A time signature is a symbol in music notation that shows how many beats of a certain type fit into each measure (bar). It tells musicians the meter of a musical piece at the level of each measure.

In a music score, the time signature is written as two numbers stacked on top of each other, like 4 (called four-four time), or as a symbol, like (called common time). It appears right after the key signature (or after the clef symbol if there is no key signature). A time signature that appears in the middle of a score, usually after a barline, shows a change in the meter.

Most time signatures are simple, meaning the beats are grouped in pairs, such as 4, 4, and 4. Others are compound, where beats are grouped in threes, like 8, 8, and 8. Some less common time signatures show more complicated, mixed, additive, or irrational meters.

Time signature notation

Most time signatures have two numbers, one placed above the other:

• The bottom number shows the type of note that the time signature is counting. This number is usually a power of 2 (such as 2, 4, or 8), though 16 is sometimes used in Baroque music. The number 2 refers to a half note (minim), 4 refers to a quarter note (crotchet), 8 refers to an eighth note (quaver), and 16 refers to a sixteenth note (semiquaver).
• The top number shows how many of these notes fit into one measure (bar).

For example, 4 means two quarter notes (crotchets) in a bar, while 8 means four eighth notes (quavers) in a bar. The most common time signatures are 4, 4, and 4.

By convention, two special symbols are sometimes used for 4 and 2:

• The symbol is sometimes used for 4 time, also called common time or imperfect time.
• The symbol is sometimes used instead of 2 and is called alla breve, or, informally, cut time or cut common time.

These symbols come from mensural time signatures, described below.

Frequently used time signatures

Simple meters are those with an upper number of 2, 3, or 4. These are sometimes called duple meter, triple meter, and quadruple meter, respectively.

In compound meter, the note values shown by the lower number are grouped into three parts. The upper number is a multiple of 3, such as 6, 9, or 12. The lower number is most often 8, as in 6/8 or 9/8.

Other upper numbers are used for irregular meters.

Music often has a repeating pulse, or beat, usually between 60 and 140 beats per minute. Depending on the tempo, this beat may match the note value shown in the time signature or a group of those note values. In simple time signatures, the beat usually matches the note value of the signature. In compound time signatures, the beat is often a dotted note value that represents three of the signature’s note values. The next smaller note value than the beat is called the subdivision.

Sometimes a bar may feel like one single beat. For example, a fast waltz written in 3/4 time might be described as having one beat per bar. At slower tempos, the beat might be a smaller note value than the one shown in the time signature.

Mathematically, time signatures like 4/4 and 8/8 are interchangeable. Simple triple time signatures, such as 6/8, 9/8, or 12/8—and compound duple time signatures, such as 6/8 or 12/8—are all equivalent in terms of the number of beats. A piece in 4/4 can be rewritten in 6/8 by halving the length of the notes.

Other time signature changes are possible, such as when simple time signatures with triplets are rewritten as compound meters.

The choice of time signature is often based on tradition. Certain time signatures are associated with specific music styles. For example, rock music is usually written in 4/4 rather than 6/8 or 2/4.

In the examples below, bold text shows the main stress in a measure, and italics show a secondary stress. Words like "and" are often used to mark the pulse between numbers.

Simple: 3/4 is a simple triple meter time signature that represents three quarter notes, usually felt as three beats. In this case, the subdivision would be the eighth note. It is felt as:

Compound: 6/8 is often felt as two beats, each being a dotted quarter note, with each beat divided into three eighth notes. It is felt as:

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

Changing the lower number while keeping the upper number the same only changes the notation, not the meaning. For example, 3/8, 3/4, 3/2, and 3/1 all represent three beats per measure, but they use different note values (eighth notes, quarter notes, half notes, or whole notes). These differences traditionally suggest different ways of performing the music and different tempo ranges. Larger numbers in the lower part of the time signature usually mean faster tempi, and smaller numbers mean slower tempi. This convention is called tempo giusto and ensures that the tempo of each note stays within a narrower, "normal" range. For example, a quarter note might correspond to 60–120 beats per minute, an eighth note to 120–240 beats per minute, and so on. These are examples, not strict rules.

This convention began during the Baroque era, when changes in tempo were shown by altering the time signature during a piece, rather than using a single time signature and changing the tempo marking.

Complex time signatures

Time signatures that do not fit simple or compound categories are called complex, asymmetric, irregular, unusual, or odd. These are general terms, and a more specific description is a meter that mixes simple and compound beats.

Irregular meters are common in some non-Western music and in ancient Greek music, such as the Delphic Hymns to Apollo. However, these time signatures rarely appeared in formal Western music until the 19th century. Early examples were found in Spain between 1516 and 1520, and in a small section of Handel's opera Orlando (1733).

The third movement of Frédéric Chopin's Piano Sonata No. 1 (1828) is an early example of 4⁄4 time in solo piano music. Anton Reicha's Fugue No. 20 from his Thirty-six Fugues, published in 1803, is also for piano and uses 8⁄8 time. The waltz-like second movement of Tchaikovsky's Pathétique Symphony (often called a "limping waltz") is a notable example of 4⁄4 time in orchestral music.

Examples from 20th-century classical music include:
– Gustav Holst's "Mars, the Bringer of War" and "Neptune, the Mystic" from The Planets (both in 4⁄4 time)
– Paul Hindemith's "Fuga secunda" in G from Ludus Tonalis (8⁄8 time)
– the ending of Stravinsky's The Firebird (4⁄4 time)
– the fugue from Heitor Villa-Lobos's Bachianas Brasileiras No. 9 (8⁄8 time)
– the themes for the Mission: Impossible television series by Lalo Schifrin (in 4⁄4 time) and for Room 222 by Jerry Goldsmith (in 4⁄4 time)

In Western popular music, unusual time signatures also appear, especially in progressive rock. Examples include the shifting meters in The Beatles' "Strawberry Fields Forever," the quintuple meter in their "Within You, Without You," and Radiohead's "Paranoid Android" (which includes 8⁄8 time).

Paul Desmond's jazz piece "Take Five," in 5⁄4 time, was one of several irregular-meter compositions performed by The Dave Brubeck Quartet. They also played pieces in 4⁄4 ("Eleven Four"), 4⁄4 ("Unsquare Dance"), and 8⁄8 ("Blue Rondo à la Turk"), which is written as 8⁄8. "Blue Rondo à la Turk" is an example of a time signature that appears compound triple but is more complex. Brubeck's title refers to the aksak meter of the Turkish karşılama dance.

However, such time signatures are unusual in most Western music. Traditional music from the Balkans uses these meters frequently. For example, Bulgarian dances include forms with 5, 7, 9, 11, 13, 15, 22, 25, and other numbers of beats per measure. These rhythms are written as additive rhythms based on simple units, usually 2, 3, and 4 beats. However, the notation does not fully describe the metric "time bending" or compound meters. See the section on additive meters for more details.

Some video examples are shown below.

Mixed meters

Time signatures usually show a regular pattern of beats that continue throughout a piece or section. However, sometimes composers change time signatures often, creating music with a very irregular rhythm. In these cases, the time signature may switch so frequently that the piece is better described as having a mix of different meters instead of one main meter. Here, the time signature helps performers but does not clearly define the meter. An example is the "Promenade" from Modest Mussorgsky's Pictures at an Exhibition (1874), where the opening measures are shown below.

Igor Stravinsky's The Rite of Spring (1913) is well-known for its complex rhythms. Five measures from "Sacrificial Dance" are shown below.

In some cases, composers choose not to include a time signature. For example, Olivier Messiaen used this in works like La Nativité du Seigneur and Quatuor pour la fin du temps. Charles Ives's Concord Sonata includes measure bars for some parts, but most of the piece has no bars.

Some pieces have no time signature because there is no clear meter. This is sometimes called "free time." A time signature (often 4) may be added to help performers read the music, with the word "free time" written as a direction. Sometimes, the word "FREE" is written vertically on the staff to show the piece uses free time. Erik Satie wrote many pieces that seem to use free time but actually follow a simple, unchanging time signature that is not stated. Later composers used this technique more clearly, creating music with little to no regular beat.

When two time signatures alternate repeatedly, they may be written together at the beginning of a piece or section, as shown below.

Additive meters

To show more complex beat patterns, such as additive rhythms, more complicated time signatures can be used. Additive meters divide beats into smaller, uneven groups. These meters are sometimes called imperfect, compared to perfect meters, where the bar is divided into equal parts.

For example, the time signature 8 means there are 8 eighth notes (quavers) in the bar. These are grouped as 3, then 2, then 3 beats. The stress pattern is counted as 1, 2, 3, 1, 2, 1, 2, 3.

This kind of time signature is often used in folk and non-Western music. In classical music, composers like Béla Bartók and Olivier Messiaen used such time signatures. The first movement of Maurice Ravel’s Piano Trio in A Minor uses 8, with beats divided into 3+2+3 to reflect Basque dance rhythms. 8 is also used in boogie-woogie music, as in the song "Beat Me Daddy, Eight to the Bar."

Romanian musicologist Constantin Brăiloiu studied compound time signatures while researching traditional music in his country. He found that these unusual meters were common in neighboring regions, like Bulgaria. He suggested these meters combine simple two-beat and three-beat patterns, with accents on the first beat of each group. In some cases, such as Bulgarian music, beat lengths may vary (1, 2, 3, or 4). When focusing only on stressed beats, simple time signatures can resemble slower, compound time. However, compound time has two beat lengths: one longer than the other (the long beat is 1.5 times the short beat, or the short beat is 2/3 the long beat). This type of meter is called aksak, a Turkish term meaning "limping," and is described as an irregular rhythm. Western musicians may find this confusing, as a measure they might see as 16 could be a three-beat aksak measure with one long and two short beats (subdivided as 2+2+3, 2+3+2, or 3+2+2).

Folk music may use metric time bends, where the actual timing of beats differs slightly from the written proportions. Depending on the playing style, these bends can range from small to large. For example, the Bulgarian tune "Eleno Mome" is written in forms like 7 (2+2+1+2), 13 (4+4+2+3), or 12 (3+4+2+3), but a performance might closely match 4+4+2+3. The Macedonian 3+2+2+3+2 meter is even more complex, with larger time bends and use of quadruples on the threes. Timing can also change based on how fast the tune is played. The Swedish Boda Polska has a typical longer second beat.

In Western classical music, metric time bends are used in Viennese waltzes. Most Western music uses simple ratios like 2:1, 3:1, or 4:1 (two-, three-, or four-beat time signatures), where all beats are equal. In contrast, ratios like 3:2 and 4:3 create distinct rhythm patterns. While Western music uses complex accents, these are often syncopation, not part of the metric structure.

Brăiloiu borrowed the term "aksak" from Turkish medieval music theory. He classified compound time signatures under "aksak rhythm," along with other terms to describe traditional rhythms. The term "aksak" is still used in Eastern Europe and appears in music worldwide, with combinations of two- and three-beat sequences. The longest aksak rhythms are found in Bulgaria, while the shortest follow a five-beat pattern (2+3 or 3+2).

Some video examples are provided below.

A method to create meters of any length was published in the Journal of Anaphoria Music Theory and Xenharmonikon 16, using techniques based on Horograms by Erv Wilson and Viggo Brun’s algorithm, developed by Kraig Grady.

Irrational meters

Irrational time signatures, also called "non-dyadic time signatures" or "odd-factored time signatures," are used for bar lengths that have a denominator not based on powers of two (such as 1, 2, 4, 8, 16, 32, etc.). These signatures divide beats into parts that are not whole numbers, like 10 or 7. For example, a time signature of 4 means a bar is divided into four equal parts of a whole note (like four quarter notes), while a time signature of 3 divides the same whole note into three equal parts. These signatures are only helpful when combined with other time signatures that have different denominators. A piece written entirely in 3 could be easier to read if rewritten in 4.

Brian Ferneyhough described metric modulation as a "somewhat distant analogy" to his use of irrational time signatures, which he used to create rhythmic complexity. It is debated whether these signatures make musical timing clearer or more confusing. Any passage using irrational time signatures can be rewritten using regular time signatures by showing how note lengths in one bar relate to those in another. However, when the relationships between bars become very complicated, irrational time signatures can make the music harder to read.

Historically, this technique was first used when composers wrote tuplets (groups of notes that divide a beat into unequal parts). For example, a bar with three triplet quarter notes could be written as a bar of 6. Henry Cowell’s piano piece Fabric (1920) used different divisions of the bar (from 1 to 9) for separate musical parts, using special note symbols to clarify the differences. However, Brian Ferneyhough is credited with pioneering the use of irrational time signatures. He said these signatures help separate changes in note density from changes in the basic tempo. Thomas Adès also used them frequently, such as in his piece Traced Overhead (1996), which includes bars with signatures like 6 and 14 alongside more common time signatures.

In musical notation, irrational time signatures are written the same way as regular tuplets. For example, a beat in a 5-time signature might be written as a quarter note, with four quarter notes completing the bar. However, the entire bar would last only 4⁄5 of a reference whole note, and each beat would be 1⁄5 of a whole note (or 4⁄5 of a regular quarter note). This is written the same way as if five quarter notes were divided into quintuplets.

The video samples below show two time signatures combined to create a polymeter, since 3 and 4 can be used together in the same piece.

Variants

Some composers have used fractional beats in their music. For example, the time signature 4 (equivalent to 8) appears in Carlos Chávez's Piano Sonata No. 3 (1928), IV, measure 1. Both 4 and 4 are found in the fifth movement of Percy Grainger's Lincolnshire Posy.

Music educator Carl Orff suggested replacing the lower number in a time signature with a picture of a note, as shown in some examples. This method removes the need for compound time signatures, which can be confusing for beginners. Although this notation is not widely used by music publishers (except in Orff's own compositions), it is commonly found in music education textbooks. Similarly, American composers George Crumb and Joseph Schwantner, among others, have used this system in their works. Émile Jaques-Dalcroze introduced this idea in his 1920 book, Le Rythme, la musique et l'éducation.

Another approach is to extend the barline above the top staff in a score when a time change occurs, writing the time signature there instead of repeating it in each instrument's staff. This saves space and effort. Henryk Górecki's Beatus Vir is an example of this method. In large scores, time signatures are sometimes written as very long, thin numbers that span the entire height of the score. This helps conductors see changes in time signatures more easily.

Early music usage

In the musical notation used during the 14th, 15th, and 16th centuries, there were no bar lines, and four basic symbols indicated the normal relationship between the lengths of different note values. Unlike modern notation, the way notes were divided could be either 2:1 or 3:1. The relationship between the breve and the semibreve was called tempus and could be perfect (a 3:1 ratio, shown with a circle) or imperfect (a 2:1 ratio, shown with a broken circle). The relationship between the semibreve and the minim was called prolatio and could be major (a 3:1 ratio, shown with a dot) or minor (a 2:1 ratio, without a dot).

Modern versions of this notation often simplify note values by a ratio of 4:1, so:
– One symbol corresponds to 8 beats per measure;
– Another symbol corresponds to 4 beats per measure;
– A third symbol corresponds to 8 beats per measure;
– A fourth symbol corresponds to 4 beats per measure.

In mensural notation, the actual length of notes depends not only on the current tempus or prolatio but also on specific rules about how notes are divided or altered. When the meaning of a symbol was unclear, a dot called a "dot of separation" was used, which looked similar to the modern "dot of augmentation" but had different effects.

These symbols not only showed how beats were organized in a piece of music but also helped indicate how fast or slow different sections should be played. Modern notation uses symbols like triplets or metric modulations for this purpose. However, the use of these symbols changed over time and in different places. For example, music historian Charles Hamm studied how Guillaume Dufay used these symbols in three different ways during his career. By the late 16th century, Thomas Morley humorously described the confusion surrounding these symbols in a made-up conversation.

In general, a slash or the number 2 shows that the tempo is doubled, while paired numbers (placed next to each other or one above the other) show ratios instead of beats per measure. In early music, the number 3, for example, did not refer to "third notes."

Some common symbols include:
– Tempus imperfectum diminutum: a 1:2 ratio (twice as fast);
– Tempus perfectum diminutum: a 1:2 ratio (twice as fast);
– Proportio tripla: a 1:3 ratio (three times as fast, similar to triplets).

When a specific symbol appeared, the beat (called tactus) changed from the usual whole note (semibreve) to the double whole note (breve), a situation called alla breve. This term is still used today, though it now means the beat is a half note (minim), which contradicts its original meaning. It still indicates that the beat has changed from a short to a longer value.

Some composers created mensuration canons, which were complex musical puzzles intentionally designed to be difficult to understand.

Irregular bar

Irregular bars are short changes in the time signature that usually last for just one bar. These bars are most often a bar with 4 beats, 3 beats, or 5 beats in a piece that usually has 4 beats per bar, or a bar with 6 beats in a piece that usually has 6 beats per bar.

If a song is entirely in 4 beats per bar, changing to 3 beats per bar for one bar will make the song feel like it has skipped a beat. Changing to 5 beats per bar will make the song feel like it adds a beat. Changing to 6 beats per bar will make that bar feel half as long as the others.

Some popular examples include "Golden Brown" by The Stranglers (3 beats in a 4 beats per bar composition), "I Love Rock 'n' Roll" originally by The Arrows (5 beats in a 4 beats per bar composition), "Hey Ya!" by Outkast (6 beats in a 6 beats per bar composition), and "Wuthering Heights" by Kate Bush (different kinds of irregular bars in a 4 beats per bar composition).