Meter (music)

Musical and lyric metre.

See also: Hymn meter and Poetic meter

The meter (or metre) of music is its rhythmic structure, the patterns of accents heard in regularly recurring measures of stressed and unstressed beats (arsis and thesis) at the frequency of the music's pulse.

A variety of systems exist throughout the world for organising and playing metrical music, such as the Indian system of tala and similar systems in Arabian and African music.

Western music inherited the concept of metre from poetry (Scholes 1977; Latham 2002b) where it denotes: the number of lines in a verse; the number of syllables in each line; and the arrangement of those syllables as long or short, accented or unaccented (Scholes 1977; Latham 2002b). The first coherent system of rhythmic notation in modern Western music was based upon rhythmic modes derived from the basic types of metrical unit in the quantitative meter of classical ancient Greek and Latin poetry (Hoppin 1978, 221).

Later music for dances such as the pavane and galliard consisted of musical phrases to accompany a fixed sequence of basic steps with a defined tempo and time signature. The English word "measure", originally an exact or just amount of time, came to denote either a poetic rhythm, a bar of music, or else an entire melodic verse or dance (Merriam-Webster 2015) involving sequences of notes, words and/or movements that may last four, eight or sixteen bars.

Metric structure

The term is not very precisely defined (Scholes 1977). MacPherson (1930, 3) preferred to speak of "time" and "rhythmic shape", Imogen Holst (1963, 17) of "measured rhythm". However, London has written a book about musical metre, which "involves our initial perception as well as subsequent anticipation of a series of beats that we abstract from the rhythm surface of the music as it unfolds in time" (London 2004, 4). This "perception" and "abstraction" of rhythmic measure is the foundation of human instinctive musical participation, as when we divide a series of identical clock-ticks into "tick-tock-tick-tock" (Scholes 1977). "Rhythms of recurrence" arise from the interaction of two levels of motion, the faster providing the pulse and the slower organizing the beats into repetitive groups (Yeston 1976, 50–52). "Once a metric hierarchy has been established, we, as listeners, will maintain that organization as long as minimal evidence is present" (Lester 1986, 77).

Metric levels: beat level shown in middle with division levels above and multiple levels below.

A definition of musical meter requires the possibility of identifying a repeating pattern of accented pulses — a "pulse-group" — which corresponds to the foot in poetry. Frequently a pulse-group can be identified by taking the accented beat as the first pulse in the group and counting the pulses until the next accent (MacPherson 1930, 5; Scholes 1977). Frequently meters can be broken down into a pattern of duples and triples (MacPherson 1930, 5; Scholes 1977).

The level of musical organisation implied by musical meter includes the most elementary levels of musical form (MacPherson 1930, 3).

Metrical rhythm, measured rhythm, and free rhythm are general classes of rhythm and may be distinguished in all aspects of temporality (Cooper 1973, 30). Metrical rhythm, by far the most common class in Western music, is where each time value is a multiple or fraction of a fixed unit (beat, see paragraph below), and normal accents re-occur regularly, providing systematic grouping (measures, divisive rhythm). Measured rhythm is where each time value is a multiple or fraction of a specified time unit but there are not regularly recurring accents (additive rhythm). Free rhythm is where there is neither (Cooper 1973, 30). Some music, including chant, has freer rhythm, like the rhythm of prose compared to that of verse (Scholes 1977). Some music, such as some graphically scored works since the 1950s and non-European music such as Honkyoku repertoire for shakuhachi, may be considered ametric (Karpinski 2000, 19). Senza misura is an Italian musical term for "without meter", meaning to play without a beat, using time to measure how long it will take to play the bar (Forney and Machlis 2007,).

Metric structure includes meter, tempo, and all rhythmic aspects that produce temporal regularity or structure, against which the foreground details or durational patterns of any piece of music are projected (Wittlich 1975, chapt. 3). Metric levels may be distinguished: the beat level is the metric level at which pulses are heard as the basic time unit of the piece. Faster levels are division levels, and slower levels are multiple levels (Wittlich 1975, chapt. 3). A rhythmic unit is a durational pattern which occupies a period of time equivalent to a pulse or pulses on an underlying metric level.

Frequently encountered types of meter

Meters classified by the number of beats per measure

Duple meter

Main article: Duple meter

In duple meter, each measure is divided into two beats, or a multiple thereof (quadruple meter). For example, in the time signature 2/4, each measure contains two (2) quarter-note (4) beats, and with the time signature 6/8, each measure contains two dotted-quarter-note beats. Corresponding quadruple meters are 4/4, with 2 × 2 = 4 quarter-note beats per measure, and 12/8, with 2 × 2 = 4 dotted-quarter-note beats per measure.

Triple meter

Main article: Triple metre

Triple meter is a meter in which each measure is divided into three beats, or a multiple thereof. For example, in the time signature 3/4, each measure contains three (3) quarter-note (4) beats, and with a time signature of 9/8, each measure contains three dotted-quarter beats.

Meters classified by the subdivisions of a beat

Simple meter and compound meter are distinguished by the way the beats are subdivided.

Simple meter

File:Simple triple drum pattern.png

Simple triple drum pattern: divides each of three beats into two

Simple meter or simple time is a meter in which each beat of the measure divides naturally into two (as opposed to three) equal parts. The top number in the time signature will be 2, 3, 4, 5, etc..

Simple quadruple drum pattern: divides each of four beats into two <phonos file="Simple duple drum pattern.mid">Play</phonos>

For example, in the time signature 3/4, each measure contains three crotchet (quarter note) beats, and each of those beats divides into two quavers (eighth notes), making it a simple meter. More specifically, it is simple triple because there are three beats in each measure; simple duple (two beats) or simple quadruple (four) are also common meters.

Compound meter

Compound triple drum pattern: divides each of three beats into three <phonos file="Compound triple drum pattern.mid">Play</phonos>

Compound meter, compound metre, or compound time (chiefly British variation), is a meter in which each beat of the measure divides naturally into three equal parts. That is, each beat contains a triple pulse (Latham 2002a). The top number in the time signature will be 6, 9, 12, 15, 18, 24, etc..

Compound duple drum pattern: divides each of two beats into three <phonos file="Compound duple drum pattern.mid">Play</phonos>

Compound meters are written with a time signature that shows the number of divisions of beats in each measure as opposed to the number of beats. For example, compound duple (two beats, each divided into three) is written as a time signature with a numerator of six, for example, 6/8. Contrast this with the time signature 3/4 which also assigns six quavers to each measure, but by convention connotes a simple triple time: 3 crotchet beats.

Examples of compound meter:

• 6/8 (compound duple meter) has two beats divided into three equal parts, i.e., a primary accent on the first quaver, and a subordinate accent on the fourth quaver.
• 9/8 (compound triple meter) has three beats divided into three parts, i.e., a primary accent on the first quaver, and subordinate accents on the fourth and seventh quavers.
• 12/8 (compound quadruple meter) has four beats divided into three equal parts, i.e., a primary accent on the first quaver, a secondary accent on the seventh quaver, and subordinate accents on the fourth and tenth quavers.

Although 3/4 and 6/8 are not to be confused, they use measures of the same length, so it is easy to "slip" between them just by shifting the location of the accents. This interpretational switch has been exploited, for example, by Leonard Bernstein, in the song "America" from West Side Story, as can be heard in the prominent motif <phonos file="Alternating time signatures2.mid">Play</phonos>:

Some works with compound meter:

• Jigs are often in 6/8 time, with Irish slip jigs in 9/8 time.

Counter-examples, not in compound meter

Compound meter divided into three parts could theoretically be transcribed into musically equivalent simple meter using triplets. Likewise, simple meter can be shown in compound through duples. In practice, however, this is rarely done because it disrupts conducting patterns when the Tempo changes. When conducting in 6/8, conductors typically provide two beats per measure. Where the tempo is slow, however, all six beats may be performed.

Compound time is associated with "lilting" and dance-like qualities. Folk dances often use compound time. Many Baroque dances are often in compound time: some gigues, the courante, and sometimes the passepied and the siciliana.

Meter in song

A German children's song shows a common fourfold multiplication of rhythmic phrases into a complete verse and melody. <phonos file="3Chinesen.mid">Play</phonos>

The concept of meter in music derives in large part from the poetic meter of song and includes not only the basic rhythm of the foot, pulse-group or figure used but also the rhythmic or formal arrangement of such figures into musical phrases (lines, couplets) and of such phrases into melodies, passages or sections (stanzas, verses) to give what Holst (1963, 18) calls "the time pattern of any song" (See also: Form of a musical passage).

Traditional and popular songs may draw heavily upon a limited range of meters, leading to interchangeability of melodies. Early hymnals commonly did not include musical notation but simply texts that could be sung to any tune known by the singers that had a matching meter. For example, The Blind Boys of Alabama rendered the hymn Amazing Grace to the setting of The Animals' version of the folk song The House of the Rising Sun. This is possible because the texts share a popular basic four-line (quatrain) verse-form called ballad meter or, in hymnals, common meter, the four lines having a syllable-count of 8:6:8:6 (Hymns Ancient and Modern Revised), the rhyme-scheme usually following suit: ABAB. There is generally a pause in the melody in a cadence at the end of the shorter lines so that the underlying musical meter is 8:8:8:8 beats, the cadences dividing this musically into two symmetrical "normal" phrases of four measures each (MacPherson 1930, 14).

In some regional music, for example Balkan music (like Bulgarian music, and the Macedonian 3+2+2+3+2 meter), a wealth of irregular or compound meters are used. Other terms for this are "additive meter" (London 2001, §I.8) and "imperfect time" (Read 1964, 147).

Meter in dance music

Typical figures of the waltz rhythm (Scruton 1997)

Meter is often essential to any style of dance music, such as the waltz or tango, that has instantly recognizable patterns of beats built upon a characteristic tempo and measure. The Imperial Society of Teachers of Dancing (1983) defines the tango, for example, as to be danced in 2/4 time at approximately 66 beats per minute.

The basic slow step forwards or backwards, lasting for one beat, is called a "slow", so that a full "right-left" step is equal to one 2/4 measure.

But step-figures such as turns, the corte and walks-in also require "quick" steps of half the duration, each entire figure requiring 3-6 "slow" beats. Such figures may then be "amalgamated" to create a series of movements that may synchronise to an entire musical section or piece. This can be thought of as an equivalent of prosody.

Meter in classical music

A sequence of steps laid against the typical rhythm of the gavotte. Stylised folk-dances from all over Europe lent their characteristic meters to the Baroque suite.

In music of the common practice period (about 1600–1900), there are four different families of time signature in common use:

• Simple duple—two or four beats to a bar, each divided by two, the top number being "2" or "4" (2/4, 2/8, 2/2 … 4/4, 4/8, 4/2 …). When there are four beats to a bar, it is alternatively referred to as "quadruple" time.
• Simple triple (<phonos file="3-4_rhythm_metre_meter_time_measure.ogg">3/4</phonos>)—three beats to a bar, each divided by two, the top number being "3" (3/4, 3/8, 3/2 …)
• Compound duple—two beats to a bar, each divided by three, the top number being "6" (6/8, 6/16, 6/4 …)
• Compound triple—three beats to a bar, each divided by three, the top number being "9" (9/8, 9/16, 9/4)

Rhythmic analysis of the metric elaboration of one phrase of a gavotte by J.S. Bach. Ebene (German: level).

If the beat is divided into two the meter is simple, if divided into three it is compound. If each measure is divided into two it is duple and if into three it is triple. Some people also label quadruple, while some consider it as two duples. Any other division is considered additively, as a measure of five beats may be broken into duple+triple (12123) or triple+duple (12312) depending on accent. However, in some music, especially at faster tempos, it may be treated as one unit of five.

Changing meter

In twentieth-century concert music, it became more common to switch meter—the end of Igor Stravinsky's The Rite of Spring is an example. A metric modulation is a modulation from one metric unit or meter to another. The use of asymmetrical rhythms also became more common: such meters include quintuple as well as more complex additive meters along the lines of 2+2+3 time, where each bar has two 2-beat units and a 3-beat unit with a stress at the beginning of each unit. Similar meters are used in various folk music as well as some music by Philip Glass. Additive meters may be conceived either as long, irregular meters or as constantly changing short meters.

Hypermeter

Hypermeter: 4-beat measure, 4-measure hypermeasure, and 4-hypermeasure verses. Hyperbeats in red.

Opening of the third movement of Beethoven's Waldstein sonata. The melodic lines in bars 1–4 and 5–8 are (almost) identical, and both form hypermetric spans. The two hyperbeats are the low Cs, in the first and fifth measures of the example.

Hypermeter is large-scale meter (as opposed to surface-level meter) created by hypermeasures which consist of hyperbeats (Stein 2005, 329). "Hypermeter is meter, with all its inherent characteristics, at the level where measures act as beats" (Neal 2000, 115). For example, the four-bar hypermeasure is the prototypical structure for country music, in and against which country songs work (Neal 2000, 115). In some styles, two- and four-bar hypermeters are common.

The term was coined, together with "hypermeasures", by Edward T. Cone (1968), who regarded it as applying to a relatively small scale, conceiving of a still larger kind of gestural “rhythm” imparting a sense of “an extended upbeat followed by its downbeat” (Berry and Van Solkema 2013, §5(vi)). London (2012, 25) contends that in terms of multiple and simultaneous levels of metrical "entrainment" (evenly spaced temporal events "that we internalize and come to expect", p. 9), there is no in-principle distinction between meter and hypermeter; instead, they are the same phenomenon occurring at different levels. Lee (1985) and Middleton have described musical meter in terms of deep structure, using generative concepts to show how different meters (4/4, 3/4, etc.) generate many different surface rhythms. For example, the first phrase of The Beatles' "A Hard Day's Night", excluding the syncopation on "night", may be generated from its meter of 4/4 (Middleton 1990, 211):

4/4					4/4
2/4	2/4				2/4	2/4	2/4	2/4
	1/4		1/4
	1/8	1/8	1/8	1/8
		It's	been	a	hard	day's	night…

The syncopation may then be added, moving "night" forward one eighth note, and the first phrase is generated ().

Polymeter

See also: Polyrhythm

Polymeter is sometimes referred to as "tactus-preserving polymeter." The measure size differs, the beat is the same. Since the beat is the same, the various meters eventually agree. (Four measures of 7/4 = seven measures of 4/4). An example is the second moment, titled "Scherzo polimetrico", of Edmund Rubbra's Second String Quartet (1951), in which a constant triplet texture holds together overlapping bars of 9/8, 12/8, and 21/8, and barlinkes rarely coincide in all four instruments (Rubbra 1953, 41).

Polyrhythm is sometimes referred to as "measure preserving polymeter". The beat varies and the measure stays constant. For example, in a 4:3 polyrhythm, one part plays 4/4 while the other plays 3/4, but the 3/4 beats are stretched so that three beats of 3/4 are played in the same time as four beats of 4/4.

More generally, sometimes rhythms are combined in a way that is neither tactus nor measure preserving—the beat differs and the measure size also differs. See Polytempi.

Research into the perception of polymeter shows that listeners often either extract a composite pattern that is fitted to a metric framework, or focus on one rhythmic stream while treating others as "noise". This is consistent with the Gestalt psychology tenet that "the figure-ground dichotomy is fundamental to all perception" (Boring 1942, 253; London 2004, 49–50). In the music, the two meters will meet each other after a specific number of beats. For example, a 3/4 meter and 4/4 meter will meet after 12 beats.

In "Toads of the Short Forest" (from the album Weasels Ripped My Flesh), composer Frank Zappa explains: "At this very moment on stage we have drummer A playing in 7/8, drummer B playing in 3/4, the bass playing in 3/4, the organ playing in 5/8, the tambourine playing in 3/4, and the alto sax blowing his nose" (Mothers of Invention 1970). "Touch And Go", a hit single by The Cars, has polymetric verses, with the drums and bass playing in 5/4, while the guitar, synthesizer, and vocals are in 4/4 (the choruses are entirely in 4/4) (Cars 1981, 15). The Swedish metal band Meshuggah makes frequent use of polymeters, with unconventionally timed rhythm figures cycling over a 4/4 base (Pieslak 2007).

Examples

Polymeters—video

Play media Beat Preserving Polymeter 5/4 with 4/4	Play media Beat Preserving Polymeter 5/4 with 3/4	Play media Beat Preserving Polymeter 3/4 with 4/4
Play media Beat Preserving Polymeter 2/4 with 3/8	Play media Beat Preserving Polymeter 4/4 with 5/8	Play media Beat Preserving Polymeter 4/4 with 7/8
Play media Measure Preserving Polyrhythm 2:3	Play media Measure Preserving Polyrhythm 4:3	Play media Measure Preserving Polyrhythm 5:4

Various meters—sound

1. sample of how <phonos file="1-4_0.3.1_rhythm_metre_meter_time_measure.ogg">1/4 meter</phonos> sounds in a tempo of 90bpm.
2. sample of how <phonos file="2-4_0.3.1_rhythm_metre_meter_time_measure.ogg">2/4 meter</phonos> sounds in a tempo of 90bpm.
3. sample of how <phonos file="3-4_0.3.1_rhythm_metre_meter_time_measure.ogg">3/4 meter</phonos> sounds in a tempo of 90bpm.
4. sample of how <phonos file="4-4_0.3.1_rhythm_metre_meter_time_measure.ogg">4/4 meter</phonos> sounds in a tempo of 90bpm.
5. sample of how <phonos file="5-8_0.3.1_rhythm_metre_meter_time_measure.ogg">5/8 meter</phonos> sounds in a tempo of 120bpm.

Various meters—video

For larger versions of the videos, click play, then go to More, then About this file

File:Video of 6o8 at 90 bpm.ogv 6/8 at tempo of 90 bpm	File:Video for 9o8 at 90 bpm.ogv 9/8 at tempo of 90 bpm	File:Video for 12o8 at 90 bpm.ogv 12/8 at tempo of 90 bpm
File:Video for 2o4 at 60 bpm.ogv 2/4 at a tempo of 60 bpm	File:Video for 3o4 at 60 bpm.ogv 3/4 at a tempo of 60 bpm	File:Video for 4o4 at 60 bpm.ogv 4/4 at a tempo of 60 bpm

See also

• Composite rhythm
• Counting (music)
• Hymns and hymn tunes
• Hymn tune
• List of musical works in unusual time signatures
• Metre (poetry)
• Tala
• Tuplet
• Wazn

Sources

• Anon. (1999). "Polymeter." Baker's Student Encyclopedia of Music, 3 vols., ed. Laura Kuhn. New York: Schirmer-Thomson Gale; London: Simon & Schuster. ISBN 0-02-865315-7. Online version 2006, archived on 27 May 2011 at http://web.archive.org/web/20110527113304/http://www.enotes.com/music-encyclopedia/polymeter.
• Anon. [2001]. "Polyrhythm". Grove Music Online. (Accessed 4 April 2009)
• Berry, David Carson, and Sherman Van Solkema (2013). "Theory". The Grove Dictionary of American Music, second edition, edited by Charles Hiroshi Garrett. New York: Oxford University Press. ISBN 978-0-19-531428-1.
• Forney, Kristine, and Joseph Machlis (2007). The Enjoyment of Music: An Introduction to Perceptive Listening, tenth edition. New York: W. W. Norton & Company, Inc. ISBN 978-0-393-92885-3 (cloth); ISBN 978-0-393-17410-6 (text w/DVD); ISBN 978-0-393-92888-4 (pbk.); ISBN 978-0-393-10757-9 (DVD
• Hindemith, Paul (1974). Elementary Training for Musicians, second edition (rev. 1949). Mainz, London, and New York: Schott. ISBN 0-901938-16-5.
• Honing, Henkjan (2002). "Structure and Interpretation of Rhythm and Timing." Tijdschrift voor Muziektheorie 7(3):227–32. (pdf)
• Hoppin, Richard H. 1978. Medieval Music. New York: W. W. Norton & Co. ISBN 0-393-09090-6.
• Larson, Steve (2006). "Rhythmic Displacement in the Music of Bill Evans". In Structure and Meaning in Tonal Music: Festschrift in Honor of Carl Schachter, edited by L. Poundie Burstein and David Gagné, 103–22. Harmonologia Series, no. 12. Hillsdale, NY: Pendragon Press. ISBN 1-57647-112-8.
• Rubbra, Edmund (1953). "String Quartet No. 2 in E flat, Op. 73: An Analytical Note by the Composer." The Music Review 14:36–44.
• Scruton, Roger (1997). The Aesthetics of Music, p. 25ex2.6. Oxford: Clarendon Press. ISBN 0-19-816638-9.
• Waters, Keith (1996). "Blurring the Barline: Metric Displacement in the Piano Solos of Herbie Hancock". Annual Review of Jazz Studies 8:19–37.

External links

• www.oddtimeobsessed.com website and Internet radio dedicated to odd meters in music. (odd time signatures)
• Video samples of various meters including polyrhythms, and mixed meters with Bounce Metronome Pro's "Gravity Bounce Conductor"