Quarter-tone arrow notation [was: Re: improving our contributing tools and workflow]

[Joseph Rushton Wakeling]

On 26/09/13 17:16, Phil Holmes wrote:
> I think it's waiting for someone to propose how it could be represented in
> LilyPond.  If _someone_ were to do that, it might progress - it was only a few
> months ago it was last looked at.

Unfortunately, it was someone putting forward a workaround which I'd already 
proposed and found lacking, as it doesn't play nice with transposition :-(

There was actually a patch submitted which tweaked the internal pitch 
representation appropriately: https://codereview.appspot.com/3789044/

... but work on it seems to have been abandoned.

_Conceptually_, the problem is this: Lilypond's pitch model consists of

     PITCH = STAFF_POSITION + ALTERATION

where alteration is some fraction of a whole tone.  (Actually there's no 
theoretical limit.  You could have 3/2 of a tone, 2 tones ... although because 
the current transposition rules have a hard-coded limit of +/- 1, it's actually 
impossible in practice to transpose into keys where you might have triple sharps 
or flats.  Hey, they do exist...:-)

That model works fine for the standard 12 chromatic pitches, and it works fine 
for microtonal notation where each microtonal alteration is represented by a 
unique accidental.  It fails for microtonal notation that essentially consists of

     PITCH = STAFF_POSTION + ALTERATION_0 + ALTERATION_1 + ... + ALTERATION_n

of which quarter-tone arrow notation is one example (you have a first-order 
alteration which is the regular accidental, and a second-order alteration which 
is the up- or down- arrows).

Ben Johnston's notation for "extended just intonation" is another example that 
very strongly relies on this hierarchy of pitch shading -- see e.g.: 
https://www.youtube.com/watch?v=0kVdgCWFJzE

... and 
http://notesfromadefeatist.blogspot.it/2010/01/just-intonation-notation.html for 
some explanation.