Multiplier

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class abjad.utilities.Multiplier.Multiplier

Multiplier.

Initializes from integer numerator:

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

Initializes from integer numerator and denominator:

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

Initializes from integer-equivalent numeric numerator:

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

Initializes from integer-equivalent numeric numerator and denominator:

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

Initializes from integer-equivalent singleton:

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

Initializes from integer-equivalent pair:

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

Initializes from other duration:

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

Intializes from fraction:

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

Initializes from solidus string:

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

Initializes from nonreduced fraction:

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

Multipliers inherit from built-in fraction:

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

Multipliers are numbers:

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

Attaching a multiplier to a score component multiplies that component’s duration:

>>> note = abjad.Note("c'1")
>>> abjad.f(note)
c'1
>>> multiplier = abjad.Multiplier(3, 8)
>>> abjad.attach(multiplier, note)
>>> abjad.f(note)
c'1 * 3/8

Attributes Summary

__mul__ Multiplier times duration gives duration.
from_dot_count Makes multiplier from dot_count.
normalized Is true when mutliplier is greater than 1/2 and less than 2.

Special methods

(Duration).__abs__(*arguments)

Gets absolute value of duration.

Returns nonnegative duration.

(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)
(Duration).__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.

(Duration).__divmod__(*arguments)

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

Returns pair.

(Duration).__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

(Duration).__format__(format_specification='')

Formats duration.

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

Returns string.

(Duration).__ge__(argument)

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

Returns true or false.

(Duration).__gt__(argument)

Is true when duration is greater than argument.

Returns true or false.

(Duration).__hash__()

Hashes duration.

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

Returns integer.

(Duration).__le__(argument)

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

Returns true or false.

(Duration).__lt__(argument)

Is true when duration is less than argument.

Returns true or false.

(Duration).__mod__(*arguments)

Modulus operator applied to duration.

Returns duration.

__mul__(*arguments)

Multiplier times duration gives duration.

Returns duration.

(Duration).__neg__(*arguments)

Negates duration.

Returns new duration.

static (Duration).__new__(class_, *arguments)

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

(Duration).__pos__(*arguments)

Get positive duration.

Returns new duration.

(Duration).__pow__(*arguments)

Raises duration to arguments power.

Returns new duration.

(Duration).__radd__(*arguments)

Adds arguments to duration.

Returns new duration.

(Duration).__rdiv__(*arguments)

Divides arguments by duration.

Returns new duration.

(Duration).__rdivmod__(*arguments)

Documentation required.

(AbjadObject).__repr__()

Gets interpreter representation of Abjad object.

Returns string.

(Fraction).__rfloordiv__(a)

a // b

(Duration).__rmod__(*arguments)

Documentation required.

(Duration).__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.

(Duration).__rpow__(*arguments)

Raises arguments to the power of duration.

Returns new duration.

(Duration).__rsub__(*arguments)

Subtracts duration from arguments.

Returns new duration.

(Duration).__rtruediv__(*arguments)

Documentation required.

Returns new duration.

(Fraction).__str__()

str(self)

(Duration).__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.

(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)
normalized()

Is true when mutliplier is greater than 1/2 and less than 2.

>>> abjad.Multiplier(3, 2).normalized()
True

Returns true or false.

(Duration).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.

(Duration).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.

(Duration).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 (Duration).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.

static from_dot_count(dot_count)

Makes multiplier from dot_count.

>>> abjad.Multiplier.from_dot_count(0)
Multiplier(1, 1)
>>> abjad.Multiplier.from_dot_count(1)
Multiplier(3, 2)
>>> abjad.Multiplier.from_dot_count(2)
Multiplier(7, 4)
>>> abjad.Multiplier.from_dot_count(3)
Multiplier(15, 8)
>>> abjad.Multiplier.from_dot_count(4)
Multiplier(31, 16)
Return type:Multiplier
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 (Duration).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 (Duration).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
(Duration).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.

(Duration).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.

(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.

(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.

(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.

(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.

(Duration).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.

(Duration).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.

(Duration).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.

(Duration).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
(Duration).pair

Gets numerator and denominator.

Gets pair:

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

Returns integer pair.

(Duration).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.

(Duration).reciprocal

Gets reciprocal.

Gets reciprocal:

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

Returns new duration.