Brief (very brief) aspects of rhythm and meter from chapter six.
Syncopation occurs when an accent comes at an unexpected moment, or when an expected event fails to occur.
Written and Perceived Meter
Sometimes, owing to syncopation, we hear (perceive) a meter that is different from what is written.
20th- and 21st-century music often employs frequently changing meter signatures.
Polymeter can be either explicit, with multiple time signatures and offset barlines, or implied through syncopation. Simultaneous use of 2/4 and 6/8 i not polymeter, but polydivision of a single meter.
Ametric music lacks a recognizable rhythmic and metric organization. The lack of a meter signature or barlines does not necessarily denote ametric music.
Additive Rhythm and Meter
Additive meter involves meters with varying beat durations, like 5/8 (which subdivides 2+3, or reversed) and 7/8 (2+2+3). 8/8 differs from 4/4 in that 8/8 implies an additive meter (3+3+2).
Additive rhythm is related but slightly different. Messiaen offers the best examples, including the example on p. 128 from the Quartet for the End of Time. Simple metrical patterns are transformed through the use of dots, short notes, or rests.
Messiaen’s Quartet for the End of Time also provides an excellent example of isorhythm in the first movement (in the Burkhart). Isorhythm refers to the use of the repeating rhythmic pattern that repeats either using different pitches, or using a pitch pattern of a different length than the rhythmic pattern.
I’ll explain this more in another post. For now, tempo modulation refers to the precise method of changing tempo by making some note value in the first tempo equal to different note value (or proportion) in the new tempo. It can also occur by changing the grouping of note values.