Time signature


The time signature is a notational convention used in Western musical notation to specify how many beats are contained in each measure, and which note value is equivalent to a beat.
In a music score, the time signature appears at the beginning as a time symbol or stacked numerals, such as or , immediately following the key signature. A mid-score time signature, usually immediately following a barline, indicates a change of meter.
There are various types of time signatures, depending on whether the music follows regular beat patterns, including simple, and compound ; or involves shifting beat patterns, including [|complex], [|mixed], [|additive], [|fractional], and [|irrational meters].

Frequently used time signatures

Simple vs. compound

Simple

Simple time signatures consist of two numerals, one stacked above the other:
For instance, means two quarter-note beats per bar, while means three eighth-note beats per bar. The most common simple time signatures are,, and.
By convention, two special symbols are sometimes used for and :
In compound meter, subdivisions of the beat are in three equal parts, so that a dotted note becomes the beat. The upper numeral of compound time signatures is commonly 6, 9, or 12. The lower number is most commonly an 8 : as in or.

Examples

In the examples below, bold denotes a more-stressed beat, and italics denotes a less-stressed beat.
Simple: is a simple triple meter time signature that represents three quarter notes. It is felt as
Compound: In principle, comprises not three groups of two eighth notes but two groups of three eighth-note subdivisions. It is felt as
These examples assume, for simplicity, that continuous eighth notes are the prevailing note values. The rhythm of actual music is typically not as regular.

Duple, triple, etc.

Time signatures indicating two beats per bar are called duple meter, while those with three beats to the bar are triple meter. Terms such as quadruple, quintuple, and so on, are also occasionally used.

Beating time signatures

To the ear, 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. Correspondingly, at slow tempos, the beat indicated by the time signature could in actual performance be divided into smaller units.
On a formal mathematical level, 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
>>

Though formally interchangeable, for a composer or performing musician, by convention, different time signatures often have different connotations. First, a smaller note value in the beat unit implies a more complex notation, which can affect ease of performance. Second, beaming affects the choice of actual beat divisions. It is, for example, more natural to use the quarter note/crotchet as a beat unit in or than the eight/quaver in or. Third, time signatures are traditionally associated with different music styles—it might seem strange to notate a rock tune in or.

Characteristics

The table below shows the characteristics of the most frequently-used time signatures.

Complex time signatures


Signatures that do not fit the usual duple or triple categories are called complex, asymmetric, irregular, unusual, or odd—though these are broad terms, and usually a more specific description is appropriate. The term odd meter, however, sometimes describes time signatures in which the upper number is simply odd rather than even, including and.
The irregular meters are common in some non-Western music, but rarely appeared in formal written Western music until the 19th century. Early anomalous examples appeared in Spain between 1516 and 1520, but the Delphic Hymns to Apollo, carved on the exterior walls of the Athenian Treasury at Delphi in 128 BC are in the relatively common cretic meter, with five beats to a foot.
The third movement of Frédéric Chopin's Piano Sonata No. 1 is an early, but by no means the earliest, example of time in solo piano music. Anton Reicha's Fugue No. 20 from his Thirty-six Fugues, published in 1803, is also for piano and is in. The waltz-like second movement of Tchaikovsky's Pathétique Symphony, often described as a "limping waltz", is a notable example of time in orchestral music.
\relative c

Examples from 20th-century classical music include:
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, as is Radiohead's "Paranoid Android".
Paul Desmond's jazz composition "Take Five", in time, was one of a number of irregular-meter compositions that The Dave Brubeck Quartet played. They played other compositions in , , and , expressed as. This last is an example of a work in 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.
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 rhythms based on simple units, usually 2, 3 and 4 beats, though the notation fails to describe the metric "time bending" taking place, or compound meters. See [|Additive meters] below.
Some video samples are shown below.'''

Mixed meters

While time signatures usually express a regular pattern of beat stresses continuing through a piece, sometimes composers place a different time signature at the beginning of each bar, resulting in music with an extremely irregular rhythmic feel. 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 is a good example. The opening measures are shown below:


Igor Stravinsky's The Rite of Spring is famous for its "savage" rhythms. Five measures from "Sacrificial Dance" are shown below:
In such cases, a convention that some composers follow 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. Sometimes one is provided 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:

Additive meters

To indicate more complex patterns of stresses, such as additive rhythms, 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 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 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
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 in A Minor is written in, in which the beats are likewise subdivided into to reflect Basque dance rhythms.
Romanian musicologist Constantin Brăiloiu had a special interest in compound time signatures, developed while studying the 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. 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, 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. This type of meter is called aksak, 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.
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: , , or , but an actual performance 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 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 —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.
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. 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.
Some video samples are shown below.
's "Blue Rondo à la Turk": It consists of three measures of followed by one measure of 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 and Xenharmonikon 16 using both those based on the Horograms of Erv Wilson and Viggo Brun's algorithm written by Kraig Grady.

Irrational meters

Irrational time signatures are used for so-called irrational bar lengths, that have a denominator that is not a power of two. 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, 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, metric modulation is "a somewhat distant analogy" to his own use of "irrational time signatures" as a sort of rhythmic dissonance. It is arguable 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' opera Nixon in China, where the sole use of irrational signatures would quickly produce massive numerators and denominators.
Historically, this device has been prefigured wherever composers wrote tuplets. For example, a bar of 3 triplet crotchets could arguably be written as a bar of. Henry Cowell's piano piece Fabric employs separate divisions of the bar for the three contrapuntal parts, using a scheme of shaped noteheads 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". Thomas Adès has also used them extensively—for example in Traced Overhead, 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 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, and a beat of one. 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, say, in isolation, is identical to.
, which is 5:3

Variants

Some composers have used fractional beats: for example, the time signature appears in Carlos Chávez's Piano Sonata No. 3 IV, m. 1. Both and appear in the fifth movement of Percy Grainger's Lincolnshire Posy.
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, 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.
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

In the 14th, 15th and 16th centuries, a period in which mensural notation was used, four basic mensuration signs determined the proportion between the two main units of rhythm. There were no measure or bar lines in music of this period; these signs, the ancestors of modern time signatures, indicate the ratio of duration between different note values. The relation between the breve and the semibreve was called tempus, and the relation between the semibreve and the minim was called prolatio. The breve and the semibreve use roughly the same symbols as our modern double whole note and whole note, but they were not limited to the same proportional values as are in use today. There are complicated rules concerning how a breve is sometimes three and sometimes two semibreves. Unlike modern notation, the duration ratios between these different values was not always 2:1; it could be either 2:1 or 3:1, and that is what, amongst other things, these mensuration signs indicated. A ratio of 3:1 was called complete, perhaps a reference to the Trinity, and a ratio of 2:1 was called incomplete.
A circle used as a mensuration sign indicated tempus perfectum, while an incomplete circle, resembling a letter C, indicated tempus imperfectum. Assuming the breve is a beat, this corresponds to the modern concepts of triple meter and duple meter, respectively. In either case, a dot in the center indicated prolatio perfecta while the absence of such a dot indicated prolatio imperfecta.
A rough equivalence of these signs to modern meters would be:
N.B.: in modern compound meters the beat is a dotted note value, such as a dotted quarter, because the ratios of the modern note value hierarchy are always 2:1. Dotted notes were never used in this way in the mensural period; the main beat unit was always a simple note value.

Proportions

Another set of signs in mensural notation specified the metric proportions of one section to another, similar to a metric modulation. A few common signs are shown:
Often the ratio was expressed as two numbers, one above the other, looking similar to a modern time signature, though it could have values such as, which a conventional time signature could not.
Some proportional signs were not used consistently from one place or century to another. In addition, certain composers delighted in creating "puzzle" compositions that were intentionally difficult to decipher.
In particular, when the sign was encountered, the tactus changed from the usual whole note to the double whole note, a circumstance called alla breve. This term has been sustained to the present day, and though now it means the beat is a half note, in contradiction to the literal meaning of the phrase, it still indicates that the beat has changed to a longer note value.