View source for Time signature

{{short description|Specification of beats in a musical bar/measure}}
{{Redirect|Time (music)|other uses|Half-time (music)}}
{{More citations needed|date=July 2025}}
{{Image frame
|width=193
|align=right
|image=Common time signatures.gif
|content=
<score> 
{ \key c \major \time 3/4 \relative c' { f a c } }
</score>
|caption=An example of a {{music|time|3|4}} time signature. The time signature indicates that there are three [[quarter note]]s (crotchets) per [[measure (music)|measure]] (bar).
|alt=Printed music staff with treble-clef symbol, {{music|time|3|4}} time signature, and 3 quarter notes: A, F, and middle C.
}}

A '''time signature''' (also known as '''meter signature''',<ref>Alexander R. Brinkman, ''Pascal Programming for Music Research'' (Chicago: [[University of Chicago Press]], 1990): 443, 450–63, 757, 759, 767. {{ISBN|978-0-226-07507-5}}; Mary Elizabeth Clark and David Carr Glover, ''Piano Theory: Primer Level'' (Miami: Belwin Mills, 1967): 12; Steven M. Demorest, ''Building Choral Excellence: Teaching Sight-Singing in the Choral Rehearsal'' (Oxford and New York: [[Oxford University Press]], 2003): 66. {{ISBN|978-0-19-516550-0}}; [[William Duckworth (composer)|William Duckworth]], ''A Creative Approach to Music Fundamentals'', eleventh edition (Boston, MA: Schirmer Cengage Learning, 2013): 54, 59, 379. {{ISBN|978-0-8400-2999-7}}; Edwin Gordon, ''Tonal and Rhythm Patterns: An Objective Analysis: A Taxonomy of Tonal Patterns and Rhythm Patterns and Seminal Experimental Evidence of Their Difficulty and Growth Rate'' (Albany: SUNY Press, 1976): 36–37, 54–55, 57. {{ISBN|978-0-87395-354-2}}; Demar Irvine, Reinhard G. Pauly, Mark A. Radice, ''Irvine’s Writing about Music'', third edition (Portland, Oregon: Amadeus Press, 1999): 209–210. {{ISBN|978-1-57467-049-3}}.</ref> '''metre signature''',<ref>[[Henry Cowell]] and David Nicholls, ''New Musical Resources'', third edition (Cambridge and New York: [[Cambridge University Press]], 1996): 63. {{ISBN|978-0-521-49651-3}} (cloth); {{ISBN|978-0-521-49974-3}} (pbk); Cynthia M. Gessele, "Thiéme, Frédéric [Thieme, Friedrich]", ''The New Grove Dictionary of Music and Musicians'', second edition, edited by [[Stanley Sadie]] and [[John Tyrrell (musicologist)|John Tyrrell]] (London: Macmillan Publishers, 2001); James L. Zychowicz, ''Mahler's Fourth Symphony'' (Oxford and New York: Oxford University Press, 2005): 82–83, 107. {{ISBN|978-0-19-518165-4}}.</ref>  and '''measure signature''')<ref>Edwin Gordon, ''Rhythm: Contrasting the Implications of Audiation and Notation'' (Chicago: GIA Publications, 2000): 111. {{ISBN|978-1-57999-098-5}}.</ref> is an indication in [[musical notation|music notation]] that specifies how many [[note value]]s of a particular type fit into each measure ([[bar (music)|bar]]). The time signature indicates the [[Metre (music)|meter]] of a musical movement at the bar level.

In a music score the time signature appears as two stacked numerals, such as {{music|time|4|4}} (spoken as ''four–four time''), or a time symbol, such as {{music|common-time}} (spoken as ''common time''). It immediately follows the [[key signature]] (or if there is no key signature, the [[clef]] symbol). A mid-score time signature, usually immediately following a [[barline]], indicates a change of [[meter (music)|meter]].

Most time signatures are either '''simple''' (the note values are grouped in pairs, like {{music|time|2|4}}, {{music|time|3|4}}, and {{music|time|4|4}}), or '''compound''' (grouped in threes, like {{music|time|6|8}}, {{music|time|9|8}}, and {{music|time|12|8}}). Less common signatures indicate [[#Complex time signatures|complex]], [[#Mixed meters|mixed]], [[#Additive meters|additive]], and [[#Irrational meters|irrational meters]].

{{TOC limit|3}}

{{Image frame
|width=310
|align=right
|content=
<score> 
{ 
   \override Score.SpacingSpanner.strict-note-spacing = ##t
    \set Score.proportionalNotationDuration = #(ly:make-moment 1/1)
   \key c \major 
   \relative c' { 
      \numericTimeSignature \time 4/4 s1
      \defaultTimeSignature \time 4/4 s1
      \numericTimeSignature \time 2/2 s1
      \defaultTimeSignature \time 2/2 s1
      \time 2/4 s2
      \time 3/4 s2.
      \time 6/8 s2.
} }
</score>
|caption=Basic time signatures: {{music|time|4|4}}, also known as ''common time'' {{nowrap|({{music|common-time}})}}; {{music|time|2|2}}, ''[[alla breve]]'', also known as ''cut time'' or ''cut-common time'' ({{music|alla-breve}}); {{music|time|2|4}}; {{music|time|3|4}}; and {{music|time|6|8}}
|alt=
}}

== Time signature notation ==
Most time signatures consist of two numerals, one stacked above the other:
<!-- Note to editors:
 We deliberately describe the lower numeral first and the upper numeral later,
 as this is clearer.  Please don't change it unless you can make it even clearer.
-->
* The ''lower'' numeral indicates the note value that the signature is counting.  This number is always a [[Power of two|power of 2]] (unless the time signature is [[Time signature#Irrational meters|irrational]]), usually 2, 4 or 8, but less often 16 is also used, usually in Baroque music. 2 corresponds to the half note (minim), 4 to the quarter note (crotchet), 8 to the eighth note (quaver), 16 to the sixteenth note (semiquaver).
* The ''upper'' numeral indicates how many such note values constitute a [[bar (music)|bar]].
For instance, {{music|time|2|4}} means two [[quarter-note]]s (crotchets) per bar, while {{music|time|4|8}} means four [[eighth-note]]s (quavers) per bar. The most common time signatures are {{music|time|2|4}}, {{music|time|3|4}}, and {{music|time|4|4}}.

=== Symbolic signatures ===
{{anchor|common time}}<!--[[Common-time]] and [[Common time]] redirect directly here.-->

{{redirect|Common time|the short story|Common Time|the Field Music album|Commontime (album){{!}}''Commontime'' (album)|the time period|Common Era}}

By convention, two special symbols are sometimes used for {{music|time|4|4}} and {{music|time|2|2}}:
* The symbol {{music|common-time}} is sometimes used for {{music|time|4|4}} time, also called ''common time'' or ''imperfect time''. 
* The symbol {{music|cut-time}} is sometimes used in place of {{music|time|2|2}} and is called ''[[alla breve]]'' or, colloquially, ''cut time'' or ''cut common time''. 
These symbols derive from [[Time signature#Mensural time signatures|mensural time signatures]], described below.

== Frequently used time signatures ==

=== Simple versus compound ===
Simple meters are those whose upper number is 2, 3, or 4, sometimes described as '''duple meter''', '''triple meter''', and '''quadruple meter''' respectively.

In [[Compound meter (music)|compound meter]], the note values specified by the bottom number are grouped into threes, and the upper number is a multiple of 3, such as 6, 9, or 12. The lower number is most commonly an 8 (an eighth-note or quaver): as in {{music|time|9|8}} or {{music|time|12|8}}.

Other upper numbers correspond to '''irregular meters'''.

=== Beat and subdivision ===
{{Main|Beat (music)}}
Musical passages commonly feature a recurring pulse, or '''beat''', usually in the range of 60–140 beats per minute. Depending on the tempo of the music, this beat may correspond to the note value specified by the time signature, or to a grouping of such note values. Most commonly, in simple time signatures, the beat is the same as the note value of the signature, but in compound signatures, the beat is usually a [[dotted note]] value corresponding to three of the signature's note values. Either way, the next lower note value shorter than the beat is called the '''subdivision'''.

On occasion a bar may seem like one singular beat. For example, a fast waltz, notated in {{music|time|3|4}} time, may be described as being ''one in a bar''. Conversely, at slow tempos, the beat might even be a smaller note value than the one enumerated by the time signature. {{example needed|date=April 2024}}

Mathematically the time signatures of, e.g., {{music|time|3|4}} and {{music|time|3|8}} are interchangeable. In a sense ''all'' simple triple time signatures, such as {{music|time|3|8}}, {{music|time|3|4}}, {{music|time|3|2}}, etc.—and all compound duple times, such as {{music|time|6|8}}, {{music|time|6|16}} and so on, are equivalent. A piece in {{music|time|3|4}} can be easily rewritten in {{music|time|3|8}}, simply by halving the length of the notes.

:<score>
    \new Staff <<
       \new voice \relative c' {
           \clef percussion
           \time 3/4
           \tempo 4 = 100       
           \stemDown \repeat volta 2 { g4 d' d }
           \time 3/8
           \tempo 8 = 100       
           \stemDown \repeat volta 2 { g,8 d' d }
       }
       \new voice \relative c'' {
           \override NoteHead.style = #'cross
           \stemUp \repeat volta 2 { a8[ a] a[ a] a[ a] }
           \stemUp \repeat volta 2 { a16 a a a a a }
       }
   >>
</score>
[[File:3-4 equals 3-8 drum pattern.mid]]

Other time signature rewritings are possible: most commonly a simple time-signature with triplets translates into a compound meter.

:<score>
    \new Staff <<
       \new voice \relative c' {
           \clef percussion
           \time 12/8
           \tempo 4. = 66       
           \stemDown \repeat volta 2 { g4. d' g, d' }
           \numericTimeSignature
           \time 4/4
           \tempo 4 = 66       
           \stemDown \repeat volta 2 { g,4 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 }
           \stemUp \repeat volta 2 { \tuplet 3/2 { a8 a a } \tuplet 3/2 { a8 a a } \tuplet 3/2 { a8 a a } \tuplet 3/2 { a8 a a } }
       }
   >>
</score>

[[File:12-8 equals 4-4 drum pattern.mid]]
{{Clear}}
The choice of time signature in these cases is largely a matter of tradition. Particular time signatures are traditionally associated with different music styles—it would seem strange to notate a conventional [[Rock music|rock]] song in {{music|time|4|8}} or {{music|time|4|2}}, rather than {{music|time|4|4}}.

=== Examples ===
In the examples below, '''bold''' denotes the primary stress of the measure, and ''italics'' denote a secondary stress. Syllables such as "and" are frequently used for pulsing in between numbers.

''Simple'': {{music|time|3|4}} is a simple [[triple meter]] time signature that represents three quarter notes (crotchets), usually perceived as three beats. In this case the subdivision would be the eighth note (quaver). It is felt as
::<big>{{music|time|3|4}}</big>: '''one''' and ''two'' and ''three'' and ...

''Compound'': Most often, <big>{{music|time|6|8}}</big> is felt as two beats, each being a dotted quarter note (crotchet), and each containing subdivisions of three eighth notes (quavers). It is felt as
::<big>{{music|time|6|8}}</big>: '''one''' two three ''four'' five six ...
The table below shows the characteristics of the most frequently used time signatures.
{| class="wikitable"
|-
! colspan="4" style="background: Silver" | Simple time signatures
|-
! Time signature
! Common uses
! Simple drum pattern
!Video representation
|-
| align="center" | <big>{{music|time|4|4}}</big> or {{music|common-time}}
(quadruple)
|| ''Common time'': Widely used in [[classical music]] and most forms of [[popular music]]. Most common time signature in [[Rock music|rock]], [[blues]], [[country music|country]], [[funk]], and [[Pop music|pop]].<ref>Scott Schroedl, ''Play Drums Today! A Complete Guide to the Basics: Level One '' (Milwaukee: Hal Leonard Corporation, 2001), p. 42. {{ISBN|978-0-634-02185-5}}.</ref>
||<score>
    \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>[[File:Characteristic rock drum pattern.mid]]
|[[File:Video_for_4o4_at_60_bpm.ogv|frameless|140x105px]]
|-
| align="center" | <big>{{music|time|2|2}}</big> or {{music|cut-time}}
(duple)
|| ''[[Alla breve]]'', ''cut time'': Used for [[march (music)|march]]es and fast orchestral music.
||<score>
    \new Staff <<
       \new voice \relative c' {
           \clef percussion
           \numericTimeSignature
           \time 2/2
           \set Score.tempoHideNote = ##t \tempo 2 = 100
           \stemDown \repeat volta 2 { g2 d' }
       }
       \new voice \relative c'' {
           \override NoteHead.style = #'cross
           \stemUp \repeat volta 2 { a4 a a a }
       }
   >></score>[[File:Half time rock pattern.mid]]
|
|-
| align="center" |<big>{{music|time|2|4}}</big>
(duple)
|| Used for [[polka]]s, [[galop]]s, [[March (music)|marches]], and many styles of [[Latin music]] (including [[bolero]], [[cumbia]], and [[Merengue music|merengue]]).
||<score>
    \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>[[File:Simple duple drum pattern.mid]]
|[[File:Video for 2o4 at 60 bpm.ogv|frameless|140x105px]]
|-
| align="center" | <big>{{music|time|3|4}}</big>
(triple)
|| {{anchor|Waltz}}<!-- [[Waltz time]] redirects here --> Used for [[waltz (music)|waltz]]es, [[minuet]]s, [[scherzo|scherzi]], [[polonaise (dance)|polonaise]]s, [[mazurka]]s, country & western ballads, R&B, and some pop
||<score>
    \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>[[File:Simple triple drum pattern.mid]]
|[[File:Video for 3o4 at 60 bpm.ogv|frameless|140x105px]]
|-
| align="center" | <big>{{music|time|3|8}}</big>
(triple)
|| Also used for the above but usually suggests higher tempo or shorter [[Metre (music)#Hypermetre|hypermeter]]. Sometimes preferred for certain folk dances such as [[cachucha]]
||<score lang="lilypond">
    \new Staff <<
       \new voice \relative c' {
           \clef percussion
           \numericTimeSignature
           \time 3/8
           \set Score.tempoHideNote = ##t \tempo 4. = 80
           \stemDown \repeat volta 2 { g8 d' d }
       }
       \new voice \relative c'' {
           \override NoteHead.style = #'cross
           \stemUp \repeat volta 2 { a16[ a] a[ a] a[ a] }
       }
   >></score>[[File:Simple triple drum pattern.mid]]
|
|-
! colspan="4" style="background: Silver" | Compound time signatures
|-
! Time signature
! Common uses
! Simple drum pattern
! Video representation
|-
| align="center" | <big>{{music|time|6|8}}</big>
(duple)
|| Double [[jig]]s, [[Jota (music)|jotas]], [[zortziko]]s, polkas,<!--Polka is also claimed under 2/4 time. RESPONSE: polkas can use either 2/4 or 6/8, depending on the subdivision of the beats (since both are duple time signatures)--> [[sega music|sega]], [[salegy]], [[tarantella]], [[March (music)|marches]], [[barcarolle]]s, [[loure]]s, and some rock music. [[Anapestic tetrameter]] poetry also fits into {{music|time|6|8}} time when said aloud.
||<score>    \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>[[File:Compound duple drum pattern.mid]]
|[[File:Video of 6o8 at 90 bpm.ogv|frameless|140x105px]]
|-
| align="center" | <big>{{music|time|9|8}}</big>
(triple)
|| ''Compound triple time'': Used in [[slip jig]]s; otherwise occurring rarely ("[[The Ride of the Valkyries]]", [[Pyotr Ilyich Tchaikovsky|Tchaikovsky]]'s [[Symphony No. 4 (Tchaikovsky)|Fourth Symphony]], and the final movement of [[Johann Sebastian Bach|J.S. Bach]]'s [[Violin Concerto in A minor (Bach)|Violin Concerto in A minor (BWV 1041)]] are familiar examples. [[Claude Debussy|Debussy]]'s "[[Clair de lune (Debussy)|Clair de lune]]" and the opening bars of ''[[Prélude à l'après-midi d'un faune]]'' are also in <big>{{music|time|9|8}})</big>
||<score>    \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>[[File:Compound triple drum pattern.mid]]
|[[File:Video for 9o8 at 90 bpm.ogv|frameless|140x105px]]
|-
| align="center" | <big>{{music|time|12|8}}</big>
(quadruple)
|| Also common in slower [[blues]] (where it is called a ''[[shuffle note|shuffle]]'') and [[doo-wop]]; also used more recently in rock music. Can also be heard in some jigs like "[[The Irish Washerwoman]]". This is also the time signature of ''Scene by the Brook'', the second movement of [[Ludwig van Beethoven|Beethoven]]'s ''[[Symphony No. 6 (Beethoven)|Pastoral Symphony]]''.
||<score>    \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>[[File:Compound quadruple drum pattern.mid]]
|[[File:Video for 12o8 at 90 bpm.ogv|frameless|140x105px]]
|}

=== Tempo giusto ===
{{main|Tempo giusto}}
While changing the bottom number and keeping the top number fixed only formally changes notation, without changing meaning – {{music|time|3|8}}, {{music|time|3|4}}, {{music|time|3|2}}, and {{music|time|3|1}} are all three beats to a meter, just noted with eighth notes, quarter notes, half notes, or whole notes – these conventionally imply different performance and different tempi. Conventionally, larger numbers in the bottom correspond to faster tempi and smaller numbers correspond to slower tempi. This convention is known as ''[[tempo giusto]]'', and means that the tempo of each note remains in a narrower, "normal" range. For illustration, a quarter note might correspond to 60–120 bpm (quintuplet 75–150, triplet 90–180 and septuplet 105–210), a half note to 30–60 bpm (triplet 45–90), a whole note to 15–30 bpm, and an eighth note to 120–240 bpm; these are not strict, but show an example of "normal" ranges.

This convention dates to the [[Baroque music|Baroque]] era, when tempo changes were indicated by changing time signature during the piece, rather than by using a single time signature and changing tempo marking.<ref>{{cite book |last=Dokter |first=Julia |title=Tempo and Tactus in the German Baroque |publisher=University of Rochester Press |year=2021 |isbn=978-1-64825-018-7 |page=[https://books.google.com/books?id=9EE3EAAAQBAJ&pg=PA144 144]}}</ref>

== Complex time signatures ==<!--[[Usual time signature]] and [[unusual time signature]] both redirect directly here.-->
{{See also|List of musical works in unusual time signatures|Quintuple meter|Septuple meter}}
{{Redirect|13/8|the date|August 13}}
{{Listen|filename=19-16 Time Drum Beat.ogg|title={{music|time|19|16}} Time Drum Beat|format=[[Ogg]]}}Signatures that do not fit the usual simple or compound categories are called ''complex'', ''asymmetric'', ''irregular'', ''unusual'', or ''odd''—though these are broad terms, and usually a more specific description is any meter which combines both simple and compound beats.<ref>{{Cite web |title=musictheory.net |url=https://www.musictheory.net/lessons/16#:~:text=8/8%20time%20contains%20two,since%20both%20have%208%20quavers. |access-date=2023-08-02 |website=www.musictheory.net}}</ref><ref>{{Cite web|title=Odd Time Signatures: A Complete Guide {{!}} Hello Music Theory|url=https://hellomusictheory.com/learn/odd-time-signatures/|access-date=2022-02-20|website=hellomusictheory.com/| date=6 March 2020 |language=en-GB}}</ref>

Irregular meters are common in some non-Western music, and in ancient Greek music such as the [[Delphic Hymns]] to Apollo, but the corresponding time signatures rarely appeared in formal written Western music until the 19th century. Early anomalous examples appeared in Spain between 1516 and 1520,<ref name="Emmons">Tim Emmons, ''Odd Meter Bass: Playing Odd Time Signatures Made Easy'' (Van Nuys: Alfred Publishing, 2008): 4. {{ISBN|978-0-7390-4081-2}}. "What is an 'odd meter'?...A complete definition would begin with the idea of music organized in repeating rhythmic groups of three, five, seven, nine, eleven, thirteen, fifteen, etc."</ref> plus a small section in Handel's opera [[Orlando (opera)|Orlando]] (1733).

The third movement of [[Frédéric Chopin]]'s [[Piano Sonata No. 1 (Chopin)|Piano Sonata No. 1]] (1828) is an early, but by no means the earliest, example of {{music|time|5|4}} time in solo piano music. [[Anton Reicha]]'s Fugue No. 20 from his ''[[36 Fugues (Reicha)|Thirty-six Fugues]]'', published in 1803, is also for piano and is in {{music|time|5|8}}. The [[waltz]]-like second movement of Tchaikovsky's [[Symphony No. 6 (Tchaikovsky)|''Pathétique'' Symphony]] (shown below), often described as a "limping waltz",<ref>{{cite web|url=http://www.classicalnotes.net/classics/pathetique.html |title=Tchaikovsky's Symphony No. 6 (''Pathetique''), Classical Classics, Peter Gutmann |publisher=Classical Notes |access-date=2012-04-20}}</ref> is a notable example of {{music|time|5|4}} time in orchestral music.

: <score sound="1">
    \relative c {
        \set Score.tempoHideNote = ##t \tempo 4 = 144
        \set Staff.midiInstrument = #"cello"
        \clef bass
        \key d \major
        \time 5/4
        fis4\mf(^\markup { \bold { Allegro con grazia } }
        g) \tuplet 3/2 { a8(\< g a } b4 cis)\!
        d( b) cis2.\>
        a4(\mf b) \tuplet 3/2 { cis8(\< b cis } d4 e)\!
        \clef tenor
        fis(\f d) e2. \break
        g4( fis) \tuplet 3/2 { e8( fis e } d4 cis)
        fis8-. [ r16 g( ] fis8) [ r16 eis( ] fis2.)
        fis4( e) \tuplet 3/2 { d8( e d } cis4) b\upbow(\<^\markup { \italic gliss. }
        b'8)\ff\> [a( g) fis-. ] e-. [ es-.( d-. cis-. b-. bes-.) ]
        a4\mf
}
</score>

Examples from [[20th-century classical music]] include:
* [[Gustav Holst]]'s "Mars, the Bringer of War" and "Neptune, the Mystic" from ''[[The Planets]]'' (both in {{music|time|5|4}})
* [[Paul Hindemith]]'s "Fuga secunda" in G from ''[[Ludus Tonalis]]'' ({{music|time|5|8}})
* the ending of [[Igor Stravinsky|Stravinsky's]] ''[[The Firebird]]'' ({{music|time|7|4}})
* the fugue from [[Heitor Villa-Lobos]]'s ''[[Bachianas Brasileiras#Bachianas Brasileiras No. 9|Bachianas Brasileiras No. 9]]'' ({{music|time|11|8}})
* the themes for the ''[[Mission: Impossible (1966 TV series)|Mission: Impossible]]'' television series by [[Lalo Schifrin]] (in {{music|time|5|4}}) and for ''[[Room 222]]'' by [[Jerry Goldsmith]] (in {{music|time|7|4}})<!--
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In the Western popular music tradition, unusual time signatures occur as well, with [[progressive rock]] in particular making frequent use of them. The use of shifting meters in [[The Beatles]]' "[[Strawberry Fields Forever]]" and the use of [[quintuple meter]] in their "[[Within You, Without You]]" are well-known examples,<ref name="Macan">Edward Macan, ''Rocking the Classics: English Progressive Rock and the Counterculture'' (New York: Oxford University Press, 1997): 48. {{ISBN|978-0-19-509888-4}}.</ref> as is [[Radiohead]]'s "[[Paranoid Android]]" (includes {{music|time|7|8}}).<ref>Radiohead (musical group). ''OK Computer'', vocal score with guitar accompaniment and tablature (Essex, England: IMP International Music Publications; Miami, Florida: Warner Bros. Publications; Van Nuys, California: Alfred Music, 1997): {{Page needed|date=March 2011}}. {{ISBN|978-0-7579-9166-0}}.</ref>
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 DO NOT ADD MORE EXAMPLES!
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[[Paul Desmond]]'s [[jazz]] composition "[[Take Five]]", in {{music|time|5|4}} time, was one of a number of irregular-meter compositions that [[The Dave Brubeck Quartet]] played. They played other compositions in {{music|time|11|4}} ("Eleven Four"), {{music|time|7|4}} ("[[Unsquare Dance]]"), and {{music|time|9|8}} ("[[Blue Rondo à la Turk]]"), expressed as {{music|time|2+2+2+3|8}}. "Blue Rondo à la Turk" is an example of a signature that, despite appearing merely compound triple, is actually more complex. Brubeck's title refers to the characteristic ''[[aksak]]'' meter of the Turkish ''[[karşılama]]'' dance.<ref>{{cite book|last1=Manuel|first1=Peter|title=Popular Musics of the Non-Western World: An Introductory Survey|date=1988|publisher=Oxford University Press|isbn=978-0-19-506334-9|page=[https://archive.org/details/popularmusicsofn0000manu/page/131 131]|edition=rev.|url=https://archive.org/details/popularmusicsofn0000manu|url-access=registration}}</ref>

However, such time signatures are only unusual in most Western music. Traditional [[music of the Balkans]] uses such meters extensively. [[Bulgarian dances]], for example, include forms with 5, 7, 9, 11, 13, 15, 22, 25 and other numbers of beats per measure. These rhythms are notated as ''[[additive rhythm]]s'' based on simple units, usually 2, 3 and 4 beats, though the notation fails to describe the [[meter (music)|metric]] "time bending" taking place, or [[compound meter (music)|compound meters]]. See [[#Additive meters|Additive meters]] below.

'''Some video samples are shown below.'''
{| class="wikitable"
|[[File:Video-of-5o4-at-60-bpm.ogv|thumb|none|{{music|time|5|4}} at 60 [[BPM (music)|bpm]]]]
|[[File:Video-for-7o4.theora.ogv|thumb|{{music|time|7|4}} at 60 bpm]]
|[[File:Video-of-11o4-at-60-bpm.ogv|thumb|none|{{music|time|11|4}} at 60 bpm]]
|}

==Mixed meters==
While time signatures usually express a regular pattern of beat stresses continuing through a piece (or at least a section), sometimes composers change time signatures often enough to result in music with an extremely irregular rhythm. The time signature may switch so much that a piece may not be best described as being in one meter, but rather as having a switching mixed meter. In this case, the time signatures are an aid to the performers and not ''necessarily'' an indication of meter. The Promenade from [[Modest Mussorgsky]]'s ''[[Pictures at an Exhibition]]'' (1874) is a good example. The opening measures are shown below:

:<score sound="1">
    { \new PianoStaff <<
        \new Staff <<
            \new voice \relative c'' {
                \set Score.tempoHideNote = ##t \tempo 4 = 112
                \clef treble \key bes \major 
				\time 5/4 
                	g4--_\f^\markup { \bold {Allegro giusto, nel modo russico; senza allegrezza, ma poco sostenuto. } } f-- bes-- c8--( f d4--)
                \time 6/4
					c8--( f d4--) bes-- c-- g-- f--
				\time 5/4
					<bes, d g>4 <a c f> <bes d bes'> \stemDown <c a'> \stemNeutral <f a d>
				\time 6/4
					\stemDown <c a'> \stemNeutral <f bes d> <d g bes> <e g c> <g, c g'> <a c f>
				}
			\new Voice \relative c'' {
                \time 5/4
					s1 s4
				\time 6/4
					s1.
				\time 5/4
					s2. \stemUp c8^( f d4)
				\time 6/4
					\stemUp c8^( f d4) s1
                }
            >>
        \new Staff <<
			\clef bass \key bes \major 
            \relative c {
                \time 5/4
					R1*5/4
				\time 6/4
					R1*6/4
				\time 5/4
					<g g'>4 <a f'> <g g'> <f f'> <d d'>
                \time 6/4
					<f f'> <bes bes'> <g g'> <c, c'> <e e'> <f f'>
				}
            >>
    >> }
</score>

:

[[Igor Stravinsky]]'s ''[[The Rite of Spring]]'' (1913) is famous for its "savage" rhythms. Five measures from "Sacrificial Dance" are shown below:

:<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>

In such cases, a convention that some composers follow (e.g., [[Olivier Messiaen]], in his ''[[La Nativité du Seigneur]]'' and ''[[Quatuor pour la fin du temps]]'') is to simply omit the time signature. [[Charles Ives]]'s ''[[Concord Sonata]]'' has measure bars for select passages, but the majority of the work is unbarred.

Some pieces have no time signature, as there is no discernible meter. This is sometimes known as [[free time (music)|free time]]. Sometimes one is provided (usually {{music|time|4|4}}) so that the performer finds the piece easier to read, and simply has "free time" written as a direction. Sometimes the word ''FREE'' is written downwards on the staff to indicate the piece is in free time. [[Erik Satie]] wrote many compositions that are ostensibly in free time but actually follow an unstated and unchanging simple time signature. Later composers used this device more effectively, writing music almost devoid of a discernibly regular pulse.

If two time signatures alternate repeatedly, sometimes the two signatures are placed together at the beginning of the piece or section, as shown below:

:[[File:Tchaikovsky String Quartet in F excerpt.png|center|thumb|460px|Detail of a score of Tchaikovsky's [[String Quartet No. 2 (Tchaikovsky)|String Quartet No.&nbsp;2 in F major]], showing a multiple time signature]]

==Additive meters==
To indicate more complex patterns of stresses, such as [[additive rhythm]]s, more complex time signatures can be used. Additive meters have a pattern of [[Beat (music)|beats]] that subdivide into smaller, irregular groups. Such meters are sometimes called ''imperfect'', in contrast to ''perfect meters'', in which the [[Bar (music)|bar]] is first divided into equal units.<ref>{{cite book|first=Gardner|last=Read|title=Music Notation: A Manual of Modern Practice|location=Boston|publisher=Allyn and Bacon, Inc.|year=1969|isbn=978-0-8008-5453-9}}{{Page needed|date=December 2010}}</ref>

For example, the time signature {{music|time|3+2+3|8}} means that there are 8 quaver beats in the bar, divided as the first of a group of three eighth notes (quavers) that are stressed, then the first of a group of two, then first of a group of three again. The stress pattern is usually counted as

:: {{music|time|3+2+3|8}}: '''one''' two three ''one'' two ''one'' two three ...

This kind of time signature is commonly used to notate folk and non-Western types of music. In classical music, [[Béla Bartók]] and [[Olivier Messiaen]] have used such time signatures in their works. The first movement of [[Maurice Ravel]]'s [[Piano Trio (Ravel)|Piano Trio in A Minor]] is written in {{music|time|8|8}}, in which the beats are likewise subdivided into {{serif|'''3+2+3'''}} to reflect [[Basque music|Basque]] dance rhythms.

Romanian [[musicologist]] [[Constantin Brăiloiu]] had a special interest in compound time signatures, developed while studying the [[Traditional music of Romania|traditional music]] of certain regions in his country. While investigating the origins of such unusual meters, he learned that they were even more characteristic of the traditional music of neighboring peoples (e.g., the [[Bulgarian Folk Music|Bulgarians]]). He suggested that such timings can be regarded as compounds of simple two-beat and three-beat meters, where an accent falls on every first beat, even though, for example in [[Bulgarian dances|Bulgarian music]], beat lengths of 1, 2, 3, 4 are used in the metric description. In addition, when focused only on stressed beats, simple time signatures can count as beats in a slower, compound time. However, there are two different-length beats in this resulting compound time, a one half-again longer than the short beat (or conversely, the short beat is {{frac|2|3}} the value of the long). This type of meter is called ''[[aksak]]'' (the Turkish word for "limping"), ''impeded'', ''jolting'', or ''shaking'', and is described as an ''irregular bichronic rhythm''. A certain amount of confusion for Western musicians is inevitable, since a measure they would likely regard as {{music|time|7|16}}, for example, is a three-beat measure in ''aksak'', with one long and two short beats (with subdivisions of {{serif|'''2+2+3'''}}, {{serif|'''2+3+2'''}}, or {{serif|'''3+2+2'''}}).<ref>Constantin Brăiloiu, ''Le rythme Aksak'', ''Revue de Musicologie'' 33, nos. 99 and 100 (December 1951): 71–108. Citation on pp. 75–76.</ref>

Folk music may make use of metric time bends, so that the proportions of the performed metric beat time lengths differ from the exact proportions indicated by the metric. Depending on playing style of the same meter, the time bend can vary from non-existent to considerable; in the latter case, some musicologists may want to assign a different meter. For example, the Bulgarian tune "[[Bulgarian dances|Eleno Mome]]" is written in one of three forms: (1) {{serif|'''7 {{=}} 2+2+1+2'''}}, (2) {{serif|'''13 {{=}} 4+4+2+3'''}}, or (3) {{serif|'''12 {{=}} 3+4+2+3'''}}, but an actual performance (e.g., "Eleno Mome"<ref>[https://folkways.si.edu/eleno-mome/world/music/track/smithsonian Audio: "Eleno Mome"] from ''The Dances of the World's Peoples, Vol. 1: Dances of the Balkans and Near East'', Smithsonian Folk Ways</ref>{{original research inline|date=June 2020}}) may be closer to {{serif|'''4+4+2+3'''}}.{{clarify|date=June 2020|reason=What does this even mean, just after 13 = 4+4+2+3 has been mentioned as one of the forms in which the music is written?}} The Macedonian {{serif|'''[[Leventikos|3+2+2+3+2]]'''}} meter is even more complicated, with heavier time bends, and use of quadruples on the threes. The metric beat time proportions may vary with the speed that the tune is played. The Swedish [[Polska (dance)|Boda Polska]] (Polska from the parish Boda) has a typical elongated second beat.

In Western classical music, metric time bend is used in the performance of the [[Viennese waltz]]. Most Western music uses metric ratios of 2:1, 3:1, or 4:1 (two-, three- or four-beat time signatures)—in other words, integer ratios that make all beats equal in time length. So, relative to that, 3:2 and 4:3 ratios correspond to very distinctive metric rhythm profiles. Complex accentuation occurs in Western music, but as [[syncopation]] rather than as part of the metric accentuation.{{Citation needed|date=January 2010}}

Brăiloiu borrowed a term from [[Music of Turkey|Turkish]] medieval music theory: ''aksak''. Such compound time signatures fall under the "aksak rhythm" category that he introduced along with a couple more that should describe the rhythm figures in traditional music.<ref name="Oprea">Gheorghe Oprea, ''Folclorul muzical românesc'' (Bucharest: Ed. Muzicala, 2002), {{Page needed|date=January 2010}} {{ISBN|978-973-42-0304-8}}</ref> The term Brăiloiu revived had moderate success worldwide, but in Eastern Europe it is still frequently used. However, aksak rhythm figures occur not only in a few European countries, but on all continents, featuring various combinations of the two and three sequences. The longest are in Bulgaria. The shortest aksak rhythm figures follow the five-beat timing, comprising a two and a three (or three and two).

'''Some video samples are shown below.'''

{| class="wikitable"
| [[File:Video-for-time-signature-3+2+3.theora.ogv|thumb|320 px|none| {{music|time|3+2+3|8}} at 120 [[BPM (music)|bpm]]]]
| [[File:Blue-Rondo-à-La-Turk.theora.ogv|thumb|320 px|none| The rhythm of [[Dave Brubeck]]'s "[[Blue Rondo à la Turk]]": It consists of three measures of {{serif|'''2+2+2+3'''}} followed by one measure of {{serif|'''3+3+3'''}} and the cycle then repeats. Taking the smallest time unit as eighth notes, the arrows on the tempo dial show the tempi for ♪, ♩, ♩. and the measure beat. Starts slow, speeds up to usual tempo]]
|}
A method to create meters of lengths of any length has been published in the Journal of Anaphoria Music Theory<ref>{{Cite web|url=http://anaphoria.com/journal.html|title = The Journal of Anaphorian Music Theory}}</ref> and Xenharmonikon 16<ref>{{Cite web|url=http://frogpeak.org/fpartists/fpchalmers.html|title=Frog Peak Artist: John Chalmers}}</ref> using both those based on the Horograms of [[Erv Wilson]] and Viggo Brun's algorithm written by  [[Kraig Grady]].

== Irrational meters ==
<!-- This section is linked from [[Stereolab]] -->
{{Image frame
|width=386
|align=right
|content=
<score>
{
\time 4/3
\times 2/3 {c''2 d'' e'' f''}
\time 4/2
c'' d'' e'' f''
}
</score>
|caption=Example of an irrational {{music|time|4|3}} time signature: here there are four (4) third notes (3) per measure. A "third note" would be one third of a whole note, and thus is a triplet half-note. The second measure of {{music|time|4|2}} presents the same notes, so the {{music|time|4|3}} time signature serves to indicate the precise speed relationship between the notes in the two measures.
|alt=Printed music staff with treble-clef symbol. The first bar has a {{music|time|4|3}} time signature, and 4 triplet half-notes: treble C, D, E, and F. The second bar is in {{music|time|4|2}} and has 4 half notes: treble C, D, E, and F.
}}
Irrational time signatures (rarely, "non-dyadic time signatures") are used for so-called ''irrational bar lengths'',<ref name="Sospeso">[https://web.archive.org/web/20110721014850/http://www.sospeso.com/contents/articles/ferneyhough_p1.html "Brian Ferneyhough"], ''The Ensemble Sospeso''</ref> that have a [[denominator]] that is not a [[power of two]] (1, 2, 4, 8, 16, 32, etc.). These are based on beats expressed in terms of fractions of full beats in the prevailing tempo—for example {{music|time|3|10}} or {{music|time|6|7}}.<ref name="Sospeso"/> For example, where {{music|time|4|4}} implies a bar construction of four quarter-parts of a whole note (i.e., four quarter notes), {{music|time|4|3}} implies a bar construction of four third-parts of it. These signatures are of utility only when juxtaposed with other signatures with varying denominators; a piece written entirely in {{music|time|4|3}} could be more legibly written out in {{music|time|4|4}}.

{{Image frame
|width=386
|align=right
|content=
<score>
{
\time 4/2
c''2 d'' e'' f'' |
c''^\markup {
  \note {1.} #1
  =
  \note {1} #1
} d'' e'' f''
}
</score>
|caption=The same example written using metric modulation instead of irrational time signatures. Three half notes in the first measure (making up a dotted whole note) are equal in duration to two half notes in the second (making up a whole note).|alt=Printed music staff with treble-clef symbol. Each bar has a {{music|time|4|2}} time signature, and 4 half notes: treble C, D, E, and F.
}}
{{Image frame
|width=386
|align=right
|content=
<score>
{
\time 4/2
c''2 d'' e'' f'' |
\time 12/4
c''2. d'' e'' f''
}
</score>
|caption=The same example written using a change in time signature.|alt=Printed music staff with treble-clef symbol. The first bar has a {{music|time|4|2}} time signature, and 4 half notes: treble C, D, E, and F. The second bar has a {{music|time|12|4}} time signature, and 4 dotted half notes: treble C, D, E, and F.
}}
According to [[Brian Ferneyhough]], [[metric modulation]] is "a somewhat distant analogy" to his own use of "irrational time signatures" as a sort of rhythmic dissonance.<ref name="Sospeso"/> It is disputed whether the use of these signatures makes metric relationships clearer or more obscure to the musician; it is always possible to write a passage using non-irrational signatures by specifying a relationship between some note length in the previous bar and some other in the succeeding one. Sometimes, successive metric relationships between bars are so convoluted that the pure use of irrational signatures would quickly render the notation extremely hard to penetrate.

Historically, this device has been prefigured wherever composers wrote [[tuplet]]s. For example, a {{music|time|2|4}} bar of 3 triplet quarter notes could be written as a bar of {{music|time|3|6}}. [[Henry Cowell]]'s piano piece ''[[Fabric (Cowell)|Fabric]]'' (1920) employs separate divisions of the bar (1 to 9) for the three [[contrapuntal]] parts, using a scheme of shaped [[notehead]]s to visually clarify the differences, but the pioneering of these signatures is largely due to [[Brian Ferneyhough]], who says that he finds that "such 'irrational' measures serve as a useful buffer between local changes of event density and actual changes of base [[tempo]]".<ref name="Sospeso"/> [[Thomas Adès]] has also used them extensively—for example in ''[[Traced Overhead]]'' (1996), the second movement of which contains, among more conventional meters, bars in such signatures as {{music|time|2|6}} and {{music|time|9|14}}.

Notationally, rather than using Cowell's elaborate series of notehead shapes, the same convention has been invoked as when normal tuplets are written; for example, one beat in {{music|time|4|5}} is written as a normal quarter note, four quarter notes complete the bar, but the whole bar lasts only {{frac|4|5}} of a reference [[whole note]], and a beat {{frac|1|5}} of one (or {{frac|4|5}} of a normal quarter note). This is notated in exactly the same way that one would write if one were writing the first four quarter notes of five quintuplet quarter notes.

'''Some video samples are shown below.'''

These video samples show two time signatures combined to make a [[polymeter]], since {{music|time|4|3}}, in isolation, is identical to {{music|time|4|4}}.

{| class="wikitable"
|- valign="top"
| [[File:Polymeter-4o4c4o3.theora.ogv|thumb|center|Polymeter {{music|time|4|4}} and {{music|time|4|3}} played together has three beats of {{music|time|4|3}} to four beats of {{music|time|4|4}}]]
| [[File:Polymeter-2o6c3o4.theora.ogv|thumb|center|Polymeter {{music|time|2|6}} and {{music|time|3|4}} played together has six beats of {{music|time|2|6}} to four beats of {{music|time|3|4}}]]
| [[File:Polymeter-2o5c2o3.theora.ogv|thumb|center|Polymeter {{music|time|2|5}} and {{music|time|2|3}} played together has five beats of {{music|time|2|5}} to three beats of {{music|time|2|3}}. The displayed numbers count the underlying [[polyrhythm]], which is 5:3]]
|}

==Variants==
Some composers have used fractional beats: for example, the time signature {{music|time|{{frac|2|1|2}}|4}} (equivalent to {{music|time|5|8}}) appears in [[Carlos Chávez]]'s Piano Sonata No. 3 (1928) IV, m. 1. Both {{music|time|{{frac|2|1|2}}|4}} and {{music|time|{{frac|1|1|2}}|4}} appear in the fifth movement of [[Percy Grainger|Percy Grainger's]] [[Lincolnshire Posy]].

[[File:Orff time signatures.gif|frame|right|Example of Orff's time signatures (traditionally, these would be notated {{music|time|3|8}} and {{music|time|6|8}} respectively)]]
Music educator [[Carl Orff]] proposed replacing the lower number of the time signature with an actual note image, as shown at right. This system eliminates the need for compound time signatures, which are confusing to beginners. While this notation has not been adopted by music publishers generally (except in Orff's own compositions), it is used extensively in music education textbooks. Similarly, American composers [[George Crumb]] and [[Joseph Schwantner]], among others, have used this system in many of their works. [[Émile Jaques-Dalcroze]] proposed this in his 1920 collection, ''Le Rythme, la musique et l'éducation''.<ref>{{cite book|last=Jaques-Dalcroze|first=Émile|author-link=Émile Jaques-Dalcroze|title=Rhythm, Music and Education|translator=Harold F. Rubenstein|location=London|publisher=Dalcroze Society|year=1967|page=84, and Appendix, example 2}} – [https://archive.org/details/lerythmelamusiqu00jaqu/page/210/mode/2up Page 210] in the French original</ref>

Another possibility is to extend the barline where a time change is to take place above the top instrument's line in a score and to write the time signature there, and there only, saving the ink and effort that would have been spent writing it in each instrument's staff. [[Henryk Górecki]]'s ''Beatus Vir'' is an example of this. Alternatively, music in a large score sometimes has time signatures written as very long, thin numbers covering the whole height of the score rather than replicating it on each staff; this is an aid to the conductor, who can see signature changes more easily.

==Early music usage==

===Mensural time signatures===
{{Main|Mensural notation#Mensurations}}
In the [[mensural notation]] of the 14th, 15th and 16th centuries there are no [[bar (music)|bar]] lines, and the four basic ''mensuration signs'' [[Image:Mensural time signature 1 (alternative).svg|x13px]], [[Image:Mensural time signature 2 (alternative).svg|x13px]], [[Image:Mensural time signature 3 (alternative).svg|x13px]], [[Image:Mensural time signature 4 (alternative).svg|x13px]] indicate the normal ratio of [[duration (music)|duration]] between different [[note value]]s.  Unlike modern notation, the subdivisions could be either 2:1 or 3:1. The relation between the ''[[Breve (music)|breve]]'' [[File:White mensural brevis.svg|x20px]] and the ''[[semibreve]]'' [[File:White mensural semibrevis.svg|x20px]] was called '''tempus''', and could be perfect ([[meter (music)#Triple meter|triple]] 3:1 indicated by circle) or imperfect ([[meter (music)#Duple meter|duple]] 2:1, with broken circle), while the relation between the ''semibreve'' and the ''[[minim (music)|minim]]'' [[File:White mensural minim.svg|x20px]] was called '''prolatio''' and could be major (3:1 or [[meter (music)#Compound meter|compound]], indicated by dot) or minor (2:1 or [[meter (music)#Simple meter|simple meter]]).

Modern transcriptions often reduce note values 4:1, such that
* [[Image:Mensural time signature 1 (alternative).svg|13px]] corresponds to {{music|time|9|8}} meter;
* [[Image:Mensural time signature 2 (alternative).svg|13px]] corresponds to {{music|time|3|4}} meter;
* [[Image:Mensural time signature 3 (alternative).svg|12px]] corresponds to {{music|time|6|8}} meter;
* [[Image:Mensural time signature 4 (alternative).svg|12px]] corresponds to {{music|time|2|4}} meter.

In mensural notation actual note values depend not only on the prevailing mensuration, but on rules for [[Mensural notation#imperfection and alteration|imperfection and alteration]], with ambiguous cases using a dot of separation, similar in appearance but not always in effect to the modern [[Dotted note|dot of augmentation]].

===Proportions===
{{Main|Mensural notation#Proportions and colorations}}
{|class="wikitable skin-invert-image" style="float:right;clear:right;"
|+Proportion signs{{sfn|Apel|1953|p=150}}
!scope="column"|Proportion
!scope="column" |Notated values
!scope="column"|equivalent to
!scope="column"|Notated values
|-
|[[File:Tempus impf prol min.svg|x30px|Semicircle without dot]] '''2''' or [[Image:Allabreve.svg|12px]]
|[[File:White mensural brevis.svg|x30px]] <br> [[File:White mensural semibrevis.svg|x30px]][[File:White mensural semibrevis.svg|x30px]]
|[[File:Tempus impf prol min.svg|x30px|Semicircle without dot]]
|[[File:White mensural semibrevis.svg|x30px]] <br>  [[File:White mensural minim.svg|x30px]] [[File:White mensural minim.svg|x30px]]
|-
|[[File:Tempus perf prol min.svg|x30px|Circle without dot]] '''2''' or  [[Image:mensural proportion 2.svg|13px]]
|[[File:White mensural brevis.svg|x30px]][[File:White mensural brevis.svg|x30px]][[File:White mensural brevis.svg|x30px]]<br>[[File:Two semibreves.svg|x30px|alt=two semibreves]][[File:Two semibreves.svg|x30px|alt=two semibreves]][[File:Two semibreves.svg|x30px|alt=two semibreves]]
|[[File:Tempus perf prol min.svg|x30px|Circle without dot]]
|[[File:Three semibreves.svg|x30px|alt=three semibreves]]<br>[[File:3x2 minims.svg|x30px|alt=three groups of two minims]]
|-
|[[File:Tempus impf prol min.svg|x30px|Semicircle without dot]] '''3'''
|[[File:White mensural brevis.svg|x30px]][[File:White mensural brevis.svg|x30px]]<br>[[File:Three semibreves.svg|x30px|alt=three semibreves]] [[File:Three semibreves.svg|x30px|alt=three semibreves]] 
|[[File:Tempus impf prol mai.svg|x30px|Semicircle with dot]]
|[[File:Two semibreves.svg|x30px|alt=two semibreves]]<br>[[File:2x3 minims.svg|x30px|alt=two groups of three minims]]
|-
|[[File:Tempus perf prol min.svg|x30px|Circle without dot]] '''3'''
|[[File:White mensural brevis.svg|x30px]][[File:White mensural brevis.svg|x30px]][[File:White mensural brevis.svg|x30px]] <br>[[File:Three semibreves.svg|x30px|alt=three semibreves]] [[File:Three semibreves.svg|x30px|alt=three semibreves]] [[File:Three semibreves.svg|x30px|alt=three semibreves]]
|[[File:Tempus perf prol mai.svg|x30px|alt=Circle with dot]]
|[[File:White mensural semibrevis.svg|x30px]][[File:White mensural semibrevis.svg|x30px]][[File:White mensural semibrevis.svg|x30px]] <br>[[File:3x3 minims.svg|x30px|alt=three groups of three minims]]
|}

Besides showing the organization of beats with [[musical meter]], the mensuration signs discussed above have a second function, which is showing tempo relationships between one section to another, which modern notation can only specify with [[tuplet]]s or  [[metric modulation]]s. This is a fraught subject, because the usage has varied with both time and place: [[Charles Hamm]]<ref>C. Hamm: ''A Chronology of the Works of Guillaume Dufay based on a Study of Mensural Practice'' (Princeton, New Jersey, 1964)</ref> was even able to establish a rough chronology of works based on three distinct usages of mensural signs over the career of  [[Guillaume Dufay]] (1397(?) – 1474). By the end of the sixteenth century [[Thomas Morley]] was able to satirize the confusion in an imagined dialogue:
<blockquote>it was a world to hear them wrangle, every one defending his own for the best. "What? <!-- … -->You keep not time in your proportions." "You sing them false. <!-- … -->What proportion is this?" "Sesquipaltry." <!-- … -->"Nay,<!-- … --> you sing you know not what; it would seem you came lately from a barber's shop where you had 'Gregory Walker' or a [[Courante|Curranta]] played in the new Proportions by them lately found out, called 'Sesquiblinda' and 'Sesquihearkenafter'."

::<small>''Plaine and Easie Introduction to Practicall Musicke'' (1597)<ref>[[Thomas Morley]]: ''Plaine and Easie Introduction to Practicall Musicke'' (1597), quoted in the unsigned "Proportions" in [[New Grove]] XV p. 307 (1980)</ref></small>
</blockquote>
In general though, a slash or the numeral 2 shows a doubling of tempo, and paired numbers (either side by side or one atop another) show ratios instead of beats per measure over note value: in early music contexts {{music|time|4|3}} for example is unrelated to 'third-notes'.{{sfn|Apel|1953|p=189}}

A few common signs are shown:{{sfn|Apel|1953|p=148}}
* [[Image:Allabreve.svg|12px]] ''tempus imperfectum diminutum'', 1:2 proportion (twice as fast);
* [[Image:mensural proportion 2.svg|13px]] ''tempus perfectum diminutum'', 1:2 proportion (twice as fast);
* [[Image:mensural proportion 5.svg|22px]] or [[Image:mensural proportion 4.svg|10px]] ''proportio tripla'', 1:3 proportion (three times as fast, similar to triplets).

In particular, when the sign [[Image:Allabreve.svg|11px]] was encountered, the [[Pulse (music)|tactus]] (beat) changed from the usual whole note (semibreve) to the double whole note (breve), a circumstance called ''[[alla breve]]''. This term has been sustained to the present day, and though now it means the beat is a [[minim (music)|half note]] (minim), in contradiction to the literal meaning of the phrase, it still indicates that the ''tactus'' has changed from a short to a doubled value.

Certain composers delighted in creating mensuration canons, "[[Puzzle canon|puzzle]]" compositions that were intentionally difficult to decipher.<ref>Ernst Friedrich Richter, ''[https://books.google.com/books?id=HNOwAAAAIAAJ A Treatise on Canon and Fugue: Including the Study of Imitation]'', translated from third German edition by  Arthur W. Foote (Boston: Oliver Ditson, 1888): 38. {{pre ISBN}}.</ref>

== Irregular bar ==
{{anchor|Irregular Bar}}
Irregular bars are a change in time signature normally for only one bar. Such a bar is most often a bar of [[Triple metre|{{music|time|3|4}}]], [[Quintuple meter|{{music|time|5|4}}]] or [[Duple meter|{{music|time|2|4}}]] in a {{music|time|4|4}} composition, or a bar of {{music|time|4|4}} in a {{music|time|3|4}} composition, or a bar of {{music|time|5|8}} in a {{music|time|6|8}} composition.

If a song is entirely in {{music|time|4|4}}, a change to {{music|time|3|4}} will make the song feel like it has skipped a beat. The opposite is true for {{music|time|5|4}}, where it feels like the song adds a beat. If a song changes to {{music|time|2|4}} is will make it feel like that bar is half as long as all the others.<ref>{{Citation |title=Songs That Skip a Beat | date=7 August 2019 |url=https://www.youtube.com/watch?v=N6Wtvs42Ne8 |language=en |access-date=2022-09-22}}</ref><ref>{{Citation |title=Songs That Add a Beat | date=8 July 2019 |url=https://www.youtube.com/watch?v=qTdCzot0fqk |language=en |access-date=2022-09-22}}</ref>

Some popular examples include "[[Golden Brown]]" by [[The Stranglers]] ({{music|time|4|4}} in a {{music|time|3|4}} composition), "[[I Love Rock 'n' Roll]]" originally by [[Arrows (British band)|The Arrows]] ({{music|time|7|4}} in a {{music|time|4|4}} composition), "[[Hey Ya!]]" by [[Outkast]] ({{music|time|2|4}} in a {{music|time|4|4}} composition), and "[[Wuthering Heights (song)|Wuthering Heights]]" by [[Kate Bush]] (different kinds of irregular bars in a {{music|time|4|4}} composition).

==See also==
*[[Schaffel]], a kind of swing in rock and techno music
*[[Tala (music)|Tala]], meter in Indian music
*[[Colotomy]], a coinage by Jap Kunst to describe the metric structure of gamelan music.

==References==
{{Reflist}}

===Sources===
*{{cite book|last=Apel|first=Willi|author-link=Willi Apel|title=The Notation of Polyphonic Music 900–1600|edition=fifth, revised and with commentary|series=The Medieval Academy of America Publication No. 38|location=Cambridge, Massachusetts|publisher=[[Medieval Academy of America]]|year=1953|isbn=978-0-910956-15-4}}

{{Rhythm and meter}}
{{Musical notation}}

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