Time has structure too.
Pitch lives in frequency. Rhythm lives in time. A time signature tells you how beats group. A subdivision tells you how beats divide. Together they create the skeleton that melody and harmony drape over. Without rhythm, music is just a list of frequencies.
Simple vs Compound
Simple meters divide each beat into two (4/4, 3/4, 2/4). Compound meters divide each beat into three (6/8, 9/8, 12/8). The difference is not the number of notes — it is how gravity pulls within each beat.
Syncopation
Accenting the weak beats or the "and" between beats. Jazz, funk, and Latin music live on syncopation. The expected beat is silence. The unexpected offbeat is sound. Tension from displaced expectation.
Asymmetric Meters
5/4, 7/8, 11/8 — meters that refuse to divide into equal halves. They feel odd because your body cannot find a symmetric pattern. Balkan folk dances live here. So does progressive rock.
Polyrhythm
Two different rhythmic patterns happening simultaneously. 3 against 2. 4 against 3. West African drumming is built on polyrhythm. Your brain hears one pattern, then the other, then both — that shift is the magic.