In modern musical parlance, a hemiola is a metrical pattern in which two bars in simple triple time (3/2 or 3/4 for example) are articulated as if they were three bars in simple duple time (2/2 or 2/4). In the example below, the third and fourth bars constitute the hemiola.
The interplay of two groups of three notes with three groups of two notes gives a distinctive pattern of 1-2-3, 1-2-3, 1-2, 1-2, 1-2. This rhythm is common in Africa and known as African hemiola style.
The word hemiola derives from the Greek adjective ἡμιόλιος - hemiolios, meaning "one and a half". This term was used in a music-theoretic context by Aristoxenus.[1] (The noun ἡμιολία - hemiolia "one and a half (fem.)" was also used by the Greeks to refer to a galley powered by one and a half banks of oars.) 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.[2] This usage was later extended to its modern sense of two bars in simple triple time articulated or phrased as if they were three bars in simple duple time. An example can be found in measures 64 and 65 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 senses that "1 2 3, 1 2 3, 1 2, 1 2, 1 2" is the musical pulse.
Hemiola is found in many Renaissance pieces at areas of cadential repose such as the compositions of Josquin des Prez and Jacob Obrecht.
The Hemiola was a common practice to end minuets in French baroque music. It is still the common practice when French baroque music is interpreted in historically correct fashion. Often the term Hemiolia is used in this case.
In the modern sense, hemiolas often occur in certain dances, particularly the courante. Composers of classical music who have used the device particularly extensively include Arcangelo Corelli, George Friedrich Handel, Carl Maria von Weber and most famously in the music of Johannes Brahms (e.g. the opening of Symphony no 3). Pyotr Ilyich Tchaikovsky frequently used hemiolas in his waltzes.
Were the metrical impulse to be not a three beat pattern changing to a two beat one (as in the Mozart example above), but one where a two-beat impulse changes to a three-beat one, the pattern of 2:3 would be known as sesquialtera. (Note, this does not specifically refer to the "sesquialtera" organ stop.)
The term "hemiola" could also be applied to patterns that are repeated, outside of the agogic stress of the written meter, creating either a temporary feeling of a meter change or one meter over another. This could be a 5-quarter-note ostinato, in a common-time piece, or any compound meter superimposed over a even one. See: Meter (music)#Polymeter.