I am also interested in the research in tuning systems other than equal temperament, which allows unusual frequency ratios to be heard in chords and melodies, which gives composers new possibilities to explore. See also
http://www.midicode.com/tunings/index.shtml
for a review of the basic concepts. Regarding the notation, I wonder why we don't simply use a numerical notation i.e. a fraction as the accidental representing the frequency ratio from a reference pitch.
This would save having to invent and learn a lot of new symbols for different ratios, and there is then no problem about extending it to new ratios that have not yet been tried. Lilypond could then convert this easily into the form required for MIDI output.
(1)The placement of a note and the usual flat and sharp symbols
would correspond to its nearest point (in terms of cents) on the equal tempered scale which is represented by standard music notation.
(2)As a simplification, the scale of 1 octave defined in this way could be printed after the time signature and before the music starts, so that in the music, the frequency ratios added to the notation would only need to be present if they were different from those in the scale.
(3)All pitches in other octaves would be initally exact multiples of 2 different from a pitch represented in the scale.
(4)It must be possible to redefine a pitch at any time e.g. bes=7/4 in the music (and perhaps another notation for doing this for all octaves simultaneously), and
(5)it may be convenient to allow redefinition of the reference pitch at any time.
The only difficulty I can think of with this is when more than two notes with different pitches but the same nearest equal tempered pitch are played simultaneously, in this case rule (1) may need to be violated or some other notation developed, hopefully this will be rare.
I would be very interested in a development of Lilypond on these lines because of its MIDI file generation capability and would be grateful of your comments.
John Nixon