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Hemiola
In music, hemiola (also hemiolia) is the ratio 3:2. The equivalent Latin term is sesquialtera. In rhythm, hemiola refers to three beats of equal value in the time normally occupied by two beats. In pitch, hemiola refers to the interval of a perfect fifth.
The word hemiola comes from the Greek adjective ἡμιόλιος, hemiolios, meaning "containing one and a half," "half as much again," "in the ratio of one and a half to one (3:2), as in musical sounds." The words "hemiola" and "sesquialtera" both signify the ratio 3:2, and in music were first used to describe relations of pitch. Dividing the string of a monochord in this ratio produces the interval of a perfect fifth. Beginning in the 15th century, both words were also used to describe rhythmic relationships, specifically the substitution (usually through the use of coloration—red notes in place of black ones, or black in place of "white", hollow noteheads) of three imperfect notes (divided into two parts) for two perfect ones (divided into three parts) in tempus perfectum or in prolatio maior.
In rhythm, hemiola refers to three beats of equal value in the time normally occupied by two beats.
The Oxford Dictionary of Music illustrates hemiola with a superimposition of three notes in the time of two and vice versa.
One textbook states that, although the word "hemiola" is commonly used for both simultaneous and successive durational values, describing a simultaneous combination of three against two is less accurate than for successive values and the "preferred term for a vertical two against three … is sesquialtera." The New Harvard Dictionary of Music states that in some contexts, a sesquialtera is equivalent to a hemiola. Grove's Dictionary, on the other hand, has maintained from the first edition of 1880 down to the most recent edition of 2001 that the Greek and Latin terms are equivalent and interchangeable, both in the realms of pitch and rhythm, although David Hiley, E. Thomas Stanford, and Paul R. Laird hold that, though similar in effect, hemiola properly applies to a momentary occurrence of three duple values in place of two triple ones, whereas sesquialtera represents a proportional metric change between successive sections.
A repeating vertical hemiola is known as polyrhythm, or more specifically, cross-rhythm. The most basic rhythmic cell of sub-Saharan Africa is the 3:2 cross-rhythm. Novotney observes: "The 3:2 relationship (and [its] permutations) is the foundation of most typical polyrhythmic textures found in West African musics." Agawu states: "[The] resultant [3:2] rhythm holds the key to understanding ... there is no independence here, because 2 and 3 belong to a single Gestalt."
In the following example, a Ghanaian gyil plays a hemiola as the basis of an ostinato melody. The left hand (lower notes) sounds the two main beats, while the right hand (upper notes) sounds the three cross-beats.
In compound time (6
8 or 6
4), where a regular pattern of two beats to a measure is established at the start of a phrase, this changes to a pattern of three beats at the end of the phrase.
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Hemiola
In music, hemiola (also hemiolia) is the ratio 3:2. The equivalent Latin term is sesquialtera. In rhythm, hemiola refers to three beats of equal value in the time normally occupied by two beats. In pitch, hemiola refers to the interval of a perfect fifth.
The word hemiola comes from the Greek adjective ἡμιόλιος, hemiolios, meaning "containing one and a half," "half as much again," "in the ratio of one and a half to one (3:2), as in musical sounds." The words "hemiola" and "sesquialtera" both signify the ratio 3:2, and in music were first used to describe relations of pitch. Dividing the string of a monochord in this ratio produces the interval of a perfect fifth. Beginning in the 15th century, both words were also used to describe rhythmic relationships, specifically the substitution (usually through the use of coloration—red notes in place of black ones, or black in place of "white", hollow noteheads) of three imperfect notes (divided into two parts) for two perfect ones (divided into three parts) in tempus perfectum or in prolatio maior.
In rhythm, hemiola refers to three beats of equal value in the time normally occupied by two beats.
The Oxford Dictionary of Music illustrates hemiola with a superimposition of three notes in the time of two and vice versa.
One textbook states that, although the word "hemiola" is commonly used for both simultaneous and successive durational values, describing a simultaneous combination of three against two is less accurate than for successive values and the "preferred term for a vertical two against three … is sesquialtera." The New Harvard Dictionary of Music states that in some contexts, a sesquialtera is equivalent to a hemiola. Grove's Dictionary, on the other hand, has maintained from the first edition of 1880 down to the most recent edition of 2001 that the Greek and Latin terms are equivalent and interchangeable, both in the realms of pitch and rhythm, although David Hiley, E. Thomas Stanford, and Paul R. Laird hold that, though similar in effect, hemiola properly applies to a momentary occurrence of three duple values in place of two triple ones, whereas sesquialtera represents a proportional metric change between successive sections.
A repeating vertical hemiola is known as polyrhythm, or more specifically, cross-rhythm. The most basic rhythmic cell of sub-Saharan Africa is the 3:2 cross-rhythm. Novotney observes: "The 3:2 relationship (and [its] permutations) is the foundation of most typical polyrhythmic textures found in West African musics." Agawu states: "[The] resultant [3:2] rhythm holds the key to understanding ... there is no independence here, because 2 and 3 belong to a single Gestalt."
In the following example, a Ghanaian gyil plays a hemiola as the basis of an ostinato melody. The left hand (lower notes) sounds the two main beats, while the right hand (upper notes) sounds the three cross-beats.
In compound time (6
8 or 6
4), where a regular pattern of two beats to a measure is established at the start of a phrase, this changes to a pattern of three beats at the end of the phrase.