Interestingly the problem happens only for quaters not for other durations.
And if I extend the quater's X-extent to that of a half note with
\override NoteHead.X-extent = #'(-0.0 . 1.377346)
(applied to Malte's code) the clash vanish.
Ofcourse this is not a workaround (the value would need adjustment for changed 
staff-sizes, the stem-attachment is off and likely other problems), but may 
point to the direction where to look for the cause of the clash.

---

And yes, first bad commit is:
commit 87eb2f9fe1be3a532675fe4b7322bbba5a60ba5c (HEAD)
Author: Carl Sorensen <[email protected]>
Date:   Sat Mar 5 21:30:46 2016 -0700

    Use a negative value of overdone_noteheads to shrink the head slightly
    
Changing recent master to the former value:

$ git diff
diff --git a/mf/feta-params.mf b/mf/feta-params.mf
index 36549e85ed..bb3dc2867f 100644
--- a/mf/feta-params.mf
+++ b/mf/feta-params.mf
@@ -250,7 +250,7 @@ slash_thick# := 2/3 * 0.48 staff_space#;
 % reduce the notehead height.  Empirically, we have determined that 
 % reducing by 10% of stafflinethickness solves the problem.
 
-overdone_heads = -0.1;
+overdone_heads = 0.0;
 noteheight# := staff_space# + (1 + overdone_heads) * stafflinethickness#;
 
 define_pixels (slash_thick);
 
 returns not clashing output.
 Ofcourse the (here reverted) patch was meant to fix a problem, which now will 
arise again...
 
  


---

** [issues:#5540] clash between staves**

**Status:** New
**Created:** Mon Jul 22, 2019 01:00 PM UTC by Werner LEMBERG
**Last Updated:** Wed Jul 24, 2019 04:05 AM UTC
**Owner:** nobody
**Attachments:**

- 
[staff-clash.png](https://sourceforge.net/p/testlilyissues/issues/5540/attachment/staff-clash.png)
 (6.0 kB; image/png)


[lilypond git 49f41bf1c64ae1e2490571e73a85cbc4b2a9fb27]

The example below exhibits a clash between staves.  It's easy to circumvent, 
but it definitely shouldn't happen, since it gets triggered by non-musical 
parameters.  Maybe a rounding issue?

~~~~
% Sizes 17 and 18 also cause a clash.
#(set-global-staff-size 16)

\paper {
  % Commenting out this line removes the clash;
  % values like 5cm and larger also remove the clash.
  indent = 4\cm
}

% The notes below trigger the clash;
% I wasn't successful in simplifying it more.
<<
  \relative c' {
    d2 d4 d |
    d8.[ d16] << { d4 } \\ { <a c> } >>
  }

  \relative c' {
     e2 e4 e |
     e4 <d b'>
  }
>>
~~~~



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