single pitch stiff string equation simulation

src/synth/Instruments/PianoString.hpp

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+
+#pragma once
+
+#include <cmath>
+
+#include "synth/Instrument.hpp"
+
+class PianoString : public Instrument {
+
+public:
+
+    PianoString() = default;
+    PianoString(ConfigService* config, LoggerService* logger);
+    ~PianoString() = default;
+    
+    void noteOn(float frequency, float velocity) override;
+    void noteOff() override;
+
+    bool isActive() override;
+
+    float process(bool& scopeTrigger) override;
+
+private:
+
+    // states
+    std::vector<float> stringY_current_;
+    std::vector<float> stringY_previous_;
+    std::vector<float> stringY_next_;
+    std::vector<float> stringX_;
+
+    // constants
+
+    // string parameters
+    size_t segmentCount_ = 30;
+    static constexpr float rho_ = 8000.0f; // density, steel, kg/m^3
+    static constexpr float radius_ = 0.001f; // meters
+    static constexpr float stringTension_ = 1200.0f; // string tension, N
+    static constexpr float stiffness_ = 0.001f; // stiffness coefficient
+    float damping_ = 0.5f; // damping coefficient
+    static constexpr float stringLength_ = 1.0f; // length of string
+    static constexpr float strikePosition_ = 0.2f; // x of impulse location
+    static constexpr float impulseWidth_ = 0.02f; // x of impulse width
+    static constexpr float impulseVelocity_ = 10000.0f; // x/t of impulse magnitude
+    static constexpr float samplePosition_ = 0.1f; // percentage along L of sampling for audio
+    float crossSectionalArea_ = pi * std::pow(radius_, 2.0f); // string cross sectional area, assuming circular
+    float mu_ = crossSectionalArea_ * rho_; // linear mass density
+    float waveVelocity_ = std::sqrt(stringTension_ / mu_); // transverse wave velocity
+
+    // eventually we'll have to dynamically tune our string according to the note that comes in
+    // an alternative is a fully built piano and then it calls voices under the instrument instead of how we do it currently
+    float f0_ = waveVelocity_ / (2.0f * stringLength_); // fundamental frequency of a non-stiff string
+    float f1_ = f0_ * std::sqrt(1.0f + stiffness_); // fundamental frequency of the stiff string
+
+    float dx_ = stringLength_ / static_cast<float>(segmentCount_);
+    float dt_ = 1.0f / sampleRate_;
+
+    // derived constants
+    float r1_ = waveVelocity_ * dt_/dx_;
+    float r2_ = std::pow(waveVelocity_ * dt_/dx_, 2.0f);
+    float s1_ = stiffness_ * dt_/std::pow(dx_, 2.0f);
+    float s2_ = std::pow(stiffness_ * dt_/std::pow(dx_, 2.0f), 2.0f);
+    float a1_ = 2.0f - 2.0f * damping_ * dt_;
+    float a2_ = 2.0f * damping_ * dt_ - 1.0f;
+
+    // keeping track of the string's activeness
+    float rms_ = 0.0f;
+
+};