbols
> per alteration, but on the basis of asuperposition of a successive
> hierarchy of symbols, each corresponding to smaller and smaller shadings
> up or down of the pitch.  For example:
>
>       sharp/flat  +  up/down arrow  +  plus/minus
>        +/- 1/2          +/- 1/4         +/- 1/8
>
> Lilypond's consideration of pitch alteration as a single number makes it
> very difficult to adequately represent such hierarchical
> pitch-alterations, and hence their corresponding notations.

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.

What is the difference between both?


I have not followed the discussion in detail, but the requirements for
any (replacement) pitch representation is:

- pitches can be transposed by pitches (deltas relative to central C),
ie. it is a representation that is closed wrt transposition
- there is a unique mapping from pitch to semitones (ie. for midi playback)
- it can represent classical pitches (ie. octave,step,alteration) unambiguously.

The current system satisfies these constraints obviously, but it
possibly does not represent well various nuances of scales that may
exist.

-- 
Han-Wen Nienhuys - address@hidden - http://www.xs4all.nl/~hanwen