Normal can be used to express natural.

Usual, normal and typical are truer synonyms.

I am curious why you say 'supernatural' rather than 'unnatural'?

In terms of flexibility, I would say 'natural' has a different set of polysemic uses to the other three cases. That there is overlap is likely due to how metaphorical usage slowly alters into literal usage overtime.

In terms of basic sturtural use 'usual' is perhaps closer to 'natural' as they both use the same prefix in 'un-' whereas the other two have more unusual (or less 'natural') structures. it does sound out of place to say 'natural' here because creativity in linguistics allows for a greater sense of flexibility in how words can be repurposed.

I would say it is abnormal for humans to have more or less than two legs, and I would say that it is unnatural for humans to have more or less than two legs.

In short:

I don't think normal is equivalent to natural (which resorts to central tendancy). — Copernicus

It can be. Just like an apple is equivalent to a banana if we are using them as examples of fruit, natural and normal are equivalent if using them as examples of commonalities only, not specifically. Reminds me of how 'little' is used more by children and 'small' more by adults--certain cultural 'norms' of use, or 'natural' uses, dictate how we receive what is being said.

I see your usage of organically/naturally, ie without external intervention. Meaning "if left to their own devices". Though the more common lay usage would mean without human intervention, ie you would have to also be removed from the equation.

Though the more common lay usage would mean without human intervention — LuckyR

And who is it, and by what means of measure, is a usage defined as "common" or "lay usage"?

Do you not see the problem? — Banno

I fail to see the solution even more.

The norm is a point of semantic balance between extremes

Why do you wish to create your own language? What purpose is this meant to serve?

Can you fully define any word, outside of mathematics? One can stipulate a definition, but it remains a definition. What a word covers is remarkably complex and is subject to expansion and change through time. I suppose the best we can do in ordinary conversation is to articulate our intuitions.

Normal, as I see it, is something like within the range of expected results or behavior. Normal often implies consistency, routine, expectedness.

But then we soon hit walls. For someone with remarkable athletic skills, say Michael Joran, a normal day playing basketball is scoring 20 (I don't know) points. That is not the average for a non-professional.

And we can expand this in all kinds of ways.

But I don't think we can provide a comprehensive definition of "normal". It's somewhat as Wittgenstein said, the meaning of a word is how we use it in language.

I fail to see the solution even more. — Copernicus

That;s what happens when you ask questions without answers.

It's normal to be abnormal.