Time Signature Duration Calculator

Clock time for a notated passage comes from three quantities: the tempo, the meter, and the bar count. Tempo in beats per minute is conventionally referenced to the quarter note, so a quarter note lasts 60/BPM seconds. The bottom number of the time signature names the note value that receives one beat, and converting between it and the quarter-note reference introduces the factor 4 divided by that number. One beat therefore lasts (60/BPM) times (4/unit) seconds, a bar lasts that times the top number, and the passage lasts the bar length times the number of bars. At 120 BPM a 4/4 bar runs 2.000 seconds while a 6/8 bar runs 1.500 seconds, because six eighth notes at 0.25 seconds each is less total value than four quarter notes. Meters are classified by how the beat divides. Simple meters such as 2/4, 3/4 and 4/4 divide each beat in two; compound meters such as 6/8, 9/8 and 12/8 group their units in threes so the felt beat is a dotted quarter; irregular meters such as 5/4, 7/8 and 11/8 mix groups of two and three. The important caveat is that the notated denominator does not always match what the performer feels, and BPM is often quoted against the felt beat instead. A 6/8 jig marked 120 usually means 120 dotted-quarter beats, not 120 eighths, which is a factor-of-three difference in duration. Treat the result as exact clock arithmetic for a fixed tempo; real performances include rubato, ritardando, fermatas and repeats that this model does not represent.

Notating relative duration at all was a medieval achievement. Franco of Cologne, writing around 1280, set out a system in which note shapes carried fixed durational values, and the fourteenth-century Ars Nova associated with Philippe de Vitry extended it with mensuration signs. Those signs, ancestors of the modern time signature, indicated whether the breve divided into two or three semibreves and were written as a circle for perfect (triple) division and a broken circle for imperfect (duple) division. The half-circle still used as the common-time C symbol is a survival of that broken circle rather than an abbreviation for the word common, and the struck-through version marking cut time descends from the proportional signs that halved note values. By the seventeenth century the mensuration signs had given way to the numeric fraction-like pair used today, with the lower figure naming a note value directly. Absolute rather than relative speed remained unspecified until mechanical timekeeping arrived: Johann Nepomuk Maelzel patented his metronome in 1815 and Beethoven began publishing metronome numbers from 1817, which for the first time made a bar of music convertible into seconds. The calculation became routine work in the twentieth century for film composers timing cues to picture and later for sequencer and digital audio workstation users, where bar and beat positions, loop lengths and tempo-synced delay times are all derived from exactly this relationship.