Ef strengurinn hefði ekki verið laus, hefði söngkonan byrjað fyrr.

It is a past counterfactual conditional.

In plain grammar terms, it describes:

• something that did not happen in the past, and
• a result that also did not happen.

So the pattern is basically:

• Ef ... hefði ..., hefði ...
• If ... had ..., would have ...

This is very similar to English If the string had not been loose, the singer would have started earlier.

Hefði is the subjunctive past form of hafa.

That matters because Icelandic uses the subjunctive in unreal, hypothetical, or contrary-to-fact situations like this one. Since the sentence is talking about something that did not actually happen, hefði is the correct choice.

Compare:

• hafði = indicative, more like plain factual past
• hefði = subjunctive, used for hypothetical/counterfactual meaning

So in this sentence, hefði helps signal: this is an unreal past situation.

Because both parts of the sentence are part of the same counterfactual past idea.

• Ef strengurinn hefði ekki verið laus = the unreal condition
• hefði söngkonan byrjað fyrr = the unreal result

Icelandic commonly uses hefði in both parts of this type of sentence, much like English uses:

• If X had happened, Y would have happened

Even though English changes form between had happened and would have happened, Icelandic often keeps hefði + past form in both clauses.

This is because Icelandic follows a verb-second pattern in main clauses.

When the sentence begins with the if-clause:

• Ef strengurinn hefði ekki verið laus, ...

that whole clause takes the first position in the sentence. Then the finite verb of the main clause must come next, in the second position:

• ..., hefði söngkonan byrjað fyrr

So the order is:

1. the fronted clause
2. the finite verb hefði
3. the subject söngkonan

If you put the main clause first, you get the more expected subject-first order:

• Söngkonan hefði byrjað fyrr ef strengurinn hefði ekki verið laus.

Both are fine, but the word order changes because of Icelandic sentence structure.

In Icelandic, ekki usually comes after the finite verb and before the non-finite verb form.

Here:

• hefði = finite verb
• verið = non-finite verb form

So the natural order is:

• hefði ekki verið

This is very common in Icelandic verb phrases:

• hann hefur ekki komið
• þau myndu ekki fara
• strengurinn hefði ekki verið laus

So ekki is in exactly the place you would expect in this kind of construction.

Because laus has to agree with strengurinn.

Here, strengurinn is:

• masculine
• singular
• nominative

So the adjective also appears in the masculine singular nominative form:

• laus

Compare:

• strengurinn er laus = masculine singular
• reipið er laust = neuter singular
• snúran er laus = feminine singular
• strengirnir eru lausir = masculine plural

In your sentence, laus is a predicate adjective after verið, but it still agrees with the noun it describes.

Both nouns have the definite article attached to the end, which is normal in Icelandic.

So:

• strengur = a string
• strengurinn = the string

and

• söngkona = a singer
• söngkonan = the singer

They are both in the nominative singular here because they are the subjects of their clauses:

• strengurinn is the subject of hefði ... verið
• söngkonan is the subject of hefði byrjað

This attached article is one of the most important features of Icelandic nouns.

Because after hafa in this kind of construction, Icelandic uses a special non-finite verb form that does not agree with the subject.

So:

• hefði verið
• hefði byrjað

stay the same regardless of whether the subject is masculine, feminine, singular, or plural.

For example:

• hann hefði byrjað
• hún hefði byrjað
• þau hefðu byrjað

The subject changes, and the auxiliary may change, but byrjað stays the same.

Fyrr means earlier or sooner.

In this sentence, it means the singer would have started earlier than she actually did.

It works very naturally as the adverb for a comparative idea:

• byrja fyrr = start earlier

A learner might compare it with áður, which often means before or previously. But here fyrr is the better choice because the sentence is comparing one possible starting time with another.

So:

• fyrr = earlier/sooner
• áður = before/previously

Yes.

A very natural alternative is:

• Söngkonan hefði byrjað fyrr ef strengurinn hefði ekki verið laus.

The meaning stays the same:

• The singer would have started earlier if the string had not been loose.

The main difference is just information order:

• starting with Ef ... foregrounds the condition
• starting with Söngkonan hefði ... foregrounds the result

Both versions are fully normal Icelandic.

No. That would be a different time reference.

Your sentence:

• Ef strengurinn hefði ekki verið laus, hefði söngkonan byrjað fyrr.
• talks about an unreal situation in the past

A present hypothetical would look more like:

• Ef strengurinn væri ekki laus, myndi söngkonan byrja fyrr.
• If the string were not loose, the singer would start earlier.

So the difference is:

• hefði verið / hefði byrjað = unreal past
• væri / myndi byrja = unreal present or future

That distinction is very important in Icelandic conditionals.