Duration

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Refers to the amount of time during which a sound event in a musical composition takes place; also referred to as time-span.

The measurement of time in Western music corresponds to the time-interval between two initiating points within a specific domain and is given in terms of number of beats. For example, the duration of the first chord in Debussy’s Nuages corresponds to the time-interval between the initiation of these two chords, that is, one-third of a beat, as defined by the time signature 6/4 (two beats corresponding to a dotted half note each).

(Prepared by Ève Poudrier, 1/14/10)

Certain theorists, such as Richard Parncutt, have attemted to quantify the durational accent (the emphasis placed on a note due to its length) with the mathematical model:

Ad(T) = (1-e-ioi(T)/τ)i

where IOI(T) represents the inter-onset interval (IOI) as a function of the length of the note (in milliseconds), τ (tau) represents the saturation duration, the point at which note duration less than a certain value results in an IOI of effectively zero (also in milliseconds), and i represents the “accent index,” a value that is adjusted to match experimental results. The equation is not fully standardized, so values for i may change depending on the source; this is typically accompanied by a change in the base number of exponential function, which also may vary between 2 and e or other numbers in the vicinity (Parncutt 1994, p430-31)