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.

\version "2.24"

#(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 }
}