utilities¶

Classes

`PitchClassSegment`	Pitch Class Segment.
`PitchClassSet`	Pitch Class Set.
`PitchSegment`	Pitch Segment.
`PitchSet`	Pitch Set.
`RatioClassSegment`	Ratio Class Segment.
`RatioClassSet`	Ratio Class Set.
`RatioSegment`	Ratio Segment.
`RatioSet`	Ratio Set.

class abjadext.microtones.utilities.PitchClassSegment(pitch_classes)[source]¶

Pitch Class Segment.

>>> from abjadext import microtones

Attributes Summary

`__add__`	Concatenates Pitch Class Segment with iterable.
`__contains__`	Returns boolean
`__getitem__`	Gets value at index
`__iter__`	Iterates contents.
`__len__`	Gets length of contents.
`__repr__`	Gets interpreter representation.
`__str__`	Gets string representation.
`complement`	Gets complement in scale.
`invert`	Gets inversion.
`multiply`	Gets multiplication.
`retrograde`	Gets retrograde.
`rotate`	Gets rotation.
`sorted`	Gets Pitch Class Segment sorted in ascending order.
`transpose`	Gets transposition.

Special methods

__add__(argument)[source]¶

Concatenates Pitch Class Segment with iterable.

>>> pc_segment = microtones.PitchClassSegment(["0", "1/2", "5/4"])
>>> pc_segment += [0, quicktions.Fraction(11, 6), quicktions.Fraction(27, 2)]
>>> print(abjad.storage(pc_segment))
microtones.PitchClassSegment(
    [
        Fraction(0, 1),
        Fraction(1, 2),
        Fraction(5, 4),
        Fraction(0, 1),
        Fraction(11, 6),
        Fraction(3, 2),
        ]
    )

__contains__(argument)[source]¶

Returns boolean

>>> pc_segment = microtones.PitchClassSegment([0, 1, 6])
>>> 6 in pc_segment
True

>>> 18 in pc_segment
False

>>> pc_segment = microtones.PitchClassSegment([0, 1, 18])
>>> 6 in pc_segment
True

>>> 18 in pc_segment
False

__getitem__(index)[source]¶

Gets value at index

>>> microtones.PitchClassSegment([0, 1, 6])[0]
Fraction(0, 1)

__iter__()[source]¶

Iterates contents.

>>> pc_set = microtones.PitchClassSegment([0, 1, 2])
>>> for item in pc_set:
...     item
... 
Fraction(0, 1)
Fraction(1, 1)
Fraction(2, 1)

__len__()[source]¶

Gets length of contents.

>>> len(microtones.PitchClassSegment([0, 1, 2]))
3

overridden __repr__()[source]¶

Gets interpreter representation.

>>> microtones.PitchClassSegment([0, 1, 2])
PitchClassSegment([Fraction(0, 1), Fraction(1, 1), Fraction(2, 1)])

overridden __str__()[source]¶

Gets string representation.

>>> str(microtones.PitchClassSegment([0, 1, 2]))
'(0, 1, 2)'

Methods

complement(scale)[source]¶

Gets complement in scale.

>>> pc_set = microtones.PitchClassSegment([0, 1, 2])
>>> input_scale = [i for i in range(12)]
>>> print(abjad.storage(pc_set.complement(input_scale)))
microtones.PitchClassSegment(
    [
        Fraction(3, 1),
        Fraction(4, 1),
        Fraction(5, 1),
        Fraction(6, 1),
        Fraction(7, 1),
        Fraction(8, 1),
        Fraction(9, 1),
        Fraction(10, 1),
        Fraction(11, 1),
        ]
    )

invert(axis=0)[source]¶

Gets inversion.

>>> print(abjad.storage(microtones.PitchClassSegment([0, 1, 3]).invert()))
microtones.PitchClassSegment(
    [
        Fraction(0, 1),
        Fraction(11, 1),
        Fraction(9, 1),
        ]
    )

>>> print(abjad.storage(microtones.PitchClassSegment([0, 1, 3]).invert(2)))
microtones.PitchClassSegment(
    [
        Fraction(4, 1),
        Fraction(3, 1),
        Fraction(1, 1),
        ]
    )

multiply(n)[source]¶

Gets multiplication.

>>> print(abjad.storage(microtones.PitchClassSegment([0, 1, 3]).multiply(2)))
microtones.PitchClassSegment(
    [
        Fraction(0, 1),
        Fraction(2, 1),
        Fraction(6, 1),
        ]
    )

retrograde()[source]¶

Gets retrograde.

>>> print(abjad.storage(microtones.PitchClassSegment([0, 1, 2]).retrograde()))
microtones.PitchClassSegment(
    [
        Fraction(2, 1),
        Fraction(1, 1),
        Fraction(0, 1),
        ]
    )

rotate(n)[source]¶

Gets rotation.

>>> print(abjad.storage(microtones.PitchClassSegment([0, 1, 2]).rotate(1)))
microtones.PitchClassSegment(
    [
        Fraction(1, 1),
        Fraction(2, 1),
        Fraction(0, 1),
        ]
    )

sorted()[source]¶

Gets Pitch Class Segment sorted in ascending order.

>>> print(abjad.storage(microtones.PitchClassSegment([2, 1, 0]).sorted()))
microtones.PitchClassSegment(
    [
        Fraction(0, 1),
        Fraction(1, 1),
        Fraction(2, 1),
        ]
    )

transpose(n)[source]¶

Gets transposition.

>>> print(abjad.storage(microtones.PitchClassSegment([0, 1, 2]).transpose(2)))
microtones.PitchClassSegment(
    [
        Fraction(2, 1),
        Fraction(3, 1),
        Fraction(4, 1),
        ]
    )

>>> print(
...     abjad.storage(
...         microtones.PitchClassSegment([0, 1, 3, 4, 5]).invert().transpose(1 + 3)
...     )
... )
microtones.PitchClassSegment(
    [
        Fraction(4, 1),
        Fraction(3, 1),
        Fraction(1, 1),
        Fraction(0, 1),
        Fraction(11, 1),
        ]
    )

class abjadext.microtones.utilities.PitchClassSet(pitch_classes)[source]¶

Pitch Class Set.

>>> from abjadext import microtones
>>> import quicktions

Attributes Summary

`__add__`	Concatenates Pitch Class Set with iterable.
`__contains__`	Returns boolean
`__getitem__`	Gets value at index
`__iter__`	Iterates contents.
`__len__`	Gets length of contents.
`__repr__`	Gets interpreter representation.
`__str__`	Gets string representation.
`complement`	Gets complement in scale.
`invert`	Gets inversion.
`multiply`	Gets multiplication.
`normal_order`	Gets normal order.
`prime_form`	Gets prime form.
`sorted`	Gets Pitch Class Set sorted in ascending order.
`transpose`	Gets transposition.

Special methods

__add__(argument)[source]¶

Concatenates Pitch Class Set with iterable.

>>> pc_set = microtones.PitchClassSet(["0", "1/2", "5/4"])
>>> pc_set += [0, quicktions.Fraction(11, 6), quicktions.Fraction(27, 2)]
>>> print(abjad.storage(pc_set))
microtones.PitchClassSet(
    [
        Fraction(0, 1),
        Fraction(1, 2),
        Fraction(5, 4),
        Fraction(11, 6),
        Fraction(3, 2),
        ]
    )

__contains__(argument)[source]¶

Returns boolean

>>> pc_set = microtones.PitchClassSet([0, 1, 6])
>>> 6 in pc_set
True

>>> 18 in pc_set
False

>>> pc_set = microtones.PitchClassSet([0, 1, 18])
>>> 6 in pc_set
True

>>> 18 in pc_set
False

__getitem__(index)[source]¶

Gets value at index

>>> microtones.PitchClassSet([0, 1, 6])[0]
Fraction(0, 1)

__iter__()[source]¶

Iterates contents.

>>> pc_set = microtones.PitchClassSet([0, 1, 2])
>>> for item in pc_set:
...     item
... 
Fraction(0, 1)
Fraction(1, 1)
Fraction(2, 1)

>>> for x in microtones.PitchClassSet(
...     ["31/2", "10", "33/4", "-5", "36/10", "113/10"]
... ).prime_form():
...     print(x)
... 
0
1/10
7/2
19/4
13/2
39/5

__len__()[source]¶

Gets length of contents.

>>> len(microtones.PitchClassSet([0, 1, 2]))
3

overridden __repr__()[source]¶

Gets interpreter representation.

>>> microtones.PitchClassSet([0, 1, 6])
PitchClassSet([Fraction(0, 1), Fraction(1, 1), Fraction(6, 1)])

overridden __str__()[source]¶

Gets string representation.

>>> str(microtones.PitchClassSet([0, 1, 6]))
'{0, 1, 6}'

Methods

complement(scale)[source]¶

Gets complement in scale.

>>> pc_set = microtones.PitchClassSet([0, 1, 2])
>>> input_scale = [i for i in range(12)]
>>> print(abjad.storage(pc_set.complement(input_scale)))
microtones.PitchClassSet(
    [
        Fraction(3, 1),
        Fraction(4, 1),
        Fraction(5, 1),
        Fraction(6, 1),
        Fraction(7, 1),
        Fraction(8, 1),
        Fraction(9, 1),
        Fraction(10, 1),
        Fraction(11, 1),
        ]
    )

invert(axis=0)[source]¶

Gets inversion.

>>> print(abjad.storage(microtones.PitchClassSet([0, 1, 3]).invert()))
microtones.PitchClassSet(
    [
        Fraction(0, 1),
        Fraction(11, 1),
        Fraction(9, 1),
        ]
    )

>>> print(abjad.storage(microtones.PitchClassSet([0, 1, 3]).invert(3)))
microtones.PitchClassSet(
    [
        Fraction(6, 1),
        Fraction(5, 1),
        Fraction(3, 1),
        ]
    )

multiply(n)[source]¶

Gets multiplication.

>>> print(abjad.storage(microtones.PitchClassSet([0, 1, 3]).multiply(2)))
microtones.PitchClassSet(
    [
        Fraction(0, 1),
        Fraction(2, 1),
        Fraction(6, 1),
        ]
    )

normal_order()[source]¶

Gets normal order.

>>> print(abjad.storage(microtones.PitchClassSet([0, 2, 1]).normal_order()))
microtones.PitchClassSet(
    [
        Fraction(0, 1),
        Fraction(1, 1),
        Fraction(2, 1),
        ]
    )

prime_form()[source]¶

Gets prime form.

>>> print(abjad.storage(microtones.PitchClassSet([1, 3, 2]).prime_form()))
microtones.PitchClassSet(
    [
        Fraction(0, 1),
        Fraction(1, 1),
        Fraction(2, 1),
        ]
    )

sorted()[source]¶

Gets Pitch Class Set sorted in ascending order.

>>> print(abjad.storage(microtones.PitchClassSet([2, 1, 0]).sorted()))
microtones.PitchClassSet(
    [
        Fraction(0, 1),
        Fraction(1, 1),
        Fraction(2, 1),
        ]
    )

transpose(n)[source]¶

Gets transposition.

>>> print(abjad.storage(microtones.PitchClassSet([0, 1, 2]).transpose(2)))
microtones.PitchClassSet(
    [
        Fraction(2, 1),
        Fraction(3, 1),
        Fraction(4, 1),
        ]
    )

>>> print(
...     abjad.storage(
...         microtones.PitchClassSet([0, 1, 3, 4, 5]).invert().transpose(1 + 3)
...     )
... )
microtones.PitchClassSet(
    [
        Fraction(4, 1),
        Fraction(3, 1),
        Fraction(1, 1),
        Fraction(0, 1),
        Fraction(11, 1),
        ]
    )

class abjadext.microtones.utilities.PitchSegment(pitches)[source]¶

Pitch Segment.

>>> from abjadext import microtones

Attributes Summary

`__add__`	Concatenates Pitch Segment with iterable.
`__contains__`	Returns boolean
`__getitem__`	Gets value at index
`__iter__`	Iterates contents.
`__len__`	Gets length of contents.
`__repr__`	Gets interpreter representation.
`__setitem__`	Sets value at index
`__str__`	Gets string representation.
`complement`	Gets complement in scale.
`invert`	Gets inversion.
`multiply`	Gets multiplication.
`retrograde`	Gets retrograde.
`rotate`	Gets rotation.
`sorted`	Gets Pitch Segment sorted in ascending order.
`transpose`	Gets transposition.

Special methods

__add__(argument)[source]¶

Concatenates Pitch Segment with iterable.

>>> p_segment = microtones.PitchSegment(["0", "1/2", "5/4"])
>>> p_segment += [0, quicktions.Fraction(11, 6), quicktions.Fraction(27, 2)]
>>> print(abjad.storage(p_segment))
microtones.PitchSegment(
    [
        Fraction(0, 1),
        Fraction(1, 2),
        Fraction(5, 4),
        Fraction(0, 1),
        Fraction(11, 6),
        Fraction(27, 2),
        ]
    )

__contains__(argument)[source]¶

Returns boolean

>>> p_segment = microtones.PitchSegment([0, 1, 6])
>>> 6 in p_segment
True

>>> 18 in p_segment
False

>>> p_segment = microtones.PitchSegment([0, 1, 18])
>>> 6 in p_segment
False

>>> 18 in p_segment
True

__getitem__(index)[source]¶

Gets value at index

>>> microtones.PitchSegment([0, 1, 6])[0]
Fraction(0, 1)

__iter__()[source]¶

Iterates contents.

>>> pc_set = microtones.PitchSegment([0, 1, 2])
>>> for item in pc_set:
...     item
... 
Fraction(0, 1)
Fraction(1, 1)
Fraction(2, 1)

__len__()[source]¶

Gets length of contents.

>>> len(microtones.PitchSegment([0, 1, 2]))
3

overridden __repr__()[source]¶

Gets interpreter representation.

>>> microtones.PitchSegment([0, 1, 2])
PitchSegment([Fraction(0, 1), Fraction(1, 1), Fraction(2, 1)])

__setitem__(index, data)[source]¶

Sets value at index

>>> s = microtones.PitchSegment([0, 1, 6])
>>> s[0] = 5
>>> print(abjad.storage(s))
microtones.PitchSegment(
    [
        Fraction(5, 1),
        Fraction(1, 1),
        Fraction(6, 1),
        ]
    )

overridden __str__()[source]¶

Gets string representation.

>>> str(microtones.PitchSegment([0, 1, 2]))
'(0, 1, 2)'

Methods

complement(scale)[source]¶

Gets complement in scale.

>>> pc_set = microtones.PitchSegment([0, 1, 2])
>>> input_scale = [i for i in range(12)]
>>> print(abjad.storage(pc_set.complement(input_scale)))
microtones.PitchSegment(
    [
        Fraction(3, 1),
        Fraction(4, 1),
        Fraction(5, 1),
        Fraction(6, 1),
        Fraction(7, 1),
        Fraction(8, 1),
        Fraction(9, 1),
        Fraction(10, 1),
        Fraction(11, 1),
        ]
    )

invert(axis=0)[source]¶

Gets inversion.

>>> print(abjad.storage(microtones.PitchSegment([0, 1, 3]).invert()))
microtones.PitchSegment(
    [
        Fraction(0, 1),
        Fraction(-1, 1),
        Fraction(-3, 1),
        ]
    )

>>> print(abjad.storage(microtones.PitchSegment([0, 1, 3]).invert(2)))
microtones.PitchSegment(
    [
        Fraction(4, 1),
        Fraction(3, 1),
        Fraction(1, 1),
        ]
    )

multiply(n)[source]¶

Gets multiplication.

>>> print(abjad.storage(microtones.PitchSegment([0, 1, 3]).multiply(2)))
microtones.PitchSegment(
    [
        Fraction(0, 1),
        Fraction(2, 1),
        Fraction(6, 1),
        ]
    )

retrograde()[source]¶

Gets retrograde.

>>> print(abjad.storage(microtones.PitchSegment([0, 1, 2]).retrograde()))
microtones.PitchSegment(
    [
        Fraction(2, 1),
        Fraction(1, 1),
        Fraction(0, 1),
        ]
    )

rotate(n)[source]¶

Gets rotation.

>>> print(abjad.storage(microtones.PitchSegment([0, 1, 2]).rotate(1)))
microtones.PitchSegment(
    [
        Fraction(1, 1),
        Fraction(2, 1),
        Fraction(0, 1),
        ]
    )

sorted()[source]¶

Gets Pitch Segment sorted in ascending order.

>>> print(abjad.storage(microtones.PitchSegment([2, 1, 0]).sorted()))
microtones.PitchSegment(
    [
        Fraction(0, 1),
        Fraction(1, 1),
        Fraction(2, 1),
        ]
    )

transpose(n)[source]¶

Gets transposition.

>>> print(abjad.storage(microtones.PitchSegment([0, 1, 2]).transpose(2)))
microtones.PitchSegment(
    [
        Fraction(2, 1),
        Fraction(3, 1),
        Fraction(4, 1),
        ]
    )

>>> print(
...     abjad.storage(
...         microtones.PitchSegment([0, 1, 3, 4, 5]).invert().transpose(1 + 3)
...     )
... )
microtones.PitchSegment(
    [
        Fraction(4, 1),
        Fraction(3, 1),
        Fraction(1, 1),
        Fraction(0, 1),
        Fraction(-1, 1),
        ]
    )

class abjadext.microtones.utilities.PitchSet(pitches)[source]¶

Pitch Set.

>>> from abjadext import microtones

Attributes Summary

`__add__`	Concatenates Pitch Set with iterable.
`__contains__`	Returns boolean
`__getitem__`	Gets value at index
`__iter__`	Iterates contents.
`__len__`	Gets length of contents.
`__repr__`	Gets interpreter representation.
`__str__`	Gets string representation.
`complement`	Gets complement in scale.
`invert`	Gets inversion.
`multiply`	Gets multiplication.
`sorted`	Gets Pitch Set sorted in ascending order.
`transpose`	Gets transposition.

Special methods

__add__(argument)[source]¶

Concatenates Pitch Set with iterable.

>>> p_set = microtones.PitchSet(["0", "1/2", "5/4"])
>>> p_set += [0, quicktions.Fraction(11, 6), quicktions.Fraction(27, 2)]
>>> print(abjad.storage(p_set))
microtones.PitchSet(
    [
        Fraction(0, 1),
        Fraction(1, 2),
        Fraction(5, 4),
        Fraction(11, 6),
        Fraction(27, 2),
        ]
    )

__contains__(argument)[source]¶

Returns boolean

>>> p_set = microtones.PitchSet([0, 1, 6])
>>> 6 in p_set
True

>>> 18 in p_set
False

>>> p_set = microtones.PitchSet([0, 1, 18])
>>> 6 in p_set
False

>>> 18 in p_set
True

__getitem__(index)[source]¶

Gets value at index

>>> microtones.PitchSet([0, 1, 6])[0]
Fraction(0, 1)

__iter__()[source]¶

Iterates contents.

>>> pc_set = microtones.PitchSet([0, 1, 2])
>>> for item in pc_set:
...     item
... 
Fraction(0, 1)
Fraction(1, 1)
Fraction(2, 1)

__len__()[source]¶

Gets length of contents.

>>> len(microtones.PitchSet([0, 1, 2]))
3

overridden __repr__()[source]¶

Gets interpreter representation.

>>> microtones.PitchSet([0, 1, 2])
PitchSet([Fraction(0, 1), Fraction(1, 1), Fraction(2, 1)])

overridden __str__()[source]¶

Gets string representation.

>>> str(microtones.PitchSet([0, 1, 2]))
'{0, 1, 2}'

Methods

complement(scale)[source]¶

Gets complement in scale.

>>> pc_set = microtones.PitchSet([0, 1, 2])
>>> input_scale = [i for i in range(12)]
>>> print(abjad.storage(pc_set.complement(input_scale)))
microtones.PitchSet(
    [
        Fraction(3, 1),
        Fraction(4, 1),
        Fraction(5, 1),
        Fraction(6, 1),
        Fraction(7, 1),
        Fraction(8, 1),
        Fraction(9, 1),
        Fraction(10, 1),
        Fraction(11, 1),
        ]
    )

invert(axis=0)[source]¶

Gets inversion.

>>> print(abjad.storage(microtones.PitchSet([0, 1, 3]).invert()))
microtones.PitchSet(
    [
        Fraction(0, 1),
        Fraction(-1, 1),
        Fraction(-3, 1),
        ]
    )

>>> print(abjad.storage(microtones.PitchSet([0, 1, 3]).invert(2)))
microtones.PitchSet(
    [
        Fraction(4, 1),
        Fraction(3, 1),
        Fraction(1, 1),
        ]
    )

multiply(n)[source]¶

Gets multiplication.

>>> print(abjad.storage(microtones.PitchSet([0, 1, 3]).multiply(2)))
microtones.PitchSet(
    [
        Fraction(0, 1),
        Fraction(2, 1),
        Fraction(6, 1),
        ]
    )

sorted()[source]¶

Gets Pitch Set sorted in ascending order.

>>> print(abjad.storage(microtones.PitchSet([2, 1, 0]).sorted()))
microtones.PitchSet(
    [
        Fraction(0, 1),
        Fraction(1, 1),
        Fraction(2, 1),
        ]
    )

transpose(n)[source]¶

Gets transposition.

>>> print(abjad.storage(microtones.PitchSet([0, 1, 2]).transpose(2)))
microtones.PitchSet(
    [
        Fraction(2, 1),
        Fraction(3, 1),
        Fraction(4, 1),
        ]
    )

>>> print(
...     abjad.storage(
...         microtones.PitchSet([0, 1, 3, 4, 5]).invert().transpose(1 + 3)
...     )
... )
microtones.PitchSet(
    [
        Fraction(4, 1),
        Fraction(3, 1),
        Fraction(1, 1),
        Fraction(0, 1),
        Fraction(-1, 1),
        ]
    )

class abjadext.microtones.utilities.RatioClassSegment(ratio_classes)[source]¶

Ratio Class Segment.

>>> from abjadext import microtones

Attributes Summary

`__add__`	Concatenates Ratio Class Segment with iterable.
`__contains__`	Returns boolean
`__getitem__`	Gets item at index
`__iter__`	Iterates contents.
`__len__`	Gets length of contents.
`__repr__`	Gets interpreter representation.
`__str__`	Gets string representation.
`complement`	Gets complement in scale.
`invert`	Gets inversion.
`multiply`	Gets multiplication.
`retrograde`	Gets retrograde.
`rotate`	Gets rotation.
`sorted`	Gets Ratio Class Segment sorted in ascending order.
`transpose`	Gets transposition.

Special methods

__add__(argument)[source]¶

Concatenates Ratio Class Segment with iterable.

>>> rc_segment = microtones.RatioClassSegment(["1", "1/2", "5/4"])
>>> rc_segment += [1, quicktions.Fraction(11, 6), quicktions.Fraction(27, 2)]
>>> s = rc_segment
>>> print(abjad.storage(s))
microtones.RatioClassSegment(
    [
        Fraction(1, 1),
        Fraction(1, 1),
        Fraction(5, 4),
        Fraction(1, 1),
        Fraction(11, 6),
        Fraction(27, 16),
        ]
    )

__contains__(argument)[source]¶

Returns boolean

>>> rc_segment = microtones.RatioClassSegment([1, 2, 6])
>>> 1 in rc_segment
True

__getitem__(index)[source]¶

Gets item at index

>>> microtones.RatioClassSegment([1, 2, 3])[0]
Fraction(1, 1)

__iter__()[source]¶

Iterates contents.

>>> pc_segment = microtones.RatioClassSegment([1, 2, 3, 3])
>>> for item in pc_segment:
...     item
... 
Fraction(1, 1)
Fraction(2, 1)
Fraction(3, 2)
Fraction(3, 2)

>>> for x in microtones.RatioClassSegment(
...     ["31/2", "10", "33/4", "36/10", "113/10"]
... ):
...     print(x)
... 
31/16
5/4
33/32
9/5
113/80

__len__()[source]¶

Gets length of contents.

>>> len(microtones.RatioClassSegment([1, 2, 3]))
3

overridden __repr__()[source]¶

Gets interpreter representation.

>>> microtones.RatioClassSegment([1, 2, 3])
RatioClassSegment([Fraction(1, 1), Fraction(2, 1), Fraction(3, 2)])

overridden __str__()[source]¶

Gets string representation.

>>> str(microtones.RatioClassSegment([1, 2, 3]))
'(1, 2, 3/2)'

Methods

complement(scale)[source]¶

Gets complement in scale.

>>> pc_segment = microtones.RatioClassSegment([1, 2, 3])
>>> input_scale = [i + 1 for i in range(11)]
>>> s = pc_segment.complement(input_scale)
>>> print(abjad.storage(s))
microtones.RatioClassSegment(
    [
        Fraction(3, 2),
        Fraction(2, 1),
        Fraction(5, 4),
        Fraction(3, 2),
        Fraction(7, 4),
        Fraction(2, 1),
        Fraction(9, 8),
        Fraction(5, 4),
        Fraction(11, 8),
        ]
    )

invert(axis=1)[source]¶

Gets inversion.

>>> s = microtones.RatioClassSegment([2, 4, 3]).invert()
>>> print(abjad.storage(s))
microtones.RatioClassSegment(
    [
        Fraction(1, 1),
        Fraction(1, 1),
        Fraction(4, 3),
        ]
    )

>>> s = microtones.RatioClassSegment([2, 4, 3]).invert(3)
>>> print(abjad.storage(s))
microtones.RatioClassSegment(
    [
        Fraction(9, 8),
        Fraction(9, 8),
        Fraction(3, 2),
        ]
    )

multiply(n)[source]¶

Gets multiplication.

>>> s = microtones.RatioClassSegment([1, 2, 3]).multiply(2)
>>> print(abjad.storage(s))
microtones.RatioClassSegment(
    [
        Fraction(2, 1),
        Fraction(2, 1),
        Fraction(3, 2),
        ]
    )

retrograde()[source]¶

Gets retrograde.

>>> s = microtones.RatioClassSegment([1, 2, 3, 3]).retrograde()
>>> print(abjad.storage(s))
microtones.RatioClassSegment(
    [
        Fraction(3, 2),
        Fraction(3, 2),
        Fraction(2, 1),
        Fraction(1, 1),
        ]
    )

rotate(n)[source]¶

Gets rotation.

>>> s = microtones.RatioClassSegment([1, 2, 3]).rotate(1)
>>> print(abjad.storage(s))
microtones.RatioClassSegment(
    [
        Fraction(2, 1),
        Fraction(3, 2),
        Fraction(1, 1),
        ]
    )

sorted()[source]¶

Gets Ratio Class Segment sorted in ascending order.

>>> s = microtones.RatioClassSegment([5, 2, 3, "1/2", 1, "1/5"]).sorted()
>>> print(abjad.storage(s))
microtones.RatioClassSegment(
    [
        Fraction(1, 1),
        Fraction(1, 1),
        Fraction(5, 4),
        Fraction(3, 2),
        Fraction(8, 5),
        Fraction(2, 1),
        ]
    )

transpose(n)[source]¶

Gets transposition.

>>> s = microtones.RatioClassSegment([1, 2, 3]).transpose(2)
>>> print(abjad.storage(s))
microtones.RatioClassSegment(
    [
        Fraction(3, 2),
        Fraction(2, 1),
        Fraction(7, 4),
        ]
    )

>>> s = microtones.RatioClassSegment([1, 2, 4, 5, 6]).invert().transpose(1 + 3)
>>> print(abjad.storage(s))
microtones.RatioClassSegment(
    [
        Fraction(5, 4),
        Fraction(5, 4),
        Fraction(5, 4),
        Fraction(7, 5),
        Fraction(4, 3),
        ]
    )

class abjadext.microtones.utilities.RatioClassSet(ratio_classes)[source]¶

Ratio Class Set.

>>> from abjadext import microtones
>>> import quicktions

Attributes Summary

`__add__`	Concatenates Ratio Class Set with iterable.
`__contains__`	Returns boolean
`__getitem__`	Gets item at index
`__iter__`	Iterates contents.
`__len__`	Gets length of contents.
`__repr__`	Gets interpreter representation.
`__str__`	Gets string representation.
`complement`	Gets complement in scale.
`invert`	Gets inversion.
`multiply`	Gets multiplication.
`sorted`	Gets Ratio Class Set sorted in ascending order.
`transpose`	Gets transposition.

Special methods

__add__(argument)[source]¶

Concatenates Ratio Class Set with iterable.

>>> rc_set = microtones.RatioClassSet(["1", "1/2", "5/4"])
>>> rc_set += [1, quicktions.Fraction(11, 6), quicktions.Fraction(27, 2)]
>>> print(abjad.storage(rc_set))
microtones.RatioClassSet(
    [
        Fraction(1, 1),
        Fraction(5, 4),
        Fraction(11, 6),
        Fraction(27, 16),
        ]
    )

__contains__(argument)[source]¶

Returns boolean

>>> rc_set = microtones.RatioClassSet([1, 2, 6])
>>> 1 in rc_set
True

__getitem__(index)[source]¶

Gets item at index

>>> microtones.RatioClassSet([1, 2, 3])[0]
Fraction(1, 1)

__iter__()[source]¶

Iterates contents.

>>> pc_set = microtones.RatioClassSet([1, 2, 3])
>>> for item in pc_set:
...     item
... 
Fraction(1, 1)
Fraction(2, 1)
Fraction(3, 2)

>>> for x in microtones.RatioClassSet(["31/2", "10", "33/4", "36/10", "113/10"]):
...     print(x)
... 
31/16
5/4
33/32
9/5
113/80

__len__()[source]¶

Gets length of contents.

>>> len(microtones.RatioClassSet([1, 2, 3]))
3

overridden __repr__()[source]¶

Gets interpreter representation.

>>> microtones.RatioClassSet([1, 2, 3])
RatioClassSet([Fraction(1, 1), Fraction(2, 1), Fraction(3, 2)])

overridden __str__()[source]¶

Gets string representation.

>>> str(microtones.RatioClassSet([1, 2, 3]))
'{1, 2, 3/2}'

Methods

complement(scale)[source]¶

Gets complement in scale.

>>> rc_set = microtones.RatioClassSet([1, 2, 3])
>>> input_scale = [i + 1 for i in range(11)]
>>> s = rc_set.complement(input_scale)
>>> print(abjad.storage(s))
microtones.RatioClassSet(
    [
        Fraction(3, 2),
        Fraction(2, 1),
        Fraction(5, 4),
        Fraction(7, 4),
        Fraction(9, 8),
        Fraction(11, 8),
        ]
    )

invert(axis=1)[source]¶

Gets inversion.

>>> s = microtones.RatioClassSet([2, 4, 3]).invert()
>>> print(abjad.storage(s))
microtones.RatioClassSet(
    [
        Fraction(1, 1),
        Fraction(4, 3),
        ]
    )

>>> s = microtones.RatioClassSet([2, 4, 3]).invert(3)
>>> print(abjad.storage(s))
microtones.RatioClassSet(
    [
        Fraction(9, 8),
        Fraction(3, 2),
        ]
    )

multiply(n)[source]¶

Gets multiplication.

>>> s = microtones.RatioClassSet([1, 2, 3]).multiply(2)
>>> print(abjad.storage(s))
microtones.RatioClassSet(
    [
        Fraction(2, 1),
        Fraction(3, 2),
        ]
    )

sorted()[source]¶

Gets Ratio Class Set sorted in ascending order.

>>> s = microtones.RatioClassSet([5, 2, 3, "1/2", 1, "1/5"]).sorted()
>>> print(abjad.storage(s))
microtones.RatioClassSet(
    [
        Fraction(1, 1),
        Fraction(5, 4),
        Fraction(3, 2),
        Fraction(8, 5),
        Fraction(2, 1),
        ]
    )

transpose(n)[source]¶

Gets transposition.

>>> s = microtones.RatioClassSet([1, 2, 3]).transpose(2)
>>> print(abjad.storage(s))
microtones.RatioClassSet(
    [
        Fraction(3, 2),
        Fraction(2, 1),
        Fraction(7, 4),
        ]
    )

>>> s = microtones.RatioClassSet([1, 2, 4, 5, 6]).invert().transpose(1 + 3)
>>> print(abjad.storage(s))
microtones.RatioClassSet(
    [
        Fraction(5, 4),
        Fraction(7, 5),
        Fraction(4, 3),
        ]
    )

class abjadext.microtones.utilities.RatioSegment(ratios)[source]¶

Ratio Segment.

>>> from abjadext import microtones

Attributes Summary

`__add__`	Concatenates Ratio Segment with iterable.
`__contains__`	Returns boolean
`__getitem__`	Gets item at index
`__iter__`	Iterates contents.
`__len__`	Gets length of contents.
`__repr__`	Gets interpreter representation.
`__setitem__`	Sets item at index
`__str__`	Gets string representation.
`complement`	Gets complement in scale.
`constrain_to_octave`	Gets Ratio Segment constrained within an octave.
`invert`	Gets inversion.
`multiply`	Gets multiplication.
`retrograde`	Gets retrograde.
`rotate`	Gets rotation.
`sorted`	Gets Ratio Segment sorted in ascending order.
`transpose`	Gets transposition.

Special methods

__add__(argument)[source]¶

Concatenates Ratio Segment with iterable.

>>> r_segment = microtones.RatioSegment(["1", "1/2", "5/4"])
>>> r_segment += [1, quicktions.Fraction(11, 6), quicktions.Fraction(27, 2)]
>>> s = r_segment
>>> print(abjad.storage(s))
microtones.RatioSegment(
    [
        Fraction(1, 1),
        Fraction(1, 2),
        Fraction(5, 4),
        Fraction(1, 1),
        Fraction(11, 6),
        Fraction(27, 2),
        ]
    )

__contains__(argument)[source]¶

Returns boolean

>>> r_segment = microtones.RatioSegment([1, 2, 6])
>>> 1 in r_segment
True

__getitem__(index)[source]¶

Gets item at index

>>> microtones.RatioSegment([1, 2, 3])[0]
Fraction(1, 1)

__iter__()[source]¶

Iterates contents.

>>> pc_segment = microtones.RatioSegment([1, 2, 3, 3])
>>> for item in pc_segment:
...     item
... 
Fraction(1, 1)
Fraction(2, 1)
Fraction(3, 1)
Fraction(3, 1)

>>> for x in microtones.RatioSegment(["31/2", "10", "33/4", "36/10", "113/10"]):
...     print(x)
... 
31/2
10
33/4
18/5
113/10

__len__()[source]¶

Gets length of contents.

>>> len(microtones.RatioSegment([1, 2, 3]))
3

overridden __repr__()[source]¶

Gets interpreter representation.

>>> microtones.RatioSegment([1, 2, 3])
RatioSegment([Fraction(1, 1), Fraction(2, 1), Fraction(3, 1)])

__setitem__(index, data)[source]¶

Sets item at index

>>> s = microtones.RatioSegment([1, 2, 3])
>>> s[1] = 5
>>> print(abjad.storage(s))
microtones.RatioSegment(
    [
        Fraction(1, 1),
        Fraction(5, 1),
        Fraction(3, 1),
        ]
    )

overridden __str__()[source]¶

Gets string representation.

>>> str(microtones.RatioSegment([1, 2, 3]))
'(1, 2, 3)'

Methods

complement(scale)[source]¶

Gets complement in scale.

>>> pc_segment = microtones.RatioSegment([1, 2, 3])
>>> input_scale = [i + 1 for i in range(11)]
>>> s = pc_segment.complement(input_scale)
>>> print(abjad.storage(s))
microtones.RatioSegment(
    [
        Fraction(4, 1),
        Fraction(5, 1),
        Fraction(6, 1),
        Fraction(7, 1),
        Fraction(8, 1),
        Fraction(9, 1),
        Fraction(10, 1),
        Fraction(11, 1),
        ]
    )

constrain_to_octave()[source]¶

Gets Ratio Segment constrained within an octave.

>>> str(microtones.RatioSegment([1, 3, "1/5"]).constrain_to_octave())
'(1, 3/2, 4/5)'

invert(axis=1)[source]¶

Gets inversion.

>>> s = microtones.RatioSegment([2, 4, 3]).invert()
>>> print(abjad.storage(s))
microtones.RatioSegment(
    [
        Fraction(1, 2),
        Fraction(1, 4),
        Fraction(1, 3),
        ]
    )

>>> s = microtones.RatioSegment([2, 4, 3]).invert(3)
>>> print(abjad.storage(s))
microtones.RatioSegment(
    [
        Fraction(9, 2),
        Fraction(9, 4),
        Fraction(3, 1),
        ]
    )

multiply(n)[source]¶

Gets multiplication.

>>> s = microtones.RatioSegment([1, 2, 3]).multiply(2)
>>> print(abjad.storage(s))
microtones.RatioSegment(
    [
        Fraction(2, 1),
        Fraction(4, 1),
        Fraction(6, 1),
        ]
    )

retrograde()[source]¶

Gets retrograde.

>>> s = microtones.RatioSegment([1, 2, 3, 3]).retrograde()
>>> print(abjad.storage(s))
microtones.RatioSegment(
    [
        Fraction(3, 1),
        Fraction(3, 1),
        Fraction(2, 1),
        Fraction(1, 1),
        ]
    )

rotate(n)[source]¶

Gets rotation.

>>> s = microtones.RatioSegment([1, 2, 3]).rotate(1)
>>> print(abjad.storage(s))
microtones.RatioSegment(
    [
        Fraction(2, 1),
        Fraction(3, 1),
        Fraction(1, 1),
        ]
    )

sorted()[source]¶

Gets Ratio Segment sorted in ascending order.

>>> s = microtones.RatioSegment([5, 2, 3, "1/2", 1, "1/5"]).sorted()
>>> print(abjad.storage(s))
microtones.RatioSegment(
    [
        Fraction(1, 5),
        Fraction(1, 2),
        Fraction(1, 1),
        Fraction(2, 1),
        Fraction(3, 1),
        Fraction(5, 1),
        ]
    )

transpose(n)[source]¶

Gets transposition.

>>> s = microtones.RatioSegment([1, 2, 3]).transpose(2)
>>> print(abjad.storage(s))
microtones.RatioSegment(
    [
        Fraction(3, 1),
        Fraction(4, 1),
        Fraction(5, 1),
        ]
    )

>>> s = microtones.RatioSegment([1, 2, 4, 5, 6]).invert().transpose(1 + 3)
>>> print(abjad.storage(s))
microtones.RatioSegment(
    [
        Fraction(5, 1),
        Fraction(9, 2),
        Fraction(17, 4),
        Fraction(21, 5),
        Fraction(25, 6),
        ]
    )

class abjadext.microtones.utilities.RatioSet(ratios)[source]¶

Ratio Set.

>>> from abjadext import microtones

Attributes Summary

`__add__`	Concatenates Ratio Set with iterable.
`__contains__`	Returns boolean
`__getitem__`	Gets item at index
`__iter__`	Iterates contents.
`__len__`	Gets length of contents.
`__repr__`	Gets interpreter representation.
`__str__`	Gets string representation.
`complement`	Gets complement in scale.
`constrain_to_octave`	Gets Ratio Set constrained within an octave.
`invert`	Gets inversion.
`multiply`	Gets multiplication.
`sorted`	Gets Ratio Class Set sorted in ascending order.
`transpose`	Gets transposition.

Special methods

__add__(argument)[source]¶

Concatenates Ratio Set with iterable.

>>> r_set = microtones.RatioSet(["1", "1/2", "5/4"])
>>> r_set += [1, quicktions.Fraction(11, 6), quicktions.Fraction(27, 2)]
>>> s = r_set
>>> print(abjad.storage(s))
microtones.RatioSet(
    [
        Fraction(1, 1),
        Fraction(1, 2),
        Fraction(5, 4),
        Fraction(11, 6),
        Fraction(27, 2),
        ]
    )

__contains__(argument)[source]¶

Returns boolean

>>> r_set = microtones.RatioSet([1, 2, 6])
>>> 1 in r_set
True

__getitem__(index)[source]¶

Gets item at index

>>> microtones.RatioSet([1, 2, 3])[0]
Fraction(1, 1)

__iter__()[source]¶

Iterates contents.

>>> pc_set = microtones.RatioSet([1, 2, 3])
>>> for item in pc_set:
...     item
... 
Fraction(1, 1)
Fraction(2, 1)
Fraction(3, 1)

>>> for x in microtones.RatioSet(["31/2", "10", "33/4", "36/10", "113/10"]):
...     print(x)
... 
31/2
10
33/4
18/5
113/10

__len__()[source]¶

Gets length of contents.

>>> len(microtones.RatioSet([1, 2, 3]))
3

overridden __repr__()[source]¶

Gets interpreter representation.

>>> microtones.RatioSet([1, 2, 3])
RatioSet([Fraction(1, 1), Fraction(2, 1), Fraction(3, 1)])

overridden __str__()[source]¶

Gets string representation.

>>> str(microtones.RatioSet([1, 2, 3]))
'{1, 2, 3}'

Methods

complement(scale)[source]¶

Gets complement in scale.

>>> r_set = microtones.RatioSet([1, 2, 3])
>>> input_scale = [i + 1 for i in range(11)]
>>> s = r_set.complement(input_scale)
>>> print(abjad.storage(s))
microtones.RatioSet(
    [
        Fraction(4, 1),
        Fraction(5, 1),
        Fraction(6, 1),
        Fraction(7, 1),
        Fraction(8, 1),
        Fraction(9, 1),
        Fraction(10, 1),
        Fraction(11, 1),
        ]
    )

constrain_to_octave()[source]¶

Gets Ratio Set constrained within an octave.

>>> str(microtones.RatioSet([1, 3, "1/5"]).constrain_to_octave())
'{1, 3/2, 4/5}'

invert(axis=1)[source]¶

Gets inversion.

>>> s = microtones.RatioSet([2, 4, 3]).invert()
>>> print(abjad.storage(s))
microtones.RatioSet(
    [
        Fraction(1, 2),
        Fraction(1, 4),
        Fraction(1, 3),
        ]
    )

>>> s = microtones.RatioSet([2, 4, 3]).invert(3)
>>> print(abjad.storage(s))
microtones.RatioSet(
    [
        Fraction(9, 2),
        Fraction(9, 4),
        Fraction(3, 1),
        ]
    )

multiply(n)[source]¶

Gets multiplication.

>>> s = microtones.RatioSet([1, 2, 3]).multiply(2)
>>> print(abjad.storage(s))
microtones.RatioSet(
    [
        Fraction(2, 1),
        Fraction(4, 1),
        Fraction(6, 1),
        ]
    )

sorted()[source]¶

Gets Ratio Class Set sorted in ascending order.

>>> s = microtones.RatioSet([5, 2, 3]).sorted()
>>> print(abjad.storage(s))
microtones.RatioSet(
    [
        Fraction(2, 1),
        Fraction(3, 1),
        Fraction(5, 1),
        ]
    )

transpose(n)[source]¶

Gets transposition.

>>> s = microtones.RatioSet([1, 2, 3]).transpose(2)
>>> print(abjad.storage(s))
microtones.RatioSet(
    [
        Fraction(3, 1),
        Fraction(4, 1),
        Fraction(5, 1),
        ]
    )

>>> s = microtones.RatioSet([1, 2, 4, 5, 6]).invert().transpose(1 + 3)
>>> print(abjad.storage(s))
microtones.RatioSet(
    [
        Fraction(5, 1),
        Fraction(9, 2),
        Fraction(17, 4),
        Fraction(21, 5),
        Fraction(25, 6),
        ]
    )