Hi Jean,

> Then I don't understand the problem. What characteristic
> of baseline-skip do you wish? Is it that it counts from
> the origin of each markup and somehow this distance is
> more convenient for you to provide? Is it that it ignores
> the extents of the markups?
> 
> Could you explain the overarching problem? To me, this
> sounds like an XY question.

This sounds like it might be related to my [long-standing] concerns about 
leading, etc., in markups: there either isn’t a convenient mechanism to deal 
with texts/markups *from their baseline [and not their reference point]*, or 
the convenient mechanism exists and isn’t sufficiently well 
exposed/documented/promoted.

{
  \override TextScript.padding = #2
  g'1^\markup { agt }
  g'1^\markup { aht }
}

Cheers,
Kieren.

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