Duration

digraph InheritanceGraph { graph [bgcolor=transparent, color=lightsteelblue2, fontname=Arial, fontsize=10, outputorder=edgesfirst, overlap=prism, penwidth=2, rankdir=LR, splines=spline, style="dashed, rounded", truecolor=true]; node [colorscheme=pastel19, fontname=Arial, fontsize=10, height=0, penwidth=2, shape=box, style="filled, rounded", width=0]; edge [color=lightslategrey, penwidth=1]; subgraph "cluster_abjad.system" { graph [label="abjad.system"]; node [color=1]; "abjad.system.AbjadObject.AbjadObject" [URL="../api/abjad/utilities/../system/AbjadObject.html#abjad.system.AbjadObject.AbjadObject", label="Abjad\nObject", target=_top]; } subgraph "cluster_abjad.utilities" { graph [label="abjad.utilities"]; node [color=2]; "abjad.utilities.Duration.Duration" [URL="../api/abjad/utilities/Duration.html#abjad.utilities.Duration.Duration", color=black, fontcolor=white, label=Duration, target=_top]; "abjad.utilities.Multiplier.Multiplier" [URL="../api/abjad/utilities/Multiplier.html#abjad.utilities.Multiplier.Multiplier", label=Multiplier, target=_top]; "abjad.utilities.Offset.Offset" [URL="../api/abjad/utilities/Offset.html#abjad.utilities.Offset.Offset", label=Offset, target=_top]; "abjad.utilities.Duration.Duration" -> "abjad.utilities.Multiplier.Multiplier"; "abjad.utilities.Duration.Duration" -> "abjad.utilities.Offset.Offset"; } subgraph cluster_builtins { graph [label=builtins]; node [color=3]; "builtins.object" [URL="https://docs.python.org/3.6/library/functions.html#object", label=object, target=_top]; } subgraph cluster_fractions { graph [label=fractions]; node [color=4]; "fractions.Fraction" [URL="https://docs.python.org/3.6/library/fractions.html#fractions.Fraction", label=Fraction, target=_top]; } subgraph cluster_numbers { graph [label=numbers]; node [color=5]; "numbers.Complex" [URL="https://docs.python.org/3.6/library/numbers.html#numbers.Complex", label=Complex, shape=oval, style=bold, target=_top]; "numbers.Number" [URL="https://docs.python.org/3.6/library/numbers.html#numbers.Number", label=Number, target=_top]; "numbers.Rational" [URL="https://docs.python.org/3.6/library/numbers.html#numbers.Rational", label=Rational, shape=oval, style=bold, target=_top]; "numbers.Real" [URL="https://docs.python.org/3.6/library/numbers.html#numbers.Real", label=Real, shape=oval, style=bold, target=_top]; "numbers.Complex" -> "numbers.Real"; "numbers.Number" -> "numbers.Complex"; "numbers.Real" -> "numbers.Rational"; } "abjad.system.AbjadObject.AbjadObject" -> "abjad.utilities.Duration.Duration"; "builtins.object" -> "abjad.system.AbjadObject.AbjadObject"; "builtins.object" -> "numbers.Number"; "fractions.Fraction" -> "abjad.utilities.Duration.Duration"; "numbers.Rational" -> "fractions.Fraction"; }

class abjad.utilities.Duration.Duration

Duration.

Initializes from integer numerator:

>>> abjad.Duration(3)
Duration(3, 1)

Initializes from integer numerator and denominator:

>>> abjad.Duration(3, 16)
Duration(3, 16)

Initializes from integer-equivalent numeric numerator:

>>> abjad.Duration(3.0)
Duration(3, 1)

Initializes from integer-equivalent numeric numerator and denominator:

>>> abjad.Duration(3.0, 16)
Duration(3, 16)

Initializes from integer-equivalent singleton:

>>> abjad.Duration((3,))
Duration(3, 1)

Initializes from integer-equivalent pair:

>>> abjad.Duration((3, 16))
Duration(3, 16)

Initializes from other duration:

>>> abjad.Duration(abjad.Duration(3, 16))
Duration(3, 16)

Intializes from fraction:

>>> abjad.Duration(abjad.Fraction(3, 16))
Duration(3, 16)

Initializes from solidus string:

>>> abjad.Duration('3/16')
Duration(3, 16)

Initializes from nonreduced fraction:

>>> abjad.Duration(abjad.NonreducedFraction(6, 32))
Duration(3, 16)

Durations inherit from built-in fraction:

>>> isinstance(abjad.Duration(3, 16), abjad.Fraction)
True

Durations are numbers:

>>> import numbers
>>> isinstance(abjad.Duration(3, 16), numbers.Number)
True

Attributes Summary

__abs__ Gets absolute value of duration.
__add__ Adds duration to arguments.
__div__ Divides duration by arguments.
__divmod__ Equals the pair (duration // arguments, duration % arguments).
__eq__ Is true when duration equals argument.
__format__ Formats duration.
__ge__ Is true when duration is greater than or equal to argument.
__gt__ Is true when duration is greater than argument.
__hash__ Hashes duration.
__le__ Is true when duration is less than or equal to argument.
__lt__ Is true when duration is less than argument.
__mod__ Modulus operator applied to duration.
__mul__ Duration multiplied by arguments.
__neg__ Negates duration.
__new__ Create and return a new object.
__pos__ Get positive duration.
__pow__ Raises duration to arguments power.
__radd__ Adds arguments to duration.
__rdiv__ Divides arguments by duration.
__rdivmod__ Documentation required.
__rmod__ Documentation required.
__rmul__ Multiplies arguments by duration.
__rpow__ Raises arguments to the power of duration.
__rsub__ Subtracts duration from arguments.
__rtruediv__ Documentation required.
__sub__ Subtracts arguments from duration.
__truediv__ Documentation required.
dot_count Gets dot count.
durations_to_nonreduced_fractions Changes durations to nonreduced fractions sharing least common denominator.
equal_or_greater_assignable Gets assignable duration equal to or just greater than this duration.
equal_or_greater_power_of_two Gets duration equal or just greater power of two.
equal_or_lesser_assignable Gets assignable duration equal or just less than this duration.
equal_or_lesser_power_of_two Gets duration of the form d**2 equal to or just less than this duration.
flag_count Gets flag count.
from_lilypond_duration_string Initializes duration from LilyPond duration string.
has_power_of_two_denominator Is true when duration is an integer power of two.
implied_prolation Gets implied prolation.
is_assignable Is true when duration is assignable.
is_token Is true when argument correctly initializes a duration.
lilypond_duration_string Gets LilyPond duration string.
pair Gets numerator and denominator.
prolation_string Gets prolation string.
reciprocal Gets reciprocal.
to_clock_string Changes duration to clock string.
to_score_markup Changes duration to score markup.
with_denominator Changes duration to nonreduced fraction with denominator.

Special methods

__abs__(*arguments)

Gets absolute value of duration.

Returns nonnegative duration.

__add__(*arguments)

Adds duration to arguments.

Returns duration when arguments is a duration:

>>> duration_1 = abjad.Duration(1, 2)
>>> duration_2 = abjad.Duration(3, 2)
>>> duration_1 + duration_2
Duration(2, 1)

Returns nonreduced fraction when arguments is a nonreduced fraction:

>>> duration = abjad.Duration(1, 2)
>>> nonreduced_fraction = abjad.NonreducedFraction(3, 6)
>>> duration + nonreduced_fraction
NonreducedFraction(6, 6)

Returns duration.

(Fraction).__bool__()

a != 0

(Fraction).__ceil__()

Will be math.ceil(a) in 3.0.

(Real).__complex__()

complex(self) == complex(float(self), 0)

(Fraction).__copy__()
(Fraction).__deepcopy__(memo)
__div__(*arguments)

Divides duration by arguments.

>>> abjad.Duration(1) / abjad.NonreducedFraction(3, 3)
NonreducedFraction(3, 3)
>>> abjad.NonreducedFraction(3, 3) / abjad.Duration(1)
NonreducedFraction(3, 3)

Returns multiplier.

__divmod__(*arguments)

Equals the pair (duration // arguments, duration % arguments).

Returns pair.

__eq__(argument)

Is true when duration equals argument.

Returns true or false.

(Rational).__float__()

float(self) = self.numerator / self.denominator

It’s important that this conversion use the integer’s “true” division rather than casting one side to float before dividing so that ratios of huge integers convert without overflowing.

(Fraction).__floor__()

Will be math.floor(a) in 3.0.

(Fraction).__floordiv__(b)

a // b

__format__(format_specification='')

Formats duration.

Set format_specification to '' or 'storage'. Interprets '' equal to 'storage'.

Returns string.

__ge__(argument)

Is true when duration is greater than or equal to argument.

Returns true or false.

__gt__(argument)

Is true when duration is greater than argument.

Returns true or false.

__hash__()

Hashes duration.

Required to be explicitly redefined on Python 3 if __eq__ changes.

Returns integer.

__le__(argument)

Is true when duration is less than or equal to argument.

Returns true or false.

__lt__(argument)

Is true when duration is less than argument.

Returns true or false.

__mod__(*arguments)

Modulus operator applied to duration.

Returns duration.

__mul__(*arguments)

Duration multiplied by arguments.

Returns a new duration when arguments is a duration:

>>> duration_1 = abjad.Duration(1, 2)
>>> duration_2 = abjad.Duration(3, 2)
>>> duration_1 * duration_2
Duration(3, 4)

Returns nonreduced fraction when arguments is a nonreduced fraction:

>>> duration = abjad.Duration(1, 2)
>>> nonreduced_fraction = abjad.NonreducedFraction(3, 6)
>>> duration * nonreduced_fraction
NonreducedFraction(3, 12)

Returns duration or nonreduced fraction.

__neg__(*arguments)

Negates duration.

Returns new duration.

static __new__(class_, *arguments)

Create and return a new object. See help(type) for accurate signature.

__pos__(*arguments)

Get positive duration.

Returns new duration.

__pow__(*arguments)

Raises duration to arguments power.

Returns new duration.

__radd__(*arguments)

Adds arguments to duration.

Returns new duration.

__rdiv__(*arguments)

Divides arguments by duration.

Returns new duration.

__rdivmod__(*arguments)

Documentation required.

(AbjadObject).__repr__()

Gets interpreter representation of Abjad object.

Returns string.

(Fraction).__rfloordiv__(a)

a // b

__rmod__(*arguments)

Documentation required.

__rmul__(*arguments)

Multiplies arguments by duration.

Returns new duration.

(Fraction).__round__(ndigits=None)

Will be round(self, ndigits) in 3.0.

Rounds half toward even.

__rpow__(*arguments)

Raises arguments to the power of duration.

Returns new duration.

__rsub__(*arguments)

Subtracts duration from arguments.

Returns new duration.

__rtruediv__(*arguments)

Documentation required.

Returns new duration.

(Fraction).__str__()

str(self)

__sub__(*arguments)

Subtracts arguments from duration.

>>> abjad.Duration(1, 2) - abjad.NonreducedFraction(2, 8)
NonreducedFraction(2, 8)
>>> abjad.NonreducedFraction(4, 8) - abjad.Duration(1, 4)
NonreducedFraction(2, 8)

Returns new duration.

__truediv__(*arguments)

Documentation required.

(Fraction).__trunc__()

trunc(a)


Methods

(Real).conjugate()

Conjugate is a no-op for Reals.

(Fraction).limit_denominator(max_denominator=1000000)

Closest Fraction to self with denominator at most max_denominator.

>>> Fraction('3.141592653589793').limit_denominator(10)
Fraction(22, 7)
>>> Fraction('3.141592653589793').limit_denominator(100)
Fraction(311, 99)
>>> Fraction(4321, 8765).limit_denominator(10000)
Fraction(4321, 8765)
to_clock_string()

Changes duration to clock string.

Changes duration to clock string:

>>> note = abjad.Note("c'4")
>>> duration = abjad.Duration(117)
>>> clock_string = duration.to_clock_string()
>>> clock_string
"1'57''"
>>> string = '"{}"'.format(clock_string)
>>> markup = abjad.Markup(string, direction=abjad.Up)
>>> abjad.attach(markup, note)
>>> abjad.show(note) 

Rounds down to nearest second.

Returns string.

to_score_markup()

Changes duration to score markup.

Changes assignable duration to score markup:

>>> markup = abjad.Duration(3, 16).to_score_markup()
>>> abjad.show(markup) 

Changes nonassignable duration to score markup:

>>> markup = abjad.Duration(5, 16).to_score_markup()
>>> abjad.show(markup) 

Override tuplet number text like this:

>>> tuplet = abjad.Tuplet((5, 7), "c'16 c' c' c' c' c' c'")
>>> abjad.attach(abjad.Beam(), tuplet[:])
>>> staff = abjad.Staff([tuplet], lilypond_type='RhythmicStaff')
>>> duration = abjad.inspect(tuplet).duration()
>>> markup = duration.to_score_markup()
>>> markup = markup.scale((0.75, 0.75))
>>> abjad.override(tuplet).tuplet_number.text = markup
>>> abjad.show(staff) 

Returns markup.

with_denominator(denominator)

Changes duration to nonreduced fraction with denominator.

Changes duration to nonreduced fraction:

>>> duration = abjad.Duration(1, 4)
>>> for denominator in (4, 8, 16, 32):
...     print(duration.with_denominator(denominator))
... 
1/4
2/8
4/16
8/32

Returns new duration.


Class & static methods

static durations_to_nonreduced_fractions(durations)

Changes durations to nonreduced fractions sharing least common denominator.

Changes durations to nonreduced fractions:

>>> durations = [abjad.Duration(2, 4), 3, (5, 16)]
>>> result = abjad.Duration.durations_to_nonreduced_fractions(durations)
>>> for x in result:
...     x
... 
NonreducedFraction(8, 16)
NonreducedFraction(48, 16)
NonreducedFraction(5, 16)
Return type:List[NonreducedFraction]
classmethod (Fraction).from_decimal(dec)

Converts a finite Decimal instance to a rational number, exactly.

classmethod (Fraction).from_float(f)

Converts a finite float to a rational number, exactly.

Beware that Fraction.from_float(0.3) != Fraction(3, 10).

static from_lilypond_duration_string(lilypond_duration_string)

Initializes duration from LilyPond duration string.

Initializes duration from LilyPond duration string:

>>> abjad.Duration.from_lilypond_duration_string('8.')
Duration(3, 16)

Returns duration.

static is_token(argument)

Is true when argument correctly initializes a duration.

Is true when expression is a duration token:

>>> abjad.Duration.is_token('8.')
True

Returns true or false.


Read-only properties

(Fraction).denominator
dot_count

Gets dot count.

Gets dot count:

>>> for n in range(1, 16 + 1):
...     try:
...         duration = abjad.Duration(n, 16)
...         sixteenths = duration.with_denominator(16)
...         dot_count = duration.dot_count
...         string = f'{sixteenths!s}\t{dot_count}'
...         print(string)
...     except abjad.AssignabilityError:
...         sixteenths = duration.with_denominator(16)
...         print(f'{sixteenths!s}\t--')
... 
1/16	0
2/16	0
3/16	1
4/16	0
5/16	--
6/16	1
7/16	2
8/16	0
9/16	--
10/16	--
11/16	--
12/16	1
13/16	--
14/16	2
15/16	3
16/16	0

Dot count defined equal to number of dots required to notate duration.

Raises assignability error when duration is not assignable.

Returns positive integer.

equal_or_greater_assignable

Gets assignable duration equal to or just greater than this duration.

Gets equal-or-greater assignable duration:

>>> for numerator in range(1, 16 + 1):
...     duration = abjad.Duration(numerator, 16)
...     result = duration.equal_or_greater_assignable
...     sixteenths = duration.with_denominator(16)
...     print(f'{sixteenths!s}\t{result!s}')
... 
1/16	1/16
2/16	1/8
3/16	3/16
4/16	1/4
5/16	3/8
6/16	3/8
7/16	7/16
8/16	1/2
9/16	3/4
10/16	3/4
11/16	3/4
12/16	3/4
13/16	7/8
14/16	7/8
15/16	15/16
16/16	1

Returns new duration.

equal_or_greater_power_of_two

Gets duration equal or just greater power of two.

Gets equal-or-greater power-of-two:

>>> for numerator in range(1, 16 + 1):
...     duration = abjad.Duration(numerator, 16)
...     result = duration.equal_or_greater_power_of_two
...     sixteenths = duration.with_denominator(16)
...     print(f'{sixteenths!s}\t{result!s}')
... 
1/16	1/16
2/16	1/8
3/16	1/4
4/16	1/4
5/16	1/2
6/16	1/2
7/16	1/2
8/16	1/2
9/16	1
10/16	1
11/16	1
12/16	1
13/16	1
14/16	1
15/16	1
16/16	1

Returns new duration.

equal_or_lesser_assignable

Gets assignable duration equal or just less than this duration.

Gets equal-or-lesser assignable duration:

>>> for numerator in range(1, 16 + 1):
...     duration = abjad.Duration(numerator, 16)
...     result = duration.equal_or_lesser_assignable
...     sixteenths = duration.with_denominator(16)
...     print(f'{sixteenths!s}\t{result!s}')
... 
1/16	1/16
2/16	1/8
3/16	3/16
4/16	1/4
5/16	1/4
6/16	3/8
7/16	7/16
8/16	1/2
9/16	1/2
10/16	1/2
11/16	1/2
12/16	3/4
13/16	3/4
14/16	7/8
15/16	15/16
16/16	1

Returns new duration.

equal_or_lesser_power_of_two

Gets duration of the form d**2 equal to or just less than this duration.

Gets equal-or-lesser power-of-two:

>>> for numerator in range(1, 16 + 1):
...     duration = abjad.Duration(numerator, 16)
...     result = duration.equal_or_lesser_power_of_two
...     sixteenths = duration.with_denominator(16)
...     print(f'{sixteenths!s}\t{result!s}')
... 
1/16	1/16
2/16	1/8
3/16	1/8
4/16	1/4
5/16	1/4
6/16	1/4
7/16	1/4
8/16	1/2
9/16	1/2
10/16	1/2
11/16	1/2
12/16	1/2
13/16	1/2
14/16	1/2
15/16	1/2
16/16	1

Returns new duration.

flag_count

Gets flag count.

Gets flag count:

>>> for n in range(1, 16 + 1):
...     duration = abjad.Duration(n, 64)
...     sixty_fourths = duration.with_denominator(64)
...     print(f'{sixty_fourths!s}\t{duration.flag_count}')
... 
1/64	4
2/64	3
3/64	3
4/64	2
5/64	2
6/64	2
7/64	2
8/64	1
9/64	1
10/64	1
11/64	1
12/64	1
13/64	1
14/64	1
15/64	1
16/64	0

Flag count defined equal to number of flags required to notate duration.

Returns nonnegative integer.

has_power_of_two_denominator

Is true when duration is an integer power of two.

Is true when duration has power-of-two denominator:

>>> for n in range(1, 16 + 1):
...     duration = abjad.Duration(1, n)
...     result = duration.has_power_of_two_denominator
...     print('{!s}\t{}'.format(duration, result))
... 
1	True
1/2	True
1/3	False
1/4	True
1/5	False
1/6	False
1/7	False
1/8	True
1/9	False
1/10	False
1/11	False
1/12	False
1/13	False
1/14	False
1/15	False
1/16	True

Returns true or false.

(Real).imag

Real numbers have no imaginary component.

implied_prolation

Gets implied prolation.

Gets implied prolation:

>>> for denominator in range(1, 16 + 1):
...     duration = abjad.Duration(1, denominator)
...     result = duration.implied_prolation
...     print('{!s}\t{!s}'.format(duration, result))
... 
1	1
1/2	1
1/3	2/3
1/4	1
1/5	4/5
1/6	2/3
1/7	4/7
1/8	1
1/9	8/9
1/10	4/5
1/11	8/11
1/12	2/3
1/13	8/13
1/14	4/7
1/15	8/15
1/16	1

Returns multipler.

is_assignable

Is true when duration is assignable.

Is true when duration is assignable:

>>> for numerator in range(0, 16 + 1):
...     duration = abjad.Duration(numerator, 16)
...     sixteenths = duration.with_denominator(16)
...     print('{!s}\t{}'.format(sixteenths, duration.is_assignable))
... 
0/16	False
1/16	True
2/16	True
3/16	True
4/16	True
5/16	False
6/16	True
7/16	True
8/16	True
9/16	False
10/16	False
11/16	False
12/16	True
13/16	False
14/16	True
15/16	True
16/16	True

Returns true or false.

lilypond_duration_string

Gets LilyPond duration string.

Gets LilyPond duration string:

>>> abjad.Duration(3, 16).lilypond_duration_string
'8.'

Raises assignability error when duration is not assignable.

Returns string.

(Fraction).numerator
pair

Gets numerator and denominator.

Gets pair:

>>> abjad.Duration(3, 16).pair
(3, 16)

Returns integer pair.

prolation_string

Gets prolation string.

Gets prolation string:

>>> abjad.Duration(3, 16).prolation_string
'16:3'

Returns string.

(Real).real

Real numbers are their real component.

reciprocal

Gets reciprocal.

Gets reciprocal:

>>> abjad.Duration(3, 7).reciprocal
Duration(7, 3)

Returns new duration.