On 27 Sep 2013, at 08:45, David Kastrup <d...@gnu.org> wrote: > 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 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) Indeed. > 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). You must be mixing me up with some microtonalist - they are well aware of this thing, though they did not use the "A" word. > 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? What I wrote is more or less equivalent to engraving microtonal symbols (leaving that as an exercise :-) ). So if you, with mathematical training, for some reason find it intractable, how do expect others here to deal with? One way would be that somebody asks questions: "hey, how does this work?". Hans _______________________________________________ lilypond-devel mailing list lilypond-devel@gnu.org https://lists.gnu.org/mailman/listinfo/lilypond-devel