Music Creating-Rhythms

Combinatorial algorithms to generate rhythms

DESCRIPTION

This package provides most of the the combinatorial algorithms described in the book, "Creating Rhythms", by Hollos. Additionally, this module provides utilities that are not part of the book but are handy nonetheless.

The comp* methods are used to generate compositions of numbers. They are "the set of combinatorial variations of the partitions of n with the duplicates removed." The arguments passed to these functions determine the specific composition that is generated.

The neck* methods generate binary necklaces of a certain length with or without specific constraints on their intervals.

The part* methods are used to generate all possible partitions of an integer into smaller parts, either with or without specific constraints on the lengths of those parts.

NB: Some arguments are switched between book and this software.

MUSICAL EXAMPLE

from music_creatingrhythms import Rhythms
from music_drummer import Drummer

r = Rhythms()
beats = 16
kick =  ''.join([str(num) for num in r.euclid(2, beats)])
snare = ''.join([str(num) for num in r.rotate_n(4, r.euclid(2, beats))])
hihat = ''.join([str(num) for num in r.euclid(11, beats)])

d = Drummer()
d.set_bpm(100)
d.set_ts()
for _ in range(8):
    d.pattern(patterns={ 'kick': kick, 'snare': snare, 'hihat': hihat })
d.sync_parts()
d.show(format='midi')

METHODS

b2int

This method takes a binary string sequence like 110100 and converts it into a list of intervals like [1,2,3].

int2b

Convert intervals of the form [2,3] into a set of binary sequences.

r.int2b([[1,2,3]]) # [[1,1,0,1,0,0]]
r.int2b([[1],[2],[3]]) # [[1],[1,0],[1,0,0]]

cfcv

This method calculates the continued fraction convergent given a set of terms. It is used to find the best rational approximations to real numbers by using their continued fraction expansions.

r.cfcv(1, 2, 2) # [7,5]

cfsqrt

Calculate the continued fraction for sqrt(n) to m digits, where n and m are integers.

r.cfsqrt(2, 3) # [1,2,2]

chsequl

Generate the upper or lower Christoffel word for p and q.

Arguments:

t: required type of word (u: upper, l: lower)
p: required numerator of slope
q: required denominator of slope
n: optional number of terms to generate, default: p+q

r.chsequl('l', 11, 5, 4) # [0,1,1,0]
r.chsequl('u', 11, 5, 4) # [1,1,1,0]

comp

Generate all compositions of n.

r.comp(4) # [1,1,1,1],[1,1,2],[1,2,1],[1,3],[2,1,1],[2,2],[3,1],[4]

A "composition" is the set of combinatorial "variations" of the partitions of n with the duplicates removed.

compa

Generate compositions of n with allowed intervals p1, p2, ... pn.

r.compa(4, 1,2) # [[1,1,1,1],[1,1,2],[1,2,1],[2,1,1],[2,2]]

Here, the "intervals" are the terms of the partition.

compam

Generate compositions of n with m parts and allowed intervals p1, p2, ... pn.

r.compam(4, 3, 1,2) # [[1,1,2],[1,2,1],[2,1,1]]

Here, the "parts" are the number of elements of each interval set.

compm

Generate all compositions of n into m parts.

r.compm(4, 2) # [[1,3],[2,2],[3,1]]

Again, the "parts" are the number of elements of each interval set.

compmrnd

Generate a random composition of n into m parts.

r.compmrnd(16, 4) # [6,1,3,6], etc.

comprnd

Generate a random composition of n.

r.comprnd(16) # [1,3,2,1,1,2,1,3,2], etc.

count_digits

Count the number of a given digit in a string or vector.

r.count_digits(0, '100110100') # 5
r.count_digits(1, [1,0,0,1,1,0,1,0,0]) # 4

count_ones

Count the number of 1s in a string or vector.

r.count_ones('100110100') # 4
r.count_ones([1,0,0,1,1,0,1,0,0]) # 4

count_zeros

Count the number of 0s in a string or vector.

r.count_zeros('100110100') # 5
r.count_zeros([1,0,0,1,1,0,1,0,0]) # 5

de_bruijn

This method generates the largest de Bruijn sequence of order n, which is a cyclic sequence containing all possible combinations of length n with no repeating subsequences.

r.de_bruijn(3) # [1,1,1,0,1,0,0,0]

euclid

Generate a Euclidean rhythm given n onsets distributed over m beats.

r.euclid(2, 4) # [1,0,1,0]

invert_at

Invert a section of a parts binary sequence at n.

r.invert_at(2, [1,0,1,0,0]) # [1,0,0,1,1]

neck

Generate all binary necklaces of length n.

r.neck(3) # [1,1,1],[1,1,0],[1,0,0],[0,0,0]

necka

Generate binary necklaces of length n with allowed intervals p1, p2, ... pn. For these "necklace" class of methods, the word "intervals" refers to the size of a number given trailing zeros. So intervals 1, 2, and 3 are represented as 1, 1,0, and 1,0,0, respectively.

r.necka(4, 1,2) # [1,1,1,1],[1,1,1,0],[1,0,1,0]

neckam

Generate binary necklaces of length n with m ones, and allowed intervals p1, p2, ... pn.

r.neckam(4, 3, 1,2) # [[1,1,1,0]]

neckm

Generate all binary necklaces of length n with m ones.

r.neckm(4, 2) # [[1,1,0,0],[1,0,1,0]]

part

Generate all partitions of n.

r.part(4) # [1,1,1,1],[1,1,2],[2,2],[1,3],[4]

parta

Generate all partitions of n with allowed intervals p1, p2, ... pn.

r.parta(4, 1,2) # [1,1,1,1],[1,1,2],[2,2]

partam

Generate all partitions of n with m parts from the intervals p1, p2, ... pn.

r.partam(4, 2, 2) # [2,2]

partm

Generate all partitions of n into m parts.

r.partm(4, 2) # [1,3],[2,2]

permi

Return all permutations of the given parts list.

r.permi([1,0,1]) # [1,0,1],[1,1,0],[0,1,1],[0,1,1],[1,1,0],[1,0,1]

pfold

Generate "paper folding" sequences, where n is the number of terms to calculate, m is the size of the binary representation of the folding function, and f is the folding function number, which can range from 0 to 2^m - 1.

r.pfold(15, 4, 0) # [0,0,1,0,0,1,1,0,0,0,1,1,0,1,1]

This method generates "paper folding" sequences, which are binary sequences that represent the creases on a piece of paper after it has been folded multiple times in different directions. The arguments passed to this function determine the specific sequence that is generated.

To quote the book, "Put a rectangular strip of paper on a flat surface in front of you, with the long dimension going left to right. Now pick up the right end of the paper and fold it over onto the left end. Repeat this process a few times and unfold the paper. [There will be] a sequence of creases in the paper, some will look like valleys and some will look like ridges... Let valley creases be symbolized by the number 1 and ridge creases by the number 0..."

reverse_at

Reverse a section of a parts sequence at n.

r.reverse_at(2, [1,0,1,0,0]) # [1,0,0,0,1]

rotate_n

Rotate a necklace of the given parts, n times.

r.rotate_n(2, [1,0,1,0,0]) # [0,0,1,0,1]

SEE ALSO

https://abrazol.com/books/rhythm1/ - "Creating Rhythms", the book.

Please see the tests.py program in this distribution for method usage.