Thanks for digging into this for me. Yes, both cases are necessary for 
typesetting shape note hymns, as illustrated by the attached scan. I believe 
the rule for this is that the notehead should be pointed up in the treble clef, 
and down in the bass clef.

Ipan ne 18 tonal tlen metstli 08 tlen xiwitl 2022, ipan 14:12 kawitl, Werner 
LEMBERG <w...@gnu.org> kiihkwilo:
> 
> >>> \partCombine #'(1 . 1)
> >>>  { \aikenHeads f'2 } 
> >>>  { \aikenHeads f'2 }
> >> 
> >> This is an interesting problem.  LilyPond's Emmentaler font
> >> contains two shapes of this glyph, namely `noteheads.d1fa` and
> >> `noteheads.u1fa`, where the 'd' and 'u' stands for 'down' and 'up',
> >> respectively (you can see the glyphs in Appendix A.8 of the
> >> Notation Reference).  It seems that the part combine engine uses
> >> the 'down' version of the glyph if two voices fall together; AFAIK,
> >> this is an arbitrary choice without a possibility to adjust.
> > 
> > Looks like it’s not the part combiner, but the core note column
> > merging logic. See note-collision.cc.
> 
> Indeed, thanks!  There is the following code in function
> `check_meshing_chords`:
> 
> ```cpp
>   /* The solfa is a triangle, which is inverted depending on stem
>      direction.  In case of a collision, one of them should be removed,
>      so the resulting note does not look like a block.
>   */
>   SCM up_style = get_property (head_up, "style");
>   SCM down_style = get_property (head_down, "style");
>   if (merge_possible
>       && (scm_is_eq (up_style, ly_symbol2scm ("fa"))
>           || scm_is_eq (up_style, ly_symbol2scm ("faThin")))
>       && (scm_is_eq (down_style, ly_symbol2scm ("fa"))
>           || scm_is_eq (down_style, ly_symbol2scm ("faThin"))))
>     {
>       Offset att = Offset (0.0, -1.0);
>       set_property (head_up, "stem-attachment", to_scm (att));
>       set_property (head_up, "transparent", SCM_BOOL_T);
>     }
> ```
> 
> So the situation in question *is* handled, making the 'up' glyph
> disappear.  This can be easily changed to do the opposite.
> 
> Benjamin, do you have real-world examples that demonstrates such
> mergings for Aiken note heads?  Please provide scans if possible!  In
> particular it would be necessary to know whether the used note head
> for merged notes is always the same.
> 
> 
>     Werner
> 

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