View source for Metre (music)

{{short description|Aspect of music}}
{{use British English|date=July 2018}}
[[File:Meter (1).svg|thumb|upright=1.5|Musical and lyric metre]]
In music, '''metre''' (British spelling) or '''meter''' (American spelling) refers to regularly recurring patterns and accents such as [[bar (music)|bars]] and [[Beat (music)|beats]]. Unlike [[rhythm (music)|rhythm]], metric onsets are not necessarily sounded, but are nevertheless implied by the performer (or performers) and expected by the listener.{{Citation needed lead|date=June 2020}}

A variety of systems exist throughout the world for organising and playing metrical music, such as the [[Music of India|Indian system]] of ''[[Tala (music)|tala]]'' and similar systems in [[Rhythm in Arabic music|Arabic]] and [[Rhythm in Sub-Saharan Africa|African music]].

[[Western culture|Western music]] inherited the concept of metre from [[poetry]],{{sfn|Scholes|1977}}{{sfn|Latham|2002b}} where it denotes the number of lines in a [[Verse (poetry)|verse]], the number of syllables in each line, and the arrangement of those syllables as long or short, accented or unaccented.{{sfn|Scholes|1977}}{{sfn|Latham|2002b}} The first coherent system of [[Chord chart|rhythmic notation]] in modern Western music was based on [[rhythmic mode]]s derived from the [[Foot (prosody)|basic types]] of [[Meter (poetry)|metrical]] unit in the [[quantitative meter|quantitative metre]] of [[Classics|classical]] [[ancient Greek poetry|ancient Greek]] and [[Latin poetry]].{{sfn|Hoppin|1978|loc=221}}

Later music for [[Renaissance dance|dances]] such as the [[pavane]] and [[galliard]] consisted of [[musical phrase]]s to accompany a [[Dance move|fixed sequence]] of [[Basic (dance move)|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{{sfn|Merriam-Webster|2015}} involving sequences of notes, words, or movements that may last four, eight or sixteen bars.{{cn|date=October 2020}}

Metre is related to and distinguished from [[pulse (music)|pulse]], [[rhythm]] (grouping), and beats:
{{Quote|Meter is the measurement of the number of pulses between more or less regularly recurring accents.<!--3--> Therefore, in order for meter to exist, some of the pulses in a series must be accented—marked for consciousness—relative to others.<!--4--> When pulses are thus counted within a metric context, they are referred to as ''beats''.{{sfn|Cooper|Meyer|1960|p=3}}}}

==Metric structure==
<!--[[Subdivision (meter)]], [[Subdivision (music)]], [[Division level]], [[Metric hierarchy]], and [[multiple level]] redirect directly here-->

The term ''metre'' is not very precisely defined.{{sfn|Scholes|1977}}  [[Stewart Macpherson|Stewart MacPherson]] preferred to speak of "time" and "rhythmic shape",{{sfn|MacPherson|1930|loc=3}} while [[Imogen Holst]] preferred "measured rhythm".{{sfn|Holst|1963|loc=17}} However, Justin 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".{{sfn|London|2004|loc=4}} This "perception" and "abstraction" of rhythmic bar is the foundation of human instinctive musical participation, as when we divide a series of identical clock-ticks into "tick–tock–tick–tock".{{sfn|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.{{sfn|Yeston|1976|loc=50–52}} In his book ''The Rhythms of Tonal Music'', Joel Lester notes that, "[o]nce a metric hierarchy has been established, we, as listeners, will maintain that organization as long as minimal evidence is present".{{sfn|Lester|1986|loc=77}}

[[File:Metric levels.svg|thumb|350px|left|Metric levels: beat level shown in middle with division levels above and multiple levels below.]]
"''Meter'' may be defined as a regular, recurring pattern of strong and weak beats. This recurring pattern of durations is identified at the beginning of a composition by a meter signature (time signature). ... Although meter is generally indicated by time signatures, it is important to realize that meter is not simply a matter of notation".{{sfn|Benward and Saker|2003|loc=9}} A definition of musical metre requires the possibility of identifying a repeating pattern of accented pulses – a "pulse-group" – which corresponds to the [[foot (poetry)|foot]] in poetry.{{cn|date=October 2020}} Frequently a pulse-group can be identified by taking the accented beat as the first pulse in the group and [[counting (music)|counting]] the pulses until the next accent.{{sfn|MacPherson|1930|loc=5}}{{sfn|Scholes|1977}}

Frequently metres can be subdivided into a pattern of duples and triples.{{sfn|MacPherson|1930|loc=5}}{{sfn|Scholes|1977}} 

For example, a {{Music|time|3|4}} metre consists of three units of a {{Music|time|2|8}} pulse group, and a {{Music|time|6|8}} metre consists of two units of a {{Music|time|3|8}} pulse group. In turn, metric bars may comprise 'metric groups' - for example, a musical phrase or melody might consist of two bars x {{Music|time|3|4}}.{{sfn|Cooper|Meyer|1960|p={{page needed|date=August 2021}}}}

The level of musical organisation implied by musical metre includes the most elementary levels of [[form (music)|musical form]].{{sfn|MacPherson|1930|loc=3}} Metrical rhythm, measured rhythm, and free rhythm are general classes of rhythm and may be distinguished in all aspects of temporality:{{sfn|Cooper|1973|loc=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 [[Accent (music)|accents]] reoccur regularly, providing systematic grouping ([[Bar (music)|bars]], [[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 time (music)|'''Free rhythm''']] is where the time values are not based on any fixed unit; since the time values lack a fixed unit, regularly recurring accents are no longer a possibility.
Some music, including [[chant]], has freer rhythm, like the rhythm of [[prose]] compared to that of [[Verse (poetry)|verse]].{{sfn|Scholes|1977}} Some music, such as some graphically scored works since the 1950s and [[World music|non-European music]] such as [[Honkyoku]] repertoire for [[shakuhachi]], may be considered ametric.{{sfn|Karpinski|2000|loc=19}} The music term ''senza misura'' is Italian for "without metre", meaning to play without a beat, using [[time]] (e.g. seconds elapsed on an ordinary clock) if necessary to determine how long it will take to play the bar.{{sfn|Forney and Machlis|2007|loc=?}}{{Page needed|date=December 2009}}

Metric structure includes metre, [[tempo]], and all [[rhythm]]ic aspects that produce temporal regularity or structure, against which the foreground details or [[Duration (music)|durational pattern]]s of any piece of music are projected.{{sfn|Wittlich|1975|loc=ch. 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.{{cn|date=October 2020}} Faster levels are division levels, and slower levels are multiple levels.{{sfn|Wittlich|1975|loc=ch. 3}} A [[rhythmic unit]] is a durational pattern which occupies a period of time equivalent to a [[Pulse (music)|pulse]] or pulses on an underlying metric level.{{cn|date=October 2020}}

==Frequently encountered types of metre==
{{anchor|Frequently encountered types of meter}}
{{more sources|section|date=October 2020}}

===Metres classified by the number of beats per measure===
{{anchor|Meters classified by the number of beats per measure}}

====Duple and quadruple metre====
{{anchor|Duple and quadruple meter}}
In [[duple metre]], each [[bar (music)|measure]] is divided into two [[beat (music)|beats]], or a multiple thereof ([[Quadruple meter|quadruple metre]]).

For example, in the time signature {{music|time|2|4}}, each bar contains two (2) [[Quarter note|quarter-note]] (4) beats. In the time signature {{music|time|6|8}}, each bar contains two [[Dotted quarter note|dotted-quarter-note]] beats.
:{|
|<score sound="1" override_midi="Simple duple drum pattern.mid">
\new Staff <<
 \new voice \relative c' {
   \clef percussion
   \numericTimeSignature
   \time 2/4
   \set Score.tempoHideNote = ##t \tempo 4 = 100
   \stemDown \repeat volta 2 { g4 d' }
  }
  \new voice \relative c'' {
   \override NoteHead.style = #'cross
   \stemUp \repeat volta 2 { a8 a a a }
   }
>>
</score>
|<score sound="1" override_midi="Compound duple drum pattern.mid">
\new Staff <<
 \new voice \relative c' {
  \clef percussion
  \numericTimeSignature
  \time 6/8
  \set Score.tempoHideNote = ##t \tempo 4. = 80
  \stemDown \repeat volta 2 { g4. d' }
  }
  \new voice \relative c'' {
  \override NoteHead.style = #'cross
  \stemUp \repeat volta 2 { a8 a a a a a }
  }
>>
</score>
|}

Corresponding quadruple metres are {{music|time|4|4}}, which has four quarter-note beats per measure, and {{music|time|12|8}}, which has four dotted-quarter-note beats per bar.

:{|
|<score sound="1" override_midi="Characteristic rock drum pattern.mid">
\new Staff <<
 \new voice \relative c' {
 \clef percussion
 \numericTimeSignature
 \time 4/4
 \set Score.tempoHideNote = ##t \tempo 4 = 100
 \stemDown \repeat volta 2 { g4 d' g, d' }
 }
 \new voice \relative c'' {
 \override NoteHead.style = #'cross
 \stemUp \repeat volta 2 { a8 a a a a a a a }
 }
>>
</score>
|<score sound="1" override_midi="Compound quadruple drum pattern.mid" lang="lilypond" vorbis="1">
\new Staff <<
 \new voice \relative c' {
 \clef percussion
 \numericTimeSignature
 \time 12/8
 \set Score.tempoHideNote = ##t \tempo 4. = 80
 \stemDown \repeat volta 2 { g4. d' g, d' }
 }
 \new voice \relative c'' {
 \override NoteHead.style = #'cross
 \stemUp \repeat volta 2 { a8 a a a a a a a a a a a }
 }
>>
</score>
|}

====Triple metre====
{{anchor|Triple meter}}
[[Triple metre]] is a metre in which each bar is divided into three beats, or a multiple thereof. For example, in the time signature {{music|time|3|4}}, each bar contains three (3) quarter-note (4) beats, and with a time signature of {{music|time|9|8}}, each bar contains three dotted-quarter beats.
:{|
|<score sound="1" override_midi="Simple triple drum pattern.mid">
\new Staff <<
 \new voice \relative c' {
 \clef percussion
 \numericTimeSignature
 \time 3/4
 \set Score.tempoHideNote = ##t \tempo 4 = 100
 \stemDown \repeat volta 2 { g4 d' d }
 }
 \new voice \relative c'' {
 \override NoteHead.style = #'cross
 \stemUp \repeat volta 2 { a8[ a] a[ a] a[ a] }
 }
>>
</score>
|<score sound="1" override_midi="Compound triple drum pattern.mid">
\new Staff <<
 \new voice \relative c' {
 \clef percussion
 \numericTimeSignature
 \time 9/8
 \set Score.tempoHideNote = ##t \tempo 4. = 80
 \stemDown \repeat volta 2 { g4. d' d }
 }
 \new voice \relative c'' {
 \override NoteHead.style = #'cross
 \stemUp \repeat volta 2 { a8 a a a a a a a a }
 }
>>
</score>
|}

==== More than four beats ====
Metres with more than four beats are called ''[[Quintuple meter|quintuple metres]]'' (5), ''[[sextuple metre]]s'' (6), ''[[Septuple meter|septuple metres]]'' (7), etc.

In classical music theory it is presumed that only divisions of two or three are perceptually valid, so a metre not divisible by 2 or 3, such as quintuple metre, say {{music|time|5|4}}, is assumed to either be equivalent to a measure of {{music|time|3|4}} followed by a measure of {{music|time|2|4}}, or the opposite: {{music|time|2|4}} then {{music|time|3|4}}. Higher metres which ''are'' divisible by 2 or 3 are considered equivalent to groupings of duple or triple metre measures; thus, {{music|time|6|4}}, for example, is rarely used because it is considered equivalent to two measures of {{music|time|3|4}}. See: [[#Hypermetre|hypermetre]] and [[additive rhythm and divisive rhythm]].

Higher metres are used more commonly in analysis, if not performance, of [[cross-rhythm]]s, as lowest number possible which may be used to count a [[polyrhythm]] is the [[lowest common denominator]] (LCD) of the two or more metric divisions. For example, much African music is recorded in Western notation as being in {{music|time|12|8}}, the LCD of 4 and 3.

===Metres classified by the subdivisions of a beat===
{{anchor|Meters classified by the subdivisions of a beat}}
Simple metre and compound metre are distinguished by the way the beats are subdivided.

====Simple metre====<!--[[Simple meter]] redirects here-->
{{anchor|Simple meter}}
Simple metre (or simple time) is a metre in which each beat of the bar divides naturally into two (as opposed to three) equal parts. The top number in the time signature will be 2, 3, 4, 5, etc.

For example, in the time signature {{music|time|3|4}}, each bar contains three quarter-note beats, and each of those beats divides into two [[eighth note]]s, making it a simple metre. More specifically, it is a simple ''triple'' metre because there are three beats in each measure; simple duple (two beats) or simple quadruple (four) are also common metres.

:{|
|<score sound="1" override_midi="Simple duple drum pattern.mid">
    \new Staff <<
       \new voice \relative c' {
           \clef percussion
           \numericTimeSignature
           \time 2/4
           \set Score.tempoHideNote = ##t \tempo 4 = 100
           \stemDown \repeat volta 2 { g4 d' }
       }
       \new voice \relative c'' {
           \override NoteHead.style = #'cross
           \stemUp \repeat volta 2 { a8 a a a }
       }
   >>
</score>
|<score sound="1" override_midi="Simple triple drum pattern.mid">
    \new Staff <<
       \new voice \relative c' {
           \clef percussion
           \numericTimeSignature
           \time 3/4
           \set Score.tempoHideNote = ##t \tempo 4 = 100
           \stemDown \repeat volta 2 { g4 d' d }
       }
       \new voice \relative c'' {
           \override NoteHead.style = #'cross
           \stemUp \repeat volta 2 { a8[ a] a[ a] a[ a] }
       }
   >>
</score>
|<score sound="1" override_midi="Characteristic rock drum pattern.mid">
    \new Staff <<
       \new voice \relative c' {
           \clef percussion
           \numericTimeSignature
           \time 4/4
           \set Score.tempoHideNote = ##t \tempo 4 = 100
           \stemDown \repeat volta 2 { g4 d' g, d' }
       }
       \new voice \relative c'' {
           \override NoteHead.style = #'cross
           \stemUp \repeat volta 2 { a8 a a a a a a a }
       }
   >>
</score>
|}

====Compound metre==== <!-- Compound_meter page links directly to here -->
{{anchor|Compound meter}}
Compound metre (or compound time), is a metre in which each beat of the bar divides naturally into three equal parts. That is, each [[beat (music)|beat]] contains a triple pulse.{{sfn|Latham|2002a}} The top number in the time signature will be 6, 9, 12, 15, 18, 24, etc.

Compound metres are written with a time signature that shows the number of ''divisions'' of beats in each bar 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, {{music|time|6|8}}. Contrast this with the time signature {{music|time|3|4}}, which also assigns six eighth notes to each measure, but by convention connotes a simple triple time: 3 quarter-note beats.

Examples of compound metre include {{music|time|6|8}} (compound duple metre), {{music|time|9|8}} (compound triple metre), and {{music|time|12|8}} (compound quadruple metre).

:{|
|<score sound="1" override_midi="Compound duple drum pattern.mid">
   \new Staff <<
       \new voice \relative c' {
           \clef percussion
           \numericTimeSignature
           \time 6/8
           \set Score.tempoHideNote = ##t \tempo 4. = 80
           \stemDown \repeat volta 2 { g4. d' }
       }
       \new voice \relative c'' {
           \override NoteHead.style = #'cross
           \stemUp \repeat volta 2 { a8 a a a a a }
       }
   >>
</score>
|<score sound="1" override_midi="Compound triple drum pattern.mid">
    \new Staff <<
       \new voice \relative c' {
           \clef percussion
           \numericTimeSignature
           \time 9/8
           \set Score.tempoHideNote = ##t \tempo 4. = 80
           \stemDown \repeat volta 2 { g4. d' d }
       }
       \new voice \relative c'' {
           \override NoteHead.style = #'cross
           \stemUp \repeat volta 2 { a8 a a a a a a a a }
       }
   >>
</score>
|<score sound="1" override_midi="Compound quadruple drum pattern.mid">
    \new Staff <<
       \new voice \relative c' {
           \clef percussion
           \numericTimeSignature
           \time 12/8
           \set Score.tempoHideNote = ##t \tempo 4. = 80
           \stemDown \repeat volta 2 { g4. d' g, d' }
       }
       \new voice \relative c'' {
           \override NoteHead.style = #'cross
           \stemUp \repeat volta 2 { a8 a a a a a a a a a a a }
       }
   >>
</score>
|}

Although {{music|time|3|4}} and {{music|time|6|8}} are not to be confused, they use bars 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 (Leonard Bernstein song)|America]]":
[[File:Alternating time signatures2.gif|center|thumb|340x340px|"[[America (West Side Story song)|I like to be in A-mer-i-ca]]" from ''[[West Side Story]]''[[File:Alternating time signatures2.mid]]]]

Compound metre divided into three parts could theoretically be transcribed into musically equivalent simple metre using [[tuplet|triplets]]. Likewise, simple metre can be shown in compound through duples. When conducting in {{music|time|6|8}}, conductors typically provide two beats per bar; however, all six beats may be performed when the tempo is very slow.

Compound time is associated with "lilting" and dancelike qualities. Folk dances often use compound time. Many [[Baroque dance]]s are often in compound time: some [[gigue]]s, the [[courante]], and sometimes the [[passepied]] and the [[siciliana]].

==Metre in song==
{{anchor|Meter in song}}
{{see also|Musical form#Levels of organization}}
[[File:3Chinesen.png|thumb|left|400x400px|The German children's song "[[Drei Chinesen mit dem Kontrabass]]" shows a common fourfold multiplication of rhythmic phrases into a complete verse and melody.[[File:3Chinesen.mid]]]]
The concept of metre in music derives in large part from the [[meter (poetry)|poetic metre]] of [[song]] and includes not only the basic rhythm of the foot, pulse-group or figure used but also the [[rhythm]]ic or [[Form (music)|formal]] arrangement of such figures into musical phrases (lines, couplets) and of such phrases into melodies, passages or sections (stanzas, verses) to give what {{harvtxt|Holst|1963}} calls "the time pattern of any song".{{sfn|Holst|1963|loc=18}}

Traditional and popular songs may draw heavily upon a limited range of metres, leading to interchangeability of melodies. Early [[hymnal]]s commonly did not include musical notation but simply texts that could be sung to any tune known by the singers that had a matching metre. 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 (poetry)|verse]]-form called ''[[ballad]] metre'' or, in hymnals, [[Meter (hymn)|''common metre'']], 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 (music)|cadence]] at the end of the shorter lines so that the underlying musical metre is 8–8–8–8 beats, the cadences dividing this musically into two symmetrical "normal" phrases of four bars each.{{sfn|MacPherson|1930|loc=14}}

In some regional music, for example [[Music of Southeastern Europe|Balkan music]] (like [[Bulgarian dances|Bulgarian music]], and the [[Macedonians (ethnic group)|Macedonian]] [[Leventikos|{{serif|3+2+2+3+2}}]] metre), a wealth of irregular or compound metres are used. Other terms for this are "additive metre"{{sfn|London|2001|loc=§I.8}} and "imperfect time".{{sfn|Read|1964|loc=147}}{{Failed verification|date=August 2013}}<!--Read is evidently the intended source, but his use of "imperfect time" does not correspond exactly to this description of additive (or aksak) metres, nor does he mention music of the Balkans at all.-->

==Metre in dance music==
{{anchor|Meter in dance music}}
{{unreferenced section|date=October 2020}}
[[File:Waltz rhythms.PNG|right|thumb|400px|Typical figures of the waltz rhythm.{{sfn|Scruton|1997}}]]
[[File:Gavotte rhythm.png|right|thumb|300x300px]]
{{listen|type=music
 | header = Dance from ''[[Terpsichore (1612)|Terpsichore]]'' ([[Michael Praetorius]], 1612)
 | filename    = Dances from Terpsichore - 6. Volte by Praetorius.ogg
 | title       = "Volte"
 | description = Includes regular metre followed by an irregular metre
}}
Metre is often essential to any style of dance music, such as the [[waltz]] or [[tango music|tango]], that has instantly recognizable patterns of beats built upon a characteristic tempo and bar. The [[Imperial Society of Teachers of Dancing]] defines the tango, for example, as to be danced in {{music|time|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 {{music|time|2|4}} bar.{{sfn|Anon.|1983|p={{page needed|date=August 2021}}}}

But step-figures such as turns, the corte and walk-ins 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 (poetry)|prosody]] (see also: [[prosody (music)]]).

==Metre in classical music==
{{anchor|Meter in classical music}}
{{unsourced section|date=October 2020}}
In music of the [[common practice period]] (about 1600–1900), there are four different families of time signature in common use:
*[[#Simple metre|Simple]] [[Duple meter|duple]]: two or four beats to a bar, each divided by two, the top number being "2" or "4" ({{music|time|2|4}}, {{music|time|2|8}}, {{music|time|2|2}} ... {{music|time|4|4}}, {{music|time|4|8}}, {{music|time|4|2}} ...). When there are four beats to a bar, it is alternatively referred to as "quadruple" time.
*Simple [[triple metre|triple]]: three beats to a bar, each divided by two, the top number being "3" ({{music|time|3|4}}, {{music|time|3|8}}, {{music|time|3|2}} ...)
*[[#Compound metre|Compound]] duple: two beats to a bar, each divided by three, the top number being "6" ({{music|time|6|8}}, {{music|time|6|16}}, {{music|time|6|4}} ...) Similarly compound quadruple, four beats to a bar, each divided by three, the top number being "12" ({{music|time|12|8}}, {{music|time|12|16}}, {{music|time|12|4}} ...)
*Compound triple: three beats to a bar, each divided by three, the top number being "9" ({{music|time|9|8}}, {{music|time|9|16}}, {{music|time|9|4}})

If the beat is divided into two the metre is ''simple'', if divided into three it is ''compound''. If each bar 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 bar 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 metre===
{{anchor|Changing meter}}
In [[20th-century classical music|20th-century concert music]], it became more common to switch metre—the end of [[Igor Stravinsky]]'s ''[[The Rite of Spring]]'' (shown below) is an example. This practice is sometimes called ''[[Mixed meter|mixed metres]]''.

{{Block indent|<score sound="1">
{ \new PianoStaff << \new Staff \relative c'' { \set Staff.midiInstrument = #"violin" \clef treble \tempo 8 = 126 \override DynamicLineSpanner.staff-padding = #4 \time 3/16 r16 <d c a fis d>-! r16\fermata | \time 2/16 r <d c a fis d>-! \time 3/16 r <d c a fis d>8-! | r16 <d c a fis d>8-! | \time 2/8 <d c a fis>16-! <e c bes g>->-![ <cis b aes f>-! <c a fis ees>-!] } \new Staff \relative c { \set Staff.midiInstrument = #"violin" \clef bass \time 3/16 d,16-! <bes'' ees,>^\f-! r\fermata | \time 2/16 <d,, d,>-! <bes'' ees,>-! | \time 3/16 d16-! <ees cis>8-! | r16 <ees cis>8-! | \time 2/8 d16^\sf-! <ees cis>-!->[ <d c>-! <d c>-!] } >> } </score>}}

A [[metric modulation]] is a [[modulation (music)|modulation]] from one metric unit or metre to another.

The use of [[asymmetrical rhythm]]s – sometimes called ''[[aksak]]'' rhythm (the Turkish word for "limping") – also became more common in the 20th century: such metres include quintuple as well as more complex [[additive meter|additive metres]] along the lines of {{serif|2+2+3}} time, where each [[bar (music)|bar]] has two 2-beat units and a 3-beat unit with a stress at the beginning of each unit. Similar metres are often used in [[Bulgarian dances|Bulgarian folk dances]] and [[Indian classical music]].

==Hypermetre==
<!--[[Hypermeter]] redirects directly here.-->
{{anchor|Hypermeter}}
[[File:Hypermeter.png|thumb|upright=2|Hypermetre: four-beat measure, four-bar hypermeasure, and four-hyperbar verses. Hyperbeats in red.]]
[[File:Waldstein.PNG|thumb|upright=2|Opening of the third movement of Beethoven's [[Piano Sonata No. 21 (Beethoven)|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 bars of the example.[[File:Waldstein.mid]]]]

Hypermetre is large-scale metre (as opposed to smaller-scale metre). [[Bar (music)#Hypermeasure|Hypermeasures]] consist of [[hyperbeat]]s.{{sfn|Stein|2005|loc=329}} "Hypermeter is metre, with all its inherent characteristics, at the level where bars act as beats".{{sfn|Neal|2000|loc=115}} For example, the four-bar hypermeasures are the prototypical structure for [[country music]], in and against which country songs work.{{sfn|Neal|2000|loc=115}} In some styles, two- and four-bar hypermetres are common.{{cn|date=October 2020}}

The term was coined, together with "hypermeasures", by [[Edward T. Cone|Edward T.]] {{harvtxt|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"{{sfn|Berry and Van Solkema|2013|loc=§5(vi)}} {{harvtxt|London|2012}} contends that in terms of multiple and simultaneous levels of metrical "entrainment" (evenly spaced temporal events "that we internalize and come to expect", p.&nbsp;9), there is no in-principle distinction between metre and hypermetre; instead, they are the same phenomenon occurring at different levels.{{sfn|London|2012|loc=25}}

{{harvtxt|Lee|1985}}{{vn|date=August 2013}} and Middleton have described musical metre in terms of [[deep structure]], using [[generative grammar|generative]] concepts to show how different metres ({{music|time|4|4}}, {{music|time|3|4}}, etc.) generate many different surface rhythms.{{cn|date=October 2020}} For example, the first phrase of [[The Beatles]]' "[[A Hard Day's Night (song)|A Hard Day's Night]]", excluding the [[syncopation]] on "night", may be generated from its metre of {{music|time|4|4}}:{{sfn|Middleton|1990|loc=211}}
:{| class="wikitable"
| colspan="5" align="center" width="33%" |{{music|time|4|4}}
| colspan="2" align="center" width="33%" |{{music|time|4|4}}
| colspan="2" align="center" width="34%" |{{music|time|4|4}}
|-
| align="center" |{{music|time|2|4}}
|colspan=4 align="center"|{{music|time|2|4}}
| align="center" |{{music|time|2|4}}
| align="center" |{{music|time|2|4}}
| align="center" width="17%" |{{music|time|2|4}}
| align="center" width="17%" |{{music|time|2|4}}
|-
|
|colspan=2 align="center"|{{music|time|1|4}}
|colspan=2 align="center"|{{music|time|1|4}}
|
|
|
|
|-
|
| align="center" |{{music|time|1|8}}
| align="center" |{{music|time|1|8}}
| align="center" |{{music|time|1|8}}
| align="center" |{{music|time|1|8}}
|
|
|
|
|-
| align="center" |{{music|halfrest}}
| align="center" |{{music|eighthrest}}
| align="center" |{{music|eighthnote}}
| align="center" |{{music|eighthnote}}
| align="center" |{{music|eighthnote}}
| align="center" |{{music|halfnote}}
| align="center" |{{music|halfnote}}
| align="center" |{{music|halfnote}}
|
|-
|
|
| align="center" |It's
| align="center" |been
| align="center" |a
| align="center" |hard
| align="center" |day's
| align="center" |night...
| [[File:A Hard Day's Night opening phrase.mid|120px]]
|}
The syncopation may then be added, moving "night" forward one eighth note, and the first phrase is generated.{{citation needed|date=October 2020}}

==Polymetre==
{{anchor|Polymeter}}
{{see also|Polyrhythm}}

With polymetre, the bar sizes differ, but the beat remains constant. Since the beat is the same, the various metres eventually agree. (Four bars of {{music|time|7|4}} = seven bars of {{music|time|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 {{music|time|9|8}}, {{music|time|12|8}}, and {{music|time|21|8}}, and barlines rarely coincide in all four instruments.{{sfn|Rubbra|1953|loc=41}}

With [[polyrhythm]], the number of beats varies within a fixed bar length. For example, in a 4:3 polyrhythm, one part plays {{music|time|4|4}} while the other plays {{music|time|3|4}}, but the {{music|time|3|4}} beats are stretched so that three beats of {{music|time|3|4}} are played in the same time as four beats of {{music|time|4|4}}.{{cn|date=October 2020}} More generally, sometimes rhythms are combined in a way that is neither tactus nor bar preserving—the beat differs and the bar size also differs. See [[Polytempo|Polytempi]].{{cn|date=October 2020}}

Research into the perception of polymetre shows that listeners often either extract a [[composite rhythm|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 (perception)|figure–ground]] dichotomy is fundamental to all perception".{{sfn|Boring|1942|loc=253}}{{vn|date=August 2013}}{{sfn|London|2004|loc=49–50}} In the music, the two metres will meet each other after a specific number of beats. For example, a {{music|time|3|4}} metre and {{music|time|4|4}} metre will meet after 12 beats.

<!--This paragraph is in danger of becoming a trivia list. There are hundreds, possibly thousands of popular-music bands who have used polyrhythm. Please think twice before adding more.-->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 {{music|time|7|8}}, drummer B playing in {{music|time|3|4}}, the bass playing in {{music|time|3|4}}, the organ playing in {{music|time|5|8}}, the tambourine playing in {{music|time|3|4}},{{Clarify|date=June 2015}}<!--How can this be describing a common beat with different-length bars? surely the players in {{music|time|7|8}} and {{music|time|5|8}} metres must be using a different counting unit from the ones in {{music|time|3|4}}.--> and the alto sax blowing his nose".{{sfn|Mothers of Invention|1970}} "Touch And Go", a [[The Cars discography|hit single]] by [[The Cars]], has polymetric verses, with the drums and bass playing in {{music|time|5|4}}, while the guitar, synthesizer, and vocals are in {{music|time|4|4}} (the choruses are entirely in {{music|time|4|4}}).{{sfn|Cars|1981|loc=15}} [[Magma (band)|Magma]] uses extensively {{music|time|7|8}} on {{music|time|2|4}} (e.g. [[Mëkanïk Dëstruktïẁ Kömmandöh]]) and some other combinations. [[King Crimson]]'s albums of the eighties have several songs that use polymetre of various combinations.{{cn|date=October 2020}}

Polymetres are a defining characteristic of the music of [[Meshuggah]], whose compositions often feature unconventionally timed rhythm figures cycling over a {{music|time|4|4}} base.{{sfn|Pieslak|2007}}

===Examples===
{|
|+Polymetres
| [[File:Polymeter-5c4.ogv|thumb|none|133px|Beat-preserving polymetre {{music|time|5|4}} with {{music|time|4|4}}]]
| [[File:Polymeter-5c3.ogv|thumb|none|133px|Beat-preserving polymetre {{music|time|5|4}} with {{music|time|3|4}}]]
| [[File:Polymeter-3c4.theora.ogv|thumb|none|133px|Measure-preserving polyrhythm {{music|time|3|4}} with {{music|time|4|4}}]]
|-
| [[File:Polymeter-2o4c3o8.ogv|thumb|none|133px|Beat-preserving polymetre {{music|time|2|4}} with {{music|time|3|8}}]]
| [[File:Polymeter-4o4c5o8.ogv|thumb|none|133px|Beat-preserving polymetre {{music|time|4|4}} with {{music|time|5|8}}]]
| [[File:Polymeter-4o4c7o8.ogv|thumb|none|133px|Beat-preserving polymetre {{music|time|4|4}} with {{music|time|7|8}}]]
|-
|[[File:Polyrhythm3c2.theora.ogv|thumb|none|133px|Measure-preserving polyrhythm 2:3]]
| [[File:Polyrhythm4c3.theora.ogv|thumb|none|133px|Measure-preserving polyrhythm 4:3]]
| [[File:Polyrhythm-5 o 4 with 4 o 4 simultaneously.ogv|thumb|none|133px|Measure-preserving polyrhythm 5:4]]
|}

{|
|+Various metres
| [[File:Video of 6o8 at 90 bpm.ogv|thumb|none|133px|{{music|time|6|8}} at tempo of 90&nbsp;bpm]]
| [[File:Video for 9o8 at 90 bpm.ogv|thumb|none|133px|{{music|time|9|8}} at tempo of 90&nbsp;bpm]]
| [[File:Video for 12o8 at 90 bpm.ogv|thumb|none|133px|{{music|time|12|8}} at tempo of 90&nbsp;bpm]]
|-
| [[File:Video for 2o4 at 60 bpm.ogv|thumb|none|133px|{{music|time|2|4}} at a tempo of 60&nbsp;bpm]]
| [[File:Video for 3o4 at 60 bpm.ogv|thumb|none|133px|{{music|time|3|4}} at a tempo of 60&nbsp;bpm]]
| [[File:Video for 4o4 at 60 bpm.ogv|thumb|none|133px|{{music|time|4|4}} at a tempo of 60&nbsp;bpm]]
|}

==See also==
* [[Metre (hymn)]]
* [[Metre (poetry)]]
* [[Hymn tune]]
* [[List of musical works in unusual time signatures]]

==References==
{{reflist|15em}}

===Sources===
{{div col|colwidth=45em}}
* {{cite book|author=Anon.|others=[[Imperial Society of Teachers of Dancing]]|year=1983|title=Ballroom Dancing|series=Teach Yourself|publisher=Hodder and Stoughton|isbn=978-0-340-22517-2}}
*{{wikicite|ref={{harvid|Benward and Saker|2003}}|reference=Benward, Bruce, and Marilyn Nadine Saker (2003). ''Music: In Theory and Practice'', Vol. 1, seventh edition. Boston: McGraw-Hill. {{ISBN|0-07-294262-2}}.}}
*{{wikicite|ref={{harvid|Berry and Van Solkema|2013}}|reference=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}}.}}
*{{Cite book |last=Boring |first=Edwin G. |year=1942 |title=Sensation and Perception in the History of Experimental Psychology |location=New York |publisher=Appleton-Century }}
*{{Cite book |last=Cars |first=The| author-link=The Cars |year=1981 |title=[[Panorama (The Cars album)|Panorama]] ''(songbook)'' |location=New York |publisher=Warner Bros. Publications}}
*{{Cite book|last=Cone|first=Edward T.|author-link=Edward T. Cone|year=1968|title=Musical Form and Musical Performance|location=New York|publisher=Norton|isbn=978-0-39309767-2}}
* {{cite book|last1=Cooper|first1=Grosvenor|last2=Meyer|first2=Leonard B.|author2-link=Leonard B. Meyer|year=1960|title=The Rhythmic Structure of Music|location=Chicago|publisher=University of Chicago Press|isbn=0-226-11521-6 |oclc=1139523}}
*{{Cite book|last=Cooper|first=Paul|year=1973|title=Perspectives in Music Theory: An Historical-Analytical Approach|location=New York|publisher=Dodd, Mead.|isbn=0-396-06752-2}}
*{{wikicite|ref={{harvid|Forney and Machlis|2007}}|reference=Forney, Kristine, and Joseph Machlis (2007). ''The Enjoyment of Music: An Introduction to Perceptive Listening'', tenth edition. New York: W. W. Norton. {{ISBN|978-0-393-92885-3}} (cloth); {{ISBN|978-0-393-17410-6}} (text with DVD); {{ISBN|978-0-393-92888-4}} (pbk.); {{ISBN|978-0-393-10757-9}} (DVD)}}
*{{Cite book |last= Holst |first= Imogen |author-link= Imogen Holst |year= 1963 |title= An ABC of Music: A Short Practical Guide to the Basic Essentials of Rudiments, Harmony, and Form' |others= [[Benjamin Britten]] (foreword) |publisher= Oxford University Press |location= London & New York |isbn= 0-19-317103-1 |url-access= registration |url= https://archive.org/details/abcofmusicshortp0000hols }}
* {{wikicite|ref={{harvid|Hoppin|1978}}|reference=Hoppin, Richard H. 1978. ''Medieval Music''. New York: W. W. Norton. {{ISBN|0-393-09090-6}}.}}
*{{cite book |last=Karpinski |first=Gary S. |year=2000 |title=Aural Skills Acquisition: The Development of Listening, Reading, and Performing Skills in College-Level Musicians. |publisher=Oxford University Press |isbn=0-19-511785-9 }}
*{{Cite book| first = Harald | last = Krebs | year = 2005 | title = Engaging Music: Essays in Music Analysis | chapter = Hypermeter and Hypermetric Irregularity in the Songs of Josephine Lang. | editor = Deborah Stein| publisher = Oxford University Press | location = New York | isbn = 0-19-517010-5 |ref={{sfnref|Stein|2005}} }}
*{{cite book |last=Latham |first=Alison |year=2002a |chapter=Compound Time [Compound Metre] |title=The Oxford Companion to Music |url=https://archive.org/details/isbn_9780198662129 |url-access=registration |editor=Alison Latham |location=Oxford and New York |publisher=Oxford University Press |isbn=0-19-866212-2 }}
*{{cite book |last=Latham |first=Alison |year=2002b |chapter=Metre |title=The Oxford Companion to Music |url=https://archive.org/details/isbn_9780198662129 |url-access=registration |editor=Alison Latham |location=Oxford and New York |publisher=Oxford University Press |isbn=0-19-866212-2 }}
*{{cite book |last=Lee |first=C. S. |year=1985 |chapter=The Rhythmic Interpretation of Simple Musical Sequences: Towards a Perceptual Model |editor3=Robert West |editor=Peter Howell |editor2=Ian Cross |title=Musical Structure and Cognition |location=London |publisher=Academic Press |isbn=978-0-12357170-0 }}
*{{Cite book| first = Joel | last = Lester | year = 1986 | title = The Rhythms of Tonal Music | publisher = Southern Illinois University Press | location = Carbondale | isbn = 0-8093-1282-4 }}
*{{cite book |last=London |first=Justin |year=2001 |chapter=Rhythm |title=[[The New Grove Dictionary of Music and Musicians]]|edition=2nd|editor1=[[Stanley Sadie]]|editor2=[[John Tyrrell (musicologist)|John Tyrrell]] |location=London |publisher=Macmillan}}
*{{Cite book| first = Justin | last = London | year = 2004 | title = Hearing in Time: Psychological Aspects of Musical Meter |edition=first |publisher = Oxford University Press | location = Oxford | isbn = 0-19-516081-9 }}
*{{Cite book| first = Justin | last = London | year = 2012 | title = Hearing in Time: Psychological Aspects of Musical Meter |edition=second|publisher = Oxford University Press | location = Oxford | isbn = 978-0-19-974437-4 }}
*{{Cite book |last=MacPherson |first=Stewart |year=1930 |title=Form in Music |location=London |publisher=Joseph Williams Ltd }}
*{{Cite web |author=Merriam-Webster|year=2015 |title=Measure|work=Dictionary |location=New York|url=http://www.merriam-webster.com/dictionary/measure}}
*{{Cite book |last=Middleton |first=Richard |author-link=Richard Middleton (musicologist)|year=1990 |title=Studying Popular Music |location=Milton Keynes |publisher=Open University Press |isbn=978-0-33515276-6 }}
*{{citation |last=Mothers of Invention |first=The |year=1970 |title=Weasels Ripped My Flesh |url=http://globalia.net/donlope/fz/lyrics/Weasels_Ripped_My_Flesh.html |format=LP |publisher=Bizarre Records / Reprise Records |id={{Discogs master|36781|MS 2028}} }}
* {{cite book |last=Neal |first=Jocelyn |editor1-first=Charles K. |editor1-last=Wolfe |editor2-first=James E. |editor2-last=Akenson |year=2000 |chapter=Songwriter's Signature, Artist's Imprint: The Metric Structure of a Country Song |title=Country Music Annual 2000 |url=https://archive.org/details/countrymusicannu00char |url-access=registration |location=Lexington, KY |publisher=University Press of Kentucky |isbn=0-8131-0989-2 }}
*{{cite journal |last=Pieslak |first=Jonathan |year=2007 |title=Re-casting Metal: Rhythm and Meter in the Music of Meshuggah |journal=[[Music Theory Spectrum]]|volume=29| issue = 2 |pages=219–45|doi=10.1525/mts.2007.29.2.219 }}
* {{Cite book |last=Read |first=Gardner |author-link=Gardner Read |year=1964 |title=Music Notation: A Manual of Modern Practice |location=Boston |publisher=Allyn and Bacon }}
* {{wikicite|ref={{harvid|Rubbra|1953}}|reference=[[Edmund Rubbra|Rubbra, Edmund]] (1953). "String Quartet No. 2 in E-flat, Op. 73: An Analytical Note by the Composer." ''The Music Review'' 14:36–44.}}
*{{cite book |last=Scholes |first=Percy |year=1977 |title=The Oxford Companion to Music |url=https://archive.org/details/oxfordcompaniont00scho |url-access=registration |others=6th corrected reprint of the 10th ed. (1970), revised and reset |editor=John Owen Ward |location=London and New York |publisher=Oxford University Press |isbn=0-19-311306-6 }}, chapters "Metre" and "Rhythm"
*{{Cite book|last= Scruton |first= Roger |author-link= Roger Scruton |year= 1997 |title= The Aesthetics of Music |page=25ex2.6|publisher= Clarendon Press |location= Oxford |isbn= 0-19-816638-9 }}
*{{Cite book| editor-first = Gary E.| editor-last = Wittlich | year = 1975 | title = Aspects of Twentieth-century Music | publisher = Prentice-Hall | location = Englewood Cliffs, New Jersey|isbn= 0-13-049346-5 }}
*{{Cite book|last= Yeston |first= Maury |author-link= Maury Yeston |year= 1976 |title= The Stratification of Musical Rhythm |publisher= Yale University Press |location= New Haven |isbn= 0-300-01884-3 }}
{{div col end}}

==Further reading==
* 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: {{webarchive |url=https://web.archive.org/web/20110527113304/http://www.enotes.com/music-encyclopedia/polymeter |date=27 May 2011}}
* Anon. [2001]. "Polyrhythm". ''[[Grove Music Online]]''. (Accessed 4 April 2009)
* [[Paul Hindemith|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):227–232. ([http://www.hum.uva.nl/mmm/papers/honing-2002.pdf pdf])
* 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, 103–122. Harmonologia Series, no. 12. Hillsdale, New York: Pendragon Press. {{ISBN|1-57647-112-8}}.
*Waters, Keith (1996). "Blurring the Barline: Metric Displacement in the Piano Solos of Herbie Hancock". ''Annual Review of Jazz Studies'' 8:19–37.

{{Rhythm and meter}}
{{Musical notation}}
{{Use dmy dates|date=September 2019}}

{{DEFAULTSORT:Meter (Music)}}
[[Category:Rhythm and meter|*]]
[[Category:Articles containing video clips]]
[[Category:Patterns]]
[[Category:Cognitive musicology]]