Re: Transposition with arrow quarter-tone notation

[Keith OHara]

Joseph Wakeling wrote:
> I've extended my 'cheat' a bit with the following rules (based on
> english.ly note names).
>
>   qs = +999/4000  (as opposed to +1/4)
>   af = -999/4000  (as opposed to -1/4)
[...]
> This setup is aimed allow for a full arrow quarter-tone notation with
> arrows being preserved across all regular transpositions
[...]
> However, transposition errors do in fact occur even with regular
> transposition:
>
> qtatest.ly:11:91: warning: Could not find glyph-name for alteration -3/2
[...]
> (I'm surprised that -3/2 or +3/2 generates an error since wouldn't this
> occur -- and be taken care of -- by transposition rules for the normal
> 12-note system?)

Lilypond preserves the triple sharp by default.  Somebody might want to define 
a triple sharp glyph for it and use it in notation.

Reduction of cisis to d, and so forth, is done with the function 
'\naturalizeMusic' 
(http://lilypond.org/doc/v2.12/Documentation/user/lilypond/Changing-multiple-pitches#Selected-Snippets-55).
  This function is not built-in to Lilypond, so you include its definition in 
your .ly file before you use it.


When arrow notation is used for quarter tones, the implication is that 
natural-up is not exactly the same pitch as sharp-down, yet a 24ET quarter-tone 
instrument is quite capable of playing the music.  This seems analogous to 
C-sharp (71cents) being not exactly D-flat (133cents) yet the piano is still a 
decent musical instrument.  So the 'cheat' above actually seems quite honest to 
me.

The difficulty with general transpositions is that successive alterations can 
generate an infinite number of different pitches within an octave.  We could 
simply decide on a way to round the alterations (like we round sharp to 
100cents in 12ET) so that they generate only a manageable set.  For arrow 
notation, I suggest :
NATURAL       0
NATURAL-RAISE 2/10 of a 12ET whole tone,
SHARP-LOWER 3/10
SHARP       1/2
SHARP-RAISE 7/10 , etc.

Then we pick glyphs for all the alterations that could result, repeating the 
natural sign to cover three possibilities -1/10, 0 and 1/10, and similarly for 
flat and sharp.  Anything larger than a semitone is reduced to an enharmonic 
equivalent using \naturalizeMusic.  Demo file, adapted from Joseph's file, is 
attached.

arrow1.ly
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arrow1.png
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