; random-walk returns a random deviation to an input value
; current-value is the starting position for the walk
; walk-distance is the maximum distance for the walk
; (note that the walk can be either in a positive or negative direction)
; the (float) function ensures that the walk is always a decimal (real) number

(defun random-walk (current-value walk-distance)
  (if (< (random 1.0) 0.5)
      (+ current-value (random (float walk-distance)))
      (- current-value (random (float walk-distance)))))

; produce a list of values generated by random walk

(defun make-random-walk (start-value steps walk-distance)
  (if (> steps 0)
      (cons start-value
	    (make-random-walk (random-walk start-value walk-distance)
			      (- steps 1)
			      walk-distance))))

; "reflect" a random walk value so that it is constrained inside
; an upper and a lower threshold

(defun barrier-test (test-value lower-boundary upper-boundary)
  (cond ((< test-value lower-boundary)
	 (barrier-test (+ lower-boundary
			  (abs (- lower-boundary test-value)))
		       lower-boundary
		       upper-boundary))
	 ((> test-value upper-boundary)
	  (barrier-test (- upper-boundary
			   (abs (- test-value upper-boundary)))
			lower-boundary
			upper-boundary))
	 (t test-value)))

; produce a list of values generated by reflected random walk

(defun make-random-walk-reflected (start-value steps walk-distance lower-boundary upper-boundary)
  (if (> steps 0)
      (cons start-value
	    (make-random-walk-reflected (barrier-test (random-walk start-value walk-distance)
						      lower-boundary
						      upper-boundary)
					(- steps 1)
					walk-distance
					lower-boundary
					upper-boundary))))

; compare an input number to a lower and higher value
; and return the closer of the two comparison values

(defun proximity-test (test-value lower-comparison upper-comparison)
  (if (>= (- test-value lower-comparison) (- upper-comparison test-value))
      upper-comparison
      lower-comparison))

(defun map-element-to-scale (value ordered-scale)
  (cond ((null ordered-scale) nil) ; if the scale is empty return nil
	((= (length ordered-scale) 1) (car ordered-scale)) ; if the scale has one value return it
	((<= value (car ordered-scale)) (car ordered-scale)) 
	; if the value is less than the first scale element, return the first scale element
	((and (> value (car ordered-scale)) (< value (cadr ordered-scale)))
	 (proximity-test value (car ordered-scale) (cadr ordered-scale)))
	 ; if the value is between the first and second scale element, try a proximity test
	(t (map-element-to-scale value (cdr ordered-scale)))))
        ; otherwise, try again, discarding the first element of the scale

(defun map-list-to-scale (value-list ordered-scale)
  (if value-list
      (cons (map-element-to-scale (car value-list) ordered-scale)
	    (map-list-to-scale (cdr value-list) ordered-scale))))

(defparameter rw-scale 
  (list 48 50 51 53 54 56 57 59 60 62 63 65 66 68 69 71 72 74 75 77 78 80 81 83 84))

#|
(map-list-to-scale (make-random-walk-reflected 60 30 6 21 109) rw-scale)
|#

(defun make-notes (start-time pitches interonsets durations amplitudes)
  ; duration is here expressed as a percentage of the interonset time: 0.0 - 1.0
  (if (and pitches interonsets durations amplitudes)
      (cons (new midi 
	      :time start-time
	      :keynum (car pitches)
	      :duration (* (car interonsets) (car durations))
	      :amplitude (car amplitudes))
	    (make-notes (+ start-time (car interonsets))
			(cdr pitches)
			(cdr interonsets)
			(cdr durations)
			(cdr amplitudes)))))

#| 
(events (make-notes 0 
		    (map-list-to-scale (make-random-walk-reflected 60 30 6 48 84) rw-scale)
		    (make-random-walk-reflected 1 30 0.2 0.2 2.4)
		    (make-random-walk-reflected 1 30 0.2 0.1 0.99)
		    (make-random-walk-reflected 1 30 0.2 0.1 0.90))
	"test.mid")

(events (append (make-notes 0 
			    (map-list-to-scale (make-random-walk-reflected 60 30 6 48 84) rw-scale)
			    (make-random-walk-reflected 1 30 0.2 0.2 2.4)
			    (make-random-walk-reflected 0.9 30 0.2 0.1 0.99)
			    (make-random-walk-reflected 1 30 0.2 0.1 0.90))
		(make-notes 0
			    (make-random-walk-reflected 60 50 6 21 109)
			    (make-random-walk-reflected 0.4 50 0.2 0.1 0.8)
			    (make-random-walk-reflected 0.9 50 0.2 0.1 0.99)
			    (make-random-walk-reflected 0.9 50 0.2 0.5 0.99))
		(make-notes 0
			    (make-random-walk-reflected 60 50 6 21 109)
			    (make-random-walk-reflected 0.4 50 0.2 0.1 0.6)
			    (make-random-walk-reflected 0.3 50 0.2 0.1 0.5)
			    (make-random-walk-reflected 0.9 50 0.2 0.3 0.99)))
	"test.mid")
|#

; next step - simulate GENDYN breakpoints as pitch contours

(defun random-walk-sequence (generations values walk-distance lower-boundary upper-boundary)
  (if (> generations 0)
      (append values 
	      (random-walk-sequence (- generations 1)
				    (mapcar #'(lambda (x) (barrier-test (random-walk x walk-distance)
									lower-boundary
									upper-boundary)) 
					    values)
				    walk-distance
				    lower-boundary
				    upper-boundary))))

#|
(events (make-notes 0
		    (random-walk-sequence 10 (list 60 62 64 66 68 70) 3 21 109)
		    (random-walk-sequence 10 (list 0.5 0.3 0.1 0.2 0.1 0.2) 0.2 0.1 1.4)
		    (random-walk-sequence 10 (list 0.5 0.6 0.7 0.8 0.9 0.8) 0.2 0.1 0.9)
		    (random-walk-sequence 10 (list 0.9 0.8 0.7 0.6 0.5 0.4) 0.2 0.3 0.9))
	"test.mid")

(events (append (make-notes 0
			    (random-walk-sequence 10 (list 60 62 64 66 68 70) 3 21 109)
			    (random-walk-sequence 10 (list 0.5 0.3 0.1 0.2 0.1 0.2) 0.2 0.1 1.4)
			    (random-walk-sequence 10 (list 0.5 0.6 0.7 0.8 0.9 0.8) 0.2 0.1 0.9)
			    (random-walk-sequence 10 (list 0.9 0.8 0.7 0.6 0.5 0.4) 0.2 0.3 0.9))
		(make-notes 0
			    (random-walk-sequence 10 (list 36 39 42 45 48 51) 3 21 109)
			    (random-walk-sequence 10 (list 0.5 0.3 0.1 0.2 0.1 0.2) 0.2 0.1 1.4)
			    (random-walk-sequence 10 (list 0.5 0.6 0.7 0.8 0.9 0.8) 0.2 0.1 0.9)
			    (random-walk-sequence 10 (list 0.5 0.4 0.3 0.2 0.3 0.4) 0.2 0.3 0.9)))
	"test.mid")

(events (append (make-notes 0
			    (random-walk-sequence 10 (list 60 62 64 66 68 70) 3 21 109)
			    (random-walk-sequence 10 (list 0.5 0.3 0.1 0.2 0.1 0.2) 0.2 0.1 1.4)
			    (random-walk-sequence 10 (list 0.5 0.6 0.7 0.8 0.9 0.8) 0.2 0.1 0.9)
			    (random-walk-sequence 10 (list 0.9 0.8 0.7 0.6 0.5 0.4) 0.2 0.3 0.9))
		(make-notes 0
			    (random-walk-sequence 10 (list 73 77 81 85 89 93) 2 21 109)
			    (random-walk-sequence 10 (list 0.5 0.3 0.1 0.2 0.1 0.2) 0.2 0.1 1.4)
			    (random-walk-sequence 10 (list 0.5 0.4 0.3 0.2 0.3 0.4) 0.2 0.1 0.9)
			    (random-walk-sequence 10 (list 0.9 0.8 0.7 0.6 0.5 0.4) 0.2 0.3 0.9))
		(make-notes 0
			    (random-walk-sequence 10 (list 36 39 42 45 48 51) 3 21 109)
			    (random-walk-sequence 10 (list 0.5 0.3 0.1 0.2 0.1 0.2) 0.2 0.1 1.4)
			    (random-walk-sequence 10 (list 0.5 0.6 0.7 0.8 0.9 0.8) 0.2 0.1 0.9)
			    (random-walk-sequence 10 (list 0.5 0.4 0.3 0.2 0.3 0.4) 0.2 0.3 0.9)))
	"test.mid")


|#