> On Aug 6, 2017, at 6:16 PM, Jordan Johnson <j...@fellowhuman.com> wrote:
> Hi all,
> I’m writing some music-related code for which I find myself using a lot of
> lookup tables, following the pattern of making an alist or hash table and
> then writing a function that consults the table. I wound up writing a macro
> for this pattern; one example of its use is:
> ;; key->fifths : PitchName -> Int[-7..7]
> ;; tells how many perfect fifths above C the given pitch is (and
> ;; therefore how many sharps or flats its key signature has)
> (define-lookup-function key->fifths
> [C 0] [G 1] [D 2] [A 3] [E 4] [B 5]
> [F# 6] [F♯ 6]
> [C# 7] [C♯ 7]
> [F -1]
> [Bb -2] [Eb -3] [Ab -4] [Db -5] [Gb -6] [Cb -7]
> [B♭ -2] [E♭ -3] [A♭ -4] [D♭ -5] [G♭ -6] [C♭ -7])
> ;; Ex:
> (key->fifths 'Gb) ;; -> -6
> This seems like a simple and common enough pattern that there must be such a
> facility in some Racket library out there already, but I haven’t found one.
> Am I reinventing a wheel here?
What I've done for situations like these is define notes like C and D not as
symbols, but as data structures that contain the numbers you need. So for
instance I would define:
(struct pitch-class [chromatic-number])
(define C (pitch-class 0))
(define C#/D♭ (pitch-class 1))
(define D (pitch-class 2))
(define D#/E♭ (pitch-class 3))
(define E (pitch-class 4))
(define F (pitch-class 5))
When the notes are defined like this, the number of fifths can be a
mathematical function instead of a lookup, if you can find the function that
maps chromatic numbers to fifths.
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