Re: Diatonic notation system

[Hans Aberg]

On 10 Dec 2008, at 07:40, Graham Breed wrote:

> > Not using key signatures will not solve that problem.
>
> I didn't say anything about not using them -- although, as it happens,
> they are trouble in microtonal music.  What I said is that they lead
> to confusion.  The main point is that learning contradictory meanings
> for existing symbols has a higher cognitive load than learning new
> symbols.

The advice is to check with the intended musicians and typeset what  
is good for them.

> > Rather which accidentals do you use?
>
> It depends on what system you use, doesn't it?

Relative Pythagorean E53 is easy. If one lets the letters C ... B  
stand for C Just major, then when changing to D Just major, then if  
one does not change the meaning of the letters, there will be a lot  
of funny accidentals. Then it is the question if musicians can work  
out such a thing - music is about playing notes, not frequencies.

> Incidentally, JI notations won't usually work with the Lilypond model
> because it only allows a single glyph for each alteration.  Pure
> sagittal can still go a long way though.

With the model I suggested, one can introduce a number of neutrals,  
and give them the same symbol. This might be useful when retuning.  
There is a principle of gravity
  http://www.maqamworld.com/maqamat.html
Scale degrees could be used to create such a retuning effect.

> > If transposition calls for say a comma below an m, and that m is  
> > computed
> > not against E53, but E12, I think there might be an error. I leave  
> > it to you
> > figure out. By contrast, if it is in E53, then I know it is right,  
> > and I do
> > not have to do that exercise.
>
> Transpositions aren't "computed against" any equal temperament.  If
> you transpose by a comma, then a comma will be added or subtracted
> from the previous alterations.  The resulting alterations will be
> calculated according to the grid you specified.  If you defined
> accidentals for them, those accidentals will be shown.  Maybe there's
> an error -- if you find it, report it as a bug.

I did it for E53 - it did not work. I attach a file.

> The difficult case is the most common one where a transposition moves
> from one scale degree to another.  In this case it can be separated
> into a "microtonal transposition" -- specified according to the
> alterations -- and a "diatonic transposition" -- where Lilypond will
> use chromatic scale steps.  A diatonic transposition will only lead to
> a change of alteration of M-m.  (I hope this is obvious.)  Lilypond
> will identify this interval as a "half step" and add or subtract 1/2
> from the alterations.  As long as you defined your alterations so that
> M-m=1/2 then all will be well.

So then one must be able to have different values here.

> > Since the name diesis has many uses, you will have to elaborate.
>
> Since even the name "enharmonic diesis" has more then one use even in
> a meantone context, I did elaborate.  I got the definition wrong
> though, because I said it was 1 step from 50.  It should be 2 steps so
> maybe that's what confused you.  It's 1 step from 19, 31, 43, 55, and
> so on adding 12 each time.  In M and m it would be 2m-M I think.

Perhaps you mean the between a sharp and a flattened M, like between  
F# and Gb, which may be positive or negative. Since I do not impose  
any such relations, those are not confused.

> > > I'm not writing it.  If I did I'd probably use Pythagorean notation
> > > with a comma accidental.
> >
> > So that would then work with the method I gave.
>
> I didn't say it wouldn't.  But, in fact, it wouldn't.  Your
> Pythagorean notation would make the comma below E indistinguishable
> from Fb.

Why would that be: m and M generate the Pythagorean system, and it  
already contains a comma if you so like, but if the comma has  
different musical function, introduce a netral second to describe it.

maqam53.ly
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