abjad.pcollections

abjad.pcollections.make_interval_class_vector(pitches)	Makes interval-class vector.
abjad.pcollections.voice_horizontally(pcs[, ...])	Voices named pcs with each pitch as close to the previous pitch as possible.
abjad.pcollections.voice_vertically(pcs[, ...])	Voices named pcs with each pitch not lower than the previous.
abjad.pcollections.PitchClassSegment([items])	Numbered pitch-class segment.
abjad.pcollections.PitchClassSet([argument])	Numbered pitch-class set.
abjad.pcollections.PitchRange([range_string])	Pitch range.
abjad.pcollections.PitchSegment([items])	Named pitch segment.
abjad.pcollections.PitchSet([argument])	Numbered pitch set.
abjad.pcollections.TwelveToneRow([items])	Twelve-tone row.

abjad.pcollections.make_interval_class_vector(pitches)

Makes interval-class vector.

abjad.pcollections.voice_horizontally(pcs: Sequence[NamedPitchClass], initial_octave: Octave = Octave(number=4)) → tuple[NamedPitch, ...]

Voices named pcs with each pitch as close to the previous pitch as possible.

>>> pcs = [abjad.NamedPitchClass(_) for _ in "c b d e f g e b a c".split()]
>>> pitches = abjad.pcollections.voice_horizontally(pcs)
>>> staff = abjad.Staff([abjad.Note(_, (1, 8)) for _ in pitches])
>>> abjad.show(staff)  

abjad.pcollections.voice_vertically(pcs: Sequence[NamedPitchClass], initial_octave: Octave = Octave(number=4)) → tuple[NamedPitch, ...]

Voices named pcs with each pitch not lower than the previous.

>>> pcs = [abjad.NamedPitchClass(_) for _ in "c ef g bf d f af".split()]
>>> pitches = abjad.pcollections.voice_vertically(pcs)
>>> staff = abjad.Staff([abjad.Note(_, (1, 8)) for _ in pitches])
>>> abjad.show(staff)  

class abjad.pcollections.PitchClassSegment(items: Sequence = ())

Numbered pitch-class segment.

>>> segment = abjad.PitchClassSegment([-2, -1.5, 6, 7, -1.5, 7])
>>> segment
PitchClassSegment([10, 10.5, 6, 7, 10.5, 7])

>>> lilypond_file = abjad.illustrate(segment)
>>> abjad.show(lilypond_file)  

invert([axis])	Inverts numbered pitch-class segment.
multiply([n])	Multiplies pitch-classes in numbered pitch-class segment by n.
retrograde()	Gets retrograde of numbered pitch-class segment.
rotate([n])	Rotates numbered pitch-class segment by index n.
transpose([n])	Transposes numbered pitch-class segment by index n.

invert(axis=None) → PitchClassSegment

Inverts numbered pitch-class segment.

>>> segment = abjad.PitchClassSegment([-2, -1.5, 6, 7, -1.5, 7])

>>> segment.invert()
PitchClassSegment([2, 1.5, 6, 5, 1.5, 5])

>>> segment.invert().invert()
PitchClassSegment([10, 10.5, 6, 7, 10.5, 7])

multiply(n=1) → PitchClassSegment

Multiplies pitch-classes in numbered pitch-class segment by n.

>>> segment = abjad.PitchClassSegment([-2, -1.5, 6, 7, -1.5, 7])
>>> segment
PitchClassSegment([10, 10.5, 6, 7, 10.5, 7])

>>> segment.multiply(n=1)
PitchClassSegment([10, 10.5, 6, 7, 10.5, 7])

>>> segment.multiply(n=5)
PitchClassSegment([2, 4.5, 6, 11, 4.5, 11])

>>> segment.multiply(n=7)
PitchClassSegment([10, 1.5, 6, 1, 1.5, 1])

>>> segment.multiply(n=99)
PitchClassSegment([6, 7.5, 6, 9, 7.5, 9])

retrograde() → PitchClassSegment

Gets retrograde of numbered pitch-class segment.

>>> segment = abjad.PitchClassSegment([-2, -1.5, 6, 7, -1.5, 7])

>>> segment.retrograde()
PitchClassSegment([7, 10.5, 7, 6, 10.5, 10])

>>> segment.retrograde().retrograde()
PitchClassSegment([10, 10.5, 6, 7, 10.5, 7])

rotate(n=0) → PitchClassSegment

Rotates numbered pitch-class segment by index n.

>>> segment = abjad.PitchClassSegment([-2, -1.5, 6, 7, -1.5, 7])

>>> segment.rotate(n=1)
PitchClassSegment([7, 10, 10.5, 6, 7, 10.5])

>>> segment.rotate(n=-1)
PitchClassSegment([10.5, 6, 7, 10.5, 7, 10])

>>> segment.rotate(n=0)
PitchClassSegment([10, 10.5, 6, 7, 10.5, 7])

transpose(n=0) → PitchClassSegment

Transposes numbered pitch-class segment by index n.

>>> segment = abjad.PitchClassSegment([-2, -1.5, 6, 7, -1.5, 7])

>>> segment.transpose(n=11)
PitchClassSegment([9, 9.5, 5, 6, 9.5, 6])

class abjad.pcollections.PitchClassSet(argument=())

Numbered pitch-class set.

>>> set_ = abjad.PitchClassSet([-2, -1.5, 6, 7, -1.5, 7])
>>> set_
PitchClassSet([6, 7, 10, 10.5])

>>> str(set_)
'PC{6, 7, 10, 10.5}'

>>> abjad.NamedPitch("fs") in set_
False

>>> abjad.NamedPitch("f") in set_
False

>>> 6 in set_
False

>>> 5 in set_
False

>>> abjad.NumberedPitchClass(5) in set_
False

>>> abjad.NumberedPitchClass(6) in set_
True

Classical operators:

>>> set_1 = abjad.PitchClassSet([0, 2, 4, 5])
>>> set_2 = abjad.PitchClassSet([4, 5, 9])

>>> set_1 & set_2
PitchClassSet([4, 5])

>>> set_1 | set_2
PitchClassSet([0, 2, 4, 5, 9])

>>> set_1 ^ set_2
PitchClassSet([0, 2, 9])

>>> set_1 - set_2
PitchClassSet([0, 2])

>>> set_2 - set_1
PitchClassSet([9])

cardinality
difference(*arguments)	Return a new set with elements in the set that are not in the others.
get_normal_order()	Gets normal order.
get_prime_form([transposition_only])	Gets prime form.
intersection(*arguments)	Return a new set with elements common to the set and all others.
invert([axis])	Inverts pitch-class set.
multiply(n)	Multiplies pitch-class set by n.
symmetric_difference(*arguments)	Return a new set with elements in either the set or other but not both.
transpose([n])	Transposes all pitch-classes in pitch-class set by index n.
union(*arguments)	Return a new set with elements from the set and all others.

cardinality

overridden difference(*arguments)

Return a new set with elements in the set that are not in the others.

get_normal_order() → PitchClassSegment

Gets normal order.

Gets normal order of empty pitch-class set:

>>> pc_set = abjad.PitchClassSet()
>>> pc_set.get_normal_order()
PitchClassSegment([])

Gets normal order:

>>> pc_set = abjad.PitchClassSet([0, 1, 10, 11])
>>> pc_set.get_normal_order()
PitchClassSegment([10, 11, 0, 1])

Gets normal order:

>>> pc_set = abjad.PitchClassSet([2, 8, 9])
>>> pc_set.get_normal_order()
PitchClassSegment([8, 9, 2])

Gets normal order of pitch-class set with degree of symmetry equal to 2:

>>> pc_set = abjad.PitchClassSet([1, 2, 7, 8])
>>> pc_set.get_normal_order()
PitchClassSegment([1, 2, 7, 8])

Gets normal order of pitch-class set with degree of symmetry equal to 4:

>>> pc_set = abjad.PitchClassSet([0, 3, 6, 9])
>>> pc_set.get_normal_order()
PitchClassSegment([0, 3, 6, 9])

get_prime_form(transposition_only=False) → PitchClassSet

Gets prime form.

Gets prime form of empty pitch-class set:

>>> pc_set = abjad.PitchClassSet()
>>> pc_set.get_prime_form()
PitchClassSet([])

>>> pc_set = abjad.PitchClassSet()
>>> pc_set.get_prime_form(transposition_only=True)
PitchClassSet([])

Gets prime form:

>>> pc_set = abjad.PitchClassSet([0, 1, 10, 11])
>>> pc_set.get_prime_form()
PitchClassSet([0, 1, 2, 3])

>>> pc_set = abjad.PitchClassSet([0, 1, 10, 11])
>>> pc_set.get_prime_form(transposition_only=True)
PitchClassSet([0, 1, 2, 3])

Gets prime form:

>>> pc_set = abjad.PitchClassSet([2, 8, 9])
>>> pc_set.get_prime_form()
PitchClassSet([0, 1, 6])

>>> pc_set = abjad.PitchClassSet([2, 8, 9])
>>> pc_set.get_prime_form(transposition_only=True)
PitchClassSet([0, 1, 6])

Gets prime form of pitch-class set with degree of symmetry equal to 2:

>>> pc_set = abjad.PitchClassSet([1, 2, 7, 8])
>>> pc_set.get_prime_form()
PitchClassSet([0, 1, 6, 7])

>>> pc_set = abjad.PitchClassSet([1, 2, 7, 8])
>>> pc_set.get_prime_form(transposition_only=True)
PitchClassSet([0, 1, 6, 7])

Gets prime form of pitch-class set with degree of symmetry equal to 4:

>>> pc_set = abjad.PitchClassSet([0, 3, 6, 9])
>>> pc_set.get_prime_form()
PitchClassSet([0, 3, 6, 9])

>>> pc_set = abjad.PitchClassSet([0, 3, 6, 9])
>>> pc_set.get_prime_form(transposition_only=True)
PitchClassSet([0, 3, 6, 9])

Gets prime form of pitch-class that is not inversion-equivalent:

>>> pc_set = abjad.PitchClassSet([0, 4, 6, 7])
>>> pc_set.get_prime_form()
PitchClassSet([0, 1, 3, 7])

>>> pc_set = abjad.PitchClassSet([0, 4, 6, 7])
>>> pc_set.get_prime_form(transposition_only=True)
PitchClassSet([0, 4, 6, 7])

Gets prime form of inversionally nonequivalent pitch-class set:

>>> pc_set = abjad.PitchClassSet([0, 4, 7])
>>> pc_set.get_prime_form()
PitchClassSet([0, 3, 7])

>>> pc_set = abjad.PitchClassSet([0, 4, 7])
>>> pc_set.get_prime_form(transposition_only=True)
PitchClassSet([0, 4, 7])

REGRESSION:

>>> pc_set = abjad.PitchClassSet([0, 1, 2, 5, 8, 9])
>>> pc_set.get_prime_form()
PitchClassSet([0, 1, 2, 5, 6, 9])

REGRESSION:

>>> pc_set = abjad.PitchClassSet([0, 1, 2, 3, 6, 7])
>>> pc_set.get_prime_form()
PitchClassSet([0, 1, 2, 3, 6, 7])

overridden intersection(*arguments)

Return a new set with elements common to the set and all others.

invert(axis=None) → PitchClassSet

Inverts pitch-class set.

>>> abjad.PitchClassSet([-2, -1.5, 6, 7, -1.5, 7]).invert()
PitchClassSet([1.5, 2, 5, 6])

multiply(n) → PitchClassSet

Multiplies pitch-class set by n.

>>> abjad.PitchClassSet([-2, -1.5, 6, 7, -1.5, 7]).multiply(5)
PitchClassSet([2, 4.5, 6, 11])

overridden symmetric_difference(*arguments)

Return a new set with elements in either the set or other but not both.

transpose(n=0) → PitchClassSet

Transposes all pitch-classes in pitch-class set by index n.

>>> set_ = abjad.PitchClassSet([-2, -1.5, 6, 7, -1.5, 7])
>>> for n in range(12):
...     print(n, set_.transpose(n))
... 
0 PC{6, 7, 10, 10.5}
1 PC{7, 8, 11, 11.5}
2 PC{0, 0.5, 8, 9}
3 PC{1, 1.5, 9, 10}
4 PC{2, 2.5, 10, 11}
5 PC{0, 3, 3.5, 11}
6 PC{0, 1, 4, 4.5}
7 PC{1, 2, 5, 5.5}
8 PC{2, 3, 6, 6.5}
9 PC{3, 4, 7, 7.5}
10 PC{4, 5, 8, 8.5}
11 PC{5, 6, 9, 9.5}

overridden union(*arguments)

Return a new set with elements from the set and all others.

class abjad.pcollections.PitchRange(range_string='[A0, C8]')

Pitch range.

Pitches from C3 to C7, inclusive:

>>> pitch_range = abjad.PitchRange("[C3, C7]")
>>> lilypond_file = abjad.illustrate(pitch_range)
>>> abjad.show(lilypond_file)  

range_string	Gets range string of pitch range.
start_pitch	Start pitch of pitch range.
stop_pitch	Stop pitch of pitch range.
voice_pitch_class(pitch_class)	Voices pitch_class.

range_string

Gets range string of pitch range.

>>> abjad.PitchRange("[C3, C7]").range_string
'[C3, C7]'

>>> abjad.PitchRange("[-inf, C7]").range_string
'[-inf, C7]'

>>> abjad.PitchRange("[C3, +inf]").range_string
'[C3, +inf]'

>>> abjad.PitchRange("[-inf, +inf]").range_string
'[-inf, +inf]'

start_pitch

Start pitch of pitch range.

>>> abjad.PitchRange("[C3, C7]").start_pitch
NamedPitch('c')

>>> abjad.PitchRange("[-inf, C7]").start_pitch is None
True

stop_pitch

Stop pitch of pitch range.

>>> abjad.PitchRange("[C3, C7]").stop_pitch
NamedPitch("c''''")

>>> abjad.PitchRange("[C8, +inf]").stop_pitch is None
True

voice_pitch_class(pitch_class)

Voices pitch_class.

Voices C three times:

>>> pitch_range = abjad.PitchRange("[C4, C6]")
>>> pitch_range.voice_pitch_class("c")
(NamedPitch("c'"), NamedPitch("c''"), NamedPitch("c'''"))

Voices B two times:

>>> pitch_range = abjad.PitchRange("[C4, C6]")
>>> pitch_range.voice_pitch_class("b")
(NamedPitch("b'"), NamedPitch("b''"))

Returns empty because B can not voice:

>>> pitch_range = abjad.PitchRange("[C4, A4)")
>>> pitch_range.voice_pitch_class("b")
()

class abjad.pcollections.PitchSegment(items: Sequence = ())

Named pitch segment.

>>> segment = abjad.PitchSegment([-2, -1.5, 6, 7, -1.5, 7])

>>> str(segment)
'<-2, -1.5, 6, 7, -1.5, 7>'

>>> lilypond_file = abjad.illustrate(segment)
>>> abjad.show(lilypond_file)  

invert([axis])	Inverts named pitch segment about axis.
multiply([n])	Multiplies pitch segment by index n.
retrograde()	Retrograde of pitch segment.
rotate([n])	Rotates pitch segment by index n.
transpose([n])	Transposes pitch segment by index n.

invert(axis=None) → PitchSegment

Inverts named pitch segment about axis.

>>> segment = abjad.PitchSegment([-2, -1.5, 6, 7, -1.5, 7])

>>> lilypond_file = abjad.illustrate(segment)
>>> abjad.show(lilypond_file)  

>>> segment = segment.invert(axis=0)

>>> str(segment)
'<2, 1.5, -6, -7, 1.5, -7>'

>>> lilypond_file = abjad.illustrate(segment)
>>> abjad.show(lilypond_file)  

multiply(n=1) → PitchSegment

Multiplies pitch segment by index n.

>>> segment = abjad.PitchSegment([-2, -1.5, 6, 7, -1.5, 7])

>>> lilypond_file = abjad.illustrate(segment)
>>> abjad.show(lilypond_file)  

>>> segment = segment.multiply(n=3)

>>> str(segment)
'<-6, -4.5, 18, 21, -4.5, 21>'

>>> lilypond_file = abjad.illustrate(segment)
>>> abjad.show(lilypond_file)  

retrograde() → PitchSegment

Retrograde of pitch segment.

>>> segment = abjad.PitchSegment([-2, -1.5, 6, 7, -1.5, 7])

>>> lilypond_file = abjad.illustrate(segment)
>>> abjad.show(lilypond_file)  

>>> segment = segment.retrograde()

>>> str(segment)
'<7, -1.5, 7, 6, -1.5, -2>'

>>> lilypond_file = abjad.illustrate(segment)
>>> abjad.show(lilypond_file)  

rotate(n=0) → PitchSegment

Rotates pitch segment by index n.

>>> segment = abjad.PitchSegment([-2, -1.5, 6, 7, -1.5, 7])

>>> lilypond_file = abjad.illustrate(segment)
>>> abjad.show(lilypond_file)  

>>> segment = segment.rotate(n=1)

>>> str(segment)
'<7, -2, -1.5, 6, 7, -1.5>'

>>> lilypond_file = abjad.illustrate(segment)
>>> abjad.show(lilypond_file)  

transpose(n=0) → PitchSegment

Transposes pitch segment by index n.

>>> segment = abjad.PitchSegment([-2, -1.5, 6, 7, -1.5, 7])

>>> lilypond_file = abjad.illustrate(segment)
>>> abjad.show(lilypond_file)  

>>> segment = segment.transpose(n=11)

>>> str(segment)
'<9, 9.5, 17, 18, 9.5, 18>'

>>> lilypond_file = abjad.illustrate(segment)
>>> abjad.show(lilypond_file)  

class abjad.pcollections.PitchSet(argument=())

Numbered pitch set.

>>> set_1 = abjad.PitchSet([-26, -2.5, 6, 7, -1.5, 7])
>>> set_2 = abjad.PitchSet([-1.5, 7, 9, 12])

>>> set_1
PitchSet([-26, -2.5, -1.5, 6, 7])

>>> set_2
PitchSet([-1.5, 7, 9, 12])

>>> str(set_1)
'{-26, -2.5, -1.5, 6, 7}'

>>> str(set_2)
'{-1.5, 7, 9, 12}'

>>> -1.5 in set_1
False

>>> abjad.NumberedPitch(-1.5) in set_1
True

>>> abjad.NumberedPitch("aqs") in set_2
False

>>> len(set_1)
5

>>> len(set_2)
4

Classical operators:

>>> set_1 = abjad.PitchSet([-26, -2.5, 6, 7, -1.5, 7])
>>> set_2 = abjad.PitchSet([-1.5, 7, 9, 12])

>>> set_1 & set_2
PitchSet([-1.5, 7])

>>> set_2 & set_1
PitchSet([-1.5, 7])

>>> set_1.intersection(set_2)
PitchSet([-1.5, 7])

>>> set_2.intersection(set_1)
PitchSet([-1.5, 7])

>>> set_1 | set_2
PitchSet([-26, -2.5, -1.5, 6, 7, 9, 12])

>>> set_2 | set_1
PitchSet([-26, -2.5, -1.5, 6, 7, 9, 12])

>>> set_1.union(set_2)
PitchSet([-26, -2.5, -1.5, 6, 7, 9, 12])

>>> set_2.union(set_1)
PitchSet([-26, -2.5, -1.5, 6, 7, 9, 12])

>>> set_1 - set_2
PitchSet([-26, -2.5, 6])

>>> set_1.difference(set_2)
PitchSet([-26, -2.5, 6])

>>> set_2 - set_1
PitchSet([9, 12])

>>> set_2.difference(set_1)
PitchSet([9, 12])

>>> set_1 ^ set_2
PitchSet([-26, -2.5, 6, 9, 12])

>>> set_2 ^ set_1
PitchSet([-26, -2.5, 6, 9, 12])

>>> set_1.symmetric_difference(set_2)
PitchSet([-26, -2.5, 6, 9, 12])

>>> set_2.symmetric_difference(set_1)
PitchSet([-26, -2.5, 6, 9, 12])

Predicates:

>>> set_1 = abjad.PitchSet([-6, -5, -3, -1])
>>> set_2 = abjad.PitchSet([-3, -1])
>>> set_3 = abjad.PitchSet([1, 3, 4])

>>> set_1.isdisjoint(set_3)
True

>>> set_2.issubset(set_1)
True

>>> set_1.issuperset(set_2)
True

Comparison:

>>> set_1 = abjad.PitchSet([-26, -2.5, 6, 7, -1.5, 7])
>>> set_2 = abjad.PitchSet([-1.5, 7, 9, 12])

>>> set_1 == set_1
True

>>> set_1 == set_2
False

>>> set_1 < set_1
False

>>> set_1 < set_2
False

>>> set_1 <= set_1
True

>>> set_1 <= set_2
False

>>> set_1 > set_1
False

>>> set_1 > set_2
False

>>> set_1 >= set_1
True

>>> set_1 >= set_2
False

Copy:

>>> import copy
>>> set_1_copy = copy.copy(set_1)
>>> set_1_copy
PitchSet([-26, -2.5, -1.5, 6, 7])

>>> set_1 == set_1_copy
True

Empty set:

>>> set_ = abjad.PitchSet()
>>> set_
PitchSet()

>>> str(set_)
'{}'

>>> len(set_)
0

>>> bool(set_)
False

difference(*arguments)	Return a new set with elements in the set that are not in the others.
intersection(*arguments)	Return a new set with elements common to the set and all others.
symmetric_difference(*arguments)	Return a new set with elements in either the set or other but not both.
union(*arguments)	Return a new set with elements from the set and all others.

overridden difference(*arguments)

Return a new set with elements in the set that are not in the others.

overridden intersection(*arguments)

Return a new set with elements common to the set and all others.

overridden symmetric_difference(*arguments)

Return a new set with elements in either the set or other but not both.

overridden union(*arguments)

Return a new set with elements from the set and all others.

class abjad.pcollections.TwelveToneRow(items: Any = (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11))

Twelve-tone row.

Initializes from defaults:

>>> row = abjad.TwelveToneRow()
>>> lilypond_file = abjad.illustrate(row)
>>> abjad.show(lilypond_file)  

Initializes from integers:

>>> numbers = [1, 11, 9, 3, 6, 7, 5, 4, 10, 2, 8, 0]
>>> row = abjad.TwelveToneRow(numbers)
>>> lilypond_file = abjad.illustrate(row)
>>> abjad.show(lilypond_file)  

Interpreter representation:

>>> row
TwelveToneRow(items=(NumberedPitchClass(1), NumberedPitchClass(11), NumberedPitchClass(9), NumberedPitchClass(3), NumberedPitchClass(6), NumberedPitchClass(7), NumberedPitchClass(5), NumberedPitchClass(4), NumberedPitchClass(10), NumberedPitchClass(2), NumberedPitchClass(8), NumberedPitchClass(0)))

invert([axis])	Inverts row about optional axis.
multiply([n])	Multiplies pitch-classes in row by n.
retrograde()	Gets retrograde of row.
rotate([n])	Rotates row by index n.
transpose([n])	Transposes row by index n.

overridden invert(axis=None) → TwelveToneRow

Inverts row about optional axis.

Example row:

>>> numbers = [1, 11, 9, 3, 6, 7, 5, 4, 10, 2, 8, 0]
>>> row = abjad.TwelveToneRow(numbers)
>>> lilypond_file = abjad.illustrate(row)
>>> abjad.show(lilypond_file)  

Inverts row about first pitch-class when axis is none:

>>> inversion = row.invert()
>>> lilypond_file = abjad.illustrate(inversion)
>>> abjad.show(lilypond_file)  

First pitch-classes are equal:

>>> row[0] == inversion[0]
True

Inverts row about pitch-class 1; same result as above:

>>> inversion = row.invert(axis=1)
>>> lilypond_file = abjad.illustrate(inversion)
>>> abjad.show(lilypond_file)  

Inverts row about pitch-class 0:

>>> inversion = row.invert(axis=0)
>>> lilypond_file = abjad.illustrate(inversion)
>>> abjad.show(lilypond_file)  

Inverts row about pitch-class 5:

>>> inversion = row.invert(axis=5)
>>> lilypond_file = abjad.illustrate(inversion)
>>> abjad.show(lilypond_file)  

overridden multiply(n=1) → TwelveToneRow

Multiplies pitch-classes in row by n.

Example row:

>>> numbers = [1, 11, 9, 3, 6, 7, 5, 4, 10, 2, 8, 0]
>>> row = abjad.TwelveToneRow(numbers)
>>> lilypond_file = abjad.illustrate(row)
>>> abjad.show(lilypond_file)  

Multiplies pitch-classes in row by 5:

>>> multiplication = row.multiply(n=5)
>>> lilypond_file = abjad.illustrate(multiplication)
>>> abjad.show(lilypond_file)  

Multiplies pitch-classes in row by 7:

>>> multiplication = row.multiply(n=7)
>>> lilypond_file = abjad.illustrate(multiplication)
>>> abjad.show(lilypond_file)  

Multiplies pitch-classes in row by 1:

>>> multiplication = row.multiply(n=1)
>>> lilypond_file = abjad.illustrate(multiplication)
>>> abjad.show(lilypond_file)  

overridden retrograde() → TwelveToneRow

Gets retrograde of row.

Example row:

>>> numbers = [1, 11, 9, 3, 6, 7, 5, 4, 10, 2, 8, 0]
>>> row = abjad.TwelveToneRow(numbers)
>>> lilypond_file = abjad.illustrate(row)
>>> abjad.show(lilypond_file)  

Gets retrograde of row:

>>> retrograde = row.retrograde()
>>> lilypond_file = abjad.illustrate(retrograde)
>>> abjad.show(lilypond_file)  

Gets retrograde of retrograde of row:

>>> retrograde = row.retrograde().retrograde()
>>> lilypond_file = abjad.illustrate(retrograde)
>>> abjad.show(lilypond_file)  

>>> retrograde == row
True

overridden rotate(n=0) → TwelveToneRow

Rotates row by index n.

Example row:

>>> numbers = [1, 11, 9, 3, 6, 7, 5, 4, 10, 2, 8, 0]
>>> row = abjad.TwelveToneRow(numbers)
>>> lilypond_file = abjad.illustrate(row)
>>> abjad.show(lilypond_file)  

Rotates row to the right:

>>> rotation = row.rotate(n=1)
>>> lilypond_file = abjad.illustrate(rotation)
>>> abjad.show(lilypond_file)  

Rotates row to the left:

>>> rotation = row.rotate(n=-1)
>>> lilypond_file = abjad.illustrate(rotation)
>>> abjad.show(lilypond_file)  

Rotates row by zero:

>>> rotation = row.rotate(n=0)
>>> lilypond_file = abjad.illustrate(rotation)
>>> abjad.show(lilypond_file)  

>>> rotation == row
True

overridden transpose(n=0) → TwelveToneRow

Transposes row by index n.

Example row:

>>> numbers = [1, 11, 9, 3, 6, 7, 5, 4, 10, 2, 8, 0]
>>> row = abjad.TwelveToneRow(numbers)
>>> lilypond_file = abjad.illustrate(row)
>>> abjad.show(lilypond_file)  

Transposes row by positive index:

>>> transposition = row.transpose(n=13)
>>> lilypond_file = abjad.illustrate(transposition)
>>> abjad.show(lilypond_file)  

Transposes row by negative index:

>>> transposition = row.transpose(n=-13)
>>> lilypond_file = abjad.illustrate(transposition)
>>> abjad.show(lilypond_file)  

Transposes row by zero index:

>>> transposition = row.transpose(n=0)
>>> lilypond_file = abjad.illustrate(transposition)
>>> abjad.show(lilypond_file)  

>>> transposition == row
True