Ratio¶

class abjad.mathtools.Ratio.Ratio(numbers=(1, 1))¶

Ratio.

Ratio of two numbers:

>>> abjad.Ratio((2, 4))
Ratio((1, 2))

Ratio of three numbers:

>>> abjad.Ratio((2, 4, 2))
Ratio((1, 2, 1))

Attributes Summary

`__eq__`	Is true when `argument` equals ratio.
`__getitem__`	Gets item or slice identified by `argument`.
`__hash__`	Hashes ratio.
`__len__`	Gets length of ratio.
`__str__`	Gets string representation of ratio.
`multipliers`	Gets multipliers of ratio.
`numbers`	Gets numbers of ratio.
`reciprocal`	Gets reciprocal.

Special methods

(NonreducedRatio).__contains__(argument)¶

Is true when ratio contains argument.

Returns true or false.

(AbjadValueObject).__copy__(*arguments)¶

Copies Abjad value object.

Returns new Abjad value object.

__eq__(argument)¶

Is true when argument equals ratio.

>>> ratio_1 = abjad.Ratio((1, 2, 1))
>>> ratio_2 = abjad.Ratio((1, 2, 1))
>>> ratio_3 = abjad.Ratio((2, 3, 3))

>>> ratio_1 == ratio_1
True

>>> ratio_1 == ratio_2
True

>>> ratio_1 == ratio_3
False

>>> ratio_2 == ratio_1
True

>>> ratio_2 == ratio_2
True

>>> ratio_2 == ratio_3
False

>>> ratio_3 == ratio_1
False

>>> ratio_3 == ratio_2
False

>>> ratio_3 == ratio_3
True

(NonreducedRatio).__format__(format_specification='')¶

Formats duration.

>>> ratio = abjad.NonreducedRatio((2, 4, 2))
>>> print(format(ratio))
abjad.NonreducedRatio((2, 4, 2))

Returns string.

__getitem__(argument)¶

Gets item or slice identified by argument.

>>> ratio = abjad.Ratio((2, 4, 2))
>>> ratio[1]
2

Returns integer or tuple.

__hash__()¶

Hashes ratio.

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

Returns integer.

(NonreducedRatio).__iter__()¶

Iterates ratio.

Returns generator.

__len__()¶

Gets length of ratio.

>>> ratio = abjad.Ratio((2, 4, 2))
>>> len(ratio)
3

Returns integer.

(NonreducedRatio).__rdiv__(number)¶

Divides number by ratio.

>>> 1 / abjad.Ratio((1, 1, 3))
[Fraction(1, 5), Fraction(1, 5), Fraction(3, 5)]

>>> abjad.Fraction(1) / abjad.Ratio((1, 1, 3))
[Fraction(1, 5), Fraction(1, 5), Fraction(3, 5)]

>>> 1.0 / abjad.Ratio((1, 1, 3))
[0.2, 0.2, 0.6]

Returns list of fractions or list of floats.

(AbjadObject).__repr__()¶

Gets interpreter representation of Abjad object.

Returns string.

(NonreducedRatio).__reversed__()¶

Iterates ratio in reverse.

Returns generator.

(NonreducedRatio).__rtruediv__(number)¶

Divides number by ratio.

>>> 1 / abjad.Ratio((1, 1, 3))
[Fraction(1, 5), Fraction(1, 5), Fraction(3, 5)]

>>> abjad.Fraction(1) / abjad.Ratio((1, 1, 3))
[Fraction(1, 5), Fraction(1, 5), Fraction(3, 5)]

>>> 1.0 / abjad.Ratio((1, 1, 3))
[0.2, 0.2, 0.6]

Returns list of fractions or list of floats.

__str__()¶

Gets string representation of ratio.

Ratio of two numbers:

>>> str(abjad.Ratio((2, 4)))
'1:2'

Ratio of three numbers:

>>> str(abjad.Ratio((2, 4, 2)))
'1:2:1'

Returns string.

Methods

(NonreducedRatio).count(argument)¶

Gets count of argument in ratio.

Returns integer.

(NonreducedRatio).index(argument)¶

Gets index of argument in ratio.

Returns integer.

Read-only properties

multipliers¶

Gets multipliers of ratio.

Ratio of two numbers:

>>> ratio = abjad.Ratio((2, 4))
>>> ratio.multipliers
(Multiplier(1, 3), Multiplier(2, 3))

Ratio of three numbers:

>>> ratio = abjad.Ratio((2, 4, 2))
>>> ratio.multipliers
(Multiplier(1, 4), Multiplier(1, 2), Multiplier(1, 4))

Returns tuple of multipliers.

numbers¶

Gets numbers of ratio.

Ratio of two numbers:

>>> ratio = abjad.Ratio((2, 4))
>>> ratio.numbers
(1, 2)

Ratio of three numbers:

>>> ratio = abjad.Ratio((2, 4, 2))
>>> ratio.numbers
(1, 2, 1)

Set to tuple of two or more numbers.

Returns tuple of two or more numbers.

reciprocal¶

Gets reciprocal.

Gets reciprocal:

>>> abjad.Ratio((3, 2)).reciprocal
Ratio((2, 3))

>>> abjad.Ratio((3, 2, 7)).reciprocal
Ratio((7, 2, 3))

Returns new ratio.