Hi everybody,
I'm connecting to this thread as it's a very similar situation:
I'm making a score consisting of fragments, and I ended up using the
\markup \fill-line \score construct.
However, when the scores are four, the distribution seems problematic,
as the scores begin to overlap. Moreover, they are not equally
distributed. I sort of get why (first and last scores are respectively
left aligned and right aligned, while second and third are not), but I
don't know how to try to distribute them in a better way.

See the following longish example, that hopefully clarifies the situation.
Thanks for any hint!
Lib

\version "2.25.19"

\markup {
  \fill-line {
    \score { {  a''8 b''8  } }
    \score { {  a''8 a''8  } }
    \score { { a''8 b''8  } }
  }
}

\markup {
  \fill-line {
    \score { {  a''8 b''8  } }
    \score { {  a''8 a''8  } }
    \score { { a''8 b''8  } }
    \score { { a''8 b''8 } }
  }
}

%here's the problematic one
\markup {
  \fill-line {
    \score { {  a''8 b''8 a''8 b''8 a''8 b''8  } }
    \score { {  a''8 a''8 a''8 b''8 a''8 b''8  } }
    \score { { a''8 b''8 a''8 b''8 a''8 b''8  } }
    \score { { a''8 b''8 a''8 b''8 a''8 b''8 } }
  }
}

\markup {
  \fill-line { 1 2 3 4}}

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