3.9. pctheory.pset
This module contains functions for working with pitch sets, or psets. A pset is represented as a set of Pitch12 or Pitch24 elements.
class Sieve12
Represents a chromatic pitch sieve in Xenakis's sieve theory. A pitch sieve is a collection of tuples (m, i), where m is a modulus and i represents a congruence‐class mod m. For example, the sieve defined by the tuples (3, 2), (4, 1) gives rise to the integer succession <1, 2, 5, 8, 9, 11...> which can be used as a scale.
Sieve12 constructor
Sieve12.__init__(tuples, base_pitch)
Constructs a Sieve12. You must provide a collection of tuples and a starting pitch (the lowest pitch in the sieve).
Sieve12 read-only properties
Sieve12.base_pitchPitch12
The lowest pitch in the sieve.
Sieve12.intervals[int]
The succession of intervals between adjacent pitches for a complete period.
Sieve12.periodint
The intervallic distance between pitch 0 and the pitch at which the sieve begins to repeat itself.
Sieve12.tuplesset
The set of tuples that define the sieve.
Sieve12 methods
Sieve12.add_tuples(*args)
Adds one or more tuples to the sieve.
Sieve12.get_range(p0, p1){Pitch12}
Gets all pitches in the sieve between p0 and p1, inclusive.
Sieve12.intersection(sieve)Sieve12
Returns the intersection of this sieve and another sieve.
Sieve12.is_in_sieve(p)bool
Whether or not a pitch is in the sieve.
Sieve12.union(sieve)Sieve12
Returns the union of this sieve and another sieve.
class Sieve24
Represents a microtonal pitch sieve in Xenakis's sieve theory. A pitch sieve is a collection of tuples (m, i), where m is a modulus and i represents a congruence‐class mod m. For example, the sieve defined by the tuples (3, 2), (4, 1) gives rise to the integer succession <1, 2, 5, 8, 9, 11...> which can be used as a scale.
Sieve24 constructor
Sieve24.__init__(tuples, base_pitch)
Constructs a Sieve24. You must provide a collection of tuples and a starting pitch (the lowest pitch in the sieve).
Sieve24 read-only properties
Sieve24.base_pitchPitch24
The lowest pitch in the sieve.
Sieve24.intervals[int]
The succession of intervals between adjacent pitches for a complete period.
Sieve24.periodint
The intervallic distance between pitch 0 and the pitch at which the sieve begins to repeat itself.
Sieve24.tuplesset
The set of tuples that define the sieve.
Sieve24 methods
Sieve24.add_tuples(*args)
Adds one or more tuples to the sieve.
Sieve24.get_range(p0, p1){Pitch24}
Gets all pitches in the sieve between p0 and p1, inclusive.
Sieve24.intersection(sieve)Sieve24
Returns the intersection of this sieve and another sieve.
Sieve24.is_in_sieve(p)bool
Whether or not a pitch is in the sieve.
Sieve24.union(sieve)Sieve24
Returns the union of this sieve and another sieve.
fb_class(pset: set, p0: int)[int]
Gets the FB‐class (figured bass) of a pset.
invert(pset: set){Pitch12}or{Pitch24}
Inverts a pset.
p_ic_matrix(pset: set)[[int]]
Gets the ic‐matrix of a pset.
p_ic_roster(pset: set){int: int}
Gets the ic‐roster of a pset.
p_set_class(pset: set, p0: int)[int]
Gets the set‐class of a pset.
pcint_class(pset: set, p0: int)[int]
Gets the PCINT‐class of a pset.
pm_similarity(pset1: set, pset2: set, ic_roster1=None, ic_roster2=None)(int, int)
Gets the pitch-measure (PM) similarity between pset1 and pset2. If ic‐rosters are not provided, they are calculated automatically.
subsets(pset: set)[{Pitch12}]or[{Pitch24}]
Gets a sorted list of subsets of the provided pset.
transform(pset: set, transformation: UTO){Pitch12}or{Pitch24}
Transforms a pset by a UTO.
transpose(pset: set, n: int){Pitch12}or{Pitch24}
Transposes a pset by n.