C. Other Notations of Large-Value Three-Against-Two

In the previous two sections, we encountered large-value three-against-two in two different forms: large-value triplets superimposed against rhythmic patterns in duple meter and large-value duplets superimposed against rhythmic patterns in triple meter. This section showcases two other ways in which large-value three-against-two is sometimes notated. The first involves 6/8 and 3/4 time signatures superimposed directly against one another in different staves. The second involves large-value hemiola patterns that imply 3/2 meter spread across a single measure of 6/4 or two measures of 3/4. Both of these notational approaches allow for easier notation of varied, nested rhythmic patterning within a large-value three-against-two framework.

3/4 Against 6/8

Exercise 5C-1: Charles Ives, “Watchman!”

Exercise 5C-2:

Exercise 5C-3:

Exercise 5C-4:

3/2 Patterning Against 6/4

Exercise 5C-5:

Exercise 5C-6:

Exercise 5C-7: