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<?php |
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declare(strict_types = 1); |
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namespace ExtendedStrings\Strings; |
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class HarmonicCalculator |
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{ |
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private $minStopDistance = 1.0; |
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private $maxStopDistance = 120.0; |
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private $minBowedDistance = 20.0; |
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private $maxSoundingNoteDifference = 50.0; |
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/** |
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* Returns a list of possible harmonics that produce a given sounding note. |
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* |
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* @param Note $soundingNote The desired sounding note of |
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* the harmonic. |
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* @param InstrumentInterface $instrument The instrument. |
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* |
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* @return Harmonic[] |
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*/ |
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public function findHarmonics(Note $soundingNote, InstrumentInterface $instrument): array |
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{ |
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$harmonics = []; |
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foreach ($instrument->getStrings() as $string) { |
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$harmonics = array_merge( |
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$harmonics, |
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$this->findNaturalHarmonics($soundingNote, $string), |
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$this->findArtificialHarmonics($soundingNote, $string) |
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); |
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} |
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$harmonics = array_filter($harmonics, function (Harmonic $harmonic) { |
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return $this->validatePhysicalDistance($harmonic); |
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}); |
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return $harmonics; |
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} |
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/** |
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* Set constraints on the physical distance between harmonic stops. |
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* |
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* @param float $minStopDistance The minimum distance between stops (mm). |
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* @param float $maxStopDistance The maximum distance between stops (mm). |
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* @param float $minBowedDistance The minimum distance between the upper |
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* harmonic stop and the bridge (mm). |
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*/ |
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public function setPhysicalDistanceConstraints(float $minStopDistance, float $maxStopDistance, float $minBowedDistance) |
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{ |
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$this->minStopDistance = $minStopDistance; |
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$this->maxStopDistance = $maxStopDistance; |
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$this->minBowedDistance = $minBowedDistance; |
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} |
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/** |
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* Set the max difference between the sounding note and natural harmonics. |
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* |
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* @param float $difference The difference in cents (default: 50.0). |
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*/ |
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public function setMaxSoundingNoteDifference(float $difference) |
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{ |
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$this->maxSoundingNoteDifference = $difference; |
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} |
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/** |
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* Check that the harmonic is within the configured distance constraints. |
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* |
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* @see HarmonicCalculator::setPhysicalDistanceConstraints() |
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* |
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* @param \ExtendedStrings\Strings\Harmonic $harmonic |
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* |
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* @return bool |
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*/ |
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private function validatePhysicalDistance(Harmonic $harmonic): bool |
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{ |
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if (!$harmonic->isNatural()) { |
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$distance = $this->getPhysicalDistanceBetweenStops($harmonic); |
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if ($distance < $this->minStopDistance || $distance > $this->maxStopDistance) { |
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return false; |
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} |
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} |
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return $this->getBowedDistance($harmonic) >= $this->minBowedDistance; |
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} |
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/** |
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* Find the physical distance between the stops of a harmonic. |
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* |
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* @param \ExtendedStrings\Strings\Harmonic $harmonic |
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* |
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* @return float |
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*/ |
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private function getPhysicalDistanceBetweenStops(Harmonic $harmonic): float |
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{ |
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return ($harmonic->getBaseStop()->getStringLength() - $harmonic->getHalfStop()->getStringLength()) |
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* $this->getPhysicalStringLength($harmonic); |
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} |
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/** |
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* Find the physical distance between a harmonic's half-stop and the bridge. |
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* |
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* @param \ExtendedStrings\Strings\Harmonic $harmonic |
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* |
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* @return float |
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*/ |
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private function getBowedDistance(Harmonic $harmonic): float |
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{ |
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return $harmonic->getHalfStop()->getStringLength() * $this->getPhysicalStringLength($harmonic); |
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} |
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/** |
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* Find the physical length of the harmonic's string. |
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* |
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* @param Harmonic $harmonic |
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* |
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* @return float |
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*/ |
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private function getPhysicalStringLength(Harmonic $harmonic): float |
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{ |
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$string = $harmonic->getString(); |
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return $string instanceof InstrumentStringInterface |
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? $string->getPhysicalLength() |
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: 500.0; |
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} |
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/** |
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* Find the artificial harmonics that produce the given sounding note. |
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* |
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* @param \ExtendedStrings\Strings\Note $soundingNote |
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* @param \ExtendedStrings\Strings\VibratingStringInterface $string |
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* |
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* @return Harmonic[] |
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*/ |
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private function findArtificialHarmonics(Note $soundingNote, VibratingStringInterface $string): array |
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{ |
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$harmonics = []; |
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$soundingNoteFrequency = $soundingNote->getFrequency(); |
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$stringFrequency = $string->getFrequency(); |
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foreach (range(6, 2) as $number) { |
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$fundamental = $soundingNoteFrequency / $number; |
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if ($fundamental > $stringFrequency) { |
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$baseStop = Stop::fromFrequency($fundamental, $string); |
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$ratio = ($number - 1) / $number; |
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$halfStop = new Stop($ratio * $baseStop->getStringLength()); |
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$harmonics[] = new Harmonic($halfStop, $baseStop, $string); |
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} |
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} |
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return $harmonics; |
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} |
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/** |
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* Find the natural harmonics that produce the given sounding note. |
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* |
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* @param \ExtendedStrings\Strings\Note $soundingNote |
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* @param \ExtendedStrings\Strings\InstrumentStringInterface $string |
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* |
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* @return Harmonic[] |
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*/ |
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private function findNaturalHarmonics(Note $soundingNote, InstrumentStringInterface $string): array |
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{ |
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$harmonics = []; |
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$soundingCents = $soundingNote->getCents(); |
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foreach (range(1, 8) as $number) { |
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// Convert harmonic number to the sounding frequency. |
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$candidateFrequency = (new Stop(1 / $number))->getFrequency($string); |
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// Calculate the difference in cents between the natural harmonic |
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// frequency and the desired sounding note. |
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$difference = abs(Cent::frequencyToCents($candidateFrequency) - $soundingCents); |
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if ($difference <= $this->maxSoundingNoteDifference) { |
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$stringLengths = Harmonic::getStringLengthsFromNumber($number, true); |
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foreach ($stringLengths as $stringLength) { |
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$harmonics[] = new Harmonic(new Stop($stringLength), null, $string); |
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} |
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} |
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} |
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return $harmonics; |
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} |
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} |
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extended-strings /
strings
