mutwo.generators.toussaint

Algorithms which are related to Canadian computer scientist G. T. Toussaint.

Functions:

alternating_hands(seed_rhythm)	Generates rhythm using the alternating hands method described by G.
euclidean(size, distribution)	Return euclidean rhythm as described in a 2005 paper by G.
paradiddle(size)	Generates rhythm using the paradiddle method described by G.

alternating_hands(seed_rhythm)

Generates rhythm using the alternating hands method described by G. T. Toussaint.

Parameters

seed_rhythm (Tuple[int, ...]) – rhythm that shall be distributed on two hands.

Returns

Return nested tuple that contains two tuple where each tuple represents one rhythm (both rhythms are complementary to each other). The rhythms are encoded in absolute time values.

Return type

Tuple[Tuple[int, …], …]

Example:

>>> from mutwo.generators import toussaint
>>> toussaint.alternating_hands((2, 2))
((0, 6), (2, 4))
>>> toussaint.alternating_hands((3, 2, 2))
((0, 5, 10), (3, 7, 12))

The alternating hands algorithm has been described by Godfried T. Toussaint in his paper ‘Generating “Good” Musical Rhythms Algorithmically’.

euclidean(size, distribution)

Return euclidean rhythm as described in a 2005 paper by G. T. Toussaint.

Parameters

• size (int) – how many beats the rhythm contains

• distribution (int) – how many beats are played

Returns

The rhythm in relative time.

Return type

Tuple[int, …]

Example:

>>> from mutwo.generators import toussaint
>>> toussaint.euclidean(8, 4)
(2, 2, 2, 2)
>>> toussaint.euclidean(7, 5)
(2, 1, 1, 2, 1)

The title of Toussaints paper is “The Euclidean Algorithm Generates Traditional Musical Rhythms”.

paradiddle(size)

Generates rhythm using the paradiddle method described by G. T. Toussaint.

Parameters

size (int) – how many beats the resulting rhythm shall last. ‘Size’ has to be divisible by 2 because of the symmetrical structure of the generated rhythm.

Returns

Return nested tuple that contains two tuple where each tuple represents one rhythm (both rhythms are complementary to each other). The rhythms are encoded in absolute time values.

Return type

Tuple[Tuple[int, …], …]

Example:

>>> from mutwo.generators import toussaint
>>> toussaint.paradiddle(8)
((0, 2, 3, 5), (1, 4, 6, 7))
>>> toussaint.paradiddle(6)
((0, 4, 5), (1, 2, 3))

The paradiddle algorithm has been described by Godfried T. Toussaint in his paper ‘Generating “Good” Musical Rhythms Algorithmically’.