interval-mapping

[AM]

i'm sure that it would also work with tonality-map,

but i was interested to code a simple version for my own to understand all the things :-)

 

;;; i wanted to map every interval-sequence to every possible pitchfield...
;;; all the sequences are "centered" (i needed that for my project)
;;; with :base  you could move up and down the center
;;; :pitchfield has to be a OMN-pitch-sequence

;;; FUNCTION
(defun interval-projection-on-pitchfield (&key pitchfield intervals (base 0))
  (let ((integers (pitch-to-integer (interval-to-pitch intervals)))
        (base-0-integers)
        (centering)
        (pos))
    (setq base-0-integers (loop for i in integers 
                            collect (+ (abs (find-min integers)) i)))
    (setq centering (if (evenp (find-max base-0-integers)) ;; finds the center of the seq
                      (/ (find-max base-0-integers) 2)
                      (/ (1+ (find-max base-0-integers)) 2)))

    (loop for i in base-0-integers
      do (setq pos (+ i (* -1 centering) base)) ;; compensating center & base

      when (< pos 0) do (setq pos 0) ;; corr if intervals to big (+/-)
      when (> pos (1- (length pitchfield))) do (setq pos (1- (length pitchfield)))
      
      collect (nth pos pitchfield))))


;;; EXAMPLE
(interval-projection-on-pitchfield :pitchfield (append 
                                                (expand-tonality '(c4 messiaen-mode5)) 
                                                (expand-tonality '(c5 messiaen-mode5)) 
                                                (expand-tonality '(c6 messiaen-mode5)))
                                             
                                   :intervals  '(1 2 3 1 2 -4 -3 -2 3 5 7 -2)
                                   :base 12)

 

short question: is there a possibilty to build this

(append (expand-tonality '(c4 messiaen-mode5)) 
        (expand-tonality '(c5 messiaen-mode5)) 
        (expand-tonality '(c6 messiaen-mode5)))

with ONE function (i need more ambitus then 1 octave)...

 

thanx, andré

 

 

 

[Stephane Boussuge]

Thank you for this very interesting function André.

 

I would love to have more easy way and tools for working with tonality on more than one octave.

 

This one is a very good one and can be very useful when working with pitchfields.

 

About your question, i don't know another way to construct your pitch field based on multiple expand-tonality into One function.

 

May be Janusz ?

 

anyway, i like very much your function.

 

Thanks again for sharing it.

 

SB.

[AM]

dear stephane

 

thanx to you! volià, here is a simple short code for this "problem"...

regards

andré

 

;;;FUNCTION

(defun multiple-expand-tonality (&key startpitch octaves tonality)
  (remove-duplicates ;remove is for "cutting" if there are too much pitches (OMN loops last octave!)
   (loop repeat octaves
     with pitch = startpitch
     append (expand-tonality (list pitch tonality))
     do (setq pitch (car (pitch-transpose 12 (list pitch)))))))

;;;EXAMPLE
(multiple-expand-tonality :startpitch 'c2 
                          :octaves 3 
                          :tonality 'messiaen-mode1)

 

[Stephane Boussuge]

Perfect, thank you but would be useful be able to create a pitch-field based on multiple tonality like that:

 

(multiple-expand-tonality :startpitch 'c2 
                          :octaves 3 
                          :tonality '(messiaen-mode1 messiaen-mode3 messiaen-mode4))

but it is already very good like that.

 

Thank you very much.

 

Stéphane

 

[AM]

violà, i think this is what you are looking for...

(defun multiple-expand-tonality (&key startpitch octaves tonality)
  (remove-duplicates ;remove is for "cutting" if there are too much pitches (OMN loops last octave!)
   (loop repeat octaves
     with pitch = startpitch
     with cnt = 0 

     when (= cnt (length tonality))
     do (setq cnt 0)

     append (expand-tonality (list pitch (nth cnt tonality)))
     do (incf cnt)
     do (setq pitch (car (pitch-transpose 12 (list pitch)))))))
     

(multiple-expand-tonality :startpitch 'c2 
                          :octaves 6 
                          :tonality '(messiaen-mode1 messiaen-mode2 messiaen-mode3))

 

[Stephane Boussuge]

Wonderful André !

 

Thank you very much.

 

i will experiment with this stuff asap next week !

 

Stéphane

[opmo]

Tonality can be any sequence:

(setf messiaen
      (append (expand-tonality '(c4 messiaen-mode1)) 
              (expand-tonality '(c5 messiaen-mode2))
              (expand-tonality '(c6 messiaen-mode3))))

(tonality-map '(messiaen :shift t)
'(c4 cs4 d4 eb4 e4 f4 fs4 g4 gs4 a4 bb4 b4 c5 cs5 d5 eb5))
=> (c4 d4 e4 fs4 gs4 bb4 c5 cs5 eb5 e5 fs5 g5 a5 bb5 c6 d6)

 

 

 

[opmo]

Examples with newly added keyword :sort (the default is t):

;;; TEST
(setf mat '(c4 cs4 d4 ds4 e4 f4 fs4 g4 gs4 a4 bb4 b4 c5 cs5 d5))
(mapcar 'pitch-to-integer
        (list
         (tonality-map '((3 0 1 4 6 11 13) :root 3 :sort nil) mat)
         (tonality-map '((3 0 1 4 6 11 13) :root 3 :sort nil :shift t) mat)
         (tonality-map '((3 0 1 4 6 11 13) :root 3 :sort t :shift t) mat)
         (tonality-map '((3 0 1 4 6 11 13) :root 3 :sort nil :fixed t) mat)
         (tonality-map '((3 0 1 4 6 11 13) :root 3 :sort t :fixed t) mat)
         ))
=> ((3 4 4 6 6 6 11 11 11 12 13 13 15 16 16)
    (3 0 1 4 6 11 13 15 12 13 16 18 23 25 27)
    (3 4 6 7 9 14 16 15 16 18 19 21 26 28 27)
    (3 4 4 6 6 6 11 11 11 13 13 13 13 13 13)
    (3 4 4 6 7 7 9 9 9 14 14 14 16 16 16))