4. Discussion
4.5 Conclusion
The implementation program runs successfully; the original purpose of this thesis is basically realized accordingly. I propose a model for algorithmic composition of monophonic pitches; the melodic contour corresponds with the law of conservation of energy. In spite of the main process of energy regulation, the input and output data in this thesis are symbolic musical pitches. They can also be, however, sub-symbolic audio
48
frequencies. We could further integrate the method with other supplementary algorithm.
I should reiterate that to reconsider the phenomena of higher levels from the point of view which we have in lower levels can assist us in composing genuinely but with imitations by adopting the principles in old styles. Above all, the domain of academic knowledge may separate again after lengthy union while it is now on the road to unite.
This thesis may be a tiny part in the giant progress; nevertheless, it strongly stands for my response to the revival.
49
Appendix: Source Code
Visual C++ Files
stdafx.h
#pragma once
#include <cmath> // for pow()
#include <time.h> // for srand(time(NULL)) and rand()
#include <fstream> // for std::ofstream
Form1.h (excerpt)
#pragma once
#include "Note.h"
#include "Score.h"
System::Void button_execute_Click(System::Object^ sender, System::EventArgs^ e) {
double countMax = pow(2.0, exponent);
// main function:
short* pitches = new short[nNote]; // pitch array
50
Note note(nNote, bottom, range, mode, tonic, center, susceptibility, similiarStepMax, contraryStepMax, stepMax, skipMax,
repetitionMax, countMax);
if (isComplete(nNote, pitches, countMax, note))
finalScore(nNote, pitches, duration); // write the result score else
finalScore(); // write a blank score delete [] pitches;
}
bool isComplete(short nNote, short* pitches, double countMax, Note note) {
else // 3. following pitches
pitches[i] = note.compose(pitches[i-2], pitches[i-1]);
// backtrack procedure:
if (pitches[i] < 0) // 1. rejectee: nextPitch_ == -1 i--; // undo the previous pitch
else // 2. pass
51 }
while (i<nNote);
return is;
}
void finalScore(short nNote, short* pitches, short duration) // write the result score {
short noteon = 0;
short pitch = 0;
Score score;
score.create();
for (short i=0; i<nNote; i++){
pitch = pitches[i];
Score score(noteon, pitch, 127, 120, 0);
// Noteon, Pitch, Velocity=127, Artdur=120, Channel=0 score.write();
noteon += duration; // whole note == 480 }
score.finish();
}
void finalScore() // write a blank score {
52 public:
Note();
Note(short nNote, short bottom, short range, short mode, short tonic, short centerPitch, short susceptibility, short consecutiveSimiliarStepTimesMax,
short consecutiveContraryStepMax,
short consecutiveStepTimesMax, short consecutiveSkipTimesMax, short repetitionTimesMax, double countMax);
short compose(); // first note creator
short compose(short firstPitch); // second note creator short compose(short previousPitch, short presentPitch);
// following note creator
bool isOnModeScale(); // pitch check: mode scale
bool isTolerableEnergyRatio(); // pitch check: energy ratio bool isAcceptableInterval(); // pitch check: interval bool isWithinRepetitionLimit(); // repetition times check
bool isWithinConsecutiveMotionLimit(); // consecutive motion check void countRepetitionTimes(); // repetition times counter
void countConsecutiveMotion(Motion motion); // consecutive motion counter private:
short nNote_; // note amount short bottom_; // bottom pitch short range_; // melody range
short mode_; // mode: 1.Ionian, 2.Aeolian short tonic_; // tonic pitch
short centerPitch_; // center pitch
short susceptibility_; // susceptibility constant
short consecutiveSimiliarStepTimesMax_; // consecutive similiar step maximum short consecutiveContraryStepTimesMax_; // consecutive contrary step maximum short consecutiveStepTimesMax_; // consecutive step maximum
short consecutiveSkipTimesMax_; // consecutive skip maximum short repetitionTimesMax_; // repetition maximum
double countMax_; // count times maximum short previousPitch_; // the previous pitch short presentPitch_; // the present pitch short nextPitch_; // the next pitch
double nextEnergyRatio_; // next energy ratio
53
double energyRatioMax_; // tolerable energy ratio maximum double energyRatioMin_; // tolerable energy ratio minmum
double tempEnergyRatioMax_; // temporary tolerable energy ratio maximum double tempEnergyRatioMin_; // temporary tolerable energy ratio minmum short nextInterval_; // next pitch interval
short consecutiveSimiliarStepTimes_; // consecutive similiar step times short consecutiveContraryTimes_; // consecutive contrary step times short consecutiveStepTimes_; // consecutive step times
short consecutiveSkipTimes_; // consecutive skip times short repetitionTimes_; // repetition times
short tempConsecutiveSimiliarStepTimes_;
// temporary consecutive similiar step times short tempConsecutiveContraryStepTimes_;
// temporary consecutive contrary step times
short tempConsecutiveStepTimes_; // temporary consecutive step times short tempConsecutiveSkipTimes_; // temporary consecutive skip times short tempRepetitionTimes_; // temporary repetition times
};
54
Note::Note(short nNote, short bottom, short range, short mode, short tonic, short centerPitch, short susceptibility,
short consecutiveSimiliarStepTimesMax, short consecutiveContraryStepMax, short consecutiveStepTimesMax, short consecutiveSkipTimesMax,
short repetitionTimesMax, double countMax) {
55
energyRatioMax_ = 4.0; // initial Max = 4
energyRatioMin_ = 0.25; // initial rMin = 4, therefore Min = 1 / 4
short Note::compose() // the first pitch {
presentPitch_ = centerPitch_;
// present pitch is the center pitch; next pitch is the first pitch double count = 0;
do {
do nextPitch_ = rand() % range_ + bottom_;
while (!isOnModeScale());
56
nextPitch_ = -1; // rejectee break;
short Note::compose(short presentPitch) // the second pitch {
presentPitch_ = presentPitch;
double count = 0;
do {
do nextPitch_ = rand() % range_ + bottom_;
while (!isOnModeScale());
if (count > countMax_) {
57 nextPitch_ = -1; // rejectee break;
short Note::compose(short previousPitch, short presentPitch) // following pitches {
do nextPitch_ = rand() % range_ + bottom_;
while (!isOnModeScale());
// reset variables of consecutive motion:
tempConsecutiveSimiliarStepTimes_ = consecutiveSimiliarStepTimes_;
58 count++;
if (count > countMax_) {
nextPitch_ = -1; // rejectee break;
short pitchClass = (nextPitch_ + 12 - tonic_) % 12;
switch (mode_)
59
else if (nextEnergyRatio_ < tempEnergyRatioMin_) is = false;
short interval = nextPitch_ - presentPitch_;
if (interval > 12) // exceed ascending octave is = false;
else if (interval < -12) // exceed descending octave is = false;
else if (interval == 6) // ascending tritone is = false;
60
else if (interval == -6) // descending tritone is = false;
else if (interval == 10) // ascending minor seven is = false;
else if (interval == -10) // descending minor seven is = false;
else if (interval == 11) // ascending major seven is = false;
else if (interval == -11) // descending major seven is = false;
tempConsecutiveStepTimes_ <= consecutiveStepTimesMax_ &&
tempConsecutiveSkipTimes_ <= consecutiveSkipTimesMax_
61 }
void Note::countRepetitionTimes() {
nextInterval_ = nextPitch_ - presentPitch_;
if (nextInterval_ == 0) // repetition
case 1 : // consecutive similiar step tempConsecutiveSimiliarStepTimes_++;
tempConsecutiveContraryStepTimes_ = 0;
tempConsecutiveStepTimes_++;
tempConsecutiveSkipTimes_ = 0;
break;
case 2 : // consecutive contrary step
tempConsecutiveSimiliarStepTimes_ = 0;
62
Frequency(short mode, short tonic, short susceptibility,
short centerPitch, short presentPitch, short nextPitch);
double allocateFrequency(short octave, short pitchClass);
double countEnergyRatioMax(double energyRatioMax); // Max
double countEnergyRatioMin(double energyRatioMin); // Min = 1 / rMin double getNextEnergyRatio();
private:
short mode_; // mode: 1.Ionian, 2.Aeolian short tonic_; // tonic pitch
short susceptibility_; // susceptibility constant short centerPitch_; // centerPitch
short presentPitch_; // present pitch short nextPitch_; // next pitch
short centerOctave_; // center pitch register location short presentOctave_ ; // present pitch register location short nextOctave_ ; // next pitch register location short centerPitchClass_; // center pitch class short presentPitchClass_; // present pitch class short nextPitchClass_; // next pitch class
double centerFrequency_; // center pitch frequency double presentFrequency_; // present pitch frequency double nextFrequency_; // next pitch frequency double presentFrequencyRatio_;
// present frequency ratio: frequency (n-1) / frequency (0)
63 double nextFrequencyRatio_;
// next frequency ratio: frequency (n) / frequency (0) double presentEnergyRatio_;
// present energy ratio: (frequency (n-1) / frequency (0))^2 double nextEnergyRatio_;
// next energy ratio: (frequency (n) / frequency (0))^2 double energyRatioInterval_; // energy ratio interval };
64
Frequency::Frequency(short mode, short tonic, short susceptibility,
short centerPitch, short presentPitch, short nextPitch) {
centerPitchClass_ = (centerPitch_ + 12 - tonic_) % 12;
presentPitchClass_ = (presentPitch_ + 12 - tonic_) % 12;
nextPitchClass_ = (nextPitch_ + 12 - tonic_) % 12;
centerOctave_ = (centerPitch_ + 12) / 12 - 1;
presentOctave_ = (presentPitch_ + 12) / 12 - 1;
nextOctave_ = (nextPitch_ + 12) / 12 - 1;
centerFrequency_ = allocateFrequency(centerOctave_, centerPitchClass_);
presentFrequency_ = allocateFrequency(presentOctave_, presentPitchClass_);
nextFrequency_ = allocateFrequency(nextOctave_, nextPitchClass_);
presentFrequencyRatio_ = presentFrequency_ / centerFrequency_;
nextFrequencyRatio_ = nextFrequency_ / centerFrequency_;
presentEnergyRatio_ = presentFrequencyRatio_ * presentFrequencyRatio_;
nextEnergyRatio_ = nextFrequencyRatio_ * nextFrequencyRatio_;
energyRatioInterval_ = nextEnergyRatio_ - presentEnergyRatio_;
}
double Frequency::allocateFrequency(short octave, short pitchClass) {
65
case 9 : frequency = 40 * pow(2.0, octave); break;
case 11 : frequency = 45 * pow(2.0, octave); break;
default : frequency = 1; break;
}
case 10 : frequency = 216 * pow(2.0, octave); break;
default : frequency = 2; break;
} break;
default : frequency = 3; break;
}
return frequency;
}
double Frequency::countEnergyRatioMax(double energyRatioMax) {
energyRatioMax = energyRatioMax - (energyRatioInterval_ * susceptibility_);
// next Max
if (energyRatioMax < 1)
energyRatioMax = 1; // Max always >=1 return energyRatioMax;
}
double Frequency::countEnergyRatioMin(double energyRatioMin) {
double reciprocalEnergyRatioMin = 1 / energyRatioMin; // present rMin reciprocalEnergyRatioMin = reciprocalEnergyRatioMin + (energyRatioInterval_
* susceptibility_); // next rMin if (reciprocalEnergyRatioMin < 1)
reciprocalEnergyRatioMin = 1; // rMin always >=1
66
energyRatioMin = 1 / reciprocalEnergyRatioMin; // next Min return energyRatioMin;
Motion(short previousPitch, short presentPitch, short nextPitch);
short identify(); // motion types identifier private:
short previousPitch_; // 0 ~ 127 short presentPitch_; // 0 ~ 127 short nextPitch_; // 0 ~ 127
short previousInterval_; // -127 ~ +127 short nextInterval_; // -127 ~ +127
bool areSimilarDirections_; // T: similiar, F: contrary short previousMotion_; // 0: repetition, 1: step, 2: skip short nextMotion_; // 0: repetition, 1: step, 2: skip };
67
Motion::Motion(short previousPitch, short presentPitch, short nextPitch) {
previousPitch_ = previousPitch;
presentPitch_ = presentPitch;
nextPitch_ = nextPitch;
previousInterval_ = presentPitch_ - previousPitch_;
nextInterval_ = nextPitch_ - presentPitch_;
// directions:
if (previousInterval_ * nextInterval_ >= 0) // not "> 0"
areSimilarDirections_ = true; // similiar
else if (previousInterval_ <= 2 && previousInterval_ >= -2) previousMotion_ = 2; // step
else
previousMotion_ = 3; // skip // next motion:
if (nextInterval_ == 0)
nextMotion_ = 1; // repetition
else if (nextInterval_ <= 2 && nextInterval_ >= -2) nextMotion_ = 2; // step
68 short identity = 0;
if (previousMotion_ == 2 && nextMotion_ == 2) {
switch (areSimilarDirections_) {
case true : identity = 1; break;// consecutive similiar step case false : identity = 2; break;// consecutive contrary step }
}
else if (previousMotion_ == 3 && nextMotion_ == 3) identity = 3; // consecutive skip
else
identity = 4; // none of above return identity;
}
Score.h
// Score Writer for the File Format of MusicSculptor by Phil Winsor
#pragma once
class Score {
public:
Score();
Score(short noteon, short pitch, short velocity, short artdur, short channel);
void create(); // output file initiator void write(); // note writer
void finish(); // output file closer private:
69
Score::Score(short noteon, short pitch, short velocity, short artdur, short channel) {
tfile<<noteon_<<' '<<pitch_<<' '<<velocity_<<' '<<artdur_<<' '<<channel_<<
std::endl;
}
70 void Score::finish()
{
// write the end flag of the output file:
std::ofstream tfile("Output.sc", std::ios::app);
tfile<<"0 -1 0 0 0"<<std::endl;
}
71
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