pctheory.pcseg

Performs an adjacent search on a corpus of pcsegs. Returns all pcsegs in the corpus that contain pcseg as an ordered sublist.

Parameters:

  • pcseg – A pcseg to search for

  • corpus – The corpus of pcsegs to search

Returns:

A sublist of pcsegs from the corpus that have pcseg in them. If an entry in the original corpus contains pcseg more than once, it will only be included once in this sublist. If no entries have pcseg in them, returns an empty list.

*Compatible with all PitchClass modulos

are_combinatorial2(row1: list, row2: list)

Determines if two rows are hexachordally combinatorial

Parameters:

  • row1 – A row

  • row2 – A row

Returns:

True or False

*Compatible only with chromatic pcsegs

are_combinatorial3(row1: list, row2: list, row3: list)

Determines if three rows are tetrachordally combinatorial

Parameters:

  • row1 – A row

  • row2 – A row

  • row3 – A row

Returns:

True or False

*Compatible only with chromatic pcsegs

are_combinatorial4(row1: list, row2: list, row3: list, row4: list)

Determines if four rows are trichordally combinatorial

Parameters:

  • row1 – A row

  • row2 – A row

  • row3 – A row

  • row4 – A row

Returns:

True or False

*Compatible only with chromatic pcsegs

bip_n(imb: list)

Gets the BIP_n of a list of set-classes generated by IMB_n

Parameters:

imb – The IMB_n list

Returns:

The BIP_n

*Compatible only with chromatic pcsegs

create_ormap(pcseg: list)

Creates the ORMAP of a row

Parameters:

pcseg – A row

Returns:

The ORMAP

*Compatible with all PitchClass modulos

generate_pcseg12_from_interval_list(interval_list: list, starting_pc=None)

Generates a pcseg from an interval list

Parameters:

  • interval_list – The interval list

  • starting_pc – The starting pitch-class. If None, a random starting pitch-class is used.

Returns:

A pcseg

*Compatible only with chromatic pcsegs

generate_pcseg24_from_interval_list(interval_list: list, starting_pc=None)

Generates a pcseg from an interval list

Parameters:

  • interval_list – The interval list

  • starting_pc – The starting pitch-class. If None, a random starting pitch-class is used.

Returns:

A pcseg

*Compatible only with microtonal pcsegs

generate_random_all_interval_row(starting_pc=None)

Generates a random all-interval row

Parameters:

starting_pc – The starting pitch-class. If None, a random starting pitch-class is used.

Returns:

An all-interval row

*Compatible only with chromatic pcsegs

generate_random_all_trichord_row(starting_pc=None)

Generates a random all-trichord row

Parameters:

starting_pc – The starting pitch-class. If None, a random starting pitch-class is used.

Returns:

An all-trichord row

*Compatible only with chromatic pcsegs

generate_random_all_trichord_babbitt_row(starting_pc=None)

Generates a random all-trichord (Babbitt) row

Parameters:

starting_pc – The starting pitch-class. If None, a random starting pitch-class is used.

Returns:

An all-trichord (Babbitt) row

*Compatible only with chromatic pcsegs

generate_random_pcseg12(length: int, non_duplicative=False, starting_pc=None)

Generates a random pcseg

Parameters:

  • length – The length of the pcseg

  • non_duplicative – Whether or not duplicate pcs may occur (must be True to generate a row)

  • starting_pc – The starting pitch-class. If None, a random starting pitch-class is used.

Returns:

A random pcseg

*Compatible only with chromatic pcsegs

generate_random_pcseg24(length: int, non_duplicative=False, starting_pc=None)

Generates a random pcseg

Parameters:

  • length – The length of the pcseg

  • non_duplicative – Whether or not duplicate pcs may occur (must be True to generate a row)

  • starting_pc – The starting pitch-class. If None, a random starting pitch-class is used.

Returns:

A random pcseg

*Compatible only with microtonal pcsegs

generate_random_pcseg_from_pcset(pcset: set)

Generates a random pcseg from a pcset

Parameters:

pcset – A pcset

Returns:

A pcseg

*Compatible with all PitchClass modulos

generate_random_ten_trichord_row(starting_pc=None)

Generates a random ten-trichord row

Parameters:

starting_pc – The starting pitch-class. If None, a random starting pitch-class is used.

Returns:

A ten-trichord row

*Compatible only with chromatic pcsegs

get_intervals(pcseg: list)

Gets the interval sequence of a pcseg

Parameters:

pcseg – The pcseg

Returns:

The interval sequence

*Compatible with all PitchClass modulos

get_row_class(row: list)

Gets all of the rows in a row-class

Parameters:

row – A row

Returns:

The row-class, as a set of rows

*Compatible with PitchClasses mod 12 and 24

get_row_dsym(row: list)

Gets the degree of symmetry of a row

Parameters:

row – A row

Returns:

The degree of symmetry of the row

*Compatible with PitchClasses mod 12 and 24

imb_n(pcseg: list, n: int)

Gets the IMB_n of a pcseg. The IMB_n is the segment of imbricated set-classes of cardinality n.

Parameters:

  • pcseg – The pcseg

  • n – The cardinality of imbrication

Returns:

The IMB_n

*Compatible with all PitchClass modulos

invert(pcseg: list)

Inverts a pcseg

Parameters:

pcseg – The pcseg

Returns:

The inverted pcseg

*Compatible with all PitchClass modulos

is_all_interval_row(pcseg: list)

Determines if a pcseg is an all-interval row

Parameters:

pcseg – The pcseg

Returns:

Whether or not the pcseg is an all-interval row

*Compatible with PitchClasses mod 12 and 24

is_all_trichord_row(pcseg: list)

Determines if a pcseg is an all-trichord row

Parameters:

pcseg – The pcseg

Returns:

Whether or not the pcseg is an all-trichord row

*Compatible only with chromatic pcsegs

is_all_trichord_babbitt_row(pcseg: list)

Determines if a pcseg is an “all-trichord” row (after Babbitt). This kind of row contains ten unique imbricated trichords, none of which are set-classes [036] or [048]. Rotation is not considered.

Parameters:

pcseg – The pcseg

Returns:

Whether or not the pcseg is an “all-trichord” row (after Babbitt)

*Compatible only with chromatic pcsegs

Determines if a row is a Link chord (an all-interval row containing the all-trichord hexachord as a subset)

Parameters:

pcseg – A pcset

Returns:

True or False

*Compatible only with chromatic pcsegs

is_row(pcseg: list)

Determines if a pcseg is a row

Parameters:

pcseg – The pcseg

Returns:

Whether or not the pcseg is a row

*Compatible with PitchClasses mod 12 and 24

is_row_generator(rgen: list)

Determines if a row generator is valid

Parameters:

rgen – A row generator

Returns:

True if the row generator is valid; false otherwise

*Compatible only with chromatic pcsegs

is_ten_trichord_row(pcseg: list)

Determines if a pcseg is a ten-trichord row. This kind of row contains ten unique imbricated trichords. Rotation is not considered.

Parameters:

pcseg – The pcseg

Returns:

Whether or not the pcseg is an “all-trichord” row (after Babbitt)

*Compatible only with chromatic pcsegs

make12(*args)

Makes a pcseg

Parameters:

args – Pcs

Returns:

A pcseg

*Compatible only with chromatic pcsegs

make_pcseg12(*args)

Makes a pcseg. Alias for make12.

Parameters:

args – Pcs

Returns:

A pcseg

*Compatible only with chromatic pcsegs

make24(*args)

Makes a pcseg

Parameters:

args – Pcs

Returns:

A pcseg

*Compatible only with microtonal pcsegs

make_pcseg24(*args)

Makes a pcseg. Alias for make24.

Parameters:

args – Pcs

Returns:

A pcseg

*Compatible only with microtonal pcsegs

multiply(pcseg: list, n: int)

Multiplies a pcseg

Parameters:

  • pcseg – The pcseg

  • n – The multiplier

Returns:

The multiplied pcseg

*Compatible with all PitchClass modulos

multiply_order(pcseg: list, n: int)

Multiplies a pcseg’s order

Parameters:

  • pcseg – The pcseg

  • n – The multiplier

Returns:

The order-multiplied pcseg

*Compatible with all PitchClass modulos

ormap(row: list, ormap: dict)

Performs the ORMAP mapping on a row, given a provided ORMAP

Parameters:

  • row – A row

  • ormap

Returns:

The ORMAP mapping for the row

*Compatible with all PitchClass modulos

prot(pcseg: list)

Generates the protocol pairs for a pcseg

Parameters:

pcseg – A pcseg

Returns:

A set of protocol pairs

*Compatible with all PitchClass modulos

retrograde(pcseg: list)

Retrogrades a pcseg

Parameters:

pcseg – The pcseg

Returns:

The retrograded pcseg

*Compatible with all PitchClass modulos

rotate(pcseg: list, n: int)

Rotates a pcseg

Parameters:

  • pcseg – The pcseg

  • n – The index of rotation

Returns:

The rotated pcseg

*Compatible with all PitchClass modulos

transform(pcseg, string)

Transforms a pcseg with a provided transformation string - Tn: transpose - I: invert - Mn: multiply - R: retrograde - rn: rotate

Parameters:

  • pcseg – The pcseg to transform

  • string – The transformation string

Returns:

The transformed pcseg

transform_hstack(pcseg, transformation_list)

Generates a really long pcseg by horizontally stacking transformed versions of it

Parameters:

  • pcseg – The pcseg to stack

  • transformation_list – A list of transformations to stack

Returns:

The stacked and transformed pcseg

transpose(pcseg: list, n: int)

Transposes a pcseg

Parameters:

  • pcseg – The pcseg

  • n – The index of transposition

Returns:

The transposed pcseg

*Compatible with all PitchClass modulos

transpositional_combination(pcseg1: list, pcseg2: list)

Transpositionally combines (TC) two pcsegs. This is Boulez’s “multiplication.”

Parameters:

  • pcseg1 – A pcseg

  • pcseg2 – A pcseg

Returns:

The TC pcset

*Compatible with all PitchClass modulos

class InvarianceMatrix

Represents an invariance matrix. Compatible with all PitchClass modulos for T and I matrices, and compatible with mod 12 and mod 24 for various M matrices (M5, M7 for mod 12; M5, M7, M11, M13, M17, M19 for mod 24)

property mx

The matrix

property pcseg_a

The pcseg A

property pcseg_b

The pcseg B

property pcseg_c

The pcseg C

__init__(self, mx_type='T', a=None, c=None)

Creates an invariance matrix

Parameters:

  • mx_type – The matrix type (T, I, M, or MI)

  • a – Pcseg A

  • c – Pcseg B

__getitem__(self, i, j)

Gets the pc at the specified row and column

Parameters:

  • i – The row

  • j – The column

Returns:

The pc

__repr__(self)

Gets a representation of the InvarianceMatrix object

Returns:

A string representation of the InvarianceMatrix object

__str__(self)

Converts the InvarianceMatrix object to string

Returns:

A string conversion of the InvarianceMatrix object

get_column(self, j)

Gets a column of the matrix

Parameters:

j – The column index

Returns:

The column

get_row(self, i)

Gets a row of the matrix

Parameters:

i – The row index

Returns:

The row

load_matrix(self, a: list, c: list)

Loads the matrix

Parameters:

  • a – Pcseg A

  • c – Pcseg C

print(self, include: list = None)

Prints the invariance matrix. You can specify to only print certain pcs to highlight invariance.

Parameters:

include – The pcs to include (if None, all pcs will be printed)

Returns:

None

class TwelveToneMatrix

Represents a twelve-tone matrix. Compatible only with mod 12 PitchClasses.

property labels_bottom

Gets the labels for the bottom of the matrix

property labels_left

Gets the labels for the left of the matrix

property labels_right

Gets the labels for the right of the matrix

property labels_top

Gets the labels for the top of the matrix

property matrix

Gets the matrix

property row

Gets the row

__init__(self, row=None)

Creates a twelve-tone matrix

Parameters:

row – A row to import

__getitem__(self, i, j)

Gets the pc at the specified row and column

Parameters:

  • i – The row

  • j – The column

Returns:

The pc

__repr__(self)

Generates a string representation of the TwelveToneMatrix that can be printed

Returns:

A string representation of the TwelveToneMatrix

__str__(self)

Generates a string representation of the TwelveToneMatrix that can be printed

Returns:

A string representation of the TwelveToneMatrix

get_column(self, j)

Gets a column of the matrix

Parameters:

j – The column index

Returns:

The column

get_row(self, i)

Gets a row of the matrix

Parameters:

i – The row index

Returns:

The row

import_row(self, row: list)

Imports a row

Parameters:

row – The row to import