Hans Aberg <haber...@telia.com> writes: > On 26 Sep 2013, at 17:16, Phil Holmes <m...@philholmes.net> wrote: > >>> The section originates with me but I got diverted into trying to >>> create a more elegant solution for how to rewrite accidentals in >>> transposed music. It was all related to the need for an effective >>> chromatic transposition solution that also worked well with >>> arbitrary microtonal accidentals. >>> >>> I was also rather discouraged by the fact that the quarter-tone >>> arrow notation issue didn't find a solution -- see: >>> https://code.google.com/p/lilypond/issues/detail?id=1278 >>> >> >> I think it's waiting for someone to propose how it could be >> represented in LilyPond. > > For one microtonal accidental, one needs, in addition to the > minor/major seconds m and M, a neutral second n. For a pitch x = r*m + > s*M + t*n, compute its degree deg(x) := r + s + t, which is its staff > position, and subtract the staff pitch. > > There remains a new pitch, which I also call x, but now with r + s + t > = 0. As sharps/flats alter with a multiple of r - s, reduce using them > so that only one of r, s is non-zero. > > Assume first that t = 1, i.e., one n. Then it must be either n - M or n - m. > > We have six microtonal symbols, sharp/natural/flat with up/down > arrows, but it will, as we shall see, suffice with four. One way to > make a choice is to conceptualize n as below or above (m + M)/2: if it > is a small or large neutral. This choice is purely formal at this > point, but will be of importance when plugging in values.
[...] > If the absolute value |t| of t is larger than 1, then one needs as > many arrows as |t|: up if t is positive, and down if t is negative. > > Two symbols where not used: sharp with up arrow and flat with down > arrow. But they conceptually fall without the region of raising a > sharp M - m or lowering with a flat -(M - m), and can in fact be > reduced using a natural with up/down arrow plus a sharp/flat. So here, > one would need notation simplification algorithm. Well, today's xkcd, at the surface more being about LilyPond's choice of extension language, still seems somewhat on-topic here: <URL:http://xkcd.com/1270/> (mark the mouse-over text) Now I appreciate that you are no longer expounding on Abelian groups here, but this still is not a text you'll find in a musician's handbook (not even if he's called Arnold). If you are interested in getting your ideas conceptualized in a manner that will make both musicians and LilyPond programmers understand them to a degree where they can work with them and actually want to do so, you need to diverge further from the abstract. I remember that my initial (and it turns out terminal) reaction to your initial group theoretic treatise a year ago or two was "I'll read this some other time". If you take into account that I'm the sort of guy who chose to do a treatise on number-theoretic transforms for convolutions as an undergraduate term paper in an engineering course, that should raise a lot of warning flags. So how do we stop this from putting a terminal halt on the discussion this time? -- David Kastrup _______________________________________________ lilypond-devel mailing list lilypond-devel@gnu.org https://lists.gnu.org/mailman/listinfo/lilypond-devel