You can create the infinity series from binary numbers. ones are added, zeros reverse sign.

Jesper

(defun inf-ser (n &optional (offset 0) &aux tmp)

(loop for i to (1- n) do

(setf tmp 0)

(loop for bin in (decimal-to-binary i)

do

(setf tmp (if (zerop bin) (- tmp) (+ tmp bin))))

;(format t "~B = ~D~%" i tmp)

collect (+ tmp offset)))

(integer-to-pitch (inf-ser 128))

(integer-to-pitch (inf-ser 128 12))

Super cool ! Thank you !

Fractal properties

;; added step

(defun inf-ser (n &key (offset 0) (step 1) &aux tmp)

(loop for i to (* (1- n) step) by step do

(setf tmp 0)

(loop for bin in (decimal-to-binary i)

do

(setf tmp (if (zerop bin) (- tmp) (+ tmp bin))))

;(format t "~B = ~D~%" i tmp)

collect (+ tmp offset)))

(setf orig (integer-to-pitch (inf-ser 128 :offset 12 :step 1)))

;;every second number = inverted series

(setf sec (integer-to-pitch (inf-ser 128 :offset 12 :step 2)))

(setf inv-sec (pitch-invert sec))

(equal orig inv-sec)

;;every 4, 16, 64… = original series

(setf fourth (integer-to-pitch (inf-ser 128 :offset 12 :step 4)))

(equal fourth orig)

Jesper