How do 'meter' and 'rhythm' affect the choice of 'Polymeter' and 'Polyrhythm'?

Question

I use chevrons (⟨⟩) to denote the concept behind the word.

[ Source :] Meter is the rhythmic structure of the music. For example, a piece of music could be in 4/4 meter, which is a strong-weak-medium-weak pattern of beats. It could be in a compound meter, where the notes are subdivided into three instead of two. It's a general structure that the music fits in. Not all music has this!

Rhythm is the actual timing of the music (relative to the tempo, I guess). For example, a rhythm for one measure of 4/4 might be a half note followed by two eighth notes and a quarter note. You can have many different rhythms within the same meter! This measure may just have a whole note as its rhythm, while that other one might have eight eighth notes.

Why was 'meter' chosen as the root in ⟨polymeter⟩ and 'rhythm' in ⟨polyrhythm⟩? In other words, why wasn't ⟨polymeter⟩ called polyrhythm instead, and ⟨polyrhythm⟩ polymeter? I understand the choice of 'poly-'.

Answer 1

I worry that your quoted source isn't the best; "meter is the rhythmic structure of the music" is not a very good definition. Here, for instance, is a better and more concise definition:

Meter refers to the grouping of accented and unaccented beats into recurring patterns. (Steven Laitz's The Complete Musician)

(Other books/authors, like Lerdahl/Jackendoff in A Generative Theory of Tonal Music, Krebs in Fantasy Pieces, and Rothstein in Phrase Rhythm in Tonal Music, have similar (but more long-winded) definitions.)

Thus, when we talk about polymeter, we're talking about multiple grouping structures. The SE answer you link displays this nicely in its example of polymeter, because there is a 5-grouped structure playing alongside a 4-grouped one, and the downbeats of the grouping structures (that is, the accents) are not aligned.

Meanwhile, the accents in the polyrhythmic example are aligned; it's just the rhythm that takes place within these accents that differs.

When viewed in this way, we see that the word roots were chosen correctly.