Time signature

Most time signatures comprise two numbers, one above the other. (When writing about time signatures, time signatures are generally written with the top number separated from the bottom by a slash (in the manner of a fraction). The example here, for example, can 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 there is no key signature). A mid-score time signature indicates a change of meter.

Basic time signatures

Time signatures can be "simple" or "compound". In simple time signatures, the upper number indicates how many beats there are in a bar, and the lower number indicates the length of that beat. The most common simple time signatures are 2/4, 3/4, and 4/4.

Compound time signatures are distinguished by a top number which is 6 or above and a multiple of three (most commonly 6, 9, or 12). Unlike simple time signatures, the upper lower and lower numbers in compound time signatures do not represent the number of beats per measure and the duration of the beat. To determine the number of beats per measure for a compound time signature, divide the upper number by three. For example, in 6/8, there are 2 beats per measure (because 6 divided by 3 equals 2). The duration of the beat (or the "beat unit") in compound time is three times the duration represented by the lower number. For example, in 6/8, the beat unit is a dotted quarter-note (because three times the value of an eighth-note is a dotted quarter-note).

In compound time, the beat unit is always a dotted value. In simple time, the beat unit is always an undotted value.

For all meters, the first beat (the "downbeat") is stressed; in time signatures with four groups in the bar (such as 4/4 and 12/8), the third beat is also stressed, though to a lesser degree. This gives a regular pattern of stressed and unstressed beats.

In some cases, the letter C (common time) is 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, indicating alla breve (cut time) for a fast duple meter.

Pieces with two beats to the bar, such as 2/4 or 6/8, are said to be in duple meter. Similarly, music with three beats to the bar (such as 3/2 or 9/8) is in triple meter. Some people also label music with four beats to the bar as quadruple meter, while some consider it as simply two duples. The latter is more consistent with the above duple/triple and simple/compound labelling system, as any other division above triple, such as quintuple, is considered as duple+triple (12123) or triple+duple (12312), depending on the accents in the musical example. However, in some music a quintuple meter, five beats per measure, may be treated and perceived as one unit of five, especially at faster tempos. Seven beats per measure would be septuple meter. These names can be combined with the simple and compound terms, so that 3/4 time can be described as simple triple, 6/8 as compound duple and so on.

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 bass note 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 bottom note can give subtle hints as to the character of the music: for example, time signatures with a longer bass-note (such as 3/2) can be used for pieces in a quick tempo to convey a sense of the time flying by.

Similarly, a piece in 2/4 can often sound like it is in 4/4 (or vice versa) and a piece in 3/4 can sound like it is in 6/8 or 12/8 time, particularly if the former is played quickly or the latter slowly. The distinction may be a matter of notation.

Examples of basic time signatures

Irregular meter time signatures

These include signatures whose upper notes are 5, 7, or other numbers other than those discussed above. Also called asymmetric meters.

Some examples in Western music are:

Paul Desmond and Dave Brubeck, 'Take Five' (Scruton 1997)

Mixed meters

While time signatures usually express a regular pattern of beat stresses continuing through a piece (or at least a section), sometimes composer 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.

Burt Bacharach's rhythmically exciting song ""Promises, Promises"" likewise features a constantly changing meter. Igor Stravinsky's The Rite of Spring is famous for its "savage" rhythms:

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

If two time signatures alternate repeatedly, sometimes the two signatures will be placed together at the beginning of the piece or section:

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 complex 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.

A few composers of orchestral music who write using mixed meters write very long, thin numbers for their time signatures rather than the standard method of writing it on each staff; this is an aid to the conductor, who can see them more easily.

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 perfectum, corresponding to simple meter and compound meter.

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 (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:

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.