Hemiola
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In modern musical parlance, a hemiola is a metrical pattern in which two bars in triple time (3/2 or 3/4 for example) are articulated as if they were three bars in duple time (2/2 or 2/4).
The word hemiola derives from the Greek hemiolios, meaning "one and a half". It was originally used in music to refer to the frequency ratio 3:2; that is, the interval of a justly tuned perfect fifth.
Later, from around the 15th century, the word came to mean the use of three breves in a bar when the prevailing metrical scheme had two dotted breves in each bar. This usage was later extended to its modern sense of two bars in triple time articulated or phrased as if they were three bars in duple time. An example can be found in the second two bars of this excerpt from the first movement of Wolfgang Amadeus Mozart's Piano Sonata, K. 332:
The effect can clearly be seen in the bottom staff, played by the left hand: the accented beats are those with two notes; hearing this passage one gets a sensation of "1 2 3, 1 2 3, 1 2, 1 2, 1 2".
Hemiolas (in the modern sense) often occur in certain dances, particularly the courante. Composers of classical music who have used the device particularly extensively include George Frideric Handel and Johannes Brahms. A more popular example of hemiola appears in "America" from Leonard Bernstein's West Side Story where bars of six beats are alternately divided into two groups of three and three groups of two ("I want to BE in a-MER-I-CA").
A hemiola is not an example of a polyrhythm.
References
- The New Grove Dictionary of Music and Musicians, ed. Stanley Sadie (sixth edition, 1980)