No! First of all, \center-align only works within a single markup and
makes sure that if you have several lines in your markup, these will
be aligned to each other.


This works for some reason, with one line in the markup:

cs'4^\markup{\center-align <\italic \bold "8va - - - - - "> }

I stay corrected! This happens since TextScripts don't fiddle with the alignment themselves. If you use the same thing together with \mark, you will not get any difference between \mark \markup{ \center-align <\italic \bold "8va - - - - - "> } and \mark \markup{ \italic \bold "8va - - - - - " } since the full rehearsal marks is centered above the bar line by default.


and \box does indeed box whatever you have without moving it to
the right.  Maybe that has something to do with \box being
able to use the bounding box of the letter without running into
others?

The \box command draws the box according to how large LilyPond thinks the content is. This is an excellent method to find out how LilyPond guesses the extent of a markup with embedde LaTeX command. Try for example \markup{ \box "\\textcircled{\\tiny 8}" } to see exactly how LilyPond fails to calculate the correct size and position of the circled number. If center the box, you'll get the box centered and the circled number misplaced exactly as much as it would be without the box.

/Mats


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