Dear Friends,

 

I´m trying to make a function to get the complementary diatonic set for a diatonic chord.
For example, if you relate the key of C major (C D E F G A B) with the chord Cmaj7 (C E G B), the complementary set is (D F A). Elliott Carter did this a lot in his Harmony Book, making all kinds of complementarities.

 

This works for comparing stuff. Is there something easier in the system ? For comparing a sequence of chords in relation to a sequence of tonalities for getting the difference ?

 

(defun compare-list-pairs (list-pairs)
  (loop for (list1 list2) in list-pairs
        collect (set-difference list1 list2 :test 'equal)))

 

(compare-list-pairs '(((c4 d4 e4) (c4 e4)) ((5 6 7 8 9) (5 7 8))))

;> ((d4) (9 6))

If you want to work to the diatonic scales as integers, this can be useful, but maybe would be easier with embbeded tonality functions.

 

(position-filter (pitch-to-integer '(e4 eb4 e4 eb4 b4 gb4 e4 db4))
'((0 2 4 5 7 9 11) (1 3 5 6 8 10 0) (2 4 6 7 9 11 1) (4 6 8 9 11 1 3) (5 7 9 10 0 2 4) (6 8 10 11 1 3 5) (7 9 11 0 2 4 6) (8 10 0 1 3 5 7) (9 11 1 2 4 6 😎 (10 0 2 3 5 7 9) (11 1 3 4 6 8 10)))

 

Any idea ?

Thanks !

I had this question before:

Here is the answer by Janusz , back in 2021. Thanks, Janusz !

I´m obssessed by the same problems over and over.

Best !

 

(let ((rem (ambitus '(c5 b5) (expand-tonality '((c5 major) (db5 major) (gb5 major)))))
      (super (ambitus '(c5 b5) '((d5 f5 a5 c6) (eb4 gb4 bb4 db4) (fs4 as4 cs4)))))
  (loop for s in super
    for r in rem
    collect (loop for i in s
              do (setf r (remove i r))
              finally (return r))))