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Good writeup, introspec. I'll add that in addition to the pin pulse method, the Squeeker method also allows for some deviations in timing, and both of these methods still work (albeit with noticable degration of sound quality and of course frequency range) at fairly low update rates, as demonstrated by nanobeep.

So as I was just about to fall asleep last night, it occurred to me that it's possible to implement a low-pass filter with variable cut-off, without using multiplication.

Assuming an engine that supports multiple volume levels per channel, the idea is as follows:

current_volume = 0
max_volume_delta = x

loop {
  new_volume = n  // use whatever standard method here
  if abs(current_volume - new_volume) > max_volume_delta {
    if new_volume > current_volume {
      new_volume = current_volume + max_volume_delta
    } else {
      new_volume = current_volume - max_volume_delta
    }
  }
  ... // output sound 
}

This could potentially be used to add filter envelope emulation to existing synthesis algorithms such as Phaser. The question though is how to efficiently implement that big fat nested conditional.

It's fairly easy for a saw wave generator, because we can assume that when (abs(current_volume - new_volume) > max_volume_delta) is true, then (new_volume < current_volume) is also true for a real-world implementation (in other words, max_volume_delta is never exceeded on the rising edge of the saw). So that's what the attached example demonstrates.

Old version of 1tracker maybe?

Qchan is pin pulse so in theory it should work. However, it may be too quiet to be properly audible, or maybe the pulses will be too short to actually switch the piezo. Could also be that the volume envelopes don't quite work as intended because some piezos have a pretty strong overshoot. Nevertheless, it's worth a try methinks. Same goes for the Octode family (except Octode PWM and Octode2k16, those are pulse interleaving), Stocker, Huby, and BuzzKick.

Engines using the pulse interleaving technique (Savage, Tritone, many others) most likely will not work on piezos. Pulse interleaving relies on inertia of the speaker cone, which is practically absent on piezos. So only engines using OR mixing (Squeeker, Squeeker Plus, PhaseSqueek, Squat) and maybe pin pulse engines will work.

That said, VZ also has tape out, right? I'd focus on using that for sound instead of the piezo.

Yay, congratulations on this achievement! And welcome to the rabbit hole of 1-bit engine making

Ehh, I wish I had Shiru's advice back in the day when I started to make my own engines. Could never wrap my head around it back in the day. Just like I couldn't figure out 16-bit dividers, lol. Speaking of which, I'd say try to figure those out next. Aside from having a greater note range, it actually makes things simpler

Of course, if you have any questions, ask away. More than happy to help.

Hi Jumperror, welcome to the forum. Wow, you're doing a lot of cool stuff! Glad to have you aboard. Looking forward to hearing more 1-bit (and other) tracks from you. I'm curious what you could come up with on some of the newer beeper engines. If you have any questions feel free to ask anytime.

Great little tune. A pity that CAFe didn't have a dedicated beeper compo though. Hmm maybe next year...

Aye, it took a while for ye olde brain. I was fixated on the "volume control" part, but it's really all about the harmonics, right?

In that case, a word of caution: Emulators are often misleading in that respect, actual hardware can sound quite different. Generally 48k tends to be more noisy, and harmonics tend to be buried under the noise. Anyway, if you're going to explore further in this direction, I can help with some hw recordings.

The question remains where these harmonics come from in the first place. Is it because at these marginal pulse width threshold overflow errors from the frequency calculation become more significant?

When I worked on those multi-core engines with many volume levels, I also noticed another effect. If there are several consecutive frames with high total volume (mimicing a DC offset), some sort of volume ramping will occur, gradually turning rectangular waves into saws. Octode2k16 is perhaps the best example of this. I tried to control this effect but it was very unreliable. Still wonder though if it can be used somehow.

Hi Dave,

In general you should be able to get away with LD ($6800),A. The thing is that, because of some hardware quirks, on the Spectrum we try to align all writes to port $FE to a multiple of 8 t-states for cleaner sound. Chances are you don't have such a requirement on your machine, so you can get away with shifting the timings a bit.

There is another problem here though. The engines that use this type of "output-and-rotate" approach heavily rely on the fact that the Speccy only looks at bit 4 for the output* and ignores the other bits. So writing the value of A directly to ($6800) probably won't work. You'd need to check bit 4 of A each time and set the output accordingly, or perhaps you could look into changing the sample format so it better suits your needs. I think if you changed the sample values as follows:

$88 -> $11
$cc -> $99
$ee -> $77
$ff -> $ff

things might work out.

* that's a bit over-simplified. Bit 3 also has an impact but often that fact is simply ignored.