Time is normal in any frame of reference. It is only relative compared to other frames of reference.

That's true, the "Speed" of light isn't actually a speed, but rather a constant.

Speeds are additive, me jogging 10 miles an hour on an airplane that's traveling 400 miles an hour makes my total speed 410 mph relative to some point on Earth.

Light on the other hand is a constant. If you flash a light while jogging 10 mph on an airplane going 400 mph, the speed the light travels is actually still just c (the constant of light) -410 mph (to adjust for the base speed relative to the constant) light is more of a structural limit than a speed.

@EnPassant gave a terse but entirely correct reply.

From my frame, would that mental “song” appear stretched out in time? — RogueAI

Yes. That's dilation, a coordinate effect. It means that from their frame, your mental song would be stretched out. 'Appear' is a loaded word since Doppler is relevant to appearances, but not relevant to time dilation. To cancel this out, I'm assuming this speedy person being observed is moving tangentially to your location.

Would it unfold more slowly to an outside observer, similar to time dilation effects?

There are no outside observers, at least not in the sense of outside of spacetime.

And would anything like a Doppler-style distortion apply

If he's moving directly towards you, Doppler effect is stronger than dilation, and his process would appear to be faster than yours. This has fooled even professional astronomers who have measured objects moving towards us to appear to be reducing the distance to us at a rate greater than c. That's Doppler effect.

I’m trying to understand how (or whether) relativity meaningfully applies to subjective mental events like imagined music, not just external physical actions.

Imagined music is just another process that takes time, same as say watching a clock. Humans are in no way special in how relativity treats any observed process.

the "Speed" of light isn't actually a speed, but rather a constant. — DifferentiatingEgg

It is expressed as a speed (not a velicity, which is frame dependent, even for light). Yes, it's a constant, and relativity theory posits (without proof) that light moves at this speed relative to any inertial frame. Note 'inertial': It can moves at different speed relative to non-inertial frames, so say light sent to the moon and back (they have reflectors up there for that) does so at slightly faster than c as measured by us.

Speeds are additive, me jogging 10 miles an hour on an airplane that's traveling 400 miles an hour makes my total speed 410 mph relative to some point on Earth.

True under Newtonian physics, but not relativity. The speeds you mention are so slow that it's really close to 410, but not exactly.

If you flash a light while jogging 10 mph on an airplane going 400 mph, the speed the light travels is actually still just c (the constant of light) -410 mph (to adjust for the base speed relative to the constant)

This is flat out wrong, in any frame. It moves locally at c relative to you, the plane, or the ground.

Time is normal in any frame of reference. — EnPassant

What does "normal" mean? That it flows at its normal 1 second per second rate?

There are no outside observers, at least not in the sense of outside of spacetime. — noAxioms

I'm pretending we have a God's-eye view outside of space-time.

I’m trying to understand how (or whether) relativity meaningfully applies to subjective mental events like imagined music, not just external physical actions. — RogueAI

If mental processes are independent of neural processes then they ought to be unaffected by the relativity of velocities. If they are not independent of neural states then they ought to be affected. Under the affect of psychedelics time dilation is a common experience, but that is an altering of the subjective sense of time.

Suppose I could somehow observe their inner mental activity directly. — RogueAI

The idea of someone observing someone else's subjective sense of time makes no sense.

perhaps the way I expressed it was poor, but what I'm saying is the light is not going at c+410 mph. That's how time dialtion works... the closer to the constant the less time you experience.

What does "normal" mean? That it flows at its normal 1 second per second rate? — RogueAI

Normal means what the first postulate of relativity means: All the normal laws apply in any inertial frame, which means there cannot be a local test for your motion. So regardless of where you are or how you're moving, everything appears 'normal' to you. Yes, time phenomenally appears to flow at its normal 1 second per second, for everybody.

I'm pretending we have a God's-eye view outside of space-time. — RogueAI

Since time is part of the universe (and not something that contains the universe), the God view isn't in time at all, and thus there is no perception of change anywhere. Also, since light cannot leave the universe, none of it gets to this god, so it isn't especially a 'view' in the sense that we have one.

If mental processes are independent of neural processes then they ought to be unaffected by the relativity of velocities. — Janus

I think the sort of dualism you suggest here is incompatible with relativity theory, which blatantly says that you can't tell if you're 'moving fast'. For instance, relativity says that if you fall into a large black hole, you cannot tell when you've crossed the event horizon. What you're suggesting is more like the experience of your body stopping as all physical processes come to a halt as the EH is approached. This would falsify all of 20th century physics, requiring a 3rd interpretation. Not even the absolutists predict that experience, regardless of one's philosophy of mind.

The idea of someone observing someone else's subjective sense of time makes no sense.

I agree, but based my reply on an assumption of mental states being in sync with (if not just being) neural states. If they're two different things that got out of sync, there would be a test for absolute motion. Your arms would be hard to move. You'd not be able to understand speech. You'd probably die if your mental states are in any way involved in life support, like say choosing to eat.

Example: Right now you're moving at ~0.997 c relative to some muon, which is part of the reason you can get to that muon before it decays in only a couple mircoseconds. This insane speed does not affect your mental abilities at all. You don't notice.

what I'm saying is the light is not going at c+410 mph. That's how time dialtion works... — DifferentiatingEgg

That's not how time dilation works.
Light moves locally at c relative to anything. So to compute light relative to the ground in your frame in the plane, you'd have to use the velocity addition formula:

sum = (v+w) / (1 + vw/c²) where v is c and w is 410

c + 410 ./ (1 + 410/c) = c

I didn't even need to bother with units to do that.

If mental processes are independent of neural processes then they ought to be unaffected by the relativity of velocities. If they are not independent of neural states then they ought to be affected. — Janus

This was my initial thought. But, funnily enough, I also went straight to psychedelic experience to note that this is perhaps simple illusion. That said, I can't see a way to litigate that. It's possible that if subjective experience isn't 1:1 eiwth neural activity that psychedelics invoke a similar effect to close-to-light-speed travel.

Yes.

I’m trying to understand how (or whether) relativity meaningfully applies to subjective mental events like imagined music, not just external physical actions. — RogueAI

Time dilation is possible within mental level. You can even travel to the past in your mental world using your own memory and imagination. But it is impossible to do so in external physical world.