how to engrave arrow over notehead?

[Bodo]

Hi,
Thanks for this awesome program. I'm new to this, so excuse me if this is
obvious, but extensive search of the docs and mailing list has not yet come
up with anything, so:

I'm trying to engrave little up- or downwards pointing arrows over
noteheads. The reason for this is to indicate tones on the harmonic scale
(overtones) that cannot be directly mapped onto tones in equal temperament.
So if the tone is close to the tempered tone, but a little higher, there
should be a little arrow pointing upwards over the notehead. Conversely, if
the tone is slightly lower than the equal-tempered tone, the arrow over the
notehead should point downwards.

I'm not sure if there is a standard name for this notation, but it has
already been used in the Overtone literature. Can this be done in Lilypond?
If not, how hard would it be to add a new engraver for a little arrow?

As a workaround, I could try to put text over the notehead and find a font
that contains arrows, but maybe there is a better way?

Thanks,
 Tucano