;; CYCLOPS.LISP
;; melodic possibilities for self-similar canons
;; --> use these with the 'scf' function in nudruz.lisp
;; to substite pitches for character placeholders

;; Drew Krause, 2004
;; drkrause@mindspring.com
;; www.wordecho.org

;; Note: these are easy to find using the gap package (www.gap-system.org)
;; gap> RequirePackage("guava");
;; gap> CyclotomicCosets(2,3); Length(last);
;; >  [ [ 0 ], [ 1, 2 ] ]
;; > 2
;; this becomes a 'cyclops' (a b b)

;; note: cyclops always works for n mod len
;; e.g., 3x4 is equiv. to 7x4, 11x4, etc.
;; ... also works for roots of n

(define cyclops3p7x4 '(a b c b))
; 3 members

(define cyclops4x5 '(a b c c b))
; 3 members

(define cyclops5x6 '(a b c d c b))
; 4 members

(define cyclops2p4x7 '(a b b c b c c))
; 3 members

(define cyclops6x7 '(a b c d d c b))
; 4 members

(define cyclops3x8 '(a b c b d e c e))
; 5 members

(define cyclops5x8 '(a b c d e b f d))
; 6 members

(define cyclops7x8 '(a b c d e d c b))
; 5 members

(define cyclops2p5x9 '(a b b c b b c b b))
; 3 members -- length 90 atx

(define cyclops4p7x9 '(a b c d b c e b c))
; 5 members -- length 252 atx

(define cyclops3p7x10 '(a b c b c d c b c b))
; 4 members -- length 210

(define cyclops3459x11 '(a b c b b b c c c b c))
; 3 members -- length 1980 atx

(define cyclops5x12 '(a b c d e b f g e h c g))
; 8 members

(define cyclops3x13 '(a b c b d c c e e b d e d))
; 5 members

(define cyclops4p10x13 '(a b c b b c c c c b b c b))
; 3 members

(define cyclops5p8x13 '(a b c c d b d d b d c c b))
; 4 members

(define cyclops9x13 '(a b c b d c c e e b d e d))
; 5 members

(define cyclops3p5x14 '(a b c b c b c d c b c b c b))
; 4 members

(define cyclops2x15 '(a b b c b d c e b c d e c e e))
; 5 members

(define cyclops3x16 '(a b c b d e c e f b f b d e f e))
; 7 members

(define cyclops5x16 '(a b c d e b f d g b c d h b f d))
; 8 members

(define cyclops5x18 '(a b c d c b e b c f c b e b c d c b))
; 6 members

(define cyclops2x21 '(a b b c b d c e b f d b c d e f b d f d d))
; 6 members

(define cyclops3p5x22 '(a b c b d b c e c b c f d e d b d e c e d e))
; 6 members

(define cyclops3x26 '(a b c d e c f g b d f d h i e i j c e g f i j g j))
; 10 members