Understanding Older Pitch Interpolation Algorithms

Warning that I’m a noob.

One of my goals is to make a sampler that can offer different pitch interpolation algorithms from past samples (so drop sample and divide-by-n clock for example). I’ve heavily referenced this thread for various numbers and formulas to play around with; https://gearspace.com/board/electronic-music-instruments-and-electronic-music-production/826280-taxonomy-early-digital-synthesizers-samplers.html

In attempting to mess with divide-by-n clock algos (using an approxmation of the fairlight’s clock speed and waveform resolution), I’ve implemented this midi implementation of pitch:

if (message.isNoteOn())
double wavSampleRate = readerSource->getAudioFormatReader()->sampleRate;
int noteNumber = message.getNoteNumber();

        double frequency = 440.0 * std::pow(2.0, (noteNumber - 69) / 12.0);
        const int m = 128;
        double adjustedSampleRate = frequency * m;

        //const double Fclk = 20e6; // 20 MHz Emulator III
        const double Fclk = 17e6; //Fairlight
        //const double Fclk = 195313; PPG

        // Calculate n using floor(Fclk/fp)
        int n = static_cast<int>(std::floor(Fclk / adjustedSampleRate));

        // Calculate pitch resolution in cents
        double pitch_resolution = 1200 * std::log2(static_cast<double>(n + 1) / n);
        double speed = 1.0/pitch_resolution;
        transportSource.setSource(readerSource.get(), 0, nullptr, 
                          readerSource->getAudioFormatReader()->sampleRate / speed);

        if (isTransportSourcePrepared)

        isFadingOut = false;
        fadeOutFactor = 1.0f;

It does give a result, but I don’t actually know if this is the correct way of implementing this formula. I don’t even know if this formula is correct, I’m simply trusting the OP of that gearspace thread. I guess I’m looking for more resources/information about these older sampler pitch algorithms. The end goal is to program something on a microcontroller and eventually develop an analog output stage, but for now I’m trying to learn/practice with JUCE plugins.