The alternative squares do exactly that, and the effects become way more obvious with distortion. Ultimately, changing phases on the same frequencies you need to build a square changes the volume due to phase cancellation and introduces some micro-changes to the sound which is what impacts the way the sound interacts with processing (distortion, compression, all that).

Also, using less frequencies to build a square overall will produce a softer and nicer square sound. Modern software really pushes it when building a proper square by adding a ton of high frequency sines to make it “textbook square” (something that wasn’t done in older hardware due to limitations). That sharpness can be easily removed to get essentially a square that doesn’t cut into your ears. Something to keep in mind if you feel the need to lowpass your squares later in the chain.

Hey man, I only know about distortion in old hardware from documentaries, it surprised me too when it produced the sound straight out of a console! I just tried one patch, but there is probably more you can do with triangles and perhaps some FM-synthesis, that’s something to feel excited about!

Insane! That’s getting added to my mental list of “things I didn’t know I needed to know, that I now know”, lol

Also, someone in the comments pointed out, the wave will interact differently with distortion and also sound differently in lower octaves. I just toyed around with it in Vital, and you can get some pretty old-school sounding imperfect square waves by randomly phaseshifting different frequencies and passing them through a clipping distortion to get back the volume. Sounds like something straight out of Atari and NES sound chips, cause I suppose the sound chips themselves on console or/and on the tv produced a ton of distortion. Playing several notes close together or in a chord and pitch shifting is completely wild, though perhaps everything I just outlined isn’t a surprise to any chiptune veterans out there.