Time signature

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The time signature (also known as "meter signature") is a notational device used in Western musical notation to specify how many beats are in each bar and what note value constitutes one beat. Time signatures indicate meter, but do not necessarily determine it.

Most time signatures comprise two numbers, one above the other. In text (as in this article), time signatures are written in the manner of a fraction: the example shown at right would be written 3/4.

In a musical score, the time signature appears at the beginning of the piece, immediately following the key signature (or immediately following the clef if the piece is in C major or A minor). A mid-score time signature, usually immediately following a barline, indicates a change of meter.

Simple and compound time signatures

A time signature defines the pulse and thus establishes the "count" of a musical work.

Time signatures can be "simple" or "compound".

Simple time signatures

In simple time signatures, each beat has the value of an undotted note.

• the upper number indicates how many beats there are in a bar ;
• the lower number indicates the note value which represents ONE beat (the "beat unit").

The most common simple time signatures are 2/4, 3/4, and 4/4. The 4 at the bottom indicates that the beat unit is the quarter note or crotchet. For example, 3/4 means three crotchet beats per measure.

Notational variations in simple time

The letter C ("common time")—deriving from the broken circle used in early music—may be used in place of the 4/4 time signature. A similar C with a vertical line through it (¢) can be used in place of 2/2, also known as "alla breve" or, colloquially in English, "cut time" or "cut common time". This "cut" symbol, doubled, is also occasionally used for 4/2, although, confusingly, some examples omit the doubling.

Compound time signatures

Compound time signatures are distinguished by an upper number which is commonly 6, 9 or 12. The most common lower number in a compound time signature is 8, meaning the time is beaten in quavers.

Unlike simple time, however, compound time uses a dotted note for the beat unit. Consequently, the upper and lower numbers in compound time signatures do not represent the number of beats per bar and the beat unit.

Interpreting compound time signatures

The upper and lower numbers in compound time signatures need to be treated as follows:

• To determine the number of beats per bar, divide the upper number by three. For example, in 6/8, there are 2 beats per measure. The pulse in a compound 6/8 will have two dotted crotchet beats, and each beat will subdivide into a group of three quavers.

• To identify the "beat unit" (i.e. which type of note represents one beat), multiply the note value represented by the lower number by three. For example, in 6/8, the lower number (8) represents the note value of a quaver. Multiplying that note value by three gives a beat unit of a dotted crotchet (i.e., 3 quavers).

For example, 12/8 time would be counted: One two three four five six seven eight nine ten eleven twelve.

In compound time, the beat unit is always a dotted note value. The most common compound time signatures are 6/8, 9/8 and 12/8, denoting two, three and four dotted quarter note beats per bar.

Beat and time

Time signatures indicating two beats per bar (whether simple or compound) are called duple time; those with three beats to the bar are triple time. Terms such as quadruple (4), quintuple (5), and so on are also occasionally used.

Most frequent time signatures

Complex time signatures

Signatures which do not fit into the usual duple or triple categories are known as complex, asymmetric, or irregular, although these are broad terms, and usually a more specific description is appropriate. Most often these can be recognised by the upper number being 5, 7, or another, larger, prime number, but this is not necessarily so; for example, the addition of two triple beats and a duple beat in a bar gives an upper number of 8. Although these more complex meters are common in non-Western music, they were rarely used in formal written Western music until the late 19th century. The earliest examples of irregular signatures are found in instrumental music by Giovanni Valentini (1582-1649) and Anton Reicha (1770-1836), written in 5/4, 9/8, etc. Both composers remained virtually unknown for centuries, however, so irregular rhythms were quite uncommon in Western music until the late 19th century when they started becoming more popular. The waltz-like second movement of Tchaikovsky's Pathétique Symphony (premiered in 1893) is one of the more famous examples of 5/4. Examples from the 20th century include Holst's "Mars, the Bringer of War," (5/4) from the orchestral suite The Planets, and the ending of Stravinsky's Firebird (7/4); examples from the Western popular music tradition include "Money" (7/4), from the progressive rock band Pink Floyd and popular metal band Soundgarden's "Outshined" (7/4). The jazz composition "Take Five", written in 5/4 time, was one of a number of irregular-meter experiments of The Dave Brubeck Quartet, which also produced compositions in 11/4 ("Eleven Four"), 7/4 ("Unsquare Dance"), and 9/8 ("Blue Rondo a la Turk"), expressed as 2+2+2+3/8, this last being a good example of a work in a signature which, despite appearing merely compound triple, is actually more complex.

It should be pointed out that such time signatures are only considered "unusual" from a Western point of view. In contrast, for example, Bulgarian dances use such meters extensively, including forms with 5, 7, 9, 11, 13, 15, 22 and other numbers of beats per measure. (These rhythms are all additive rhythms based on simple units of 2 and 3 beats; see Variations below.)

For more examples, see List of works in unusual time signatures.

Mixed meters

While time signatures usually express a regular pattern of beat stresses continuing through a piece (or at least a section), 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, not an indication of meter. The Promenade from Mussorgsky's Pictures at an Exhibition is a good example:

Burt Bacharach's rhythmically exciting song "Promises, Promises" likewise features a constantly changing meter.

Igor Stravinsky's aforementioned The Rite of Spring is famous for its "savage" rhythms:

Some composers (and even Hymnals) simply omit the time signature in such cases. Many songs in Bertolt Brecht's plays also follow this convention.

Some pieces have no time signature, as there is no discernible rhythm. This is commonly known as free time. Sometimes one is provided (usually 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 stave to indicate the piece is in free time. Erik Satie wrote many compositions which are ostensibly in free time, but actually follow an unstated and unchanging simple time signature throughout. Later composers have made more effective use of this device, writing music which is almost devoid of any discernable regularity of pulse.

If two time signatures alternate repeatedly, sometimes the two signatures will be placed together at the beginning of the piece or section, as in this example, the theme from the song "America" from West Side Story:

Variations

To indicate more complex patterns of stresses, such as additive rhythms, more complex time signatures can be used. For example, the signature

which can be written 3+2+3/8, means that the first of a group of three quavers (eighth notes) is to be 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, italics indicating stresses. 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 are examples of composers who have used such time signatures.

Some composers have used fractional beats; for example, the time signature (2 1/2)/4 appears in Carlos Chávez's Sonata No. 3 (1928) IV, m. 1.

Music educator Carl Orff proposed replacing the lower number of the time signature with the actual note value, as shown at right. This system eliminates the need for compound time signatures (described above), 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.

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.

 

"Irrational" meters

These are time signatures which have a denominator which is not a power of two (1, 2, 4, 8, 16, 32, etc.). These are used to express the division of a whole note (UK "semibreve") into equal parts just as ordinary signatures do. For example, where 4/4 implies a bar construction of four quarter-parts of a whole note i.e. four quarter notes, 4/3 implies a bar construction of four third-parts of it. These signatures are only of utility when juxtaposed with other signatures with varying denominators; a piece written entirely in 4/3, say, could be more legibly written out in 4/4.

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 (1987), where the sole use of "irrational" signatures would quickly produce massive numerators and denominators.

Historically, this device has been prefigured wherever composers have written tuplets; for example, a 2/4 bar consisting of 3 triplet crotchets could arguably more sensibly be written as a bar of 3/6. Henry Cowell's piano piece "Fabric" (1920) throughout employs separate divisions of the bar (anything from 1 to 9) for the three contrapuntal parts, using a scheme of shaped noteheads to make the differences visually clear, but the pioneering of these signatures is largely due to Brian Ferneyhough. Thomas Adès has also made extensive use of them, for example in his piano work "Traced Overhead" (1996), the second movement of which contains, amongst more conventional meters, bars in such signatures as 2/6, 9/14 and 5/24. A gradual process of diffusion into less rarefied musical circles seems to be underway, hence for example, John Pickard's work "Eden", commissioned for the 2006 finals of the National Brass Band Championships of Great Britain, which contains bars of 3/10.

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 4/5 is written as a normal quarter note, four quarter notes complete the bar, but the whole bar lasts only 4/5 of a reference whole note, and a beat 1/5 of one (or 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.

The appropriateness of the term "irrational" is moot; an irrational number is one that cannot be written as a ratio of whole numbers, a rational number is one that can. By definition, these signatures are far better represented by the concept of rationality than irrationality. Nevertheless, the term appears to be established now, and the only potential problem is that of nomenclature should someone write a piece with a proportion such as the square root of 2 involved in a signature; a further hyperbolism would be necessary to describe these. In fact, at least one such piece already exists; one of Conlon Nancarrow's "Studies for Player Piano" contains a canon where one part is augmented in the ratio sqrt(42):1.

Stress and meter

For all meters, the first beat (the downbeat, ignoring any anacrusis) is usually stressed (though not always, for example in reggae where the offbeat are stressed); in time signatures with four groups in the bar (such as 4/4 and 12/8), the third beat is often also stressed, though to a lesser degree. This gives a regular pattern of stressed and unstressed beats, although notes on the "stressed" beats are not necessarily louder or more important.

Rewriting meters

There is a sense in which all simple triple time signatures, be they 3/8, 3/4, 3/2 or anything else, and all compound duple times, such as 6/8, 6/16 and so on, are equivalent – a piece in 3/4 can be easily rewritten in 3/8 simply by halving the length of the notes. Sometimes, the choice of beat unit is simply down to tradition: the minuet, for example, is generally written in 3/4, and though examples in 3/8 do exist, a minuet in 3/2 would be highly unconventional.

At other times, the choice of beat unit (the bottom number of a time signature) note can give subtle hints as to the character of the music: for example, time signatures with a longer beat unit (such as 3/2) can be used for pieces in a quick tempo to convey a sense of the time flying by. This may be counter-intuitive, but in the Baroque and Classical periods, typically meters with long note values (such as 3/2) were fast tempos, while slow movements were typically written with the eighth note as the beat.

Similarly, a piece in 2/4 can often sound as if it is in 4/4 (or vice versa) and a piece in 3/4 can sound as if it is in 6 or 12 compound time, particularly if the former is played quickly or the latter slowly. The distinction may be a matter of notation.

Early music usage

Mensural time signatures

In the 13th through 16th centuries, a period in which mensural notation was used, there were four basic time signatures, which determined the proportion between the two main units of rhythm. There were no measures or barlines 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. 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 these mensural signatures indicated. A ratio of 3:1 was called perfect, perhaps a reference to the Trinity, and a ratio of 2:1 was called imperfect.

A circle used as a time signature indicated tempus perfectum (a circle being a symbol of perfection), while an incomplete circle, resembling a letter C, indicated tempus imperfectum. Assuming the breve to be 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 perfectum while the absence of such a dot indicated prolatio imperfectum, corresponding to simple meter and compound meter.

A rough equivalence of these signs to modern meters would be:

• corresponds to 9/8 meter
• corresponds to 3/4 meter
• corresponds to 6/8 meter
• corresponds to 2/4 meter

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 (undotted) 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:

• 1:2 proportion (twice as fast)
• 1:3 proportion (three times as fast)
• 2:3 proportion (similar to triplets)

Often the ratio was expressed as two numbers, one above the other, looking similar to a modern time signature, although it could have values such as 4/3, which a time signature could not.

There is still controversy regarding the meaning of some proportional signs, and they may not have been used consistently from one place or century to another. In addition, certain composers delighted in creating "puzzle" compositions which were intentionally difficult to decipher.

In particular, when the sign was encountered, the tactus (beat) changed from the usual semibreve to the breve, a circumstance called alla breve. This term has been sustained to the present day, and although now it means the beat is a minim (half note), in contradiction to the literal meaning of the phrase, it still indicates that the beat has changed to a longer note value.

In the 17th century, additional signs such as also indicated proportions like this.

See also

• Math rock
• List of works in irregular time signatures
• Schaffel beat

External links

• Grateful Dead songs with unusual time signatures (Grateful Dead)
• Doctor Nerve: Skin Scorebook featuring a score which uses unusual time signatures (Nick Didkovsky)