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The time signature, or meter of a musical entity is an indicator as to how the measure is to be rythmically interpreted relative to the tempo. The time signature has existed since the advent of modern musical notation, and has persisted to today in much the same form as it first appeared in.
Elements of a time signature, common meters
Music is commonly divided up into measures, each of which are defined by the most recently indicated time signature. Each measure is composed of a certain number of beats lasting a certain duration (in relation to the tempo). The time signature presents two numerical values that define both variables. Below is an example of a common time signature:
<music> \time 2/4 e2 </music>
The bottom number indicates what the beat represents. A simple way to determine this is to use this number as the denominator of a fraction: in this case, 1/4. We now know that one beat represents one quarter note. The top number indicates the number of beats in a measure. In this case, the time signature indicates there are two beats to a measure. Putting these two elements together, we learn that one measure of 2/4 contains two quarter notes:
<music> \time 2/4 ees4 ges4 a2 bes2 (bes2) </music>
A measure of 3/4 contains three quarter-notes beats, 4/4 four (4/4 can be indicated by the letter C ):
<music> \time 3/4 c4 d4 e4 </music> <music> \time 4/4 d4 fis4 a4 g4 fis1 </music>
A measure of 12/8 contains twelve 8th-note beats, 9/8 nine:
<music> \time 12/8 ees8 ees8 ees8 e8 e8 e8 f8 f8 f8 fis8 fis8 fis8 </music> <music> \time 9/8 g'8 g8 g8 gis8 gis8 gis8 a8 a8 a8 </music>
A measure of 3/2 contains three half-note beats, 2/2 two (2/2 is sometimes denoted by the letter C, with a line drawn through it):
<music> \time 3/2 b'2 a2 g2 </music> <music> \time 2/2 e2 f2 </music>
The more common meters used in music are, for the most part, those listed above: 2/2, 3/2, 2/4, 3/4, 4/4, 3/8 6/8, 9/8, 12/8 (3/16, 6/16) . Other time signatures exist and are used, however, they are not as common as the ones previously listed. Time signatures that have an even number indicating the number of beats to a measure are termed duple meters, while those that have a factor of 3 are termed triple meters.
Less common meters
As there are a very large number of possibilities for time signatures, meters other than the common ones listed above may be written. Some possibilities include 5/4, 7/4, 5/8, 7/8, 5/16, 7/16, etc.
<music> \time 5/4 d4 e4 f4 fis4 g4 </music> <music> \time 7/8 aes'4 g8 d8 fis8 gis4 </music> <music> \time 7/16 r16 cis'16 e,16 des8 bes16 a'16 </music>
Accents within the measure
Usually, the meter of a measure doesn't only define its speed and its value in relation to the tempo. It also serves as an indicator of rhythmic accent, indicating which beats to emphasize. In duple meters, the first notes of a pair are rhythmically emphasized:
<music> \time 2/4 ees->d c->d </music> <music> \time 4/4 d->e f->gis a->d f->e </music>
When the meter is made up of more than one pair of beats, the first pair receives stronger emphasis than the second (this is an important distinction between 2/4 and 4/4, the third beat being less accented than the first in the latter).
Triple meters generally recieve accent on the first beat of the measure:
<music> \time 3/4 f4->a4 cis4 </music>
However, ternary meters that can be grouped into two ore more untis of three smaller values (usually eigth notes) are generally considered, and counted, as a larger duple or triple meter. The examples below demonstrate 12/8 counted in the same accented manner as 4/4 (one beat to every dotted quarter note), 9/8 as 3/4 and 6/8 as 2/4.
<music> \time 12/8 c8->c8 c8 d8 e8 f8 fis8->fis8 fis8 g8 g8 g8 </music> <music> \time 9/8 f8->g8 a8 g8 a8 bes8 a8 c8 a8 </music> <music> \time 6/8 ees8-> ees8 ees8 bes8 bes8 bes8 </music>
Time signatures not indicating a number of beats to the measure that finds itself to be a factor of 2 or 3 are termed asymmetrical meters. These meters can be counted with a single accent on the first beat of the measure:
<music> \time 7/4 d4->e4 fis4 e4 f4 a4 d4 </music>
Or, they may be broken up into triple and duple meters. Below, a measure of 5/8 is divided into one measure of 2/8 and one measure of 3/8.
<music> \time 5/8 ges8->aes8 bes8 aes8->des8 </music>
Asymmetrical meters counted in this way may also be indicated with time signatures that "add up" a triple and duple meter. For example, 7/4 could be notated as 3+2+2/4 to signify the following accent pattern:
<music> \time 7/4 g'4-> a4 b4 a4->g4 f4->e4 </music>
Effect of tempo upon the measure
The tempo is usually indicated by a rhythm and a number indicating how many times that rhythm can be played in one minute at that given tempo (e.g. quarter note = 100). While the tempo is usually indicated with the same rhythm used in the time signature (4/4 using tempo at the quarter note, 3/2 using tempo at the half note, etc.), often the tempo uses different rhythmic values than are indicated by the time signature. This occurs mostly when a measure of smaller values is considered as one large triple or duple meter (a possibility previously discussed). For example, a measure of 12/8, counted and accented as 4/4 would be, could use a tempo counted at the dotted quarter note (equivalent to three eigth notes). Thus, the measure would be counted as 4/4 would be, however the subdivisions of each beat would be different. Likewise, a measure of 3/4 or 3/8 could be counted using a tempo at the dotted half note or dotted quarter note, respectively.
When the tempo remains constant, the use of different time signatures affects the speed at which notes are played. For example, at the ssme tempo of quarter note = 60, a measure of 3/4 will be played more slowly than a measure of 3/8 with the same melodic content. However, meters that are rhythmically equivalent, such as 4/4 and 2/2, will be played at the same speed if the same tempo is used.
Historical evolution of the time signature
Before the advent of modern musical notation, the usual notions of tempo, measures, bar lines and beats were absent from the then-used mensural notation. Rather, a symbol placed before the text indicated the ratio between the durations of the note values, the tempus being the ration between the duration of the breve (double whole note) and the semibreve (whole note), the prolatio being the ratio between the duration of the semibreve (whole note) and the minim (half note). A circle placed at the begining of the text indicated tempus perfectum (corresponding to triple meter, a 3:1 ratio betweeen the durations of the breve and semibreve), while a half circle indicated tempus imperfectum (corresponding to duple meter). A dot placed inside the circle or half-circle indicated prolatio perfecta (corresponding to a 3:1 ratio between the durations of the semibreve and minim), the absence of a dot indicating prolatio imperfecta (corresponding to a 2:1 ratio between the durations of the semibreve and minim).
The modern time signature came into existence during the Rennaissance and Baroque periods, the meters used being the ones most commonly found today (i.e. 4/4, 2/4, 3/4, etc.). More complex meters came into use during the late romantic and early 20th century periods, and the use of asymmetrical meter can be found in works such as Moussorgsky's Pictures at an Exhibition and Stravinsky's Rite of Spring. Today, complex meters are frequently seen in works of a more modernist character.