I'm teaching on the IB Music Diploma Programme and am looking at an examiner's markscheme for a question about the Dixieland jazz piece "Tiger Rag" (similar to this version:) on a past listening exam paper. In the markscheme, the examiner states the first section is made up of 4 X 2-bar phrases, which makes 8 bars in total (0:00 - 0-16 in link version). However, my previous understanding of this type of piece is that it uses ragtime form, which is based on a 16-bar strain (not 8). If you look at this version with a scrolling score: , you can see that it uses 2/4 time and the first section is indeed 16 bars (0:00-0:18). This examiner seems to be using 4/4 time, resulting in it being analysed as 8 bars instead of 16. Can this examiner's analysis also be acceptable, meaning either 2/4 or 4/4 can be used for this piece or should it always be 2/4 for this particular type of jazz piece?
From looking at lots of tangos and ragtimes from the 1890-1950 era, I find that the use of 2/4 vs 4/4 is somewhat sloppy. Sometimes a piece will really be in two, successions of two-beat patterns (some marches in general). These are usually notated in cut time or 2/4 with either the half-note or quarter-note getting one beat. Sometimes they are in either common or 4/4 time but taken in two. Some pieces have four beat counts but are notated in 2/4 with an eighth note pulse (very common) and some four-beat songs will be in 4/4 with quarter-note pulse (more common in later works.) A few cases (four-beat pulse) will just write in 2/4 and use pairs of measures (in which case, the wrong parity may be used).
You have to just play the music and see what's appropriate.
In your case, as it's now the Twenty-First Century, you can just write in 4/4 with quarter beat pulse. (Or 2/4 with two beat pulse.)