Re: [tablatures] harmonics in tablature

[Marc Hohl <marc@xxxxxxxxxx>]

Hi Patrick, hi tablature users,

just a short sign of life - I am still working on the problem. For now, 
lilypond computes
the correct pitches and transposes the notes accordingly, but I didn't 
manage to get
the 'HarmonicEvent on the right place within the music expression. The 
simplest case

\harmonicByRatio #1/2 e,,4

would work, but neither

\harmonicByRatio #1/2 { e,,4 a, } nor
\harmonicByRatio #1/2 { < d g >4 }

If this is solved, I'll have to adapt the fret number. Here I am not 
sure how to get this done -
I have some ideas, but didn't yet find the time to test it.

Attached is my work-in-progress so you can see how it works. If you have 
some ideas/corrections/solutions,
let me know!

Greetings

Marc

\version "2.13.32"

#(define node-positions
  ;; for the node on m/n-th of the string length, we get the corresponding
  ;; (exact) fret position by calculating p=(-12/log 2)*log(1-(m/n));
  ;; since guitarists normally use the forth fret and not the 3.8th, here
  ;; are rounded values, ordered by
  ;; 1/2
  ;; 1/3 2/3
  ;; 1/4 2/4 3/4 etc.
  ;; The value for 2/4 is irrelevant in practical, bacause the string sounds
  ;; only one octave higher, not two, but since scheme normalizes the fractions
  ;; anyway, these values are simply placeholders for easier indexing.
  ;; According to the arithmetic sum, the position of m/n is at 1/2*(n-2)(n-1)+(m-1)
  ;; if we start counting from zero
  (vector 12
           7   19
           5   12    24
           4    9    16   28
           3    7    12   19    31
           2.7  5.8  9.7  14.7  21.7  33.7
           2.3  5    8    12    17    24    36
           2    4.4  7    10    14    19    26  38 ))

#(define partial-pitch
  (vector '(0 0 0)
          '(1 0 0)
          '(1 4 0)
          '(2 0 0)
          '(2 2 0)
          '(2 4 0)
          '(2 6 -1/2)
          '(3 0 0)
          '(3 1 0)))

#(define fret-partials
  '(("0" . 0)
    ("12" . 1)
    ("7" . 2)
    ("19" . 2)
    ("5" . 3)
    ("24" . 3)
    ("4" . 4)
    ("9" . 4)
    ("16" . 4)
    ("3" . 5)
    ("2.7" . 6)
    ("2.3" . 7)
    ("2" . 8)))

#(define (ratio->fret ratio)
  (let* ((nom (numerator ratio))
         (den (denominator ratio))
         (index (+ (* (- den 2)
                      (- den 1)
                      1/2)
                   nom -1)))
     (number->string (vector-ref node-positions index))))

#(define (ratio->pitch ratio)
  (let* ((partial (1- (denominator ratio)))
         (pitch (vector-ref partial-pitch partial)))

  (ly:make-pitch (first pitch)
                 (second pitch)
                 (third pitch))))

#(define (fret->pitch fret)
  (let* ((partial (assoc-get fret fret-partials 0))
         (pitch (vector-ref partial-pitch partial)))

  (ly:make-pitch (first pitch)
                 (second pitch)
                 (third pitch))))

#(define (calc-harmonic-pitch pitch music)
  (let ((es (ly:music-property music 'elements))
        (e (ly:music-property music 'element))
        (p (ly:music-property music 'pitch)))

    (if (pair? es)
        (ly:music-set-property! music 'elements
                                (map (lambda (x) (calc-harmonic-pitch pitch x)) es)))
    (if (ly:music? e)
        (ly:music-set-property! music 'element (calc-harmonic-pitch pitch e)))
    (if (ly:pitch? p)
        (begin
          (set! p (ly:pitch-transpose p pitch))
          (ly:music-set-property! music 'pitch p)))
    music))


harmonicByRatio = #(define-music-function (parser location ratio music) (number? ly:music?)
  (let ((pitch (ratio->pitch ratio)))

  (calc-harmonic-pitch pitch music))
)

harmonicByFret = #(define-music-function (parser location fret music) (number? ly:music?)
  (let ((pitch (fret->pitch (number->string fret))))

  (calc-harmonic-pitch pitch music))
)


test = {
  c4 \harmonicByRatio #1/4  c4
  c4 \harmonicByFret #2.3  c4
}

\score {
  <<
    \new Staff {
      \new Voice {
        \clef "treble_8"
        \test
      }
    }
    \new TabStaff {
      \new TabVoice {
        \test
      }
    }
  >>
}