Jeg er interesseret i musik.

• Jeg = I
• er = am / are / is (the present tense of to be)
• interesseret = interested
• i = in
• musik = music

So the full sentence means I am interested in music.

In Danish, jeg is the subject pronoun I, and er is the present tense of the verb at være (to be).

So:

• jeg er = I am
• du er = you are
• han er = he is
• hun er = she is

Unlike English, Danish does not have different present forms like am / is / are. It just uses er for all persons.

Interesseret is the normal predicate form here, used after er.

In Jeg er interesseret i musik, interesseret describes the subject jeg after the verb er, just like interested in English.

You will often see:

• Jeg er interesseret i kunst.
• Han er interesseret i sport.
• Vi er interesserede i politik.

A useful thing to notice is that Danish sometimes changes the adjective ending in the plural:

• singular: interesseret
• plural: interesserede

So:

• Jeg er interesseret i musik.
• Vi er interesserede i musik.

Because Danish uses interesseret i to mean interested in.

This is just the standard combination:

• interesseret i noget = interested in something

Examples:

• Jeg er interesseret i film.
• Hun er interesseret i historie.
• De er interesserede i sprog.

So if you want to say what someone is interested in, i is the usual preposition.

Yes. Jeg interesserer mig for musik is also correct, and it means roughly I am interested in music or Music interests me depending on context.

There is a small difference in structure:

• Jeg er interesseret i musik
  = adjective-based expression: I am interested in music

• Jeg interesserer mig for musik
  = verb-based expression: literally something like I interest myself in music, but naturally just I am interested in music

A learner will probably hear both, but Jeg er interesseret i musik is very common and straightforward.

Notice the preposition changes:

• interesseret i
• interessere sig for

Because musik is being used as an uncountable noun here, just like music in English.

You normally do not say:

• a music
• en musik

So Danish says:

• Jeg er interesseret i musik.

If you were talking about a specific kind of music, you might add more information:

• Jeg er interesseret i klassisk musik.
• Jeg er interesseret i dansk musik.

But musik by itself does not need an article here.

A rough learner-friendly guide is:

• Jeg ≈ yai or yaiy
• er ≈ air said quickly, often weaker
• interesseret ≈ in-te-re-SE-ret with the stress around -se-
• i = ee
• musik ≈ mu-SEEK

A more important point is that spoken Danish is often less clear-cut than the spelling suggests. In natural speech, some sounds get reduced.

If you are a beginner, it is enough at first to aim for something like:

yai air in-te-re-SE-ret ee mu-SEEK

Then improve by listening to native audio.

No, this is basic Danish word order in a main clause:

Subject + verb + complement

So:

• Jeg = subject
• er = verb
• interesseret i musik = complement

This is very similar to English:

• I am interested in music

Danish word order becomes more noticeable when something else comes first:

• I musik er jeg interesseret is not natural in ordinary speech.
• Normal order is Jeg er interesseret i musik.

You usually put ikke after the verb er:

• Jeg er ikke interesseret i musik.
  = I am not interested in music.

This is a very common Danish pattern:

• Jeg er glad. → Jeg er ikke glad.
• Hun er træt. → Hun er ikke træt.

So the placement of ikke is important:

• Jeg er ikke interesseret i musik.

In Danish yes/no questions, the verb usually comes before the subject:

• Er jeg interesseret i musik?
  = Am I interested in music?

This is the same kind of inversion as in English:

• I am interested in music.
• Am I interested in music?

If you ask someone else:

• Er du interesseret i musik?
  = Are you interested in music?

You only need to change the subject pronoun, and sometimes the adjective ending in the plural.

Examples:

• Jeg er interesseret i musik. = I am interested in music.
• Du er interesseret i musik. = You are interested in music.
• Han er interesseret i musik. = He is interested in music.
• Hun er interesseret i musik. = She is interested in music.
• Vi er interesserede i musik. = We are interested in music.
• De er interesserede i musik. = They are interested in music.

Notice:

• singular often uses interesseret
• plural often uses interesserede

Yes. Musik can refer to music in general, just like English music.

Examples:

• Jeg kan godt lide musik. = I like music.
• Jeg er interesseret i musik. = I am interested in music.

If you want to be more specific, you add a type:

• rockmusik = rock music
• klassisk musik = classical music
• popmusik = pop music

So in this sentence, musik is broad and general.

Yes, it is completely natural. It is a standard and idiomatic way to say I am interested in music.

It sounds neutral and normal in everyday speech and writing. A Dane would understand it immediately.

You could also say more specific things, such as:

• Jeg interesserer mig for musik.
• Jeg går meget op i musik. = I’m really into music.

But Jeg er interesseret i musik is correct, natural, and useful.