What's the name of this rhythm? There's an embedded 4:3 polyrhythm, where the two voices will arrive together on beats 1 and 4 of each bar. It reminds me of a clave (2:3), but it's not.
I personally call rhythmic patterns like that systematically according to the number of rhythmic pulses in each note. This one would be 3-3-3-3-4. Other examples are 3-3-2 and 3-1, which are common bass and kick drum patterns for faking many sorts of Latin-American and African rhythms. If the pattern starts with a rest, I write it in parentheses, but I don't know how to pronounce it easily. Another favorite kick drum pattern of mine is: (3)-3-2 where the kick is NOT played on the one.
Here's another example of this descriptive naming style: Is there a name for a 3-3-2-2-2 rhythm?
Not to be confused with "3-2 clave" and "2-3 clave" where the numbers don't mean note lengths in pulses, but number of notes (hits) per 2/4 bar. See https://en.wikipedia.org/wiki/Clave_(rhythm)#The_3%E2%80%932/2%E2%80%933_clave_concept_and_terminology
Calling it cross rhythm or polyrhythm... This is just my opinion, but I wouldn't give this simple pattern that status, because the three-pulse rhythm is reset at the beginning of every bar. You should continue it much longer, 3-3-3-3-3-3-3-3-3-3-3-3-3-3-3-3-... etc.
I’d like to add that if you are notating this rhythm it should be done this way for clarity and ease of sight reading. Here are 16th and 8th note versions:
This is a fairly common rhythm. The most prominent use of it is in this recording by Sammy Davis Jr. although it is played staccato on that recording.
It is also used in many rock tunes but usually with two eighth notes in place of the final quarter note (or two quarters if written in eighth notes instead of 16ths). The second two bars of the 4 bar ending vamp of “Stairway to Heaven” is a classic example.
There is no special name given to this 4:3 relationship. It is an example of cross rhythm.
Cross-rhythm refers to systemic polyrhythm. The New Harvard Dictionary of Music states that cross-rhythm is: "A rhythm in which the regular pattern of accents of the prevailing meter is contradicted by a conflicting pattern and not merely a momentary displacement that leaves the prevailing meter fundamentally unchallenged" (1986: 216). The physical basis of cross-rhythms can be described in terms of interference of different periodicities.
Other cross-rhythms are 4:3 (with 4 dotted eight notes over 3 quarter notes...)1
1The quotation specifies 3/4 time. To the best of my knowledge, the 3/4 time aspect is not critical.