Violinens lyd er ikke lige så høj som trommernes.

Because violinens is the genitive form, meaning the violin’s.

• violinen = the violin
• violinens = the violin’s

So Violinens lyd literally means the violin’s sound.

In Danish, the genitive is usually made by adding -s to the noun, including nouns that already have the definite ending:

• bogen = the book
• bogens = the book’s

Because lyd is being used in a possessive phrase: Violinens lyd = the violin’s sound.

In Danish, when a noun is modified by a genitive phrase, it is usually indefinite, just like in English:

• the violin’s sound
• not the violin’s the sound

So:

• violinens lyd = the violin’s sound
• not violinens lyden

It means not as ... as.

In this sentence:

• ikke = not
• lige så høj som = as loud as

So the pattern is:

• X er ikke lige så [adjective] som Y
• X is not as [adjective] as Y

Examples:

• Han er ikke lige så gammel som mig. = He is not as old as me.
• Bilen er ikke lige så hurtig som toget. = The car is not as fast as the train.

Yes, høj often means high or tall, but with sound it can mean loud.

So in this sentence:

• høj lyd = loud sound

This is similar to English, where words about height or level sometimes extend into sound-related meanings.

A useful contrast:

• en høj bygning = a tall building
• høj musik = loud music

Trommernes is the genitive plural definite form, meaning the drums’.

So:

• trommerne = the drums
• trommernes = the drums’

The full underlying phrase is:

• trommernes lyd = the drums’ sound

But in the sentence, lyd is left out because it is understood from the earlier part of the sentence.

So:

• Violinens lyd er ikke lige så høj som trommernes.
• literally: The violin’s sound is not as loud as the drums’ [sound].

Yes. It stands for trommernes lyd.

This is a common kind of omission when the noun is obvious from context. English does the same thing:

• The violin’s sound is not as loud as the drums’.

The word sound is omitted after drums’, because it would be repetitive.

So Danish is being quite natural here.

Here som means as in a comparison.

In the structure:

• lige så ... som = as ... as

So:

• lige så høj som = as loud as

Be careful, because som can also mean who, which, or that in other sentences. Its meaning depends on context.

Because in a normal Danish main clause, the finite verb usually comes in second position. This is the well-known V2 word order.

Here the structure is:

• Violinens lyd = subject
• er = finite verb
• ikke = negation
• lige så høj som trommernes = comparison phrase

So:

• Violinens lyd er ikke lige så høj som trommernes.

This placement of ikke after the finite verb is very common in Danish main clauses.

Yes, that would also be grammatical, but it changes the wording slightly.

• ikke lige så høj som = not as loud as
• lavere end = lower/quieter than

Both can express a similar idea in context, but they are not always identical in tone.

Compare:

• Violinens lyd er ikke lige så høj som trommernes.

• The violin’s sound is not as loud as the drums’.

• Violinens lyd er lavere end trommernes.
• The violin’s sound is lower/quieter than the drums’.

The first is often the most direct match for not as ... as.

Because violinens lyd is already a complete noun phrase meaning the violin’s sound. Danish does not need an extra den here.

In other words, the genitive phrase itself makes the reference specific enough.

So:

• violinens lyd = the violin’s sound
• not den violinens lyd

That extra article would be wrong here.

Yes, it is normal and correct Danish.

It is a fairly clear, standard sentence structure. In everyday speech, people might also choose slightly different wording depending on context, for example:

• Violinen er ikke lige så høj som trommerne.
• The violin is not as loud as the drums.

That version is a little less precise, because instruments themselves are being compared rather than their sound, but in normal conversation it often works fine.

Your original sentence is more exact because it specifically talks about the sound.