How should I understand iii-iv-i7-v progression?

[Functional]

Is it by any means possible that you would either have a modulation going on, or the tonic root is actually somewhere other than A?

No, I don't think there's any modulation. You can hear it yourself if you wish: https://picosong.com/wJEKM/

[mystran]

My brain wants to parse the 3rd bar into two chords (Amin and Cmaj) and the last bar seems to at least suggests Emin into G major, giving I (parallel minor), II, VI resolving into I (now major) and III (into V?) in the general scale of C major.

At this point it is rather well-known that there is something wrong with my brain, so I don't know if other people are going to hear it like that... but the progression that results seems quite logical.

[jancivil]

The tonal center, is, well, not so much a center. I don't find any home there really, after hearing it. The chief figure is a minor third in the motif at the start, which gets replicated a tone up and that is the passage's center afaic.

[jancivil]

So even my assessment of the red herring of a i7b5 (a ii, functionally subdominant in minor) is a red herring since I can't get a i out of it.
a iiø7 as i is modulatory, 'ii is the new i' but this hasn't any home to move away from, it's a wanderlust.
There's no real use for shoehorning it conceptually into function, it is what it is.

[Functional]

My brain wants to parse the 3rd bar into two chords (Amin and Cmaj) and the last bar seems to at least suggests Emin into G major, giving I (parallel minor), II, VI resolving into I (now major) and III (into V?) in the general scale of C major.

At this point it is rather well-known that there is something wrong with my brain, so I don't know if other people are going to hear it like that... but the progression that results seems quite logical.

Okay so that chord progression in terms of purely being a chord progression actually would work on top of this better than what I had in mind, so that's surely something. I'm not sure if I will need one though, but if I do, you have helped there

So even my assessment of the red herring of a i7b5 (a ii, functionally subdominant in minor) is a red herring since I can't get a i out of it.
a iiø7 as i is modulatory, 'ii is the new i' but this hasn't any home to move away from, it's a wanderlust.
There's no real use for shoehorning it conceptually into function, it is what it is.

If this song would be in English and theme wouldn't be cultism, wanderlust would have been a perfect name!

But, I guess I did something right for once if the point was to create something that sounds mysterious. Does modal interchange (if that is what it is?) give often such results? I mean, this is probably very mild compared to what one can do with that, but I've kept myself away from doing that

[stillshaded]

Uh..

Could you just write out the chord progression? The way you’re wording this is really confusing.

[Functional]

Uh..

Could you just write out the chord progression? The way you’re wording this is really confusing.

I have already, but at this point I think the answer is "no need to think about it in terms of harmonic functions"

[mystran]

My brain wants to parse the 3rd bar into two chords (Amin and Cmaj) and the last bar seems to at least suggests Emin into G major, giving I (parallel minor), II, VI resolving into I (now major) and III (into V?) in the general scale of C major.

At this point it is rather well-known that there is something wrong with my brain, so I don't know if other people are going to hear it like that... but the progression that results seems quite logical.

Okay so that chord progression in terms of purely being a chord progression actually would work on top of this better than what I had in mind, so that's surely something. I'm not sure if I will need one though, but if I do, you have helped there

Well, it's hard to say. You asked why it works, I tried to explain why it works for me. What you have right now is clearly open for interpretation, I just offered one possibility. If you make the chords more explicit (whatever those chords might be), then you might actually make it less "mysterious" and therefore less interesting. You could also add more ambiguity by adding additional elements that do not fit into the established framework, to make it even more confusing, for better or worse.

I think the important point here is that ultimately, the actual chords don't even matter that much, as long as there is just enough harmonic structure to suggest that it makes sense, one way or another. Judging by the track, you can clearly hear what works and what doesn't and I feel like that's a whole lot more important than trying to fit things into some rigid framework.