Waveshaping always implies non-linearities.
Non-linearity, however, does not imply waveshaping. AM and FM, for example, are non-linear processes. But they aren't waveshapers.
Also, if you use a straight line as the transfer function, it's still a waveshaper, but it can be linear.
But that "becoming squarer" is closely related to the "new" samplerate
And how do you explain that the "harmonics" always meet at the f_ny_new (or at f_sr_new), if there was no relation to it...
The harmonics begin at the new SR, an extend beyond it. The only frequency that aliases at the new Nyquist is that of the sine wave (the fundamental of the distorted wave).
Take a look at my patch again. Starting at 0 Hz, as you increase frequency you will immediately see the first harmonic pop up at the "new SR". As you increase, some partials will increase in frequency while others decrease. Those decreasing once are folding over from the global sample rate, not the [samphold~] one. Once the [osc~] frequency goes above 2756.25, it aliases, and you see that frequency moving back toward zero. Everything above 2756.25 is distortion, and the only reason there are partials that fall below 5512.5 is because they were aliased at 22050. You can see this because the partials between 2756.25 and 5512.5 always go in the opposite direction of the lowest frequency, whether it has been aliased or not.
Take a look at the modified attached patch. I added a high-order Chebychev filter to act like an anti-aliasing filter would at the dac. It's not perfect because 1) no anti-aliasing filter is, and 2) there's still a global sampling rate, which would not be the case in a good dac. But it does illustrate some important points. First, the anti-aliasing filter fixes those steps so that the sinewave is reconstructed. Second, it shows that only the [osc~] frequency aliases at the new SR. If the other frequencies were aliasing, the level of that one remaining unfiltered partial would start to decrease as you increased the frequency. But it doesn't. It stays at the same level (plus or minus the filter ripple and slope). You can push it well beyond the SR and it will be a sine wave at the same level (except if you push WAY too high, but that's because of floating-point madness).
It's obvious: Just change the new samplerate and watch the loundest partials fold at the new sr (and its multiples)...
The loudest partial is the fundamental, i.e. the [osc~] frequency. It's the only one that folds over at that new Nyquist.
The more quiet a sound the more negligible!
That's because they're quiet. The amplitude range is limited by the bit depth. Also, they're just quiet.
And the aliasing I hear is far from being quiet!!!
That's not the aliasing you hear at the new SR you hear. It's the distortion. That artificial SR created by [samphold~] does not mean everything between that Nyquist and the global Nyquist don't exist.
...and beside that negligible "crap" from the original sr-aliasing, it just behaves nicely 'relative' to the f_sr_new.
In that it never aliases at that SR.
You don't like the timedomain, do you?
Sure I do. Most of what I do ends up being in the time domain. I just think it's important to know which domain is useful for what purpose.
...since shure it is: Sampling each "0.2 period" is the same as sampling each "1.2 period" since an offset of 1 period doesn't change anything..
But in a signal with more than one harmonic, you can't tell which of those harmonics were aliasing in the time domain. Also, as I mention before, .2 and 1.2 are technically the same thing in discrete time. You don't really even know which one it is.
...I wonder why the saw is called SAW... (and not like "shark-tooth" or sth.)
Hmm...maybe that's a hard-synced saw?
A synth with just one osc (and filters) is a little lame, don't you think?!
So when there is another osc to mix with, phase becomes important, too.
Yeah, in that case it might matter. But it doesn't have to be a perfect saw shape. Just a collection of harmonics with 1/n amplitude up until Nyquist that are phase-aligned.
By the way, if you see an oversampled-and-filtered sawtooth that just has a smooth transition where the discontinuity would be and no ripple, that means it used a filter that doesn't have a linear phase, and so the phase alignment gets fucked up anyway. A linear phase FIR filter will have some ripple, similar to a limited sum of sine waves, and it won't look like a perfect saw, either.