5.4. Duration types

Abjad publishes duration information about all score components.

5.4.1. Written duration

Abjad uses written duration to refer to the face value of notes, rests and chords prior to prolation. Abjad written duration corresponds to the informal names most frequently used when talking about note duration.

These sixteenth notes are worth a sixteenth of a whole note:

abjad> measure = Measure((5, 16), Note(0, (1, 16)) * 5)
abjad> spannertools.BeamSpanner(measure)
abjad> staff = stafftools.RhythmicStaff([measure])
abjad> note = measure[0]
abjad> note.written_duration
Duration(1, 16)

These sixteenth notes are worth more than a sixteenth of a whole note:

abjad> tuplet = tuplettools.FixedDurationTuplet(Duration(5, 16), Note(0, (1, 16)) * 4)
abjad> spannertools.BeamSpanner(tuplet)
abjad> measure = Measure((5, 16), [tuplet])
abjad> staff = stafftools.RhythmicStaff([measure])
abjad> note = tuplet[0]
abjad> note.written_duration
Duration(1, 16)

The notes in these examples are ‘sixteenth notes’ that carry different prolated durations. Abjad written duration captures the fact that the note heads and flag counts of the two examples match.

Written duration is a user-assignable rational number. Users can assign and reassign the written duration of notes, rests and chords at initialization and at any time during the life of the note, rest or chord. Written durations must be assignable; see the chapter on assignability for details. Note that Abjad containers do not carry written duration.

5.4.2. Prolated duration

Prolation refers to the duration-scaling effects of tuplets and special types of time signature. Prolation is a way of thinking about the contribution that musical structure makes to the duration of score objects. All durated Abjad objects carry a prolated duration. Prolated duration is an emergent property of notes, tuplets and other durated objects. The prolated duration of notes, rests and chords equals the product of the written duration and prolation of those objects. The prolated duration of tuplets, measures and other containers equals the the container’s duration interface multiplied by the container’s prolation.

5.4.3. Contents duration

Abjad defines the contents duration of tuplets, measures, voices, staves and other containers equal to the sum of the preprolated duration of each of the elements in the container.

The measure here contains two eighth notes and tuplet. These elements carry preprolated durations equal to 1/8, 1/8 and 2/8, respectively:

abjad> notes = Note(0, (1, 8)) * 2
abjad> spannertools.BeamSpanner(notes)
abjad> tuplet = tuplettools.FixedDurationTuplet(Duration(2, 8), Note(0, (1, 8)) * 3)
abjad> spannertools.BeamSpanner(tuplet)
abjad> measure = Measure((4, 8), notes + [tuplet])
abjad> staff = stafftools.RhythmicStaff([measure])
abjad> measure.contents_duration
Duration(1, 2)

The contents duration of the measure here equals 1/8 + 1/8 + 2/8 = 4/8.

5.4.4. Target duration

Abjad defines the target duration of fixed-duration tuplets equal to composer-settable duration to which the tuplet prolates its contents.

This fixed-duration tuplet carries a target duration equal to 4/8:

abjad> tuplet = tuplettools.FixedDurationTuplet(Duration(4, 8), Note(0, (1, 8)) * 5)
abjad> spannertools.BeamSpanner(tuplet)
abjad> measure = Measure((4, 8), [tuplet])
abjad> staff = stafftools.RhythmicStaff([measure])
abjad> print tuplet.contents_duration
5/8
abjad> tuplet.target_duration
Duration(1, 2)

The tuplet contents sum to 5/8. But tuplet target duration always equals 4/8.

5.4.5. Multiplied duration

Abjad defines the multiplied duration of notes, rests and chords equal to the product of written duration and leaf multiplier.

The first two notes below carry leaf mulitipliers equal to 2/1:

abjad> notes = Note(0, (1, 16)) * 4
abjad> notes[0].duration_multiplier = Fraction(2, 1)
abjad> notes[1].duration_multiplier = Fraction(2, 1)
abjad> measure = Measure((3, 8), notes)
abjad> spannertools.BeamSpanner(measure)
abjad> staff = stafftools.RhythmicStaff([measure])
abjad> note = measure[0]
abjad> note.written_duration
Duration(1, 16)

abjad> note.duration_multiplier
Fraction(2, 1)

abjad> note.written_duration * note.duration_multiplier
Duration(1, 8)
abjad> note.multiplied_duration
Duration(1, 8)

The written duration of these first two notes equals 1/16 and so the multiplied duration of these first two notes equals 1/16 * 2/1 = 1/8.