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## Re: Slanted Beams thickness

 From: Luca Fascione Subject: Re: Slanted Beams thickness Date: Fri, 25 Mar 2022 14:05:57 +0100

```Carl,
If you look at the video I posted, could you explain how you see using that
instrument non along its tooling direction? (Like, "diagonally" wrt cutting
edge at the tip) seemd to me it would be very hard to get a straight line
doing so...

L

On Fri, 25 Mar 2022, 13:52 Carl Sorensen, <carl.d.sorensen@gmail.com> wrote:

> 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
>

```