Duration types — Abjad v1.1.1 documentation

### Navigation

- index
- modules |
- next |
- previous |
- Project Abjad »
- Abjad v1.1.1 documentation »
- Durations »

# Duration types

Abjad publishes duration information about notes, rests, chords and skips, and also about tuplets, measures, voices, staves and the other containers. Abjad groups duration information about notes, rests, chords and skips into the `_LeafDurationInterface` class; duration information about tuplets, measures, voices, staves and other containers groups together inside some type of `_ComponentDurationInterface` interface.

## Written duration

Abjad uses written duration to refer to the face value of notes, rests, chords and skips without prolation. Abjad written duration corresponds to the informal names we use when talking about duration.

The sixteenth notes here are worth exactly a sixteenth of a whole note.

    abjad> measure = RigidMeasure((5, 16), Note(0, (1, 16)) * 5)
    abjad> Beam(measure)
    abjad> staff = RhythmicStaff([measure])
    abjad> note = measure[0]
    abjad> print note.duration.written
    1/16

The sixteenth notes here are worth more than a sixteenth of a whole note.

    abjad> tuplet = FixedDurationTuplet((5, 16), Note(0, (1, 16)) * 4)
    abjad> Beam(tuplet)
    abjad> measure = RigidMeasure((5, 16), [tuplet])
    abjad> staff = RhythmicStaff([measure])
    abjad> note = tuplet[0]
    abjad> print note.duration.written
    1/16

The notes in these examples carry different durations. But we probably still call them all sixteenths anyway. Abjad written duration captures the fact that these notes write the same way before prolation.

Abjad notes, rests, chords and skips all make written duration available as `duration.written`. Written duration is a user-assignable rational number. Users can assign and reassign the written duration of notes, rests, chords and skips at initialization and at any time during the life of the note, rest, chord or skip. Notes, rests, chords and skips admit a degree of input flexibility; Abjad `Rational` instances, rational tokens, and integers are all allowed; see the chapter on duration initialzation for details. Written durations must always be notehead-assignable; see the chapter on assignability for details. The written duration of notes, rests, chords and skips corresponds more closely to our usual understanding of musical duration than do any of the other Abjad duration attributes. Abjad containers do not carry written duration.

## 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 as duration.prolated. Prolated duration is an emergent property of notes, tuplets and other durated objects. The prolated duration of notes, rests, chords and skips equals the product of the written duration and prolation of those objects. The prolated duration of tuplets, measures and other containers equals the product of the container duration interface itself and the prolation of the container in question.

## 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> Beam(notes)
    abjad> tuplet = FixedDurationTuplet((2, 8), Note(0, (1, 8)) * 3)
    abjad> Beam(tuplet)
    measure = RigidMeasure((4, 8), notes + [tuplet])
    abjad> staff = RhythmicStaff([measure])
    abjad> print measure.duration.contents
    1/2

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

## Target duration

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

The fixed-duration tuplet here carries a target duration equal to 4/8.

    abjad> tuplet = FixedDurationTuplet((4, 8), Note(0, (1, 8)) * 5)
    abjad> Beam(tuplet)
    measure = RigidMeasure((4, 8), [tuplet])
    abjad> staff = RhythmicStaff([measure])
    abjad> print tuplet.duration.contents
    5/8
    abjad> print tuplet.duration.target
    1/2

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

## Multiplied duration

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

The first two notes here carry leaf mulitipliers equal to 2/1.

    abjad> notes = Note(0, (1, 16)) * 4
    abjad> notes[0].duration.multiplier = Rational(2, 1)
    abjad> notes[1].duration.multiplier = Rational(2, 1)
    measure = RigidMeasure((3, 8), notes)
    abjad> Beam(measure)
    abjad> staff = RhythmicStaff([measure])
    abjad> note = measure[0]
    abjad> print note.duration.written
    1/16

    abjad> print note.duration.multiplier
    2

    abjad> print note.duration.written * note.duration.multiplier
    1/8
    abjad> print note.duration.multiplied
    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.

### Navigation

- index
- modules |
- next |
- previous |
- Project Abjad »
- Abjad v1.1.1 documentation »
- Durations »