Duration¶

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.