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I've implemented Miller Puckette's time-domain pitch shifting algorithm (http://msp.ucsd.edu/techniques/v0.11/book-html/node125.html) in PureData's help files in C++ (my code here: https://github.com/aparks5/synthcastle/blob/main/src/pitchshift_timedomain.cpp)

I've been playing around with it, and noted that introducing feedback into the delay line produces some interesting effects. I could describe it is a "bloom" but it is probably more clearly described as a pitch-shifter with (exponentially?) further increasing pitch over time.

However, because of the assumptions made about the phase of the envelope and the phase of the unipolar sawtooth which modulates the delay time, when feedback is introduced, the assumptions about phase that allow this splicing to occur cleanly without discontinuities no longer holds.

How can I introduce feedback into a pitch-shifting delay line without introducing further clicks?

I don't expect it's going to sound "clean" without Phase Vocoding, I just simply want a better idea of how I can modify the envelope to compensate for the feedback path.

Anecdotally, I think this effect must be possible because it was implemented on the Boss RPS-10 Pitch-Shifter Delay, and I have to imagine such an effect worked in the time domain.

Here is my code pasted below

#include "pitchshift_timedomain.h"

#include "gain.h"

PitchShift::PitchShift(size_t fs)
    : Module(fs)
    , m_delay(fs, 1.0f)
    , m_delayInv(fs, 1.f)
    , m_saw(fs)
    , m_shiftSemitones(7)
{ 
    m_delay.update(0.f, 0.0f);
    m_delayInv.update(0.f, 0.0f);
    // http://msp.ucsd.edu/techniques/v0.11/book-html/node125.html
    float semi = m_shiftSemitones;
    float temp = expf(semi * 0.05776f) - 1;
    temp = temp / 0.08; // window
    m_saw.freq(temp);
}
float PitchShift::operator()(float in) {

    // http://msp.ucsd.edu/techniques/v0.11/book-html/node125.html
    float delay1Modulation = m_saw();
    // make saw unipolar
    delay1Modulation = (delay1Modulation * 0.5f) + 0.5f;

    // add 90 degree offset, wrap around 1
    float delay2Modulation = 0.5f + delay1Modulation;
    if (delay2Modulation > 1) {
        delay2Modulation -= 1;
    }

    m_delay.update((delay1Modulation * 80) + 67, 0.0f);
    m_delayInv.update((delay2Modulation * 80) + 67, 0.0f);

    float temp = m_delay();
    // restrict cosine from -.25 to .25
    float env = cosf(2*M_PI * ((delay1Modulation - 0.5f) * 0.5f));
    temp *= env;
    
    float tempInv = m_delayInv();
    float envInv = cosf(2*M_PI * ((delay2Modulation - 0.5f) * 0.5f));
    tempInv *= envInv;

    m_delay.write(in);
    m_delayInv.write(in);
    return (temp + tempInv) * 0.707;
}
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    $\begingroup$ Please vote on this meta question to get code highlighting activated on this site. $\endgroup$ Commented Dec 31, 2021 at 19:42
  • $\begingroup$ I guess perhaps my expectations are unrealistic in the time domain, all of these time domain based guitar effects have a similar kind of noise buildup when feedback is introduced into the pitch shift $\endgroup$
    – panthyon
    Commented Dec 31, 2021 at 20:47
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    $\begingroup$ I guess I don't quite grok the question. The pitch shifter should be defined as an encapsulated block that itself has some mean delay. Now you can surround that block with feedback and a summing node at the pitch shifter input. Now if you're doing something different than that, you need to explain to us how it's different and why it's done that way. $\endgroup$ Commented Jan 1, 2022 at 6:18
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    $\begingroup$ pitch shifting with feedback is not an uncommon effect for chorussing guitars and also for a sorta crystal "tinkling" effect. if there is no discontinuity in the mathematics of the variable delay or in the crossfading in the delay line (that time-domain pitch shifters do), and if the audio contains no clicks, I dunno where a click would come from. $\endgroup$ Commented Jan 1, 2022 at 6:26
  • $\begingroup$ I voted to close this question because I think what I am hearing is not a true discontinuity but simply the sound of the effect. After listening to demos of similar guitar effects I'm convinced this is simply how it sounds (you may ask, how did I expect it to sound? I think with more 'glissando') $\endgroup$
    – panthyon
    Commented Jan 4, 2022 at 16:02

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