Learn Hardcore Finnish: Jos olisin korjannut kuulokkeet aikaisemmin, musiikki olisi ollut selkeämpää. - If I had fixed the headphones earlier, the music would have been clearer.

Jos introduces the protasis (the “if” clause) of a conditional sentence. Olisin korjannut is the past conditional (conditional perfect) of korjata, expressing an unfulfilled action in the past (“if I had fixed”).

How is the past conditional (conditional perfect) formed in Finnish?

You take the conditional form of olla (here olisin) and add the active past participle of the main verb (here korjannut). Together they form olisin korjannut (“I would have fixed”).

Why isn’t the clause Jos korjasin kuulokkeet aikaisemmin or Jos korjaisin kuulokkeet aikaisemmin?

Jos korjasin is simple past (“if I fixed”), not counterfactual.
Jos korjaisin is present conditional (“if I would fix now”), not referring to a completed past action.
To express “if I had fixed” (a past, unfulfilled condition), Finnish uses the past conditional Jos olisin korjannut.

Why does the result clause use musiikki olisi ollut instead of just musiikki olisi?

Oisi ollut is the conditional perfect of olla (“to be”), so musiikki olisi ollut means “the music would have been.” Using only musiikki olisi (“the music would be”) would be a present conditional and wouldn’t match the past-time reference set by Jos olisin korjannut.

Why is the adjective selkeämpää in the partitive case instead of nominative?

Comparative adjectives in predicate position with olla typically take the partitive singular. Selkeämpi (“clearer”) becomes selkeämpää in the partitive to express “would have been clearer.”

Why is kuulokkeet in that form (ending in -t) and not another case?

Kuulokkeet is the direct object of korjata (“to fix”). In Finnish, a definite plural object often appears in the accusative, which looks identical to the nominative plural (ending in -t). Hence kuulokkeet marks “the headphones” as the thing being fixed.

Why isn’t a pronoun like minä used for the subject?

Finnish is a pro-drop language: the verb ending -isin in olisin korjannut already indicates first person singular. Explicitly saying minä (“I”) is optional and often omitted for conciseness.

Can the clauses be swapped, for example Musiikki olisi ollut selkeämpää, jos olisin korjannut kuulokkeet aikaisemmin?

Yes. Finnish allows relatively free word order. You can place the main clause (apodosis) before the protasis without altering the meaning.

What does aikaisemmin mean, and how does it differ from aiemmin?

Both mean “earlier” or “before.”

Aikaisemmin is slightly more formal or emphatic.
Aiemmin is more common in spoken Finnish.
In this sentence, you could use either without a significant change in meaning.