| Re: [tablatures] harmonics in tablature |
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Hi Marc,
Am 23.09.2010 um 21:27 schrieb Marc Hohl:
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.
I'm not sure it it's relevant here but the IR (1.1.28 HarmonicEvent)
states:
Not accepted by any engraver.
The simplest case
\harmonicByRatio #1/2 e,,4
(All ratios for the defined partials work!)
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.
Hm, don't be offended by the naivety of my thoughts ;-): In the case
of \harmonicByFret the fret number to be engraved should equal the
value of \harmonicByFret, i.e. e.g. 7 in the following example:
\harmonicByFret #7 e,\6
This way the user can decide whether the finger should be placed e.g.
over the 7th or 19th fret to get the second harmonic.
In the case of \harmonicByRatio the fret positions should correspond
to the node positions rather than to the fret position of the
sounding pitch. But I'm sure you know all of this already.
I feel sorry for not being able to help you, here.
Greetings
patrick
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
}
}
}