music.Peals

class music.Peals(nelements=4, method='dimino')

Bases: InterestingPermutations, GenericPeal

Uses permutations to make peals and represents peals as permutations.

Holds peals by name, which is the model GenericPeal provides act and act_all for – act("some_peal", domain). That is a different operation from PlainChanges.act(), which acts the one peal the object was built from and takes the domain first.

Notes

Core reference: - http://www.gutenberg.org/files/18567/18567-h/18567-h.htm

Also check peal rules, such as conditions for trueness. - Wikipedia seemed ok last time.

__init__(nelements=4, method='dimino')

Initializes a Peals object.

Parameters:

nelementsint, optional

How many elements the permutations act on, by default 4. This also sizes the default domain that act and act_all build.

methodstr, optional

The generation method passed to InterestingPermutations.

Methods

__init__([nelements, method])	Initializes a Peals object.
act(peal[, domain])	Acts a specific peal on the specified domain.
act_all([domain])	Acts all peals on the specified domain.
an_eight_and_forty()	Placeholder for an eight and forty peal implementation.
even_odd(sequence)	Determines if a permutation is even or odd.
get_alternating()	Generates permutations in the alternating group.
get_full_symmetry()	Generates permutations with full symmetry.
get_mirrors()	Generates mirror permutations.
get_rotations()	Generates rotations of permutations.
get_swaps()	Generates swap permutations.
transpositions_peal(permutation[, peal_name])	Generates a peal from transpositions of a permutation.
twenty_all_over()	Placeholder for a 20 all over peal implementation.

Attributes

permutations_by_sizes
permutations
neighbor_swaps
swaps_by_stepsizes
swaps_as_comes
swaps
rotations
mirrors
dihedral
peals	name -> list of permutations.
acted_peals

transpositions_peal(permutation, peal_name='transposition_peal')

Generates a peal from transpositions of a permutation.

Parameters:

permutationPermutation

The permutation to generate transpositions from.

peal_namestr, optional

The name of the peal. Defaults to “transposition_peal”.

Returns:

list

The transpositions, as permutations over the same domain.

Notes

sympy’s transpositions() yields index pairs, which are cycle notation rather than array form: Permutation((0, 1)) is the identity and Permutation((0, 2)) raises. The pairs are expanded with the original size, so composing them in reverse rebuilds the permutation they came from.

twenty_all_over()

Placeholder for a 20 all over peal implementation.

an_eight_and_forty()

Placeholder for an eight and forty peal implementation.