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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 $minDistance = 1.0; |
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private $maxDistance = 120.0; |
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private $minBowedDistance = 20.0; |
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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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* @param float $tolerance The maximum deviation (cents) |
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* between the desired sounding |
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* note and a natural harmonic. |
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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, float $tolerance = 50.0): array |
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{ |
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$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, $tolerance), |
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$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 $this->validateDistance($harmonic); |
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}); |
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return $harmonics; |
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} |
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/** |
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* Set the minimum and maximum distance between harmonic stops (in mm). |
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* |
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* @param float $minDistance |
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* @param float $maxDistance |
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* @param float $minBowedDistance |
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*/ |
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public function setDistanceConstraints(float $minDistance, float $maxDistance, float $minBowedDistance) |
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{ |
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$this->minDistance = $minDistance; |
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$this->maxDistance = $maxDistance; |
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$this->minBowedDistance = $minBowedDistance; |
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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::setDistanceConstraints() |
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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 validateDistance(Harmonic $harmonic): bool |
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{ |
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$physicalLength = $this->getPhysicalStringLength($harmonic); |
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$basePhysical = $harmonic->getBaseStop()->getStringLength() * $physicalLength; |
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$halfStopPhysical = $harmonic->getHalfStop()->getStringLength() * $physicalLength; |
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$distance = $basePhysical - $halfStopPhysical; |
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$bowedDistance = $halfStopPhysical; |
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return ( |
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$harmonic->isNatural() |
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|| ($distance >= $this->minDistance && $distance <= $this->maxDistance) |
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) && $bowedDistance >= $this->minBowedDistance; |
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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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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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* @param float $tolerance |
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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, float $tolerance = 50.0): array |
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{ |
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$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 <= $tolerance) { |
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$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
