Function for direction/trajectory?

[eboats]

What function would I use if I have a list of ascending pitches and I want to generate a sequence that would gradually work its way up from lowest to highest pitch ( or vice versa), with some control over volatility and how quickly the seq goes from low to highest?   So far I've found the brownian motion sample function with a "drift" arg for doing something like this.  Are there other functions for doing this kind of thing? 

 

What I have in mind is something like the first 13 bars of Varese's Density 21.5, where there's a gradual upward trajectory in pitch, culminating in bar 13. 

 

https://petruccilibrary.ca/files/imglnks/caimg/c/c0/IMSLP405195-PMLP656047-Varèse_-_Density_21.5_(flute).pdf

 

 

[AM]

a quick idea: if you would do it with rnd-walk and use it as positions  in a pitchfield, you have a some global control over all parameters.

pitchfields are - in my opinion - useful, because you have some nice vertical control. you don't have this if you simply have the random walk out of the pitches directly.

 

(progn
  ;; do a rnd-walk with tendency
  (setf walk (gen-walk 24 :step '(1 2 3) :backward 0.3 :forward 0.7))

  ;; transform it to positions in a pitchfield and "reset list" if min-val < 0
  (setf positions (cumulative-sums walk))
  (setf positions (if (< (find-min positions) 0)
                       (x+b positions (abs (find-min positions)))
                      positions))

  ;; define a pitchfield (or chord)
  (setf pitchfield (append (expand-tonality '(b3 messiaen-mode6))
                           (expand-tonality '(b4 messiaen-mode5))
                           (expand-tonality '(b5 messiaen-mode4))
                           (expand-tonality '(b6 messiaen-mode3))))
  
  ;; reading pitchfield by positions
  (position-filter (cumulative-sums walk) pitchfield))

 

[Stephane Boussuge]

Here's  function I've made few years ago, hope it help:

 

;;;===================================
;;; PITCH-TRAJECTORY
;;;===================================
;;; SB 1.11.21
;;;===================================
(defun pitch-trajectory (nbpitch range tendency 
                                 &key 
                                 (variance 0.5) 
                                 (type :around) 
                                 (quantize 1/2) 
                                 (smooth 1)
                                 filter-repeat
                                 seed
                                 (output 'pitch)
                                 (int-range '(0 24))
                                 )
  (setf seed (rnd-seed seed))
  (do-verbose ("pitch-trajectory :seed ~s" seed)
  (let* ((values (gen-tendency nbpitch tendency :variance variance :type type 
                           :seed (seed)))
         (smoothedval (vector-smooth smooth values))
         (out (cond ((equal output 'pitch)
                     (vector-to-pitch range smoothedval :quantize quantize))
                    ((equal output 'int)
                     (vector-round (car int-range) (cadr int-range) smoothedval)))))
         
    (if filter-repeat 
      (filter-repeat filter-repeat out)
      out))))


#|
;;; Test du bon fonctionnement du seed
(progn
(init-seed 1)
(rnd-sample 4 '(c4 d4 e4 f4))
(rnd-sample 4 '(c4 d4 e4 f4))
(pitch-trajectory 32 '(c4 g5) '(0.1 1 0.1))
(init-seed nil)
)

;;; Tests divers
(pitch-trajectory 32 '(c4 g5) '(0.1 1 0.1) :seed 1234)
(pitch-trajectory 32 '(c4 g5) '(0.1 1 0.1) :seed 1234 :filter-repeat 1)
(pitch-trajectory 32 '(c4 g5) '(0.1 1 0.1) :seed 1234 
                  :filter-repeat 1
                  :variance 1
                  )
(pitch-trajectory 32 '(c4 g5) '(0.1 1 0.1) :seed 1234 
                  :filter-repeat 1
                  :variance 0.1
                  )
(pitch-trajectory 32 '(c4 g5) '(0.1 1 0.1) :seed 1234 
                  :filter-repeat 1
                  :smooth 0.1
                  )
(pitch-trajectory 32 '(c4 g5) '(0.1 1 0.1) :seed 1234 
                  :filter-repeat 1
                  :quantize 1/4
                  )
(pitch-trajectory 32 '(c4 g5) '(0.1 1 0.1) :seed 1234 
                  :filter-repeat 1
                  :quantize 1/8
                  )
(pitch-trajectory 32 '(c4 g5) '(0.1 1 0.1) :seed 1234 
                  :filter-repeat 1
                  :variance 1
                  :quantize 1/8
                  )



(gen-filter-change 
 (pitch-trajectory 
  32 '(c4 g5) '(0.1 1 0.1) :seed 1234)
 's)

;;; pitch-ouput 

(pitch-list-plot
 (pitch-trajectory 128 '(fs3 g5) '(0.1 1 0.1) 
                   :filter-repeat 1
                   :variance 0.8
                   :output 'pitch
                   ))

;;; integer-output for MAPPING

(list-plot
 (pitch-trajectory 128 '(fs3 g5) '(0.1 1 0.1) 
                   :filter-repeat 1
                   :variance 0.8
                   :output 'int
                   :int-range '(0 23)
                   ))



;;; MAPPING the integers on a scale or pitchfield

(loop 
  for i in (pitch-trajectory 128 '(fs3 g5) '(0.1 1 0.1) 
                   :filter-repeat 1
                   :variance 0.8
                   :output 'int
                   :int-range '(0 23))
  with scale = (make-scale 'c2 24 :alt '(1 2))
  collect (nth i scale))


(loop 
  for i in (pitch-trajectory 128 '(fs3 g5) '(0.1 3 0.1) 
                   :filter-repeat 1
                   :variance 0.9
                   :output 'int
                   :int-range '(0 23))
  with scale = (make-scale 'c2 24 :alt '(2 1 6 5 4))
  collect (nth i scale))


;;; an example with MAPPING and SAMPLING

(progn
  (setf seq (loop 
              for i in (pitch-trajectory 64 '(fs2 g6) '(0.1 3 0.1) 
                                          :filter-repeat 1
                                          :variance 0.4
                                          :output 'int
                                          :int-range '(0 23))
            with scale = (make-scale 'c2 24 :alt '(2 1 6 5 4))
              collect (nth i scale)))
  
  (make-omn :pitch (flatten (loop repeat 20 collect (rnd-sample-seq (rnd-pick '(11 17 29)) seq)))
            :length (rnd-sample 20 '((s s s s)(t t t t t t t t)(e e)))
            ))
|#

It comes from this interesting discussion with Andre:

 

[eboats]

Thank you all, will have a look.  Am hoping a function like this could be included/simplified as an OM system function, since the idea of a direction/trajectory seems basic and something others would want too.  

[Stephane Boussuge]

4 hours ago, eboats said:

Thank you all, will have a look.  Am hoping a function like this could be included/simplified as an OM system function, since the idea of a direction/trajectory seems basic and something others would want too.  

Iti is very easy with OM to do pitch trajectories by generating some vectors and use vector-map to map then on anything. A good suggestion for controlled vector generation could be gen-tendency function.