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the ABS module is a full rectifier, i.e. it doubles the frequency of the already existing waveform. If I feed it a triangular waveform, it will probably output a triangular waveform with twice the frequency. Plus it will be offset

The twice frequency should not be an issue, unless you want something over 10kHz, and you can use a hipass filter to remove the offset …

I was thinking that you could adjust the mark-space ratio to get the look you wanted. Of course, you can always use audio math modules to generate pretty much what ever you want. For example if you followed an LFO with some kind of level detector and a SWITCH driven by the detector you could create a range of sawtooth effects.