Re: Distance of secondary beams

[Noeck]

Hi Abraham,

Am 17.01.2017 um 17:30 schrieb Abraham Lee:
> 
> I'm not sure why the calculation for this is so convoluted.

I am not sure if this is the "why" you are looking for (if this is the
answer to what you were wondering about). But I think the equation can
be explained by the following snippet:

\version "2.19.50"

{
  %\override Beam.length-fraction = 0.4
  %\override Beam.beam-thickness = 0.2
  \repeat unfold 2 a8
  \repeat unfold 4 a16
  \repeat unfold 8 a32
  \repeat unfold 16 a64
  \repeat unfold 32 a128
  \repeat unfold 2 g8
  \repeat unfold 4 g16
  \repeat unfold 8 g32
  \repeat unfold 16 g64
  \repeat unfold 32 g128
}

General goals:
Beams look well aligned if they are top-, bottom- or center-aligned with
a staff line (at least cover staff lines instead of being placed
completely in the staff space). A beam distance where you put one beam
per staff line is too wide, two beams per staff line are too narrow. So
a compromise has to be found depending on the number of beams. (These
goals for beam placement are based on my aesthetics but I think
something similar lead to the existing traditional rules, lilypond
implements for beam spacing.)

For the number of beams this results in:
1 beam is easy: it is center-aligned.
2 beams: I cannot decide what looks best (see the example for LP's decision)
3 beams fill 2 staff spaces (i.e. bottom/center/top-aligned)
4 beams fill 3 staff spaces (the outer two are bottom/top-aligned, the
inner two at least cover the staff lines)
>4 beams use the same spacing as 4 of them are inside the staff and the
others do not interfere with staff lines.

This leads to the formulae. You need to take into account the staff
space, the staff line thickness and the beam width to correctly align
the beams.

However, what happens to the g128 looks strange to me. I don't see why
it shouldn't look just like the a128.

Also interesting:
http://blog.steinberg.net/2015/03/development-diary-part-10/

Cheers,
Joram


PS: While we are at it: LilyPond has flags until 1/128 (5 ‘flaglets’).
Shorter durations (1/256, 1/512, etc.) are actually understood and
typeset when they have beams. I gave up checking after 1/131072 =
1/2^17. It took to typeset 32768 such notes. The Frescobaldi
highlighting recognizes durations until 1/2048.