Mater dicit lyram suaviorem esse, sed pater citharam clarius audiri.

Because Latin has no articles. It does not have separate words for the or a/an.

So mater can mean:

• mother
• the mother
• a mother

and context tells you which is most natural. The same is true for pater, lyram, and citharam.

They are accusative because Latin is using indirect statement after a verb of saying.

After dicit (says), Latin often does not use a that-clause the way English does. Instead, it uses:

• accusative for the subject of the reported statement
• infinitive for the verb of the reported statement

So:

• lyram suaviorem esse = that the lyre is sweeter
• citharam clarius audiri = that the cithara is heard more clearly

Even though lyram and citharam are the logical subjects of those ideas, they appear in the accusative because of this construction.

It is called the accusative and infinitive construction, often shortened to A+I or AcI.

It is the standard Latin way to report a statement after verbs like:

• dico = say
• puto = think
• scio = know
• audio = hear

English usually says:

• Mother says that the lyre is sweeter

Latin usually says:

• Mater dicit lyram suaviorem esse

Because in indirect statement, Latin changes the reported verb into an infinitive.

Compare the likely direct statements:

• Lyra suavior est = The lyre is sweeter
• Cithara clarius auditur = The cithara is heard more clearly

After dicit, those become:

• lyram suaviorem esse
• citharam clarius audiri

So est becomes esse, and auditur becomes audiri.

Suaviorem is the comparative adjective from suavis.

Its basic comparative form is:

• masculine/feminine: suavior = sweeter, more pleasant
• neuter: suavius

But here it must agree with lyram, which is:

• feminine
• singular
• accusative

So the form becomes suaviorem.

In other words, suaviorem agrees with lyram just as sweeter in English belongs to lyre.

Because clarius modifies audiri, not citharam.

The idea is not:

• the clearer cithara

but:

• the cithara is heard more clearly

So Latin uses the comparative adverb clarius = more clearly.

A helpful contrast:

• citharam clariorem = the clearer cithara / the cithara [which is] clearer
• citharam clarius audiri = the cithara to be heard more clearly

So:

• suaviorem is an adjective
• clarius is an adverb

Because the instrument is being heard; it is not doing the hearing.

So:

• audiri = to be heard

This fits the meaning:

• pater citharam clarius audiri = father [says] that the cithara is heard more clearly

If Latin used the active infinitive audire, the meaning would be different. It would suggest someone hears the cithara more clearly, with that someone left implied.

So the passive is the natural choice when the instrument itself is the thing being perceived.

Yes, it is understood.

The full version would be:

• Mater dicit lyram suaviorem esse, sed pater dicit citharam clarius audiri.

Latin often omits a repeated word when it is obvious from the context. This is called ellipsis.

So after sed pater, you should mentally supply dicit.

The comparison is left implicit.

In context, the most natural idea is that each parent is comparing one instrument with the other:

• mother says the lyre is sweeter
• father says the cithara is heard more clearly

Latin often leaves the second term of comparison unstated if it is obvious from the situation.

So suaviorem and clarius can work without an expressed quam here because the listener can infer the comparison from the two instruments already mentioned.

Because the two clauses are describing different kinds of ideas.

In the first clause, the statement is about a quality of the lyre itself:

• lyram suaviorem esse = the lyre is sweeter / more pleasant

That naturally uses an adjective.

In the second clause, the statement is about the manner in which the cithara is heard:

• citharam clarius audiri = the cithara is heard more clearly

That naturally uses an adverb.

So the grammar changes because the meaning changes:

• what the instrument is like vs.
• how it is perceived

Because they express an action or state that is simultaneous with dicit.

So:

• dicit ... esse = says ... is
• dicit ... audiri = says ... is heard

The present infinitive in indirect statement usually represents something happening at the same time as the main verb.

If the statement referred to an earlier time, Latin would normally use a perfect infinitive instead.

Yes. Latin word order is fairly flexible because the endings show the grammatical relationships.

For example, you could also say:

• Mater lyram suaviorem esse dicit, sed pater citharam clarius audiri dicit.

That means essentially the same thing.

The given order helps highlight the contrast:

• mater ... sed pater
• lyram ... citharam

So the word order is doing some stylistic work, but the endings are what tell you the grammar.