RootedChordClass

class tonalanalysistools.RootedChordClass(root=None, *arguments)

A rooted chord class.

G major triad in root position:

>>> tonalanalysistools.RootedChordClass('g', 'major')
GMajorTriadInRootPosition

G dominant seventh in root position:

>>> chord_class = tonalanalysistools.RootedChordClass('g', 'dominant', 7)

Note that notions like a G dominant seventh represent an entire class of chords because there are many different spacings and registrations of a G dominant seventh.

Lineage

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Attribute summary

bass Bass of rooted chord-class.
cardinality Cardinality of rooted chord-class.
cardinality_to_extent(cardinality) Change cardinality to extent.
chord_quality Chord quality of rooted chord-class.
copy() Copies typed frozen set.
difference(argument) Typed frozen set set-minus argument.
extent Extent of rooted chord-class.
extent_to_cardinality(extent) Change extent to cardinality.
extent_to_extent_name(extent) Change extent to extent name.
figured_bass Figured bass of rooted chord-class.
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.
inversion Inversion of rooted chord-class.
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.
markup Markup of rooted chord-class.
multiply(n) Multiplies pitch-class set by n.
order_by(pitch_class_segment) Orders pitch-class set by pitch_class_segment.
quality_pair Quality pair of rooted chord-class.
root Root of rooted chord-class.
root_string Root string of rooted chord-class.
symmetric_difference(argument) Symmetric difference of typed frozen set and argument.
transpose() Transpose rooted chord-class.
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__(arg) Is true when arg is a rooted chord-class with root, chord quality and inversion equal to those of this rooted chord-class.
__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 rooted chord-class.
__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__(arg) Is true when rooted chord-class does not equal arg.
__or__(argument) Logical OR of typed frozen set and argument.
__repr__() Gets interpreter representation of rooted chord-class.
__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

RootedChordClass.bass

Bass of rooted chord-class.

>>> chord_class.bass
NamedPitchClass('g')

Returns named pitch-class.

RootedChordClass.cardinality

Cardinality of rooted chord-class.

>>> chord_class.cardinality
4

Returns nonnegative integer.

RootedChordClass.chord_quality

Chord quality of rooted chord-class.

>>> chord_class.chord_quality
DominantSeventhInRootPosition('P1', '+M3', '+P5', '+m7')

Returns chord quality.

RootedChordClass.extent

Extent of rooted chord-class.

>>> chord_class.extent
ChordExtent(number=7)

Returns chord extent.

RootedChordClass.figured_bass

Figured bass of rooted chord-class.

>>> chord_class.figured_bass
'7'

Returns string.

RootedChordClass.inversion

Inversion of rooted chord-class.

>>> chord_class.inversion
0

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.

RootedChordClass.markup

Markup of rooted chord-class.

>>> show(chord_class.markup) 

Returns markup.

RootedChordClass.quality_pair

Quality pair of rooted chord-class.

>>> chord_class.quality_pair
('dominant', 'seventh')

Returns pair.

RootedChordClass.root

Root of rooted chord-class.

>>> chord_class.root
NamedPitchClass('g')

Returns

RootedChordClass.root_string

Root string of rooted chord-class.

>>> chord_class.root_string
'G'

Returns string.

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.

RootedChordClass.transpose()

Transpose rooted chord-class.

Not yet implemented.

Will return new rooted chord-class.

(TypedFrozenset).union(argument)

Union of typed frozen set and argument.

Returns new typed frozen set.

Class & static methods

static RootedChordClass.cardinality_to_extent(cardinality)

Change cardinality to extent.

Tertian chord with four pitch classes qualifies as a seventh chord:

>>> tonalanalysistools.RootedChordClass.cardinality_to_extent(4)
7

Returns integer.

static RootedChordClass.extent_to_cardinality(extent)

Change extent to cardinality.

Tertian chord with extent of seven comprises four pitch-clases:

>>> tonalanalysistools.RootedChordClass.extent_to_cardinality(7)
4

Returns integer.

static RootedChordClass.extent_to_extent_name(extent)

Change extent to extent name.

Extent of seven is a seventh:

>>> tonalanalysistools.RootedChordClass.extent_to_extent_name(7)
'seventh'

Returns string.

(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.

(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.

RootedChordClass.__eq__(arg)

Is true when arg is a rooted chord-class with root, chord quality and inversion equal to those of this rooted chord-class. 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.

RootedChordClass.__hash__()

Hashes rooted chord-class.

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

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.

RootedChordClass.__ne__(arg)

Is true when rooted chord-class does not equal arg. Otherwise false.

Returns true or false.

(TypedFrozenset).__or__(argument)

Logical OR of typed frozen set and argument.

Returns new typed frozen set.

RootedChordClass.__repr__()

Gets interpreter representation of rooted chord-class.

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.