Microtonality (was: improving our contributing tools and workflow)

[David Kastrup]

Hans Aberg <address@hidden> writes:

> On 26 Sep 2013, at 17:16, Phil Holmes <address@hidden> 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