3.3. pctheory.group
This module contains a class representing a group of operators.
class OperatorGroup
Represents a group of TnMm operators. Operator groups are mathematical groups; that is, they have an operation (operator concatenation), they have an identity element (T0M1), they are associative, and for every operator TnMm in the group, there is an inverse operator (TnMm)‐1 in the group. The TTOs (twelve-tone operators) are a mathematical group, as well as smaller subgroups of the TTOs.
OperatorGroup constructor
OperatorGroup.__init__(utos: list = None, num_pcs: int = 12)
Constructs an OperatorGroup. You can initialize the group with a list of UTOs that form a group. You can also specify whether this is a group of chromatic UTOs or microtonal UTOs. Once this is specified in the constructor, it cannot be changed.
OperatorGroup read-only properties
OperatorGroup.namestr
Gets the name of the operator group. For example, the group of all TTOs is G*/*/*/*.
OperatorGroup.utos{UTO}
Gets the UTOs in the operator group as a set.
OperatorGroup methods
OperatorGroup.get_orbits()[PitchClass12]or[PitchClass24]
Gets the orbits of an operator group. Let U be the universal set of all chromatic pitch-classes or of all microtonal pitch-classes. Then the orbits of an operator group G are the disjoint subsets of U, such that for any pitch-class s in a subset S of U, the operations in G only transform s into another element t ∈ S.
OperatorGroup.left_coset(uto: transformations.UTO)[UTO]
Gets the left coset of G by a UTO.
OperatorGroup.load_utos(utos: list)
Loads a list of UTOs into a group. Note that when the OperatorGroup was initialized, the number of possible pcs was specified. If this is a group of chromatic operators, you cannot load microtonal operators into the group, and vice versa.
OperatorGroup.right_coset(uto: UTO)[UTO]
Gets the right coset of G by a UTO.
OperatorGroup overloaded special functions
Overloaded special functions include __repr__() and __str__(). The str() implementation allows OperatorGroup objects to be printed.