abjad.setclass

abjad.setclass.SetClass([cardinality, rank, ...])

Set-class.

class abjad.setclass.SetClass(cardinality: int = 1, rank: int = 1, lex_rank: bool = False, transposition_only: bool = False)[source]

Set-class.

Makes SG2 set-class from Forte rank:

>>> set_class = abjad.SetClass(4, 29)
>>> print(set_class)
SC(4-29){0, 1, 3, 7}

Makes SG2 set-class from lex rank:

>>> set_class = abjad.SetClass(4, 29, lex_rank=True)
>>> print(set_class)
SC(4-29){0, 3, 6, 9}

Makes SG1 set-class:

>>> set_class = abjad.SetClass(4, 29, transposition_only=True, lex_rank=True)
>>> print(set_class)
SC(4-29){0, 2, 6, 7}

Makes aggregate:

>>> set_class = abjad.SetClass(12, 1, transposition_only=True, lex_rank=True)
>>> print(set_class)
SC(12-1){0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}

Lists SG2 tetrachords, pentachords, hexachords by Forte rank:

>>> set_classes = abjad.SetClass.list_set_classes(cardinality=4)
>>> for set_class in set_classes:
...     print(set_class)
... 
SC(4-1){0, 1, 2, 3}
SC(4-2){0, 1, 2, 4}
SC(4-3){0, 1, 3, 4}
SC(4-4){0, 1, 2, 5}
SC(4-5){0, 1, 2, 6}
SC(4-6){0, 1, 2, 7}
SC(4-7){0, 1, 4, 5}
SC(4-8){0, 1, 5, 6}
SC(4-9){0, 1, 6, 7}
SC(4-10){0, 2, 3, 5}
SC(4-11){0, 1, 3, 5}
SC(4-12){0, 2, 3, 6}
SC(4-13){0, 1, 3, 6}
SC(4-14){0, 2, 3, 7}
SC(4-15){0, 1, 4, 6}
SC(4-16){0, 1, 5, 7}
SC(4-17){0, 3, 4, 7}
SC(4-18){0, 1, 4, 7}
SC(4-19){0, 1, 4, 8}
SC(4-20){0, 1, 5, 8}
SC(4-21){0, 2, 4, 6}
SC(4-22){0, 2, 4, 7}
SC(4-23){0, 2, 5, 7}
SC(4-24){0, 2, 4, 8}
SC(4-25){0, 2, 6, 8}
SC(4-26){0, 3, 5, 8}
SC(4-27){0, 2, 5, 8}
SC(4-28){0, 3, 6, 9}
SC(4-29){0, 1, 3, 7}

>>> set_classes = abjad.SetClass.list_set_classes(cardinality=5)
>>> for set_class in set_classes:
...     print(set_class)
... 
SC(5-1){0, 1, 2, 3, 4}
SC(5-2){0, 1, 2, 3, 5}
SC(5-3){0, 1, 2, 4, 5}
SC(5-4){0, 1, 2, 3, 6}
SC(5-5){0, 1, 2, 3, 7}
SC(5-6){0, 1, 2, 5, 6}
SC(5-7){0, 1, 2, 6, 7}
SC(5-8){0, 2, 3, 4, 6}
SC(5-9){0, 1, 2, 4, 6}
SC(5-10){0, 1, 3, 4, 6}
SC(5-11){0, 2, 3, 4, 7}
SC(5-12){0, 1, 3, 5, 6}
SC(5-13){0, 1, 2, 4, 8}
SC(5-14){0, 1, 2, 5, 7}
SC(5-15){0, 1, 2, 6, 8}
SC(5-16){0, 1, 3, 4, 7}
SC(5-17){0, 1, 3, 4, 8}
SC(5-18){0, 1, 4, 5, 7}
SC(5-19){0, 1, 3, 6, 7}
SC(5-20){0, 1, 3, 7, 8}
SC(5-21){0, 1, 4, 5, 8}
SC(5-22){0, 1, 4, 7, 8}
SC(5-23){0, 2, 3, 5, 7}
SC(5-24){0, 1, 3, 5, 7}
SC(5-25){0, 2, 3, 5, 8}
SC(5-26){0, 2, 4, 5, 8}
SC(5-27){0, 1, 3, 5, 8}
SC(5-28){0, 2, 3, 6, 8}
SC(5-29){0, 1, 3, 6, 8}
SC(5-30){0, 1, 4, 6, 8}
SC(5-31){0, 1, 3, 6, 9}
SC(5-32){0, 1, 4, 6, 9}
SC(5-33){0, 2, 4, 6, 8}
SC(5-34){0, 2, 4, 6, 9}
SC(5-35){0, 2, 4, 7, 9}
SC(5-36){0, 1, 2, 4, 7}
SC(5-37){0, 3, 4, 5, 8}
SC(5-38){0, 1, 2, 5, 8}

>>> set_classes = abjad.SetClass.list_set_classes(cardinality=6)
>>> for set_class in set_classes:
...     print(set_class)
... 
SC(6-1){0, 1, 2, 3, 4, 5}
SC(6-2){0, 1, 2, 3, 4, 6}
SC(6-3){0, 1, 2, 3, 5, 6}
SC(6-4){0, 1, 2, 4, 5, 6}
SC(6-5){0, 1, 2, 3, 6, 7}
SC(6-6){0, 1, 2, 5, 6, 7}
SC(6-7){0, 1, 2, 6, 7, 8}
SC(6-8){0, 2, 3, 4, 5, 7}
SC(6-9){0, 1, 2, 3, 5, 7}
SC(6-10){0, 1, 3, 4, 5, 7}
SC(6-11){0, 1, 2, 4, 5, 7}
SC(6-12){0, 1, 2, 4, 6, 7}
SC(6-13){0, 1, 3, 4, 6, 7}
SC(6-14){0, 1, 3, 4, 5, 8}
SC(6-15){0, 1, 2, 4, 5, 8}
SC(6-16){0, 1, 4, 5, 6, 8}
SC(6-17){0, 1, 2, 4, 7, 8}
SC(6-18){0, 1, 2, 5, 7, 8}
SC(6-19){0, 1, 3, 4, 7, 8}
SC(6-20){0, 1, 4, 5, 8, 9}
SC(6-21){0, 2, 3, 4, 6, 8}
SC(6-22){0, 1, 2, 4, 6, 8}
SC(6-23){0, 2, 3, 5, 6, 8}
SC(6-24){0, 1, 3, 4, 6, 8}
SC(6-25){0, 1, 3, 5, 6, 8}
SC(6-26){0, 1, 3, 5, 7, 8}
SC(6-27){0, 1, 3, 4, 6, 9}
SC(6-28){0, 1, 3, 5, 6, 9}
SC(6-29){0, 1, 3, 6, 8, 9}
SC(6-30){0, 1, 3, 6, 7, 9}
SC(6-31){0, 1, 3, 5, 8, 9}
SC(6-32){0, 2, 4, 5, 7, 9}
SC(6-33){0, 2, 3, 5, 7, 9}
SC(6-34){0, 1, 3, 5, 7, 9}
SC(6-35){0, 2, 4, 6, 8, 10}
SC(6-36){0, 1, 2, 3, 4, 7}
SC(6-37){0, 1, 2, 3, 4, 8}
SC(6-38){0, 1, 2, 3, 7, 8}
SC(6-39){0, 2, 3, 4, 5, 8}
SC(6-40){0, 1, 2, 3, 5, 8}
SC(6-41){0, 1, 2, 3, 6, 8}
SC(6-42){0, 1, 2, 3, 6, 9}
SC(6-43){0, 1, 2, 5, 6, 8}
SC(6-44){0, 1, 2, 5, 6, 9}
SC(6-45){0, 2, 3, 4, 6, 9}
SC(6-46){0, 1, 2, 4, 6, 9}
SC(6-47){0, 1, 2, 4, 7, 9}
SC(6-48){0, 1, 2, 5, 7, 9}
SC(6-49){0, 1, 3, 4, 7, 9}
SC(6-50){0, 1, 4, 6, 7, 9}

There are 352 SG1 set-classes and 224 SG2 set-classes.

Gets cardinality of SG2 set-class with Forte rank:

>>> set_class = abjad.SetClass(4, 29)
>>> print(set_class)
SC(4-29){0, 1, 3, 7}

>>> set_class.cardinality
4

Gets cardinality of SG2 set-class with lex rank:

>>> set_class = abjad.SetClass(
...     4,
...     29,
...     lex_rank=True,
... )
>>> print(set_class)
SC(4-29){0, 3, 6, 9}

>>> set_class.cardinality
4

Gets cardinality of SG1 set-class:

>>> set_class = abjad.SetClass(
...     4,
...     29,
...     lex_rank=True,
...     transposition_only=True,
... )
>>> print(set_class)
SC(4-29){0, 2, 6, 7}

>>> set_class.cardinality
4

Initializes SG2 set-class with Forte rank:

>>> set_class = abjad.SetClass(4, 29)
>>> print(set_class)
SC(4-29){0, 1, 3, 7}

Initializes SG2 set-class with lex rank:

>>> set_class = abjad.SetClass(
...     4,
...     29,
...     lex_rank=True,
... )
>>> print(set_class)
SC(4-29){0, 3, 6, 9}

Initializes SG1 (transposition-only) set-class:

>>> set_class = abjad.SetClass(
...     4,
...     29,
...     lex_rank=True,
...     transposition_only=True,
... )
>>> print(set_class)
SC(4-29){0, 2, 6, 7}

`is_inversion_equivalent`	Is true when set-class is inversion-equivalent.
`prime_form`	Gets prime form.

is_inversion_equivalent

Is true when set-class is inversion-equivalent.

Is inversion-equivalent:

>>> set_class = abjad.SetClass(4, 29)
>>> print(set_class)
SC(4-29){0, 1, 3, 7}

>>> pitch_class_set = set_class.prime_form
>>> inverted_pitch_class_set = pitch_class_set.invert()
>>> inverted_set_class = abjad.SetClass.from_pitches(inverted_pitch_class_set)
>>> print(inverted_set_class)
SC(4-29){0, 1, 3, 7}

>>> set_class.is_inversion_equivalent
True

Is inversion-equivalent:

>>> set_class = abjad.SetClass(
...     4,
...     29,
...     lex_rank=True,
... )
>>> print(set_class)
SC(4-29){0, 3, 6, 9}

>>> pitch_class_set = set_class.prime_form
>>> inverted_pitch_class_set = pitch_class_set.invert()
>>> inverted_set_class = abjad.SetClass.from_pitches(
...     inverted_pitch_class_set,
...     lex_rank=True,
... )
>>> print(inverted_set_class)
SC(4-29){0, 3, 6, 9}

>>> set_class.is_inversion_equivalent
True

Is not inversion-equivalent:

>>> set_class = abjad.SetClass(
...     4,
...     29,
...     lex_rank=True,
...     transposition_only=True,
... )
>>> print(set_class)
SC(4-29){0, 2, 6, 7}

>>> pitch_class_set = set_class.prime_form
>>> inverted_pitch_class_set = pitch_class_set.invert()
>>> inverted_set_class = abjad.SetClass.from_pitches(
...     inverted_pitch_class_set,
...     lex_rank=True,
...     transposition_only=True,
... )
>>> print(inverted_set_class)
SC(4-15){0, 1, 5, 7}

>>> set_class.is_inversion_equivalent
False

prime_form

Gets prime form.

Gets prime form of SG2 set-class with Forte rank:

>>> set_class = abjad.SetClass(4, 29)
>>> print(set_class)
SC(4-29){0, 1, 3, 7}

>>> set_class.prime_form
PitchClassSet([0, 1, 3, 7])

Gets prime form of SG2 set-class with lex rank:

>>> set_class = abjad.SetClass(
...     4,
...     29,
...     lex_rank=True,
... )
>>> print(set_class)
SC(4-29){0, 3, 6, 9}

>>> set_class.prime_form
PitchClassSet([0, 3, 6, 9])

Gets prime form of SG1 set-class:

>>> set_class = abjad.SetClass(
...     4,
...     29,
...     lex_rank=True,
...     transposition_only=True,
... )
>>> print(set_class)
SC(4-29){0, 2, 6, 7}

>>> set_class.prime_form
PitchClassSet([0, 2, 6, 7])