How is the synth that plays at the very start of the tune programmed? Is it an FM synth? Is there a flange effect applied to it? I wish to program something similar in Logic Pro X. How would you recommend I go about it?
Oscillator is probably a single pulse wave with pulse width adjusted a little bit from pure square for that slightly brittle metallic timbre. I think this slight adjustment in pulse width is what makes you think of FM.
Amp envelope should just have decay and release set to something fairly short. No sustain.
Gently turn down the filter (low pass with gentle slope), but with a bit of envelope on cutoff as well for that distinct attack. Like the amp envelope it should just have a bit of decay and release. Play with the envelope times, amount of modulation and cutoff controls until you find something close. You could try to apply just a little hint of resonance but I think it should be close to zero.
I also think you should let the cutoff follow keyboard pitch in order for the octaved notes to sound right.
This should at least get you somewhere close and should be possible with any simple subtractive synthesizer.
Sounds like a very basica analog synth patch to me. Possibly just a single square wave or pulse wave with no modulation, very little to no filter (cutoff set very high), and resonance set very low.