3s and 2s: Hemiola and Other Across-the-Beat Rhythms
In a previous section, we looked at how 3s and 2s can interact through mixed meter and tuplets (triplets and duplets). Here, we’ll take a look at a few additional ways 3s and 2s can interact.
The first, called “hemiola,” is particularly associated with (broadly defined) classical music. Hemiola technically just refers to the ratio of 3:2, but it is most often used to describe a shift, usually temporary, from “two groups of three” to “three groups of two.” In notated music, this most often means one of the following:
- When in a compound duple meter such as six-eight (two beats of three eighth notes each), there may be a shift to a simple triple meter such as three-four (three beats of two eighth notes each). This might be notated as a meter change, or there might simply be an implication of three-four by the use of three quarter notes within six-eight.
- In music notated in a simple triple meter like 3/4, measures/cycles often seem to group in pairs, creating “two groups of three” (two measures with three beats each); hemiola in this case would mean suddenly using half notes and pairs of quarter notes tied across the barline, since now two measures will be filled with “three groups of two.”
The second type of 3/2 interaction we’ll address here is particularly associated with popular music. In this type, a simple meter melody uses a bunch of “threes” (dotted notes), syncopating or contrasting against the beat, only to use some number of “twos” at the end of a cycle to “reset” to the downbeat. For example, in 4/4, the rhythm might be dotted quarter-dotted quarter-quarter (3-3-2, measured in eighth notes) or dotted eighth-dotted eighth-dotted eighth-dotted eighth-eighth-eighth (3-3-3-3-2-2, measured in sixteenth notes).
Perform hemiolas from notation
Goal: Get used to how hemiolas feel in performance.
Before you start: You’ll need a source of notated rhythms or melodies with hemiolas. Many sight-reading anthologies have chapters on hemiola; hemiolas are also reasonably common in triple-meter music by Johannes Brahms and some varieties of European Medieval and Renaissance music. You can do this activity vocally or on an instrument.
Instructions:
- Note the meter and set it up internally.
- Scan the notation for a hemiola, looking for a spot where groups of three (typically dotted notes) are supplanted by groups of three (likely undotted notes).
- Practice transitioning into the hemiola; it may help to practice abstractly at first, counting 1-la-li-2-la-li-1-and-2-and-3-and. Make sure your beat divisions remain the same length.
- Perform the rhythm.
Activity: Identify contrasting 3s and 2s in music
Goal: Identify hemiolas and other contrasting 3s and 2s in sounding music.
Instructions: Listen to a song from the playlist below. Each song features either hemiolas or, within a simple meter, several “three” notes followed by 1–2 “two” notes; the latter case is usually a cycle that repeats over and over. Identify which device you hear in each song. Optionally, notate the relevant phrase.
