/* * C S O U N D * * L I C E N S E * * This software is free software; you can redistribute it and/or * modify it under the terms of the GNU Lesser General Public * License as published by the Free Software Foundation; either * version 2.1 of the License, or (at your option) any later version. * * This software is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU * Lesser General Public License for more details. * * You should have received a copy of the GNU Lesser General Public * License along with this software; if not, write to the Free Software * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */ #ifndef CSOUND_VOICELEAD_HPP #define CSOUND_VOICELEAD_HPP #include "Platform.hpp" #ifdef SWIG %module CsoundAC %{ #include "Event.hpp" #include "CppSound.hpp" #include <vector> #include <algorithm> #include <cmath> %} %include "std_vector.i" %template(ChordVector) std::vector< std::vector<double> >; #else #include "Event.hpp" #include <vector> #endif namespace csound { /** * This class contains facilities for * voiceleading, harmonic progression, * and identifying chord types. * * See: http://ruccas.org/pub/Gogins/music_atoms.pdf */ 00049 class Voicelead { public: /** * Return the pitch-class of the pitch. * Pitch is measured in semitones, and * the octave is always 12 semitones, * so the pitch-class is the pitch modulo 12. * If the pitch is an integral number of semitones, * and the number of divisions per octave is also 12, * then the pitch-class of a pitch is an integer. * If the pitch is not an integral number of semitones, * or the number of divisions per octave is not 12, * then the pitch-class is not necessarily an integer. */ static double pc(double pitch, size_t divisionsPerOctave = 12); /** * Return the voice-leading vector (difference) * between chord1 and chord2. */ static std::vector<double> voiceleading(const std::vector<double> &chord1, const std::vector<double> &chord2); /** * Return the simpler (fewer motions) of the voiceleadings * between source chord and either destination1 or destination2, * optionally avoiding parallel fifths. */ static const std::vector<double> &simpler(const std::vector<double> &source, const std::vector<double> &destination1, const std::vector<double> &destination2, bool avoidParallels); /** * Return the smoothness (distance by taxicab or L1 norm) * of the voiceleading between chord1 and chord2. */ static double smoothness(const std::vector<double> &chord1, const std::vector<double> &chord2); /** * Return the Euclidean distance between two chords, * which must have the same number of voices. */ static double euclideanDistance(const std::vector<double> &chord1, const std::vector<double> &chord2); /* * Return whether the progression between chord1 and chord2 * contains a parallel fifth. */ static bool areParallel(const std::vector<double> &chord1, const std::vector<double> &chord2); /** * Return the closer, first by smoothness then by simplicity., * of the voiceleadings between source and either * destination1 or destination2, optionally avoiding * parallel fifths. */ static const std::vector<double> &closer(const std::vector<double> &source, const std::vector<double> &destination1, const std::vector<double> &destination2, bool avoidParallels); /** * Return the chord with the first note rotated to the last note. */ static std::vector<double> rotate(const std::vector<double> &chord); /** * Return the set of all rotations of the chord. */ static std::vector< std::vector<double> > rotations(const std::vector<double> &chord); /** * Return the chord as the list of its pitch-classes. * Although the list is nominally unordered, it is * returned sorted in ascending order. Note that pitch-classes * may be doubled. */ static std::vector<double> pcs(const std::vector<double> &chord, size_t divisionsPerOctave = 12); /** * Return the chord as the list of its pitch-classes. * Although the list is nominally unordered, it is * returned sorted in ascending order. Note that pitch-classes * are NOT doubled. */ static std::vector<double> uniquePcs(const std::vector<double> &chord, size_t divisionsPerOctave = 12); /** * Convert a chord to a pitch-class set number * M = sum over pitch-classes of (2 ^ pitch-class). * These numbers form a multiplicative monoid. * Arithmetic on this monoid can perform many * harmonic and other manipulations of pitch. */ static double pitchClassSetToM(const std::vector<double> &chord, size_t divisionsPerOctave = 12); /** * Convert a pitch-class set number M = sum over pitch-classes of (2 ^ pitch-class) * to a pitch-class set chord. */ static std::vector<double> mToPitchClassSet(double pcn, size_t divisionsPerOctave = 12); /** * Convert a pitch-class set to a prime chord number and a transposition. * Note that the prime chord numbers, and transpositions, each form an additive cyclic group. */ static std::vector<double> pitchClassSetToPandT(const std::vector<double> &pcs, size_t divisionsPerOctave = 12); /** * Convert a prime chord number and transposition to a pitch-class set. */ static std::vector<double> pAndTtoPitchClassSet(double prime, double transposition, size_t divisionsPerOctave = 12); /** * Return the closest voiceleading within the specified range, * first by smoothness then by simplicity, * between the source chord any of the destination chords, * optionally avoiding parallel fifths. */ static const std::vector<double> closest(const std::vector<double> &source, const std::vector< std::vector<double> > &destinations, bool avoidParallels); /** * Return the closest voiceleading within the specified range, * first by smoothness then by simplicity, * between the source chord and the target pitch-class set, * optionally avoiding parallel fifths. * The algorithm uses a brute-force search through all * unordered chords, which are stored in a cache, * fitting the target pitch-class set within * the specified range. Although the time complexity * is exponential, this is still usable for non-real-time * operations in most cases of musical interest. */ static std::vector<double> voicelead(const std::vector<double> &source, const std::vector<double> &targetPitchClassSet, double lowest, double range, bool avoidParallels, size_t divisionsPerOctave = 12); /** * Return the closest voiceleading within the specified range, * first by smoothness then by simplicity, * between the source chord and the target pitch-class set, * optionally avoiding parallel fifths. * The algorithm uses a brute-force search through all * unordered chords, which are recursively enumerated, * fitting the target pitch-class set within * the specified range. Although the time complexity * is exponential, the algorithm is still usable * for non-real-time operations in most cases of musical interest. */ static std::vector<double> recursiveVoicelead(const std::vector<double> &source, const std::vector<double> &targetPitchClassSet, double lowest, double range, bool avoidParallels, size_t divisionsPerOctave = 12); /** * Return the pitch in pitches that is closest to the specified pitch. */ static double closestPitch(double pitch, const std::vector<double> &pitches); /** * Return the pitch that results from making the minimum adjustment * to the pitch-class of the pitch argument that is required to make * its pitch-class the same as one of the pitch-classes in the * pitch-class set argument. I.e., "round up or down" to make * the pitch fit into a chord or scale. */ static double conformToPitchClassSet(double pitch, const std::vector<double> &pcs, size_t divisionsPerOctave = 12); /** * Invert by rotating the chord and adding an octave to its last pitch. */ static std::vector<double> invert(const std::vector<double> &chord); /** * Return as many inversions of the pitch-classes in the chord * as there are voices in the chord. */ static std::vector< std::vector<double> > inversions(const std::vector<double> &chord); /** * Return the chord transposed so its lowest pitch is at the origin. */ static std::vector<double> toOrigin(const std::vector<double> &chord); /** * Return the normal chord: that inversion of the pitch-classes in the chord * which is closest to the orthogonal axis of the Tonnetz for that chord. * Similar to, but not identical with, "normal form." */ static std::vector<double> normalChord(const std::vector<double> &chord); /** * Return the prime chord: that inversion of the pitch-classes in the chord * which is closest to the orthogonal axis of the Tonnetz for that chord, * transposed so that its lowest pitch is at the origin. * Similar to, but not identical with, "prime form." */ static std::vector<double> primeChord(const std::vector<double> &chord); /** * Return C = (sum over pitch-classes of (pitch-class ^ 2)) - 1 * (additive cyclic group for pitch-class sets) * for the named pitch-class set. */ static double nameToC(std::string name, size_t divisionsPerOctave_); /** * Return C = (sum over pitch-classes of (pitch-class ^ 2)) - 1 * (additive cyclic group for non-empty pitch-class sets) * for M = sum over pitch-classes of (2 ^ pitch-class) * (multiplicative monoid for pitch-class sets). */ static double mToC(double M, size_t divisionsPerOctave); /** * Return M = sum over pitch-classes of (2 ^ pitch-class) * (multiplicative monoid for pitch-class sets) * for C = (sum over pitch-classes of (pitch-class ^ 2)) - 1 * (additive cyclic group for non-empty pitch-class sets). */ static double cToM(double C, size_t divisionsPerOctaven = 12); /** * Return C = (sum over pitch-classes of (pitch-class ^ 2)) - 1 * (additive cyclic group for non-empty pitch-class sets) * for P = index of prime chords. * If an exact match is not found the closest match is returned. */ static double cToP(double C, size_t divisionsPerOctave = 12); /** * Return P = index of prime chords * for C = (sum over pitch-classes of (pitch-class ^ 2)) - 1 * (additive cyclic group for non-empty pitch-class sets). * If an exact match is not found the closest match is returned. */ static double pToC(double Z, size_t divisionsPerOctave = 12); /** * Return a copy of the chord where each pitch is replaced by its corresponding pitch-class. * The voices remain in their original order. */ static std::vector<double> orderedPcs(const std::vector<double> &chord, size_t divisionsPerOctave = 12); /** * Return a copy of the chord sorted by ascending distance from its first pitch-class. */ static std::vector<double> sortByAscendingDistance(const std::vector<double> &chord, size_t divisionsPerOctave = 12); /** * Return the closest crossing-free, non-bijective voiceleading * from the source chord to the pitch-classes in the target chord, * using Dimitri Tymoczko's linear programming algorithm. * Because voices can be doubled, the source chord * is returned along with result. * The algorithm does not avoid parallel motions, * and does not maintain the original order of the voices. * The return value contains the original chord, the voiceleading vector, * and the resulting chord, in that order. */ static std::vector< std::vector<double> > nonBijectiveVoicelead(const std::vector<double> &sourceChord, const std::vector<double> &targetPitchClassSet, size_t divisionsPerOctave = 12); /** * Return the prime chord for the index P. */ static std::vector<double> pToPrimeChord(double P, size_t divisionsPerOctave = 12); static void initializePrimeChordsForDivisionsPerOctave(size_t divisionsPerOctave); /** * Return the voiced chord for the prime chord index P, transposition T, * and voicing index V within the specified range for the indicated number of tones per octave. * The algorithm finds the zero voicing * (the lowest octave transposition * of the normal chord of the chord * that is no lower than the lowest pitch, * which has voicing index V = 0) and the zero * iterator (the lowest (in all voices) * unordered voicing of the chord that is no lower * (in all voices) than the lowest pitch, * which has enumeration index = 0). Thus, * V of a voicing equals the enumeration index of that * voicing minus the enumeration index of the zero voicing. * The algorithm enumerates the voicings, and thus V, until V is matched. * If V is greater than the maximum V, its modulus is used. */ static std::vector<double> ptvToChord(size_t P, size_t T, size_t V_, size_t lowest, size_t range, size_t divisionsPerOctave = 12); /** * Return the voiced chord for the prime chord index P, transposition T, * and voicing index V within the specified range for the indicated number of tones per octave. * The algorithm finds the zero voicing * (the lowest octave transposition * of the normal chord of the chord * that is no lower than the lowest pitch, * which has voicing index V = 0) and the zero * iterator (the lowest (in all voices) * unordered voicing of the chord that is no lower * (in all voices) than the lowest pitch, * which has enumeration index = 0). Thus, the * V of a voicing equals the enumeration index of that * voicing minus the enumeration index of the zero voicing. * The algorithm enumerates the voicings until the chord is matched. */ static std::vector<double> chordToPTV(const std::vector<double> &chord, size_t lowestPitch, size_t highestPitch, size_t divisionsPerOctave = 12); /** * Return an enumeration of all voicings of the chord * that are greater than or equal to the lowest pitch, * and less than the highest pitch, by adding octaves. * Voicings are ordered, but note that normally * in this module chords are considered to be unordered. * Note that complex chords and/or wide ranges may require * more memory than is available. * The index of voicings V forms an additive cyclic group. * Arithmetic on this group can perform many operations * on the voices of the chord such as revoicing, arpeggiation, and so on. */ static std::vector< std::vector<double> > voicings(const std::vector<double> &chord, double lowest, double highest, size_t divisionsPerOctave); /** * Add an octave to a voicing; can be * iterated to enumerate the voicings of a chord. * The lowest voicing must initially be set equal to the original voicing. * The algorithm treats a chord as a 'numeral' that increments * with a radix equal to the number of octaves in the total range of pitches. * Returns an empty voicing if adding an octave would * create a voicing that exceeds the maximum pitch, * i.e. when the highest-order voice needs to 'carry.' */ static bool addOctave(const std::vector<double> &lowestVoicing, std::vector<double> &newVoicing, size_t maximumPitch, size_t divisionsPerOctave); /** * Wrap chord tones that exceed the highest pitch around to the bottom of the range orbifold. */ static std::vector<double> wrap(const std::vector<double> &chord, size_t lowestPitch, size_t highestPitch, size_t divisionsPerOctave = 12); /** * Return the chord transposed by the indicated number of semitones. */ static std::vector<double> transpose(const std::vector<double> &chord, double semitones); /** * Return the pitch-class transposition of pitch p by n semitones. */ static double T(double p, double n); /** * Return the pitch-class transposition of chord c by n semitones. */ static std::vector<double> T(const std::vector<double> &c, double n); /** * Return the pitch-class inversion of pitch p by n semitones. */ static double I(double p, double n); /** * Return the pitch-class inversion of chord c by n semitones. */ static std::vector<double> I(const std::vector<double> &c, double n); /** * Invert chord c by exchange. */ static std::vector<double> K(const std::vector<double> &c); /** * Return whether chord Y is a transposed form of chord X; g is the generator of * transpositions. */ static bool Tform(const std::vector<double> &X, const std::vector<double> &Y, double g=1.0); /** * Return whether chord Y is an inverted form of chord X; g is the generator of * inversions. */ static bool Iform(const std::vector<double> &X, const std::vector<double> &Y, double g=1.0); /** * Contextually transpose chord c with respect to chord s by n semitones; g is the generator of * transpositions. */ static std::vector<double> Q(const std::vector<double> &c, double n, const std::vector<double> &s, double g=1.0); /** * Size of the octave in semitones. */ 00457 static const double semitonesPerOctave; }; } #endif

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