PitchClassSet

class pitchtools.PitchClassSet(items=None, item_class=None)

Pitch-class set.

Initializes numbered pitch-class set:

>>> numbered_pitch_class_set = PitchClassSet(
...     items=[-2, -1.5, 6, 7, -1.5, 7],
...     item_class=NumberedPitchClass,
...     )
>>> numbered_pitch_class_set
PitchClassSet([6, 7, 10, 10.5])

Initializes named pitch-class set:

>>> named_pitch_class_set = PitchClassSet(
...     items=['c', 'ef', 'bqs,', 'd'],
...     item_class=NamedPitchClass,
...     )
>>> named_pitch_class_set
PitchClassSet(['c', 'd', 'ef', 'bqs'])

Lineage

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Attribute summary

cardinality Gets cardinality of set.
copy() Copies typed frozen set.
difference(argument) Typed frozen set set-minus argument.
from_selection(class_, selection[, item_class]) Makes pitch-class set from selection.
get_normal_order() Gets normal order.
get_prime_form([transposition_only]) Gets prime form.
intersection(argument) Set-theoretic intersection of typed frozen set and argument.
invert([axis]) Inverts pitch-class set.
is_transposed_subset(pcset) Is true when pitch-class set is transposed subset of pcset.
is_transposed_superset(pcset) Is true when pitch-class set is transposed superset of pcset.
isdisjoint(argument) Is true when typed frozen set shares no elements with argument.
issubset(argument) Is true when typed frozen set is a subset of argument.
issuperset(argument) Is true when typed frozen set is a superset of argument.
item_class Gets item class of collection.
items Gets items in collection.
multiply(n) Multiplies pitch-class set by n.
order_by(pitch_class_segment) Orders pitch-class set by pitch_class_segment.
symmetric_difference(argument) Symmetric difference of typed frozen set and argument.
transpose([n]) Transposes all pitch-classes in pitch-class set by index n.
union(argument) Union of typed frozen set and argument.
yield_all_pitch_class_sets() Yields all pitch-class sets.
__and__(argument) Logical AND of typed frozen set and argument.
__contains__(item) Is true when typed collection contains item.
__eq__(argument) Is true when argument is a typed collection with items that compare equal to those of this typed collection.
__format__([format_specification]) Formats Abjad object.
__ge__(argument) Is true when typed frozen set is greater than or equal to argument.
__gt__(argument) Is true when typed frozen set is greater than argument.
__hash__() Hashes pitch-class set.
__illustrate__() Illustrates pitch-class set.
__iter__() Iterates typed collection.
__le__(argument) Is true when typed frozen set is less than or equal to argument.
__len__() Gets length of typed collection.
__lt__(argument) Is true when typed frozen set is less than argument.
__ne__(argument) Is true when typed frozen set is not equal to argument.
__or__(argument) Logical OR of typed frozen set and argument.
__repr__() Gets interpreter representation of Abjad object.
__str__() Gets string representation of pitch-class set.
__sub__(argument) Subtracts argument from typed frozen set.
__xor__(argument) Logical XOR of typed frozen set and argument.

Read-only properties

(Set).cardinality

Gets cardinality of set.

Defined equal to length of set.

Returns nonnegative integer.

(TypedCollection).item_class

Gets item class of collection.

Collection coerces items according to item_class.

Returns class.

(TypedCollection).items

Gets items in collection.

Returns list.

Methods

(TypedFrozenset).copy()

Copies typed frozen set.

Returns new typed frozen set.

(TypedFrozenset).difference(argument)

Typed frozen set set-minus argument.

Returns new typed frozen set.

PitchClassSet.get_normal_order()

Gets normal order.

Gets normal order of empty pitch-class set:

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

Gets normal order:

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

Gets normal order:

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

Returns pitch-class segment.

PitchClassSet.get_prime_form(transposition_only=False)

Gets prime form.

Gets prime form of empty pitch-class set:

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

Gets prime form:

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

Gets prime form:

>>> pc_set = PitchClassSet([2, 8, 9])
>>> pc_set.get_prime_form()
PitchClassSet([0, 1, 6])
>>> pc_set = 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 = PitchClassSet([1, 2, 7, 8])
>>> pc_set.get_prime_form()
PitchClassSet([0, 1, 6, 7])
>>> pc_set = 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 = PitchClassSet([0, 3, 6, 9])
>>> pc_set.get_prime_form()
PitchClassSet([0, 3, 6, 9])
>>> pc_set = 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 = PitchClassSet([0, 4, 6, 7])
>>> pc_set.get_prime_form()
PitchClassSet([0, 1, 3, 7])
>>> pc_set = PitchClassSet([0, 4, 6, 7])
>>> pc_set.get_prime_form(transposition_only=True)
PitchClassSet([0, 4, 6, 7])

Returns new pitch-class set.

(TypedFrozenset).intersection(argument)

Set-theoretic intersection of typed frozen set and argument.

Returns new typed frozen set.

PitchClassSet.invert(axis=None)

Inverts pitch-class set.

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

Returns numbered pitch-class set.

PitchClassSet.is_transposed_subset(pcset)

Is true when pitch-class set is transposed subset of pcset. Otherwise false:

>>> pitch_class_set_1 = PitchClassSet(
...     [-2, -1.5, 6, 7, -1.5, 7],
...     )
>>> pitch_class_set_2 = PitchClassSet(
...     [-2, -1.5, 6, 7, -1.5, 7, 7.5, 8],
...     )
>>> pitch_class_set_1.is_transposed_subset(pitch_class_set_2)
True

Returns true or false.

PitchClassSet.is_transposed_superset(pcset)

Is true when pitch-class set is transposed superset of pcset. Otherwise false:

>>> pitch_class_set_1 = PitchClassSet(
...     [-2, -1.5, 6, 7, -1.5, 7],
...     )
>>> pitch_class_set_2 = PitchClassSet(
...     [-2, -1.5, 6, 7, -1.5, 7, 7.5, 8],
...     )
>>> pitch_class_set_2.is_transposed_superset(pitch_class_set_1)
True

Returns true or false.

(TypedFrozenset).isdisjoint(argument)

Is true when typed frozen set shares no elements with argument. Otherwise false.

Returns true or false.

(TypedFrozenset).issubset(argument)

Is true when typed frozen set is a subset of argument. Otherwise false.

Returns true or false.

(TypedFrozenset).issuperset(argument)

Is true when typed frozen set is a superset of argument. Otherwise false.

Returns true or false.

PitchClassSet.multiply(n)

Multiplies pitch-class set by n.

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

Returns new pitch-class set.

PitchClassSet.order_by(pitch_class_segment)

Orders pitch-class set by pitch_class_segment.

Returns pitch-class segment.

(TypedFrozenset).symmetric_difference(argument)

Symmetric difference of typed frozen set and argument.

Returns new typed frozen set.

PitchClassSet.transpose(n=0)

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

Returns new pitch-class set.

(TypedFrozenset).union(argument)

Union of typed frozen set and argument.

Returns new typed frozen set.

Class & static methods

classmethod PitchClassSet.from_selection(class_, selection, item_class=None)

Makes pitch-class set from selection.

>>> staff_1 = Staff("c'4 <d' fs' a'>4 b2")
>>> staff_2 = Staff("c4. r8 g2")
>>> selection = select((staff_1, staff_2))
>>> PitchClassSet.from_selection(selection)
PitchClassSet(['c', 'd', 'fs', 'g', 'a', 'b'])

Returns pitch-class set.

static PitchClassSet.yield_all_pitch_class_sets()

Yields all pitch-class sets.

Yields all pitch-class sets:

>>> class_ = PitchClassSet
>>> pcsets = list(class_.yield_all_pitch_class_sets())
>>> len(pcsets)
4096
>>> for pcset in pcsets[:20]:
...   pcset
... 
PitchClassSet([])
PitchClassSet([0])
PitchClassSet([1])
PitchClassSet([0, 1])
PitchClassSet([2])
PitchClassSet([0, 2])
PitchClassSet([1, 2])
PitchClassSet([0, 1, 2])
PitchClassSet([3])
PitchClassSet([0, 3])
PitchClassSet([1, 3])
PitchClassSet([0, 1, 3])
PitchClassSet([2, 3])
PitchClassSet([0, 2, 3])
PitchClassSet([1, 2, 3])
PitchClassSet([0, 1, 2, 3])
PitchClassSet([4])
PitchClassSet([0, 4])
PitchClassSet([1, 4])
PitchClassSet([0, 1, 4])

There are 4096 pitch-class sets.

This is U* in [Morris 1987].

Returns generator.

Special methods

(TypedFrozenset).__and__(argument)

Logical AND of typed frozen set and argument.

Returns new typed frozen set.

(TypedCollection).__contains__(item)

Is true when typed collection contains item. Otherwise false.

Returns true or false.

(TypedCollection).__eq__(argument)

Is true when argument is a typed collection with items that compare equal to those of this typed collection. Otherwise false.

Returns true or false.

(AbjadObject).__format__(format_specification='')

Formats Abjad object.

Set format_specification to ‘’ or ‘storage’. Interprets ‘’ equal to ‘storage’.

Returns string.

(TypedFrozenset).__ge__(argument)

Is true when typed frozen set is greater than or equal to argument. Otherwise false.

Returns true or false.

(TypedFrozenset).__gt__(argument)

Is true when typed frozen set is greater than argument. Otherwise false.

Returns true or false.

PitchClassSet.__hash__()

Hashes pitch-class set.

Returns integer.

PitchClassSet.__illustrate__()

Illustrates pitch-class set.

Illustrates numbered segment:

>>> set_ = PitchClassSet([-2, -1.5, 6, 7, -1.5, 7])
>>> show(set_) 

Illustrates named set:

>>> items = ['c', 'ef', 'bqs,', 'd']
>>> set_ = PitchClassSet(
...     items=items,
...     item_class=NamedPitchClass,
...     )
>>> show(set_) 

Returns LilyPond file:

>>> prototype = lilypondfiletools.LilyPondFile
>>> isinstance(set_.__illustrate__(), prototype)
True
(TypedCollection).__iter__()

Iterates typed collection.

Returns generator.

(TypedFrozenset).__le__(argument)

Is true when typed frozen set is less than or equal to argument. Otherwise false.

Returns true or false.

(TypedCollection).__len__()

Gets length of typed collection.

Returns nonnegative integer.

(TypedFrozenset).__lt__(argument)

Is true when typed frozen set is less than argument. Otherwise false.

Returns true or false.

(TypedFrozenset).__ne__(argument)

Is true when typed frozen set is not equal to argument. Otherwise false.

Returns true or false.

(TypedFrozenset).__or__(argument)

Logical OR of typed frozen set and argument.

Returns new typed frozen set.

(AbjadObject).__repr__()

Gets interpreter representation of Abjad object.

Returns string.

PitchClassSet.__str__()

Gets string representation of pitch-class set.

Gets string of set sorted at initialization:

>>> pc_set = PitchClassSet([6, 7, 10, 10.5])
>>> str(pc_set)
'PC{6, 7, 10, 10.5}'

Gets string of set not sorted at initialization:

>>> pc_set = PitchClassSet([10.5, 10, 7, 6])
>>> str(pc_set)
'PC{6, 7, 10, 10.5}'

Returns string.

(TypedFrozenset).__sub__(argument)

Subtracts argument from typed frozen set.

Returns new typed frozen set.

(TypedFrozenset).__xor__(argument)

Logical XOR of typed frozen set and argument.

Returns new typed frozen set.