can someone point me to complete documentation for the partial command argument syntax?

[Sam Roberts]

I'm still baffled by it. After experimentation, I found this worked:

\time 3/4 \partial 1 c4 |

But "1"? 1 what? The pickup is a 2, and if I do this barcheck passes,
as I expect:

\time 3/4  c2 c4 |

So from the doc examples I'd expect "\partial 2" to indicate a
half/note pickup, but it fails.

https://music.stackexchange.com/questions/106875/how-to-write-a-pickup-measure-with-5-16-duration-in-lilypond
has some examples using the star operator, but I haven't found any ref
for how to specify rationals. I don't really understand what's on the
left and right of the "*", and I don't understand if the fractions are
true fractions, or note fractions. Not sure what the right term for
that, but in 3/4 time there are 3 1/4 notes in a whole bar, so the
pickup in above is 2/3 of a bar, but is two 1/4 notes, or one 1/2 note
(which takes 2/3 of the bar). I tried to use both approaches, no luck.

These fails the bar check, an attempt at saying 2 quarter notes:

\partial 2*1/4 c'4 |

This is syntax failure:

\partial 2/3 c'4 |

wrong type for argument 1.  Expecting duration, found (cons 2 3)

I've searched for docs on the duration syntax, but I'm not succeeding yet.

Can someone point me to docs, or perhaps explain the syntax?

https://lilypond.org/doc/v2.21/Documentation/learning/advanced-rhythmic-commands#partial-measure
as an example, just has a couple examples, but not a complete syntax.


Thank you,
Sam