I often hear this rhythm in accompaniments in contemporary music:
|x---x---x---x---| Beat |--x--x--x--x--x-| Lead 1.:.2.:.3.:.4.:.
That is, it's a 4:3 polyrhythm but with a single quarter note every five notes to even out to four beats. Variations will shift the beats around, but always have the same 3-3-3-3-4 progression.
Is there a special name for this "polyrhythm"?
For an actual example: this video at 0:34.
The pattern you describe is a 2:3 version of the bossa nova pattern (or clave), also called Brazilian clave.
Shift the order of the first and second halves and you have the original 3:2 bossa nova pattern.
See also Bossa Nova
Note: If the link doesn't bring you to the section about the bossa nova pattern on the Wikipesia page on claves, then just search for it or use the table of contents.
On first glance, your rhythm appears to be a slightly-modified 2/3 clave. As you can see from the linked article, the clave rhythms (so named because, in some styles, the rhythm is played on the claves) are a subject of some controversy. One way to classify clave rhythms is "2/3" versus "3/2", depending whether the first half of the pattern contains two notes or three, respectively. In this case, the first half of your pattern has two notes, and the second half has three, hence the 2/3 clave designation. As the article states, in standard notation, the clave patterns are often written over a span of two bars of alla breve rather than one bar of 4/4 time. However, that is a matter of notation, not sound. I would hesitate to call a pattern over eight beats (e.g., two bars of 4/4) rather than four a clave rhythm, but you are describing a pattern comprising four beats.
Your rhythm differs slightly from the more "traditional" 2/3 clave in that the second note is a little late, producing the near-symmetry that you describe while containing a repeatable pattern within four beats. To my ear, this pattern still retains the character of the 2/3 clave.
The clave patterns occur in many musical styles, often in one of the percussion instruments associated with a "hand-clap" effect (e.g., the snare drum of a drum kit, perhaps even using rim shots instead of just hitting the drum head normally).
I wouldn't really call it a polyrhythm, since it's not being repeated at a regular interval. If only the first three beats were being repeated and we were in 3/4, you'd be correct.
However, in this case I'd just call it a rhythm, closely related to a 2+3 clave, making use of dotted-eighth-note syncopation. It's a fairly common occurrence in Latin-influenced music like the piece you linked.
That's not to say that practicing polyrhythms won't help to learn this; on the contrary, practicing polyrhythms is a fantastic tool for learning odd syncopations.
I have written a dictionary of over 8700 rhythm families and this rhythm family is called 'Longfu'. The Normal form of Longfu is your pattern 1001001001001000 but you can create other forms by starting the cyclical pattern in other places (the second intermediate form 1001001000100100 is quite fun)
