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Parsimonious Voice Leading (again): attempts to provide an algorithm ;;In a previous post I deleted, I was trying to find a good way to ensure the minimal parsimonious Voice-Leading (VL) between a sequence of chords. ;;In this post I will try to explain my second attempt. ;Let's take a look at a sequence of chords, spreaded out almost in a random way, with no VL (setf chordstovl2 '(b3eb5g3 cs6e7gs3 b4f5g6 f7e5c2 d4f7e4 gs7e2a8) ;lLet's specify and evaluate a variable for the number of voices used: (setf voices 3) ;Let's try to think the best way to connect this pitches with minimal movement. I will apply the following expression to ensure a better and less ambiguous result when applying the Chord-Closest-Path Function ;;;Evaluate voices before (setf voices 3) ;;;Then (setf chordized (mclist (chordize-list (gen-divide voices (setf vlfinal (integer-to-pitch (modus (interval-to-pitch (replace-map '((-11 1) (-10 2) (-9 3) (-8 4) (-7 5) (7 -5) (8 -4) (9 -3)(10 -2)(11 -1)) (integer-to-interval (modus (pitch-to-midi (setf chordmelo (pitch-melodize chordstovl2)))))) :start (car chordmelo))))))))) ;;; Please note the use of the replace-map function ensuring that no movement will be greater than a tritone away. This means that a movement like "C to G" (7 semitones) will be convertet in a G to C (5 semitones). This ensure a modulo 12 (octave constraint) reduction of all the material and also a constraint in terms of the size of the movements that will not exceed 6 semitones. ;;;Finally, I will apply the Chord-Closest-Path Function (chord-closest-path (car chordized) (chordize-list (gen-divide voices vlfinal))) Hope it help some VL efforts. Best, Julio Herrlein
Dear All, HAPPY 2018 !! With the new PCS organization in Opusmodus is possible to implement a concept of my book, called Combinatorial Voiceleading of Hexachords. From a Hexachord Set, is possible to find 10 different ways to combine the notes in the for of voice-leading sets. Each hexachord is divided in (3 + 3) way. This expression: (setf hexavl (mclist (chordize-list (integer-to-pitch (remove-duplicates (sort-asc (gen-divide 3 (flatten (permute (pcs '6-32))))) :test #'equal))))) Will result in this combination of the 6-32 hexachord, similar to the idea in the book. In the book, the material is organized in 70 pages of melodic and harmonic exercises. Here is a litte sample: CH_HERRLEIN.pdf The entire book: https://www.melbay.com/Products/Default.aspx?bookid=30042BCDEB Best ! Julio Herrlein