Time signatures consist of two numbers: the lower number indicates the note value that represents one beat (the "beat unit"); the upper number indicates how many of these beats there are in a bar.
Note values are traditionally classified as simple (2/4 and 3/4) and other time signatures, including perfect (for example, 4/4=2/4+2/4), triple, complex, and changing time signatures. Note: The Finnish term 'yhdistetty tahtilaji' is not the same as the English 'compound meter'.
Besides providing the time values and their number, a time signature defines the metric structure in a bar. In compound metres, the main beat is divided into parts, which are longer than the beat unit. For example, time signatures 6/8, 9/8 and 12/8 almost always consist of 3/8 units; in other words, the beat unit is not a quaver or an eighth note but a dotted crotchet or fourth note. It is only in slow tempos that a quaver or an eighth note is perceived as a natural beat unit in these time signatures.
Shorter or longer note values can also be applied as beat units, and their numbers can be different from that shown in the chart.
Time signatures in brackets often use a beat unit other than that on the line. For example, a dotted minim or half note is a frequent beat unit in high tempo ¾ time signatures. A dotted crotchet or fourth note is often used as a beat unit in 6/8 time signatures. The sign denotesa 4/4 time signature; stands for 2/2 (alla breve).
In notation, metric structure is presented according to history and tradition. It is important to point out a difference between, for example, 3/4 and 6/8 time signatures: Even though both time signatures consist of the same calculatory number of note values, the former is divided into three beats, the latter into two beats. To be more precise, modern notation sometimes applies a note instead of a time value to present the beat unit.
Rhythm/metre has been and still is perceived and explained in various ways. The traditional terms used in Finnish music theory to describe metrics, iskuala (by Krohn) and metrinen kaava (by Oksala) do not correspond to the hierarchical pulse structure presented as dots below.
The dots on the top line denote the shortest time value in use (fast pulse). Four dots on top of each other denote the note with the strongest accent or emphasis (after the barline); according to the hierarchical structure, three dots on top of each other get a stronger accent than two dots. It is typical that one of these beats with a weaker accent represents the pulse defining the beat unit.
Figure A shows a perfect time signature; in 4/4 time, the dots are quavers or eighth notes, in 2/4 time, they are semiquavers or sixteenth notes.
While figure B can be a 6/8 time signature, it can also be perceived as ¾ time, typically consisting of pairs with a weaker latter part.
Figure C can be perceived as ¾ time if it denotes a swing rhythm (jazz waltz).
Figure D can be a 12/8 time signature (with quaver dots) or a typical swing 4/4 time (with crotchet triplets). In figures B, C, and D, the bar is divided into two, three, and four parts, but they all have the same number of notes with the shortest time value.
The four divisions of time mentioned above were known as early as the 14th century as tempus and prolatio.
The divisions shown above are often applied to musical units larger than a bar. It is common in popular music with African-American origins that bars form pairs and further clusters of four, eight, twelve, and sixteen bars with accented beginnings.
To perceive the metric structure of music, it is good to be familiar with beat units, and to note anacruses and incomplete bars, groupings of time values (with beams or ties), and different symbols for phrasing.
Tempo is also an important factor for the perception of metric structure and for the writing of time signatures: when a slow melody in ¾ time is accelerated, it is wise to write a dotted crotchet as the beat unit and 6/8 as the time signature. Further accelerated, a natural time signature would be 12/8. When the tempo is fast enough to blur the subdivisions of the beat, the time signature will be 4/4; with the speeded-up tempo, a triple time becomes a simple time!