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The notation snippet below is from the cover of a Composition textbook. The cover has a pale blue background and pale green notes, so I changed it to be black on white to make it easier to read.
From the lower stave, it looks as though the time signature is 5/16
But I can't work out what's going on in the upper stave. There seems so be some sort of clash between the beams and I can't work out what that 16th rest applies to.
Can anyone make sense of it?
These are bars 10 and 11 from Chopin's first Prelude (a larger snippet from IMSLP):
Different editions vary on exactly how they place the beams - the original screenshot seems quite poorly typeset.
The time signature is 2/8; the initial three LH semiquavers form an unmarked triplet (tuplet markings are often omitted like this; the first bar has them explicitly but the remaining bars are left implicit).
The upper stave contains three voices, but the rests for some of them have been omitted to avoid cluttering the score:
The (triplet) semiquaver rest applies to both the lower two voices; the upper voice's initial quaver rest is omitted.
The lowermost voice's "dotted quaver" is not actually a literal dotted quaver since it takes the span of four triplet semiquavers (4/3 of a quaver) and not the usual span of three semiquavers (3/2 of a quaver). This sort of technically-wrong notation is often used when the intent is "clear", and when the actually-correct notation would be too confusing to read quickly. (There's no "triplet-dot" notation; a double-dotted quaver would also be wrong; two tied triplet-quavers would be correct but would clutter the RH a lot and, I think, obscure the similarity between the lowermost and uppermost RH voices.)
In this case the original score tells us everything - it has the explicit triplet markings in the first bar, and the time signature - but how might you figure this out if you don't know what piece the original screenshot is taken from? There is just about enough information in the bars given to make a decent guess, I think.
The top G in the RH lines up with the LH quaver rest, indicating that they probably occur at the same point in time. The LH is grouped into two chunks (a set of beamed semiquavers, and a rest) and the middle voice in the RH has a beam-break in its semiquavers at that point, strongly suggesting that the LH quaver rest, and the second half of the RH bar, form a new beat. (From the left hand, therefore: probably two beats in the bar?)
From the LH, this beat is one quaver long, and the RH middle voice fits three semiquavers into this time period - which points to either an unmarked triplet in the RH, or an unmarked duplet rest in the LH. There's definitely something tuplet-related going on, though.
So, ignoring the RH lowermost voice for the moment, we're probably looking at one of:
Unmarked triplets in piano music are very common, so the topmost of these is quite likely; unmarked duplets and unmarked tuplet rests are pretty rare, so the second is unlikely.
I think the third is also quite unlikely - a piece with both triplet-semiquavers and normal-semiquavers-beamed-in-threes would probably specify the triplets explicitly everywhere for safety - but not impossible. (I could see a piece notated with a time signature of (3+2)/16, with frequent triplets in the second beat in one voice, leaving those triplet markings implicit after a while and relying on the established pattern to "make things clear".
So: most likely in 2/8 with unmarked triplets, but possibly a 5/16 with some unmarked triplets notated in an unfriendly way.
Turning back to the initial semiquaver rest in the first half of the bar: it, followed by the two semiquavers in the middle RH voice, line up perfectly with the LH semiquavers, suggesting that it goes with those (either as an unmarked triplet, in the 2/8 case, or as literal semiquavers, in the 5/16 case). The bottom-most RH voice shares its first notehead with the middle voice; it's reasonable to assume it's also sharing the rest.
The topmost RH voice comes out of nowhere in the middle of the bar and should have a corresponding rest for the first half of the bar - but I think it's clear enough from how the voices line up vertically that that's what's happening. (If that rest was present, it would settle the 2/8-vs-5/16 issue, since we'd expect it to be a quaver rest in the first case and a dotted-quaver rest in the second case.)
The RH lowermost voice is a problem either way: regardless of how you try and interpret the other voices, the lowermost voice doesn't add up, so we don't really have any choice but to shrug and assume it's a "technically-incorrect, but clear enough in context" notational convenience and leave it out of our analysis - and, indeed, even with the original score, the lowermost RH voice is just as problematic to interpret literally.
