Hemiola turns out to be fairly strictly defined (see Sources and Definitions, below). The key distinction from other 3:2 relationships is that it is a metrical event, as opposed to a rhythmic one. That is, hemiola temporarily redefines the meter of a piece by affecting the beat level or without changing the primary subdivision pulse.
Thus, the following would be hemiola
at the beat level
X: 1
T: Hemiola
T: 6/8 to 3/4
M: 6/8
L: 1/8
K: C clef=perc stafflines=1
!>!BBB !>!BBB | !>!BB!>!B B!>!BB |
X: 1
T: Hemiola
T: 2/4 to 3/4
M: 2/4
L: 1/4
K: C clef=perc stafflines=1
!>!B B | !>!B B | B2- | B B- | B2 |
or at the subdivision level
X: 1
T: Hemiola
T: 2/4 to 3/16 (sixteenths to triplets)
M: 2/4
L: 1/16
K: C clef=perc stafflines=1
!>!BBBB !>!BBBB | !>!BBB!>!B BB!>!BB | B!>!BBB !>!BBB!>!B | BB!>!BB B!>!BBB |
Note that in all cases, the predominant rhythmic pulse doesn't change, but the metric accent does.
By contrast, the following are not hemiola, because the 3 and 2 divisions comprise different subdivisions from each other.
X: 1
T: Not Hemiola
T: eighths versus triplets
M: 2/4
L: 1/4
K: C clef=perc stafflines=1
V:V1
V:V2 name="basic subdivisions"
[V:V1] B/2B/2 B/2B/2 | (3BBB |
[V:V2] B/2B/2 B/2B/2 | (3B/2B/2B/2 (3B/2B/2B/2 |
X: 1
T: Not Hemiola
T: eighths versus triplets
M: 2/4
L: 1/4
K: C clef=perc stafflines=1
[V:V1] B/2B/2 B/2B/2 | B B | (3BBB |
[V:V2] B/2B/2 B/2B/2 | B/2B/2 B/2B/2 | B/2B/2 B/2B/2 |
Because these examples rely on duple versus triple subdivisions of the same basic pulse, they affect the rhythm but not the meter. Thus, by the strict definition, they are not hemiola.
Sources and Definitions
It is not immediately obvious from any individual source the metrical quality which distinguishes hemiola. Some sources describe it as "rhythmic." However, in all cases, it is described as affecting meter, all examples are metrical, and no examples of, say, duplets against triplets are give.
1. The Oxford Companion to Music, edited by Alison Latham (Oxford University Press, 2002), page 579.
A term denoting the ratio 3:2. In modern notation, a hemiola occurs when two bars in triple meter (e.g. 3/2) are performed as if they were notated as three bars in duple meter (6/4), or vice versa.
2. The Norton/Grove Consice Encyclopedia of Music, edited by Stanley Sadie (Macmillan Press, 1994), page 359.
In the modern metrical system it denotes the articulation of two bars in triple meter as if they were three bars in duple.
3. Stephen G. Laitz, The Complete Musician, 2nd ed. (Oxford University Press, 2008), page 63.
Another type of metrical disturbance, closely related to syncopation, is the hemiola. In a hemiola, the established meter temporarily is displaced by a competing meter.
4. Edward Aldwell and Carl Schachter, Harmony and Voice Leading, 2nd ed. (Harcourt Brace Jovanovich, 1989), page 41.
In triple and compound meters, shifted accents sometimes transform two groups of three beats into three groups of two beats. ... The technical name for this rhythmic device is hemiola.
(Note the description as "rhythmic" device, although the example given in the book is metric. That "rhythmic" and "metric" are used interchangeably is, I believe, the source of ambiguity in defining the term.)
5. Richard Hoffman, The Rhythm Book, 2nd ed. (Richard Hoffman, 2009), page 70.
Hemiola is a special form of syncopation describing the use of three even durations in place of two. ... [For example,] regroupings within the measure of triple meter.