Time signature

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.

Two staves with time signature highlighted in blue

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

Basic 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 or measure;
*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 (UK crotchet). For example, 3/4 means three quarter-note beats per measure.

Counting in simple time

In simple time, counting is done by taking the beat unit (the note value designated by the bottom number of the time signature) and repeating it the number of times given by the top number. For instance, in "common" (4/4) time, the beat unit is a quarter note (crotchet), and there are four of them in each measure.

While one could count simple time this way (using the 4/4 example):

One — two — three — four

it is more usual to count simple time in eight notes (quavers), like this:

One and two and three and four and

where each syllable represents an eighth note (quaver). The spoken numbers represent the beats in the measure.

Notational variations in simple time

The letter C ("common time") - in actuality, a broken circle - 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, indicating alla breve or "cut time"; however, this symbol is also sometimes used for 4/2.

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 eighth notes.

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 measure and the beat unit.

Compound meter gets its name by combining two or more simple meter measures to form a compound measure. (Historically, 4/4 was once considered a compound meter: 2/4 + 2/4 = 4/4.) Today when we refer to compound meters, we refer only to the 'compounding' of two (or more) simple triple measures.

3/8 + 3/8 = 6/8

3/8 + 3/8 + 3/8 = 9/8

3/8 + 3/8 + 3/8 + 3/8 = 12/8

Interpreting compound time signatures

The upper and lower numbers in compound time signatures need to be factored as follows:
*To determine the number of beats per measure, 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 quarter beats, each beat will subdivide into a group of three eighth notes. The count is technically correct as "1-2-3, 2-2-3". One can reproduce the same result in simple duple (2/4) meter by using triplets to count. The meter is exactly the same, but usually it will be counted as "1 trip-let, 2 trip-let" or "1 and-a, 2 and-a".
*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 an eighth note (quaver). Multiplying that note value by three gives a beat unit of a dotted quarter note (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 measure respectively.

There are occasions when a compound time signature is interpreted as simple time, without the factoring. In such cases, 6/8 would be have 6 equally stressed eighth note (quaver) beats per bar. A 6/8 measure in simple meter would be counted as "1-2-3-4-5-6".

The "beat unit" in compound time signatures

The choice of the note for the "beat unit" (quarter note, eighth note, etc.) in compound time signatures may seem arbitrary: why is some music written in 9/8, for instance, and other music written in 9/16? Keeping in mind that these are essentially the same meter, only with a different "denominator", the answer is simple: faster music uses smaller beat units. So it can be seen, given these two examples, that a piece in 9/16 will generally have a faster tempo than one written in 9/8. This is by no means a hard and fast rule, but instead a compositional convention that serves to give performers helpful clues as to how a piece should be played.

Beat and meter

Time signatures indicating two beats per bar (whether simple or compound) are called duple meter; those with three beats to the bar are triple meter. Terms such as quadruple, septuple, and so on are also occasionally used. See Metre (music).

Most frequent time signatures

Simple time signatures
4/4	common time: widely used in classical music; the norm in rock, jazz, country, and bluegrass, and most modern pop or dance music
2/2	alla breve, cut time: used for marches and fast orchestral music. Frequently occurs in musical theater. Sometimes called "in 2".
4/2	rare in music since 1600, although Brahms and other conservative composers used it occasionally.
2/4	used for polkas or marches
3/4	used for waltzes, minuets, scherzi, and country & western ballads.
Compound time signatures
6/8	double jigs, fast waltzes, marches and some rock music.
9/8	"compound triple time", used in triple ("slip") jigs, otherwise occurring rarely (The Sorcerer's Apprentice is a familiar example)
12/8	common in blues and doo-wop, also used more recently in rock music.

Unusual meters

The piano intro to "Take Five" – Listen to this piece.

These include signatures whose upper notes are 5, 7, or numbers other than those discussed above. Also called asymmetric meters or irregular time signatures. 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. Some notable examples are "Money" (7/4), from the progressive rock band Pink Floyd, popular metal band Soundgarden's "Outshined" (7/4), Holst's "Mars, the Bringer of War," (5/4) from the orchestral suite The Planets, and the ending of Stravinsky's Firebird (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 sported 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).

It should be pointed out that such time signatures are only considered "unusual" from a Western point of view: for instance, 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:

Mussorgsky's Pictures at an Exhibition "Promenade"

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::

Stravinsky, The Rite of Spring, "Sacrificial Dance"

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 in free time.

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:

Alternating_time_signatures2.gif

Variations

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

Additive_time_signature.png

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.

example Orff time signatures

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 option for dealing with mixed meters is to extend the barline where the change is to take place above the top instrument's line and write the time signature there once, thus saving the ink that would've been spent writing it in each instrument's staff. Henryk Górecki's Beatus Vir does this.

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.

Stress and meter

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, 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 6/8 or 12/8 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:
*

Mensural_ts2.gif

corresponds to 9/8 meter
*

Mensural_ts1.gif

corresponds to 3/4 meter
*

Mensural_ts3.gif

corresponds to 6/8 meter
*

Mensural_ts4.gif

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:
*

Mensural_proportion1.gif

1:2 proportion (twice as fast)
*

Mensural_proportion2.gif

1:3 proportion (three times as fast)
*

Mensural_proportion4.gif

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