8/4 time?

[jancivil]

One benefit of notating it 4/4 rather than 8/8 would be that it allows the performer to interpret a bit of swing on the second note

On the other hand 8/8 would imply that it can be treated as a compound time; a conductor might interpret that by beating only the three strong beats!

Sorry for being… inarticulate and/or harsh there. This convention “beats” tends to indicate uniformity of that metric. EG: 12/8 as compound time = 4 dotted quarter beats. 8/8’s beats amount to 2, 4, or 8.
The general term will be *accents*, ‘the three [strong] accents’ in the aforedescribed 8/8.

There's no restricted list of "allowed" time signatures, you should pick one that indicates how the bar should be counted. 4/2 is not unusual if you go back to Renaissance stuff and sometimes makes sense for a slow section in a longer piece.

True, and a good point, but also “cut time”, signed by the C for “common time” with a vertical line through the middle indicates 2/2 typically double time, as in marching band convention.

(Hmm, I wonder if "compound time" could mean other products of two prime numbers, such as 10 or 21?)

Conventionally it means a factor of two and a factor of three compounding.

But I think of numbers other than 2 mixed with 3, eg., 5 and 3 like a compound of {but not necessarily in a time signature*}. Zappa called that “the mystery hemiola” (*: might occur in 4/4 for that matter).

[atwoslottoaster]

As it is quite fast tempo - but it's purely esthetic - I would use 8th notes. So 3/8+3/8+2/8 rather than 3/4+3/4+2/4. That's for exemple why scherzo are written in 3/8 rather than 3/4.

Because of the faster tempo you could also feel it as 3/8+5/8 too! It's a little less clunky than including a 2/8 measure.

[jancivil]

not if the musical idea is 3+3+2 it isn’t. which is an extremely common idea. and very probably most common in common time, 4/4 (8/8).