Re: Slanted Beams thickness

[Carl Sorensen]

On Thu, Mar 24, 2022 at 6:46 PM Valentin Petzel <valentin@petzel.at> wrote:

> Hello,
>
> Lilypond handles slanted Beams in a geometrically weird way, that is, the
> thickness is not measured as the shortest distance between the opposing
> sides
> of the boundary, but as vertical distance. This results in Beams getting
> optically thinner and closer the higher the slope is. But we can very
> easily
> factor this out by adjusting the thickness to the slope. In fact if we
> want to
> achieve a real thickness theta the adjusted thickness would need to be
> theta·sqrt(1 + slope²). See attached an experimental example.
>

I think LilyPond handles beams not in a geometrically weird way, but in a
geometrically correct way.

If I understand correctly, I think that the slanted beams are defined not
by the perpendicular thickness, but by the vertical "thickness", and that
this is intentional.

When the end of a beam sits on a staff, it should take up a fixed
percentage of the staff space, which we call the beam thickness.  In
actuality, it is not the perpendicular thickness of the beam (the dimension
perpendicular to the beam center line) but the vertical thickness (the
dimension perpendicular to the staff lines.  Of course, this does lead to a
reduced perpendicular thickness, which might be considered the optical
thickness.

This models hand engraving, where chisels of a fixed width were used, and
the chisels were always held with the ends perpendicular to the staff
lines, so that the ends of the beams were vertical.

If we want to have a setting to change that, I'm fine.  But I don't think
we should change the default, without strong evidence from good
hand-engraved scores that this is the proper way to do it.

The same is true of beam spacing.  Beam spacing needs to match the vertical
staff spacing, not the perpendicular spacing.  Lilypond uses beam quanting
to make sure that the beams interact properly with the staff lines.

I note that Dorico offers "optical beaming" for slanted beams, but can't
find any discussion of it.

Thanks,

Carl