Gen - sharing work - antialiased OSC (similar to tri~) with flexible oversampling

Awesome demo! :)

Amazing! Thanks so much for this.

I feel like i'm about to ask stupid questions(it's ok though: feeling stupid is what i do best in life 🥺😜), but i don't understand how you came up with the values particularly in this line:

os = int ((48000 / samplerate) * (2 + (14 * (scale(in1, 200, 12000, 0, 1, 0.5)))));

in particular, how did you figure out where the '14' comes into play? and since i stop understanding there, i wonder how i'd figure out the "2 +..." also... and how did you know to use "0.5" for the exponential curvature of 'scale'?
i guess i can sort of see that the input to 'scale' will be an effective range in Hz?

maybe they're all part of the same question: i don't understand how i could come up with that line of code myself to apply to other instances(i realize i probably could just copy/paste, but i don't like to do that 😋)

maybe a better question would be: where can i read more, in order to learn the basics of this math?

So to the line os is the amount of how much it will be oversampled. And on how I came up with this is:
48000 is my "standartsamplerate" so if you would use a higher rate you'll need less oversampling.
for the second part, it will scale the incoming frequenci to a range from 0 to 1, so evrything from 200 hertz and below will only be oversampled 2 times, and evrything obove 1200 Hertz will be oversampled 16 times. It is flexible because there is more alising on higher basfrequencis than on lower, so we can use less oversamoling on those lower frewquencies and safe some CPU. So 16 as highest oversamplingrate and 0.5 for curvature are just vThe specific values where just For the specific values I was just trying around and they did work fine. If someone has better mathknowledge this whole thing could probably be optimised a bit more. And where can you read more? Hmm I don't know, like i said it was more try and error than actual math

perfect, that explains everything i needed 🙌
(i also reread some relevant stuff in Musimathics Vol 2. just now and with your explanation it helps me realize the "2 + (14*..." leads to 16x for the highest need here... i had never seen it parsed out to different parts of the spectrum before using 'scale' etc.. everything below 200 oversampled twice, while everything above 12000 oversampled 16x ... that's genius!🙇‍♂️)

now i completely understand. thanks again so much!

Thanks a lot for sharing. Could you briefly explain what these 2 lines of code are doing:
Audio = wrap(phase, 0, 1);
phase = fixdenorm(Audio + (in1 / sr));
Thanks a lot!

These two lines are a recreation of the phasor object.
The reoson phasor can't be used here is that it is internaly getting the samplingrate at which in which the whole patch is running. But in this situation we want it to run at a higher sampling rate, so it needs this recreatin to be abel to use a higher samplerate.

Thanks!

Probably a stupid comment, but I will make it anyway: as far as I understand, the gen patch outputs at sample level and your for loop enables you to calculate steps in between (=oversampling). The only benefit, which could come out of the oversampling is, if any of the calculations make between two sample outputs uses historical data . Since the triangle object only reads out data from a wavetable, the generation of the triangle does not benefit (or change) from (due to) the oversampling. It is just the output after the low-pass filter that benefits from the oversampling since it makes use of historical data. For some reason I had this false impression that you could also reduce the aliasing effect if you were to oversample just the triangle object.

Here's the exact C++ code of triangle:

inline t_sample triangle(t_sample phase, t_sample p1) {
    phase = wrap(phase, 0., 1.);
    p1 = clamp(p1, 0., 1.);
    if (phase < p1)
        return t_sample((p1) ? phase/p1 : 0.);
    else
        return t_sample((p1==1.) ? phase : 1. - ((phase - p1) / (1. - p1)));
}

So you see it's not a wavetable. May be with the max-triangle but not the gen-triangle.
And you also see, it dose not ask for a samplerate, so this is why it can be oversampled.
If you look in to the patch I did make the same thing without oversampling and you can hear the difference. However the filter has to be oversampled as well, if you wouldn't do it would create the alising when going down to the original samplerate, so you have to filter out the unwanted frequencies before going to the original samplerate. But even a wavetable would benefit from the oversampling.