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Transposing pitches with minimum accidentals (“smart” transpose) ¶

This example uses some Scheme code to enforce enharmonic modifications for notes in order to have the minimum number of accidentals. In this case, the following rules apply:

• double accidentals should be removed
• b sharp → c
• e sharp → f
• c flat → b
• f flat → e

In this manner, the most natural enharmonic notes are chosen.

#(define (naturalize-pitch p)
   (let ((o (ly:pitch-octave p))
         ;; `ly:pitch-alteration` returns quarter tone steps.
         (a (* 4 (ly:pitch-alteration p)))
         (n (ly:pitch-notename p)))
     (cond
      ((and (> a 1)
            (or (eqv? n 6) (eqv? n 2)))
       (set! a (- a 2))
       (set! n (+ n 1)))
      ((and (< a -1)
            (or (eqv? n 0) (eqv? n 3)))
       (set! a (+ a 2))
       (set! n (- n 1))))
     (cond
      ((> a 2)
       (set! a (- a 4))
       (set! n (+ n 1)))
      ((< a -2)
       (set! a (+ a 4))
       (set! n (- n 1))))
     (when (< n 0)
       (set! o (- o 1))
       (set! n (+ n 7)))
     (when (> n 6)
       (set! o (+ o 1))
       (set! n (- n 7)))
     (ly:make-pitch o n (/ a 4))))

#(define (naturalize music)
   (let ((es (ly:music-property music 'elements))
         (e (ly:music-property music 'element))
         (p (ly:music-property music 'pitch)))
     (when (pair? es)
       (ly:music-set-property! music 'elements
                               (map naturalize es)))
     (when (ly:music? e)
       (ly:music-set-property! music 'element
                               (naturalize e)))
     (when (ly:pitch? p)
       (set! p (naturalize-pitch p))
       (ly:music-set-property! music 'pitch p))
     music))

naturalizeMusic =
#(define-music-function (m) (ly:music?)
   (naturalize m))

music = \relative c' { c4 d e g }

\new Staff {
  \transpose c ais { \music }
  \naturalizeMusic \transpose c ais { \music }
  \transpose c deses { \music }
  \naturalizeMusic \transpose c deses { \music }
}