Re: Microtonal accidentals

[Keith OHara]

Joseph Rushton Wakeling <joseph.wakeling <at> webdrake.net> writes:

> On 03/11/13 11:20, Hans Aberg wrote:
> > 1. http://www.newmusicbox.org/assets/72/HelmholtzEllisLegend.pdf
> > 2. http://www.marcsabat.com/pdfs/notation.pdf
> > 3. http://www.marcsabat.com/
> > 4. https://en.wikipedia.org/wiki/Just_intonation

> [...]
> Short version: in many microtonal notations, the number of enharmonic 
pitches is 
> expanded -- but Lilypond has no way to represent these enharmonics.

Let's see about that.

Harmonic systems like Helmholtz's and Ben Johnston's introduce a new symbol 
for each new prime factor they want to include in the frequency ratios of 
the intervals.  Each symbol represents a different size of alteration, so 
there are no enharmonic equivalences.

With equal divisions of the octave, we name pitches based on the closest 
harmonic pitch.  31-equal-temperament can use names 
 { c  cih  cis des  deh  d }  or  
 { c deses cis ces cisis d }
for the same set of pitches.  LilyPond distinguishes the enharmonic 
equivalents cih and deses in this tuning system just fine.

LilyPond handles 24-equal-temperament with the half-flat symbols 
similarly.  Even in atonal music we might prefer one of the spellings deh 
or cisih over the other to better show the melodic line.  The notation 
using arrows on accidentals might similarly use D-natural-down or C-sharp-
up, whichever choice puts the pitch on a staff-line to best clarify the 
melodic line.  LilyPond keeps track.  

The arrow notation also gives two options for the half-flat: natural-down-
arrow and flat-up-arrow.  If someone uses both options for the half-flat in 
the same piece, LilyPond can keep track of the choice by using a tuning 
system that has them at slightly different pitches.

If in addition we ask LilyPond to transpose a melody, containing both C-
natural-down-arrow and a C-flat-up-arrow, down by another arrow, 
and if we want these two formerly-distinguished pitches to /both/ be 
represented by C-flat, then LilyPond finally needs some help.

In this case we need to explicitly enter a second reference to the flat 
glyph into the table of accidental glyphs at the numerical value for the 
alteration that is 2 times the down-arrow alteration.