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@stevenstrogatz An analogy between musical and poetic rhythm may help. 6/8 and 3/4 both refer to rhythms in which each "line" of a musical "poem" has six "syllables." But in the former case, the the stress is as in "elegant discipline," whereas in the latter, it's as in "nothing really matters."
@stevenstrogatz To a poet, the distinction is between six syllables as two dactyls (which is what you get with 6/8) and six syllables as three trochees (which is what you get with 3/4.) 6/8 therefore refers to a duple rhythm, with two stressed beats per line, and 3/4 to a triple one, with three.
@stevenstrogatz Musicians use the word "hemiola" to refer to the alternation or layering of duple and triple rhythms. Certain composers were especially fond of the effect, and used it extensively. Here is an exquisite example from Brahms, in 6/4 alternating with 3/2: bit.ly/2Gl8ahL
@stevenstrogatz It may be that the fascination of hemiola lies precisely in its subtlety; it's one of those musical phenomena that one hardly notices until it's pointed out explicitly -- whereupon one notices it everywhere.
