Another popular rhythmic displacement technique common to all musical styles is known as hemiola, which involves superimposing a repetitive, but contrasting rhythmic grouping over a reference beat. The most common hemiola is three-against-four. This could refer to three quarter-notes, three eighth-notes, or three sixteenth-notes repeated over a 4/4 pulse until they recycle back to their starting point.
For instance, a 3/8 hemiola would look and sound like Ex. 1, and recycle every three measures. Why? Count the eighth-notes and do the math. Three bars of 4/4 will house 12 quarter-notes or 24 eighth-notes, which can be grouped as three groups of eight (3 x 8 = 24), or as eight groups of three (8 x 3 = 24). The latter grouping forms a 3/8 hemiola, which displaces itself eight times over the course of three bars of the 4/4 reference beat before starting over again at its point of origin. This example uses three repetitive chromatic eighth-notes to illustrate (think b7-to- 7-to-root in E, or 4-b5-5 in A), but any notes may be applied to any hemiola. You can also substitute swing eighths for straight eighths.
Not every note in a hemiola has to be played. The figure in Ex. 2a replaces the third eighth-note of each 3/8 grouping with a rest, while Ex. 2b simply shifts the replacement rest to the first eighth-note of each 3/8 grouping. Both examples produce hemiolas that are equally applicable to styles from blues to bossa nova. (Tip: Try replacing the single notes with a jazzy chord progression, such as Dm9-G7#5-C6/9.) You can also shift the rest to the second eighth-note of each 3/8 grouping. Replace each pair of notes with a broken oblique bend—i.e., a D-to-E bend followed by an unbent unison E—and play them with a swing feel to form trademark T-Bone Walker and Chuck Berry rhythms.
Sixteenth-notes can also function as the common denominator in a hemiola, as shown in the 3/16 adaptation of Ex. 2a illustrated in Ex. 3. Think the “I know, I know, I know, etc.” vocal line from Bill Withers’ “Ain’t No Sunshine.” (Tip: Ex. 2b can be adapted to 3/16 in the same manner.) Repetitive 3/16 hemiolas like the one in Ex. 4a are commonplace in the blues-rock vernacular, and Ex. 4b demonstrates how to squeeze one more note into the same hemiola by subdividing the third sixteenth-note into two thirty-second- notes. You can also mix combinations of sixteenths and eighths in any 3/8 hemiola, as shown in the Example 4c’s jazz-organ-inspired A blues lick.
Partial hemiolas, which only last for a bar or two and don’t completely recycle, also abound in all musical styles. Some real-world examples include the intro to Hendrix’s “Crosstown Traffic,” whose sixteenth-plus-eighth 3/16 hemiola is simulated in Ex. 5a. Note how this partial version uses two eighth-notes on beat four of bar 2 to break out of the repetitive sixteenth-plus-eighth pattern. Ex. 5b shows a Johnny Winter-inspired V-chord turnaround in A that uses a partial hemiola derived from the 3/16 version of Ex. 2b, while the one in Ex. 5c, which features a partial 3/16 hemiola that begins on the and of beat one, is based on Rick Derringer’s pre-verse figure from his classic “Rock and Roll Hoochie Koo.” For extra credit, reference this month’s Under Investigation and You’re Playing It Wrong and see if you can pick out the partial hemiolas contained in Examples 3a, 4e, and 5a of the former and Ex. 7b of the latter. Once you discover that any rhythmic grouping that adds up to three eighth- or sixteenth-notes can be used to create a hemiola, you’ll discover that they’re everywhere!