A cross-staff beam is a beam which begins on notes in
one staff, and extends through the gap between the
staves onto notes in another neighbouring staff. A
kneed beam is a beam that connects notes with a mixture
of up stems and down stems.
Here are some examples of cross-staff kneed beams in
Lilypond:
Notes for future implementation:
Auto-kneeing is the process of deciding whether to use
a kneed beam. If the slope of a beam between two
note-heads, which may be either on the same stave or on
two neighbouring staves and which are to be beamed
together, exceeds the maximum allowable slope threshold
then:
1) a kneed beam is used with its midpoint at a height corresponding to the vertical halfway point between the two note-heads, and 2) the stems of the notes on different staves are made to face in opposite directions in order to minimise the slope of the kneed beam.
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I've been thinking about this one, as it is on my list of Things Rosegarden Can't Do With Any Amount of LilyPond Export Hackery.
I've concluded that this one is probably something we have to leave to the dedicated notation editors, and shouldn't ever even contemplate.
I'll leave this open though.