Neither the NES nor the SID employs FM synthesis. I'm not even sure what the collective noun is for these. Wikipedia tells me it's PSG (programmable sound generator).

The same behavior could be (also was) teased out of a MOD player if you choose samples with a handful of sample points, like 12. You could also draw up a sawtooth in paint and use that as a sample. These are down-to-earth honest true Scotsman chiptunes.

Those are SID etc. tunes. Not chiptunes.