Re: Contemporary music required feature #1: chromatic transposition

[Hans Aberg]

On 22 Sep 2009, at 13:44, Joseph Wakeling wrote:

> > So I think you need to add a choice of glyph. LilyPond is too  
> > primitive
> > to treat # and b and other accidentals as operators acting on all
> > intervals.
>
> Well, the point is that a glyph for 5/4 sharp is nonsensical.  A
> contemporary music player would be pissed off enough at seeing a
> double-sharp in non-tonal music, to say nothing of a 5/4-sharp symbol.

The original staff system is generated by pure fifths and octaves. It  
can be recomputed in terms of major M and minor m seconds, which add  
one to the scale degree. The sharps and flats alter by the interval M  
- m, and do not change the scale degree.

The original staff system is algebraic, and does not subsume any  
particular tuning. If one substitutes values for the intervals, then  
one has to be careful with that algebraic structure, because it is  
still there, but may be hidden by the explicit values.

So you originally had two sharps and transposed up an intermediate  
interval, and so that is what you get. The sharp only get the value 1  
in E12. But E12 does not respect the scale degrees of the original  
staff system.

> > I think one needs to think through carefully how one wants to  
> > enharmonic
> > equivalences be applied. It may vary with context. On most  
> > instruments,
> > it can be used to simplify key signatures. On a harp, it may have  
> > to be
> > applied note-by-note, as double sharps and flats are not available.  
> > If
> > the tuning is other than E12, it implies a small slip in pitch.
>
> Yes, that's a good point I hadn't considered.  The naturalizeMusic
> function serves the harp's needs well, where 3/4-sharps and flats are
> not possible.  (Was that the motivation for this function?)
>
> So basically we are talking about a 'modulo effect', i.e. to constrain
> every accidental to 'modulo a' where a is an alteration: for the harp,
> to modulo 1/2, for standard chromatic transposition, to modulo 1.
>
> That might actually be the best way of looking at it -- relative to a
> maximum acceptable size of alteration.  (Tricky would be
> less-than-or-equal-to versus less-than.)

I think that the intervals, at least in E12 are computed internally so  
that an octave is 6. Thine if an offset is more than 1, you want to  
reduce it, and add 1 to the scale degree. So you should perhaps tweak  
the naturalizeMusic to do that instead. Then first transpose and apply  
this once afterwards. Just a guess.

  Hans