score.sieves — kunstmusik/score 0.5.0-SNAPSHOT

"...sieve theory is the study of the internal symmetries of a series of points either constructed intuitively, given by observation, or invented completely from moduli of repetition." - Xenakis, Formalized Music, pp. 276

Sieve functions based on work by Iannis Xenakis. Sieves are represented as a 2-vector of [modulo index]. U and I are used to create Union and Intersection Sieves. Sieves may also be nil, though are factored out when a Sieve is simplified, and generates no sequence when gen-sieve is called.

Code Consulted:

• C Code from "Sieves" article below.
• Haskell Music Theory (https://hackage.haskell.org/package/hmt-0.15)
• athenaCL (http://www.flexatone.org/athena.html)
• Music21 (http://web.mit.edu/music21/)

Literature:

• Xenakis and Rahn. "Sieves". Perspectives of New Music, Vol. 28, No. 1 (Winter, 1990), pp. 58-78.
• Xenakis. "Formalized Music". pp. 268-288.

analyze-sieve clj

(analyze-sieve pts)

Analyzes the formula of the sieve for a given sequence pts of number values. Sequence pts should be finite.

Returns a map containing:

• :analysis - vector of sieve vectors containing [modulus index points-covered].
• :sieve - Union sieve of analysis vectors
• :period - period of the sieve

gen-sieve clj

(gen-sieve sieve)

(gen-sieve n sieve)

Generate sequence using sieve. Can optionally provide number n of elements to produce.

I clj

(I & sieves)

Create new sieve that is the intersection of sieves

Intersection clj

Sieve clj protocol

Protocol for Sieves

element? clj

(element? s n)

Determines if number n is an element of this Sieve

normalize clj

(normalize s)

Reduces Sieves in [mod index] form to its normalized form

period clj

(period s)

Returns the period of the Sieve.

reduce-sieve clj

(reduce-sieve s)

Reduces the Sieve to its simplest form

simplified clj

(simplified sieve)

Returns simplified (normalized and reduce) version of sieve

U clj

(U & sieves)

Create new sieve that is the union of sieves

Union clj