The time signature (also known as meter signature, metre signature, or measure signature) is a notational convention used in Western musical notation to specify how many beats (pulses) are to be contained in each bar and which note value is to be given one beat. In a musical score, the time signature appears at the beginning of the piece, as a time symbol or stacked numerals, such as or 3/4 (read common time and three four time, respectively), immediately following the key signature or immediately following the clef symbol if the key signature is empty.
There are various types of time signatures, including: simple (such as 3/4 or 4/4), compound (e.g., 9/8 or 12/8), complex (e.g., 5/4 or 7/8), mixed (e.g., 5/8 & 3/8 or 6/8 & 3/4), additive (e.g., 3+2+3/8), fractional (e.g., 2½/4), and irrational meters (e.g., 3/10 or 5/24).
Simple Time Signatures
The most common simple time signatures are 2/4, 3/4, and 4/4.
Notational Variations in Simple Time
The symbol is sometimes used for 4/4 time, also called common time or imperfect time. The symbol is derived from a broken circle used in music notation from the 14th through 16th centuries, where a full circle represented what today would be written in 3/2 or 3/4 time, and was called tempus perfectum (perfect time). The symbol is also a carry-over from the notational practice of late-Medieval and Renaissance music, where it signified tempus imperfectum diminutum (diminished imperfect time)—more precisely, a doubling of the speed, or proportio dupla, in duple meter. In modern notation, it is used in place of 2 and is called alla breve or, colloquially, cut time or cut common time.
Compound Time Signatures
In compound meter, subdivisions of the main beat (the upper number) split into three, not two, equal parts, so that a dotted note (half again longer than a regular note) becomes the beat unit. Compound time signatures are named as if they were simple time signatures, in which the one-third part of the beat unit is the beat, so the top number is commonly 6, 9 or 12 (multiples of 3). The lower number is most commonly an 8 (an eighth-note): as in 9/8 or 12/8.
3/4 is a simple signature that represents three quarter notes. It has a basic feel of (Bold denotes a stressed beat):
one two three (as in a waltz)
Each quarter note might comprise two eighth-notes (quavers) giving a total of six such notes, but it still retains that three-in-a-bar feel:
one and two and three and
6/8: Theoretically, this can be thought of as the same as the six-quaver form of 3/4 above with the only difference being that the eighth note is selected as the one-beat unit. But whereas the six quavers in 3/4 had been in three groups of two, 6/8 is practically understood to mean that they are in two groups of three, with a two-in-a-bar feel (Bold denotes a stressed beat):
one and a, two and a
one two three, four five six
Beat and Time
Time signatures indicating two beats per bar (whether they are simple or compound) are called duple time; those with three beats to the bar are triple time. To the ear, a bar may seem like one singular beat. For example, a fast waltz, notated in 3/4 time, may be described as being one in a bar. Terms such as quadruple (4), quintuple (5), and so on are also occasionally used.
Actual Beat Divisions
As mentioned above, though the score indicates a 3/4 time, the actual beat division can be the whole bar, particularly at faster tempos. Correspondingly, at slow tempos the beat indicated by the time signature could in actual performance be divided into smaller units.
Interchangeability, Rewriting Meters
On a formal mathematical level, the time signatures of, for example, 3/4 and 3/8 are interchangeable.
In a sense, all simple triple time signatures, such as 3/8, 3/4, 3/2, etc.—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. Other time signature rewritings are possible: most commonly a simple time signature with triplets translates into a compound meter.
Though formally interchangeable, for a composer or performing musician, 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 6/4 or 2/2 than the eight/quaver in 6/8 or 2/4. Third, time signatures are traditionally associated with different music styles—it might seem strange to notate a rock tune in 4/8 or 4/2.
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 offbeats 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, though notes on stressed beats are not necessarily louder or more important.