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## Re: Slanted Beams thickness

 From: Mats Bengtsson Subject: Re: Slanted Beams thickness Date: Fri, 25 Mar 2022 14:52:43 +0100 User-agent: Mozilla/5.0 (X11; Linux x86_64; rv:91.0) Gecko/20100101 Thunderbird/91.7.0

```   On 2022-03-25 01:44, Valentin Petzel wrote:

Subject:
Slanted Beams thickness
From:
Valentin Petzel [1]<valentin@petzel.at>
Date:
2022-03-25 01:44

To:
[2]lilypond-devel@gnu.org

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.

Cheers,
Valentin

A couple of points, on top of what has already been brought up.

As has already been said, you will hardly notice any difference unless
the slope is very high, which is a situation that you anyway try to
avoid as much as possible, which also makes it hard to find examples in
typeset scores. After all, that's one of the main reasons to use kneed
beams.

My gut feeling is that a mathematically exact solution is not likely to
provide the most pleasing effect to the eye. There are already a number
of optical corrections applied in LilyPond to handle other such
discrepancies between the mathematically most obvious solution and the
visually most pleasing solution. Something in between the current and
the newly proposed approach is likely to look best.

Even though a general guiding approach for Lilypond's layout decisions
is to imitate old hand engraved scores, we shouldn't necessarily copy
layout decisions that were caused by technical limitations in the hand
engraving process, if we have a general agreement that something else
looks better.

/Mats

References

1. mailto:valentin@petzel.at
2. mailto:lilypond-devel@gnu.org

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