Generate pulses based on the prime series

Hello,

Below is a method I use a lot in generating rhythms in my compositions.

It generates a list of pulses of n units, where the pulses are assigned to prime indexes only.

I hope you find it useful.

All the best,

Jawher Matmati

;;; ====================================================

(defun gen-prime-pulses (nb &key (unit 's))

"Return a list of Nb OMN lengths:

index i is UNIT if i is prime, otherwise the corresponding rest (-UNIT).

Example: (gen-prime-pulses 10 :unit 's)

=> (-s -s s s -s s -s s -s -s -s)

NB: 0 and 1 are not prime; primes start at 2.

UNIT may be an OMN length symbol (s e q h w …) or a rational like 1/16."

(labels

((primep (n)

(and (> n 1)

(loop for d from 2 to (isqrt n)

never (zerop (mod n d)))))

(rest-of (u)

;; If UNIT is a symbol like 's -> make symbol '-s.

;; If UNIT is a ratio (e.g. 1/16) -> return negative ratio for rest.

(typecase u

(symbol (intern (format nil "-~a" u))) ; => -S (case-insensitive)

(rational (- u))

(integer (- u))

(float (- u)))))

(loop for i from 0 to (- nb 1)

collect (if (primep i) unit (rest-of unit)))))

;;; ====================================================