3.7. pctheory.poset
This module contains functionality for working with posets, or partially ordered sets. For the purposes of this module, a poset is a list that contains one or more of the following: sets, lists, and individual pitch-classes. The two functions in this module are useful for generating posets that match certain criteria.
filter_poset_positions(posets: list, position_filter: list, exclude=False)list
Filters a list of posets. The position_filter must be a list of the same length as each element in posets. Each element in position_filter corresponds to an element in any single poset in posets. The filter is either an inclusion or exclusion filter. If it is an inclusion filter (default), each element in any single poset in posets must be an improper subset of the corresponding element in position_filter. If the filter is an exclusion filter, each element in any single poset in posets must be disjoint with the corresponding element in position_filter. The filter type is determined by the exclude parameter.
generate_chains_weak(p0: PitchClass12, sc_list: list, max_2_similarity: float = 0.4, min_2_similarity: float = 0, max_3_similarity: float = 0.4, min_3_similarity: float = 0, pn=False)list
Generates a list of weak pcset chains. A “weak pcset chain” is an ordered succession of pcsets, such that each pair of adjacent pcsets has at least one element in common. This element is extracted from both pcsets and positioned in between them in the chain. For example, suppose we have a list of pcsets [{059A}, {358B}, {1234}]. The corresponding weak pcset chain is [{09A}, 5, {8B}, 3, {124}]. We can specify the starting pc, so we will choose 9 for that. And we will also choose an ending pc (although this is not strictly necessary, the algorithm will do this). So the weak pcset chain becomes [9, {0A}, 5, {8B}, 3, {14}, 2]. This is a poset. The single pcs and sets are ordered with respect to each other. The elements inside the sets are not ordered with respect to each other.
The parameter p0 specifies the initial pc of the chain. sc_list is a list of set‐classes (each successive pcset in the chain must be a member of its corresponding set‐class in sc_list. The max and min similarity parameters specify the percentage of elements that can be the same in 2 or 3 adjacent pcsets. Finally, pn is the ending pc (if it is not specified, there will be no ending pc specified).
This function will generate every possible chain that matches the input criteria.