Hi,
About enharmonicity:
2011/6/20 Benkő Pál <benko....@gmail.com>:
>
> with an algebraic pitch representation the test and adjustment would
> look like as follows:
> two pitches are enharmonic iff their interval is in the subspace spanned
> by the enharmonic interval (default: diminished second) and the scale
> period (default: pure octave). to make it a bit more difficult, the
> scale period coefficient must be integer, while the enharmonic interval
> coefficient may be rational. the scale period coefficient also gives the
> necessary adjustment.
>
Enharmonicity is just an equivalence relation respecting the abelian
group structure of intervals/transpositions. You can represent it by a
quotient map or by its kernel.
Your approach is representing the kernel, via its generators. This
is complicated.
A much simpler idea is to represent the quotient map, which is a
particularly simple kind of function.
I am attaching a modified version of your code which expresses the
idea. I believe that the code can get even cleaner, but I am leaving
that work to you (or someone else), since I have a very low fluency
in Lisp.
Explaining the code:
{enharmonic-class} corresponds to the quotient map. {et12-class}
and {et31-class} are examples. The important thing is that these
procedures return the same value for enharmonic equivalent pitches
modulo octave.
{enharmonic-octaves} is used in the octave adjustment. It is supposed
to receive a pitch which is enharmonic to an integer number of octaves,
and return that number.
Note how {enharmonic} became trivial. This means that
{enharmonic-from} reduces to a dictionary look-up. I leave to someone
else to reimplement this in the best possible way.
Hope it helps.
If you have any questions, please ask.
Regards,
Felipe
\version "2.15.3"
#(define (extract-pitch-sequence music)
"Recurse through @var{music}, extracting pitches.
Returns a list of pitch objects, e.g
@code{'((ly:make-pitch 0 2 0) (ly:make-pitch 0 4 0) ... )}
Typically used to construct a scale for input to transposer-factory
(see).
"
(let ((elements (ly:music-property music 'elements))
(element (ly:music-property music 'element))
(pitch (ly:music-property music 'pitch)))
(cond
((ly:pitch? pitch)
pitch)
((pair? elements)
(map
(lambda (x) (extract-pitch-sequence x))
elements))
((ly:music? element)
(extract-pitch-sequence element)))))
#(define (enharmonic pitch0 pitch1 enharmonic-class)
"Whether two pitches are enharmonic."
(equal? (enharmonic-class pitch0) (enharmonic-class pitch1)))
%TODO: implement this with a dictionary.
#(define (enharmonic-from scale pitch enharmonic-class enharmonic-octaves)
"The first enharmonic equivalent of pitch from scale."
(if (pair? scale)
(let ((pitch1 (caar scale)))
(if (enharmonic pitch pitch1 enharmonic-class)
; adjust octave of pitch1
(ly:pitch-transpose
pitch1 (ly:make-pitch
(enharmonic-octaves (ly:pitch-diff pitch pitch1))
0 0))
(enharmonic-from (cdr scale) pitch enharmonic-class enharmonic-octaves)))
pitch))
#(define (enharmonize-pitch pitch scale enharmonic-class enharmonic-octaves)
(let ((p (ly:music-property pitch 'pitch)))
(if (ly:pitch? p)
(ly:music-set-property!
pitch 'pitch
(enharmonic-from scale p enharmonic-class enharmonic-octaves)))
pitch))
#(define (enharmonize scale music enharmonic-class enharmonic-octaves)
"Replaces pitches in music by their enharmonic counterpart in scale."
(let ((s (extract-pitch-sequence scale)))
(music-map (lambda (x) (enharmonize-pitch x s enharmonic-class enharmonic-octaves)) music)))
enharmonizeMusic =
#(define-music-function (parser location scale music enharmonic-class enharmonic-octaves)
(ly:music? ly:music? procedure? procedure?)
(_i "Replace pitches in @var{music} by their enharmonic counterpart in @var{scale}.")
(enharmonize scale music enharmonic-class enharmonic-octaves))
#(define (frac x) (- x (floor x)))
#(define (alg-alteration pitch)
"Second coefficient of an algebraic pitch representation modulo octave,"
" the first one being (ly:pitch-notename pitch)"
(+ (ly:pitch-alteration pitch)
(if (> (ly:pitch-notename pitch) 2)
-1/2 0)))
#(define (et12-value pitch)
"Auxiliary."
(* 1/6 (+ (ly:pitch-notename pitch) (alg-alteration pitch))))
#(define (et12-class pitch)
"pitch modulo octave in ET12, represented as a fraction of the octave"
(frac (et12-value pitch)))
#(define (et12-octaves pitch)
"If pitch is equivalent to an integer number of octaves in ET12,"
" returns that value. Otherwise, return value is unspecified."
(+ (ly:pitch-octave pitch)
(et12-value pitch)))
#(define (et31-value pitch)
"Auxiliary."
(+ (* 5/31 (ly:pitch-notename pitch)) (* 4/31 (alg-alteration pitch))))
#(define (et31-class pitch)
"pitch modulo octave in ET31, represented as a fraction of the octave"
(frac (et31-value pitch)))
#(define (et31-octaves pitch)
"If pitch is equivalent to an integer number of octaves in ET31,"
" returns that value. Otherwise, return value is unspecified."
(+ (ly:pitch-octave pitch)
(et31-value pitch)))
esMinor = { es f ges as bes ces des }
mus = { dis' feses' c'' aisis' }
mu = { bisis' feses' }
{
\key es \minor
\mus
\enharmonizeMusic \esMinor \mus #et12-class #et12-octaves
\enharmonizeMusic \esMinor \transpose es es' \mus #et12-class #et12-octaves
\enharmonizeMusic \esMinor \transpose es' es \mus #et12-class #et12-octaves
% example for 31-step equal temperament
\mu
\enharmonizeMusic
{ deses cis des cisis eses dis es disis } \mu #et31-class #et31-octaves
}
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