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A time signature (also known as meter signature, metre signature, and measure signature) is an indication in
music notation Musical notation is any system used to visually represent music. Systems of notation generally represent the elements of a piece of music that are considered important for its performance in the context of a given musical tradition. The proces ...
that specifies how many
note value In music notation, a note value indicates the relative duration (music), duration of a note (music), note, using the texture or shape of the ''notehead'', the presence or absence of a ''stem (music), stem'', and the presence or absence of ''flags ...
s of a particular type fit into each measure (
bar Bar or BAR may refer to: Food and drink * Bar (establishment), selling alcoholic beverages * Candy bar ** Chocolate bar * Protein bar Science and technology * Bar (river morphology), a deposit of sediment * Bar (tropical cyclone), a laye ...
). The time signature indicates the
meter The metre (or meter in US spelling; symbol: m) is the base unit of length in the International System of Units (SI). Since 2019, the metre has been defined as the length of the path travelled by light in vacuum during a time interval of of ...
of a musical movement at the bar level. In a music score the time signature appears as two stacked numerals, such as (spoken as ''four–four time''), or a time symbol, such as (spoken as ''common time''). It immediately follows the
key signature In Western musical notation, a key signature is a set of sharp (), flat (), or rarely, natural () symbols placed on the staff at the beginning of a section of music. The initial key signature in a piece is placed immediately after the cl ...
(or if there is no key signature, the
clef A clef (from French: 'key') is a musical symbol used to indicate which notes are represented by the lines and spaces on a musical staff. Placing a clef on a staff assigns a particular pitch to one of the five lines or four spaces, whic ...
symbol). A mid-score time signature, usually immediately following a
barline In musical notation, a bar (or measure) is a segment of music bounded by vertical lines, known as bar lines (or barlines), usually indicating one or more recurring beats. The length of the bar, measured by the number of note values it contains, ...
, indicates a change of
meter The metre (or meter in US spelling; symbol: m) is the base unit of length in the International System of Units (SI). Since 2019, the metre has been defined as the length of the path travelled by light in vacuum during a time interval of of ...
. Most time signatures are either simple (the note values are grouped in pairs, like , , and ), or compound (grouped in threes, like , , and ). Less common signatures indicate
complex Complex commonly refers to: * Complexity, the behaviour of a system whose components interact in multiple ways so possible interactions are difficult to describe ** Complex system, a system composed of many components which may interact with each ...
, mixed,
additive Additive may refer to: Mathematics * Additive function, a function in number theory * Additive map, a function that preserves the addition operation * Additive set-function see Sigma additivity * Additive category, a preadditive category with fin ...
, and
irrational meters Irrationality is cognition, thinking, talking, or acting without rationality. Irrationality often has a negative connotation, as thinking and actions that are less useful or more illogical than other more rational alternatives. The concept of ...
.


Time signature notation

Most time signatures consist of two numerals, one stacked above the other: * The ''lower'' numeral indicates the note value that the signature is counting. This number is always a
power of 2 A power of two is a number of the form where is an integer, that is, the result of exponentiation with number two as the base and integer  as the exponent. In the fast-growing hierarchy, is exactly equal to f_1^n(1). In the Hardy hie ...
(unless the time signature is
irrational Irrationality is cognition, thinking, talking, or acting without rationality. Irrationality often has a negative connotation, as thinking and actions that are less useful or more illogical than other more rational alternatives. The concept of ...
), 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 Bar or BAR may refer to: Food and drink * Bar (establishment), selling alcoholic beverages * Candy bar ** Chocolate bar * Protein bar Science and technology * Bar (river morphology), a deposit of sediment * Bar (tropical cyclone), a laye ...
. For instance, means two quarter-notes (crotchets) per bar, while means four
eighth-note 180px, Figure 1. An eighth note with stem extending up, an eighth note with stem extending down, and an eighth rest. 180px, Figure 2. Four eighth notes beamed together. An eighth note ( American) or a quaver (British) is a musical note play ...
s (quavers) per bar. The most common time signatures are , , and .


Symbolic signatures

By convention, two special symbols are sometimes used for and : * The symbol is sometimes used for time, also called ''common time'' or ''imperfect time''. * The symbol is sometimes used in place of and is called ''
alla breve ''Alla breve'' also known as cut time or cut common timeis a Meter (music), musical meter notated by the time signature symbol (a C) with a vertical line through it, which is the equivalent of . The term is Italian language, Italian for "on t ...
'' or, colloquially, ''cut time'' or ''cut common time''. These symbols derive from 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, 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 or . Other upper numbers correspond to irregular meters.


Beat and subdivision

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 In Western musical notation, a dotted note is a Musical note, note with a small dot written after it. In modern practice, the first dot increases the duration (music), duration of the original note by half of its note value, value. This makes a ...
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 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. Mathematically the time signatures of, e.g., and are interchangeable. In a sense ''all'' simple triple time signatures, such as , , , etc.—and all compound duple times, such as , and so on, are equivalent. A piece in can be easily rewritten in , simply by halving the length of the notes. : \new Staff << \new voice \relative c' \new voice \relative c'' >> Other time signature rewritings are possible: most commonly a simple time-signature with triplets translates into a compound meter. : \new Staff << \new voice \relative c' \new voice \relative c'' >> 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 Rock most often refers to: * Rock (geology), a naturally occurring solid aggregate of minerals or mineraloids * Rock music, a genre of popular music Rock or Rocks may also refer to: Places United Kingdom * Rock, Caerphilly, a location in Wale ...
song in or , rather than .


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'': is a simple
triple meter Triple is used in several contexts to mean "threefold" or a " treble": Sports * Triple (baseball), a three-base hit * A basketball three-point field goal * A figure skating jump with three rotations * In bowling terms, three strikes in a row ...
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 ::: one and ''two'' and ''three'' and ... ''Compound'': Most often, 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 ::: one two three ''four'' five six ... The table below shows the characteristics of the most frequently used time signatures.


Tempo giusto

While changing the bottom number and keeping the top number fixed only formally changes notation, without changing meaning – , , , and 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 ''Tempo giusto'' () is a musical term that means 'in correct time'.David Fallows. 'Tempo giusto' in Grove Music Online. Oxford University Press. www.oxfordmusiconline.com. Accessed 20 Feb 2015. General In the 17th and 18th centuries (Baroque an ...
'', 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 The Baroque ( , , ) is a Western Style (visual arts), style of Baroque architecture, architecture, Baroque music, music, Baroque dance, dance, Baroque painting, painting, Baroque sculpture, sculpture, poetry, and other arts that flourished from ...
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.


Complex time signatures

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. Irregular meters are common in some non-Western music, and in ancient Greek music such as the
Delphic Hymns The Delphic Hymns are two musical compositions from Ancient Greece, which survive in substantial fragments. They were long regarded as being dated and 128 BC, respectively, but recent scholarship has shown it likely they were both written f ...
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,Tim Emmons, ''Odd Meter Bass: Playing Odd Time Signatures Made Easy'' (Van Nuys: Alfred Publishing, 2008): 4. . "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." plus a small section in Handel's opera
Orlando Orlando commonly refers to: * Orlando, Florida, a city in the United States Orlando may also refer to: People * Orlando (given name), a masculine name, includes a list of people with the name * Orlando (surname), includes a list of people wit ...
(1733). The third movement of
Frédéric Chopin Frédéric François Chopin (born Fryderyk Franciszek Chopin; 1 March 181017 October 1849) was a Polish composer and virtuoso pianist of the Romantic period who wrote primarily for Piano solo, solo piano. He has maintained worldwide renown ...
's Piano Sonata No. 1 (1828) is an early, but by no means the earliest, example of time in solo piano music.
Anton Reicha Anton (Antonín, Antoine) Joseph Reicha (Rejcha) (26 February 1770 – 28 May 1836) was a Czech-born, Bavarian-educated, later naturalization, naturalized French composer and music theorist. A contemporary and lifelong friend of Ludwig van Be ...
's Fugue No. 20 from his '' Thirty-six Fugues'', published in 1803, is also for piano and is in . The
waltz The waltz ( , meaning "to roll or revolve") is a ballroom dance, ballroom and folk dance, in triple (3/4 time, time), performed primarily in closed position. Along with the ländler and allemande, the waltz was sometimes referred to by the ...
-like second movement of Tchaikovsky's ''Pathétique'' Symphony (shown below), often described as a "limping waltz", is a notable example of time in orchestral music. : \relative c Examples from
20th-century classical music 20th-century classical music is Western art music that was written between the years 1901 and 2000, inclusive. Musical style diverged during the 20th century as it never had previously, so this century was without a dominant style. Modernism, i ...
include: *
Gustav Holst Gustav Theodore Holst (born Gustavus Theodore von Holst; 21 September 1874 â€“ 25 May 1934) was an English composer, arranger and teacher. Best known for his orchestral suite ''The Planets'', he composed many other works across a range ...
's "Mars, the Bringer of War" and "Neptune, the Mystic" from ''
The Planets ''The Planets'', Op. 32, is a seven- movement orchestral suite by the English composer Gustav Holst, written between 1914 and 1917. In the last movement the orchestra is joined by a wordless female chorus. Each movement of the suite is name ...
'' (both in ) *
Paul Hindemith Paul Hindemith ( ; ; 16 November 189528 December 1963) was a German and American composer, music theorist, teacher, violist and conductor. He founded the Amar Quartet in 1921, touring extensively in Europe. As a composer, he became a major advo ...
's "Fuga secunda" in G from ''
Ludus Tonalis ''Ludus Tonalis'' ("Play of Tones", "Tonal Game", or "Tonal Primary School" after the Latin ''Ludus Litterarius''), subtitled ''Kontrapunktische, tonale, und Klaviertechnische Übungen'' (''Counterpoint, tonal and technical studies for the piano ...
'' () * the ending of Stravinsky's ''
The Firebird ''The Firebird'' (; ) is a ballet and orchestral concert work by the Russian composer Igor Stravinsky. It was written for the 1910 Paris season of Sergei Diaghilev's Ballets Russes company; the original choreography was by Michel Fokine, who c ...
'' () * the fugue from
Heitor Villa-Lobos Heitor Villa-Lobos (March 5, 1887November 17, 1959) was a Brazilian composer, conductor, cellist, and classical guitarist described as "the single most significant creative figure in 20th-century Brazilian art music". Villa-Lobos has globally bec ...
's '' Bachianas Brasileiras No. 9'' () * the themes for the '' Mission: Impossible'' television series by
Lalo Schifrin Boris Claudio "Lalo" Schifrin (born June 21, 1932) is an Argentine-American pianist, composer, arranger, and conductor. He is best known for his large body of film and TV scores since the 1950s, incorporating jazz and Music of Latin America, Lati ...
(in ) and for ''
Room 222 ''Room 222'' is an American comedy-drama television series produced by 20th Century Fox Television that aired on American Broadcasting Company, ABC for 112 episodes, from September 17, 1969, until January 11, 1974. The show was broadcast on 1969 ...
'' by
Jerry Goldsmith Jerrald King Goldsmith (February 10, 1929July 21, 2004) was an American composer, conductor and orchestrator with a career in film and television scoring that spanned nearly 50 years and over 200 productions, between 1954 and 2003. He was consid ...
(in ) In the Western popular music tradition, unusual time signatures occur as well, with
progressive rock Progressive rock (shortened as prog rock or simply prog) is a broad genre of rock music that primarily developed in the United Kingdom through the mid- to late 1960s, peaking in the early-to-mid-1970s. Initially termed " progressive pop", the ...
in particular making frequent use of them. The use of shifting meters in
The Beatles The Beatles were an English Rock music, rock band formed in Liverpool in 1960. The core lineup of the band comprised John Lennon, Paul McCartney, George Harrison and Ringo Starr. They are widely regarded as the Cultural impact of the Beatle ...
' "
Strawberry Fields Forever "Strawberry Fields Forever" is a song by the English Rock music, rock band the Beatles, written by John Lennon and credited to Lennon–McCartney. It was released on 13 February 1967 as a double A-side single with "Penny Lane". It represented ...
" and the use of
quintuple meter Quintuple meter or quintuple time is a musical meter (music), meter characterized by five Beat (music), beats in a measure, whether variably or equally stressed. Like the more common Duple meter, duple, triple meter, triple, and quadruple meter, ...
in their " Within You, Without You" are well-known examples,Edward Macan, ''Rocking the Classics: English Progressive Rock and the Counterculture'' (New York: Oxford University Press, 1997): 48. . as is
Radiohead Radiohead are an English rock band formed in Abingdon-on-Thames, Abingdon, Oxfordshire, in 1985. The band members are Thom Yorke (vocals, guitar, piano, keyboards); brothers Jonny Greenwood (guitar, keyboards, other instruments) and Colin Gre ...
's "
Paranoid Android "Paranoid Android" is a song by English alternative rock band Radiohead, released as the lead single from their third studio album, '' OK Computer'' (1997), on 26 May 1997. The lyrics were written by singer Thom Yorke following an unpleasant e ...
" (includes ).
Paul Desmond Paul Desmond (born Paul Emil Breitenfeld; November 25, 1924 – May 30, 1977) was an American jazz alto saxophonist and composer and proponent of cool jazz. He was a member of the Dave Brubeck Quartet and composed the group's biggest hit, " ...
's
jazz Jazz is a music genre that originated in the African-American communities of New Orleans, Louisiana, in the late 19th and early 20th centuries. Its roots are in blues, ragtime, European harmony, African rhythmic rituals, spirituals, h ...
composition "
Take Five "Take Five" is a jazz standard composed by Paul Desmond in 5 beat per measure, the melody relying on the blues scale, with harmony E-flat minor. It was first recorded in 1959 and is the third track on ''Time Out'' by the Dave Brubeck Quartet. ...
", in time, was one of a number of irregular-meter compositions that
The Dave Brubeck Quartet David Warren Brubeck (; December 6, 1920 – December 5, 2012) was an American jazz pianist and composer. Often regarded as a foremost exponent of cool jazz, Brubeck's work is characterized by unusual time signatures and superimposing contrasti ...
played. They played other compositions in ("Eleven Four"), (" Unsquare Dance"), and ("
Blue Rondo à la Turk Blue is one of the three primary colours in the RYB colour model (traditional colour theory), as well as in the RGB (additive) colour model. It lies between violet and cyan on the spectrum of visible light. The term ''blue'' generally d ...
"), expressed as . "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 In Ottoman musical theory, ''aksak'' () is a rhythmic system in which pieces or sequences, executed in a fast tempo, are based on the uninterrupted reiteration of a matrix, which results from the juxtaposition of rhythmic cells based on the alter ...
'' meter of the Turkish ''
karşılama Karsilamas (; ) is a folk dance spread all over Northwest Turkey and carried to Greece by Anatolian Greek immigrants. The term "karşılama" means "encounter, welcoming, greeting" in Turkish. The dance is popular in Northwestern areas of Turkey, ...
'' dance. However, such time signatures are only unusual in most Western music. Traditional music of the Balkans uses such meters extensively.
Bulgarian dances Bulgarian folk dances are intimately related to the music of Bulgaria. This distinctive feature of Balkan folk music is the asymmetrical meter, built up around various combinations of 'quick' and 'slow' beats. The music, in Western musical nota ...
, 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 In music, the terms ''additive'' and ''divisive'' are used to distinguish two types of both rhythm and meter: * A divisive (or, alternately, multiplicative) rhythm is a rhythm in which a larger period of time is divided into smaller rhythmic unit ...
s'' based on simple units, usually 2, 3 and 4 beats, though the notation fails to describe the
metric Metric or metrical may refer to: Measuring * Metric system, an internationally adopted decimal system of measurement * An adjective indicating relation to measurement in general, or a noun describing a specific type of measurement Mathematics ...
"time bending" taking place, or compound meters. See
Additive meters Additive may refer to: Mathematics * Additive function, a function in number theory * Additive map, a function that preserves the addition operation * Additive set-function see Sigma additivity * Additive category, a preadditive category with fin ...
below. Some video samples are shown below.


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 Modest Petrovich Mussorgsky (; ; ; – ) was a Russian composer, one of the group known as "The Five (composers), The Five." He was an innovator of Music of Russia, Russian music in the Romantic music, Romantic period and strove to achieve a ...
's ''
Pictures at an Exhibition ''Pictures at an Exhibition'' is a piano suite in ten movements, plus a recurring and varied Promenade theme, written in 1874 by Russian composer Modest Mussorgsky. It is a musical depiction of a tour of an exhibition of works by architect and ...
'' (1874) is a good example. The opening measures are shown below: : :
Igor Stravinsky Igor Fyodorovich Stravinsky ( – 6 April 1971) was a Russian composer and conductor with French citizenship (from 1934) and American citizenship (from 1945). He is widely considered one of the most important and influential 20th-century c ...
's ''
The Rite of Spring ''The Rite of Spring'' () is a ballet and orchestral concert work by the Russian composer Igor Stravinsky. It was written for the 1913 Paris season of Sergei Diaghilev's Ballets Russes company; the original choreography was by Vaslav Nijinsky ...
'' (1913) is famous for its "savage" rhythms. Five measures from "Sacrificial Dance" are shown below: : In such cases, a convention that some composers follow (e.g.,
Olivier Messiaen Olivier Eugène Prosper Charles Messiaen (, ; ; 10 December 1908 – 27 April 1992) was a French composer, organist, and ornithology, ornithologist. One of the major composers of the 20th-century classical music, 20th century, he was also an ou ...
, in his ''
La Nativité du Seigneur ''La Nativité du Seigneur, neuf méditations pour orgue'' (''The Birth of the Lord, nine meditations for organ'') is an important work for organ, written by the French composer Olivier Messiaen in 1935 in Grenoble. It is a testament to Messiaen ...
'' and ''
Quatuor pour la fin du temps ''Quatuor pour la fin du Temps'' (), originally ''Quatuor de la fin du Temps'' ("''Quartet of the End of Time''"), also known by its English title ''Quartet for the End of Time'', is an eight-movement piece of chamber music by the French composer ...
'') is to simply omit the time signature.
Charles Ives Charles Edward Ives (; October 20, 1874May 19, 1954) was an American modernist composer, actuary and businessman. Ives was among the earliest renowned American composers to achieve recognition on a global scale. His music was largely ignored d ...
's ''
Concord Sonata The Piano Sonata No. 2, ''Concord, Mass., 1840–60'' (commonly known as the ''Concord Sonata'') is a piano sonata by Charles Ives. It is one of the composer's best-known and most highly regarded pieces. A typical performance of the piece lasts ar ...
'' 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 Leisure (, ) has often been defined as a quality of experience or as free time. Free time is time spent away from business, work, job hunting, domestic chores, and education, as well as necessary activities such as eating and sleeping. Leis ...
. Sometimes one is provided (usually ) 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 Eric Alfred Leslie Satie (born 17 May 18661 July 1925), better known as Erik Satie, was a French composer and pianist. The son of a French father and a British mother, he studied at the Conservatoire de Paris, Paris Conservatoire but was an undi ...
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: :


Additive meters

To indicate more complex patterns of stresses, such as
additive rhythm In music, the terms ''additive'' and ''divisive'' are used to distinguish two types of both rhythm and meter: * A divisive (or, alternately, multiplicative) rhythm is a rhythm in which a larger period of time is divided into smaller rhythmic unit ...
s, more complex time signatures can be used. Additive meters have a pattern of beats that subdivide into smaller, irregular groups. Such meters are sometimes called ''imperfect'', in contrast to ''perfect meters'', in which the
bar Bar or BAR may refer to: Food and drink * Bar (establishment), selling alcoholic beverages * Candy bar ** Chocolate bar * Protein bar Science and technology * Bar (river morphology), a deposit of sediment * Bar (tropical cyclone), a laye ...
is first divided into equal units. For example, the time signature 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 :: : 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 Béla Viktor János Bartók (; ; 25 March 1881 – 26 September 1945) was a Hungarian composer, pianist and ethnomusicologist. He is considered one of the most important composers of the 20th century; he and Franz Liszt are regarded as Hunga ...
and
Olivier Messiaen Olivier Eugène Prosper Charles Messiaen (, ; ; 10 December 1908 – 27 April 1992) was a French composer, organist, and ornithology, ornithologist. One of the major composers of the 20th-century classical music, 20th century, he was also an ou ...
have used such time signatures in their works. The first movement of
Maurice Ravel Joseph Maurice Ravel (7 March 1875 – 28 December 1937) was a French composer, pianist and conductor. He is often associated with Impressionism in music, Impressionism along with his elder contemporary Claude Debussy, although both composer ...
's Piano Trio in A Minor is written in , in which the beats are likewise subdivided into to reflect
Basque Basque may refer to: * Basques, an ethnic group of Spain and France * Basque language, their language Places * Basque Country (greater region), the homeland of the Basque people with parts in both Spain and France * Basque Country (autonomous co ...
dance rhythms. Romanian
musicologist Musicology is the academic, research-based study of music, as opposed to musical composition or performance. Musicology research combines and intersects with many fields, including psychology, sociology, acoustics, neurology, natural sciences, f ...
Constantin Brăiloiu had a special interest in compound time signatures, developed while studying the
traditional music Folk music is a music genre that includes traditional folk music and the contemporary genre that evolved from the former during the 20th-century folk revival. Some types of folk music may be called world music. Traditional folk music has b ...
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
Bulgarians Bulgarians (, ) are a nation and South Slavs, South Slavic ethnic group native to Bulgaria and its neighbouring region, who share a common Bulgarian ancestry, culture, history and language. They form the majority of the population in Bulgaria, ...
). 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 music The music of Bulgaria refers to all forms of music associated with the country of Bulgaria, including classical, folk, popular music, and other forms. Classical music, opera, and ballet are represented by composers Emanuil Manolov, Pancho Vladi ...
, 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 the value of the long). This type of meter is called ''
aksak In Ottoman musical theory, ''aksak'' () is a rhythmic system in which pieces or sequences, executed in a fast tempo, are based on the uninterrupted reiteration of a matrix, which results from the juxtaposition of rhythmic cells based on the alter ...
'' (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 , for example, is a three-beat measure in ''aksak'', with one long and two short beats (with subdivisions of , , or ). 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 " Eleno Mome" is written in one of three forms: (1) , (2) , or (3) , but an actual performance (e.g., "Eleno Mome") may be closer to . The Macedonian 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 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 Viennese waltz () is a genre of ballroom dance. At least four different meanings are recognized. In the historically first sense, the name may refer to several versions of the waltz, including the earliest waltzes done in ballroom dancing, dance ...
. 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 In music, syncopation is a variety of rhythms played together to make a piece of music, making part or all of a tune or piece of music off-beat (music), off-beat. More simply, syncopation is "a disturbance or interruption of the regular flow of ...
rather than as part of the metric accentuation. Brăiloiu borrowed a term from 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.Gheorghe Oprea, ''Folclorul muzical românesc'' (Bucharest: Ed. Muzicala, 2002), 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. A method to create meters of lengths of any length has been published in the Journal of Anaphoria Music Theory and Xenharmonikon 16 using both those based on the Horograms of
Erv Wilson Ervin Wilson (June 11, 1928 – December 8, 2016) was a Mexican/ American (dual citizen) music theorist. Early life Ervin Wilson was born iColonia Pacheco a small village in the remote mountains of northwest Chihuahua, Mexico, where he lived u ...
and Viggo Brun's algorithm written by
Kraig Grady Kraig Grady (born 1952) is a US-Australian composer/ sound artist. He has composed and performed with an ensemble of microtonal instruments of his own design and also worked as a shadow puppeteer, tuning theorist, filmmaker, world music radio D ...
.


Irrational meters

Irrational time signatures (rarely, "non-dyadic time signatures") are used for so-called ''irrational bar lengths'',"Brian Ferneyhough"
''The Ensemble Sospeso''
that have a
denominator A fraction (from , "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, thre ...
that is not a
power of two A power of two is a number of the form where is an integer, that is, the result of exponentiation with number 2, two as the Base (exponentiation), base and integer  as the exponent. In the fast-growing hierarchy, is exactly equal to f_1^ ...
(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 or . For example, where implies a bar construction of four quarter-parts of a whole note (i.e., four quarter notes), 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 , say, could be more legibly written out in . According to
Brian Ferneyhough Brian John Peter Ferneyhough (; born 16 January 1943) is an English composer. Ferneyhough is typically considered the central figure of the New Complexity movement. Ferneyhough has taught composition at the Hochschule für Musik Freiburg and ...
,
metric modulation In music, metric modulation is a change in pulse rate (tempo) and/or pulse grouping ( subdivision) which is derived from a note value or grouping heard before the change. Examples of metric modulation may include changes in time signature across ...
is "a somewhat distant analogy" to his own use of "irrational time signatures" as a sort of rhythmic dissonance. 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. Good examples, written entirely in conventional signatures with the aid of between-bar specified metric relationships, occur a number of times in
John Adams John Adams (October 30, 1735 – July 4, 1826) was a Founding Fathers of the United States, Founding Father and the second president of the United States from 1797 to 1801. Before Presidency of John Adams, his presidency, he was a leader of ...
' opera ''
Nixon in China ''Nixon in China'' is an opera in three acts by John Adams with a libretto by Alice Goodman. Adams's first opera, it was inspired by U.S. president Richard Nixon's 1972 visit to the People's Republic of China. The work premiered at the Houston ...
'' (1987), where the sole use of irrational signatures would quickly produce massive numerators and denominators. Historically, this device has been prefigured wherever composers wrote
tuplet In music, a tuplet (also irrational rhythm or groupings, artificial division or groupings, abnormal divisions, irregular rhythm, gruppetto, extra-metric groupings, or, rarely, contrametric rhythm) is "any rhythm that involves dividing the beat ...
s. For example, a bar of 3 triplet quarter notes could be written as a bar of .
Henry Cowell Henry Dixon Cowell (; March 11, 1897 – December 10, 1965) was an American composer, writer, pianist, publisher, teacher Marchioni, Tonimarie (2012)"Henry Cowell: A Life Stranger Than Fiction" ''The Juilliard Journal''. Retrieved 19 June 2022.C ...
's piano piece ''
Fabric Textile is an umbrella term that includes various fiber-based materials, including fibers, yarns, filaments, threads, and different types of fabric. At first, the word "textiles" only referred to woven fabrics. However, weaving is no ...
'' (1920) employs separate divisions of the bar (1 to 9) for the three
contrapuntal In music theory, counterpoint is the relationship of two or more simultaneous Part (music), musical lines (also called voices) that are harmonically dependent on each other, yet independent in rhythm and Pitch contour, melodic contour. The term ...
parts, using a scheme of shaped
notehead In music, a notehead is the part of a note, usually elliptical in shape, whose placement on the staff indicates the pitch, to which modifications are made that indicate duration. Noteheads may be the same shape but colored completely b ...
s to visually clarify the differences, but the pioneering of these signatures is largely due to
Brian Ferneyhough Brian John Peter Ferneyhough (; born 16 January 1943) is an English composer. Ferneyhough is typically considered the central figure of the New Complexity movement. Ferneyhough has taught composition at the Hochschule für Musik Freiburg and ...
, 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 In musical terminology, tempo (Italian for 'time'; plural 'tempos', or from the Italian plural), measured in beats per minute, is the speed or pace of a given musical composition, composition, and is often also an indication of the composition ...
".
Thomas Adès Thomas Joseph Edmund Adès (born 1 March 1971) is a British composer, pianist and conductor. Five compositions by Adès received votes in the 2017 Classic Voice poll of the greatest works of art music since 2000: ''The Tempest (opera), The T ...
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 , and . A gradual process of diffusion into less rarefied musical circles seems underway. For example, John Pickard's ''Eden'', commissioned for the 2005 finals of the
National Brass Band Championships of Great Britain National may refer to: Common uses * Nation or country ** Nationality – a ''national'' is a person who is subject to a nation, regardless of whether the person has full rights as a citizen Places in the United States * National, Maryland, ce ...
, contains bars of and . 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 is written as a normal quarter note, four quarter notes complete the bar, but the whole bar lasts only of a reference
whole note A whole note (American) or semibreve (British) in musical notation is a single note equivalent to or lasting as long as two half notes or four quarter notes. Description The whole note or semibreve has a note head in the shape of a hollow ov ...
, and a beat of one (or 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 In music, metre (British spelling) or meter (American spelling) refers to regularly recurring patterns and accents such as bars and beats. Unlike rhythm, metric onsets are not necessarily sounded, but are nevertheless implied by the performer ( ...
, since , say, in isolation, is identical to .


Variants

Some composers have used fractional beats: for example, the time signature appears in
Carlos Chávez Carlos Antonio de Padua Chávez y Ramírez (13 June 1899 – 2 August 1978) was a Mexican composer, conducting, conductor, music theorist, educator, journalist, and founder and director of the Mexican Symphonic Orchestra. He was influence ...
's Piano Sonata No. 3 (1928) IV, m. 1. Both and appear in the fifth movement of Percy Grainger's
Lincolnshire Posy ''Lincolnshire Posy'' is a musical composition by Percy Grainger for concert band commissioned in 1937 by the American Bandmasters Association. Considered by John Bird, the author of Grainger's biography, to be his masterpiece, the work has six ...
. Music educator
Carl Orff Carl Heinrich Maria Orff (; 10 July 1895 – 29 March 1982) was a German composer and music educator, who composed the cantata ''Carmina Burana (Orff), Carmina Burana'' (1937). The concepts of his Orff Schulwerk, Schulwerk were influential for ...
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 George Henry Crumb Jr. (24 October 1929 – 6 February 2022) was an American composer of avant-garde contemporary classical music. Early in his life he rejected the widespread modernist usage of serialism, developing a highly personal musical ...
and
Joseph Schwantner Joseph Clyde Schwantner (born March 22, 1943) is an American composer, educator and a member of the American Academy of Arts and Letters since 2002. He was awarded the 1970 Charles Ives Prize. Schwantner is prolific, with many works to his cred ...
, among others, have used this system in many of their works.
Émile Jaques-Dalcroze Émile Jaques-Dalcroze (6 July 1865 – 1 July 1950) was a Swiss composer, musician, and music educator who developed Dalcroze eurhythmics, an approach to learning and experiencing music through movement. Dalcroze eurhythmics influenced Carl O ...
proposed this in his 1920 collection, ''Le Rythme, la musique et l'éducation''. 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 Henryk Mikołaj Górecki ( , ; 6 December 1933 – 12 November 2010) was a Polish composer of contemporary classical music. According to critic Alex Ross, no recent classical composer has had as much commercial success as Górecki. He became a l ...
'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

In the
mensural notation Mensural notation is the musical notation system used for polyphony, polyphonic European vocal music from the late 13th century until the early 17th century. The term "mensural" refers to the ability of this system to describe precisely measur ...
of the 14th, 15th and 16th centuries there are no
bar Bar or BAR may refer to: Food and drink * Bar (establishment), selling alcoholic beverages * Candy bar ** Chocolate bar * Protein bar Science and technology * Bar (river morphology), a deposit of sediment * Bar (tropical cyclone), a laye ...
lines, and the four basic ''mensuration signs'' , , , indicate the normal ratio of duration between different
note value In music notation, a note value indicates the relative duration (music), duration of a note (music), note, using the texture or shape of the ''notehead'', the presence or absence of a ''stem (music), stem'', and the presence or absence of ''flags ...
s. Unlike modern notation, the subdivisions could be either 2:1 or 3:1. The relation between the ''
breve A breve ( , less often , grammatical gender, neuter form of the Latin "short, brief") is the diacritic mark , shaped like the bottom half of a circle. As used in Ancient Greek, it is also called , . It resembles the caron (, the wedge or in ...
'' and the ''
semibreve A whole note (American) or semibreve (British) in musical notation is a single note equivalent to or lasting as long as two half notes or four quarter notes. Description The whole note or semibreve has a note head in the shape of a hollow o ...
'' was called tempus, and could be perfect (
triple Triple is used in several contexts to mean "threefold" or a " treble": Sports * Triple (baseball), a three-base hit * A basketball three-point field goal * A figure skating jump with three rotations * In bowling terms, three strikes in a row * I ...
3:1 indicated by circle) or imperfect ( duple 2:1, with broken circle), while the relation between the ''semibreve'' and the '' minim'' was called prolatio and could be major (3:1 or
compound Compound may refer to: Architecture and built environments * Compound (enclosure), a cluster of buildings having a shared purpose, usually inside a fence or wall ** Compound (fortification), a version of the above fortified with defensive struc ...
, indicated by dot) or minor (2:1 or
simple meter In music, metre (British spelling) or meter (American spelling) refers to regularly recurring patterns and accents such as bars and beats. Unlike rhythm, metric onsets are not necessarily sounded, but are nevertheless implied by the performer ( ...
). Modern transcriptions often reduce note values 4:1, such that * corresponds to meter; * corresponds to meter; * corresponds to meter; * corresponds to meter. In mensural notation actual note values depend not only on the prevailing mensuration, but on rules for imperfection and alteration, with ambiguous cases using a dot of separation, similar in appearance but not always in effect to the modern dot of augmentation.


Proportions

Besides showing the organization of beats with
musical meter 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 ar ...
, 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 In music, a tuplet (also irrational rhythm or groupings, artificial division or groupings, abnormal divisions, irregular rhythm, gruppetto, extra-metric groupings, or, rarely, contrametric rhythm) is "any rhythm that involves dividing the beat ...
s or
metric modulation In music, metric modulation is a change in pulse rate (tempo) and/or pulse grouping ( subdivision) which is derived from a note value or grouping heard before the change. Examples of metric modulation may include changes in time signature across ...
s. This is a fraught subject, because the usage has varied with both time and place:
Charles Hamm Charles Edward Hamm (April 21, 1925 – October 16, 2011) was an American musicologist, writer, composer, and music educator. He is credited with being the first music historian to seriously study and write about American popular music. He also w ...
was even able to establish a rough chronology of works based on three distinct usages of mensural signs over the career of
Guillaume Dufay Guillaume Du Fay ( , ; also Dufay, Du Fayt; 5 August 1397 – 27 November 1474) was a composer and music theorist of early Renaissance music, who is variously described as French or Franco-Flemish. Considered the leading European composer of h ...
(1397(?) – 1474). By the end of the sixteenth century
Thomas Morley Thomas Morley (1557 – early October 1602) was an English composer, music theory, theorist, singer and organist of late Renaissance music. He was one of the foremost members of the English Madrigal School. Referring to the strong Italian inf ...
was able to satirize the confusion in an imagined dialogue:
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 Curranta played in the new Proportions by them lately found out, called 'Sesquiblinda' and 'Sesquihearkenafter'." ::''Plaine and Easie Introduction to Practicall Musicke'' (1597)
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 for example is unrelated to 'third-notes'. A few common signs are shown: * ''tempus imperfectum diminutum'', 1:2 proportion (twice as fast); * ''tempus perfectum diminutum'', 1:2 proportion (twice as fast); * or ''proportio tripla'', 1:3 proportion (three times as fast, similar to triplets). In particular, when the sign was encountered, the tactus (beat) changed from the usual whole note (semibreve) to the double whole note (breve), a circumstance called ''
alla breve ''Alla breve'' also known as cut time or cut common timeis a Meter (music), musical meter notated by the time signature symbol (a C) with a vertical line through it, which is the equivalent of . The term is Italian language, Italian for "on t ...
''. This term has been sustained to the present day, and though now it means the beat is a
half note In music, a half note (American) or minim (British) is a Musical note, note played for half the duration of a whole note (or semibreve) and twice the duration of a quarter note (or crotchet). It was given its Latin name (''minima'', meaning "le ...
(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 A puzzle is a game, problem, or toy that tests a person's ingenuity or knowledge. In a puzzle, the solver is expected to put pieces together ( or take them apart) in a logical way, in order to find the solution of the puzzle. There are differe ...
" compositions that were intentionally difficult to decipher.


Irregular bar

Irregular bars are a change in time signature normally for only one bar. Such a bar is most often a bar of , or in a composition, or a bar of in a composition, or a bar of in a composition. If a song is entirely in a change to will make the song feel like it has skipped a beat, the opposite is true for where it feels like the song adds a beat. If a song changes to is will make it feel like that bar is half as long as all the others Some popular examples include "
Golden Brown "Golden Brown" is a song by the English rock music, rock band the Stranglers, released as a 7-inch single on EMI's Liberty Records, Liberty label in 1982. Noted for its distinctive harpsichord instrumentation, it was the second single release ...
" by
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( in a composition), "
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" originally by The Arrows ( in a composition), "
Hey Ya! "Hey Ya!" is a song by American hip hop duo Outkast, performed by its member André 3000, who wrote and produced the song. Along with " The Way You Move", recorded by Outkast's other member Big Boi and which featured Sleepy Brown, "Hey Ya! ...
" by
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( in a composition), and "
Wuthering Heights ''Wuthering Heights'' is the only novel by the English author Emily Brontë, initially published in 1847 under her pen name "Ellis Bell". It concerns two families of the landed gentry living on the West Yorkshire moors, the Earnshaws and the ...
" by
Kate Bush Catherine Bush (born 30 July 1958) is an English singer, songwriter, record producer, and dancer. Bush began writing songs at age 11. She was signed to EMI Records after David Gilmour of Pink Floyd helped produce a demo tape. In 1978, at the ...
(different kinds of irregular bars in a composition).


See also

* Schaffel, a kind of swing in rock and techno music * Tala, meter in Indian music *
Colotomy ''Colotomy'' is an Indonesian description of the rhythmic and metric patterns of gamelan music. It refers to the use of specific instruments to mark off nested time intervals, or the process of dividing rhythmic time into such nested cycles. I ...
, a coinage by Jap Kunst to describe the metric structure of gamelan music.


References


Sources

* {{DEFAULTSORT:Time Signature Musical notation * Articles containing video clips Music theory