Learn Hardcore Portuguese (Portugal): A música ajuda a acalmar o Pedro.

This use of a (feminine singular article) before música is normal when you’re talking about music in general, not one specific song. In English we typically drop the article in this kind of general statement, but in Portuguese (especially European Portuguese) it’s usual to keep it:

A música é importante. – Music is important.
A água é essencial. – Water is essential.

So A música here is just music in general, not that specific music.

There are two a’s: A música ajuda a acalmar.... Are they the same word?

No, they are different words with different functions:

A música – here a is the feminine singular definite article (“the”) agreeing with música (a feminine noun).
ajuda a acalmar – here a is the preposition a (“to”) that introduces the infinitive acalmar.

So:

A (article) + música (noun) = The music
ajuda (verb “helps”) + a (preposition “to”) + acalmar (infinitive “to calm”)
= helps to calm

They just happen to look the same in writing, but grammatically they are different.

Why is acalmar in the infinitive form? Could I use a different structure, like que acalma o Pedro?

The verb ajudar is normally followed by a + infinitive when it means “to help (to) do something”:

ajudar a estudar – to help (to) study
ajudar a cozinhar – to help (to) cook
ajudar a acalmar o Pedro – to help (to) calm Pedro down

So ajuda a acalmar = helps to calm.

You could say A música ajuda que o Pedro se acalme, but:

it sounds unnatural or overly formal/odd in most everyday contexts
ajudar + que + subjunctive is not the usual pattern here

The natural, standard structure is ajudar a + infinitive, which is why acalmar is in the infinitive.

Why is it acalmar o Pedro and not just acalmar Pedro?

In European Portuguese, personal names usually take a definite article (o / a / os / as) in normal speech, both as subject and as object:

O Pedro chegou. – Pedro arrived.
Vi a Ana ontem. – I saw Ana yesterday.

So:

acalmar o Pedro – calm (down) Pedro

Dropping the article (acalmar Pedro) is possible, but in European Portuguese it tends to sound:

more written/formal, or
somewhat “marked” (e.g. for emphasis or style)

In everyday European Portuguese, o Pedro with the article is the default.

In English we usually say “calm himself down”. Why isn’t it acalmar-se here?

Portuguese has two related verbs:

acalmar – to calm (something/someone)
acalmar-se – to calm down / to become calm (reflexive: the subject calms itself)

Your sentence:

A música ajuda a acalmar o Pedro.
Literally: The music helps to calm Pedro.
Implicitly: helps to calm him down.

We don’t have to make it reflexive because we already say o Pedro as the direct object – the music calms him.

If you want to emphasize that Pedro calms himself (with the help of music), you could say:

A música ajuda o Pedro a acalmar-se. – The music helps Pedro calm down (calm himself).

Both are possible; the original sentence just focuses on the music actively calming him, not on him calming himself.

Could I say A música ajuda o Pedro a acalmar instead of ajuda a acalmar o Pedro?

Yes, that is also grammatically correct:

A música ajuda a acalmar o Pedro.
A música ajuda o Pedro a acalmar.

Nuance:

ajuda a acalmar o Pedro: the focus is a bit more on the action of calming Pedro.
ajuda o Pedro a acalmar: the focus is a bit more on Pedro being the one who calms (with help from the music).

In everyday speech both can be used and are usually understood the same way. The original version is slightly more common and “neutral” sounding.

If I don’t want to mention Pedro’s name, how would I say “Music helps calm him down”?

You can replace o Pedro with the unstressed object pronoun o (“him”) attached to acalmar:

A música ajuda a acalmá-lo.

Notice:

acalmar + o → acalmá-lo
The final -r of acalmar drops and an accent appears on á when the clitic pronoun o is attached.

Similarly:

A música ajuda a acalmá-la. – Music helps calm her down.
A música ajuda a acalmá-los. – Music helps calm them (masc./mixed) down.
A música ajuda a acalmá-las. – Music helps calm them (fem.) down.

How would the sentence change if Pedro were female, e.g. Ana?

You mainly change the article before the name to the feminine form a:

A música ajuda a acalmar a Ana.

Breakdown:

A música – the music
ajuda – helps
a acalmar – to calm
a Ana – Ana (with the feminine article)

All the verbs stay the same; only the article with the name changes.

Is ajuda here a verb or a noun? How can I tell?

In Portuguese, ajuda can be:

a verb form: 3rd person singular of ajudar (ele/ela ajuda – he/she helps)
a noun: ajuda (“help”)

Here, ajuda is clearly a verb, because:

it comes right after the subject A música
it is followed by a + infinitive (a acalmar), which is typical after the verb ajudar

Structure:

A música (subject)
ajuda (verb)
a acalmar o Pedro (verbal complement)

If it were a noun, you’d expect a different structure, for example with a form of ser (to be):

A música é uma ajuda para acalmar o Pedro. – The music is a help to calm Pedro down.

How is the sentence pronounced in European Portuguese?

In a careful European Portuguese pronunciation, you might hear something like:

[ɐ ˈmuzikɐ ɐˈʒuðɐ ɐ ɐkɐɫˈmaɾ u ˈpeðɾu]

Word by word (approximate):

A – [ɐ] (a very short, unstressed “uh”)
música – [ˈmuzikɐ] (ú is stressed: MOO-zee-kɐ)
ajuda – [ɐˈʒuðɐ] (zh-OO-dɐ; j like French je)
a – [ɐ]
acalmar – [ɐkɐɫˈmaɾ] (ah-kɐL-MAR; lh-like dark l in -cal-)
o – [u] (“oo”)
Pedro – [ˈpeðɾu] (PEH-dhru; d is soft, almost like “th”)

In natural speech, many of these vowels will be quite reduced and the words link together smoothly.

Is this sentence specifically European Portuguese? Would it look different in Brazilian Portuguese?

The sentence is perfectly correct in both varieties, but there are two main differences in typical use:

Article with names
- European Portuguese: o Pedro is very common.
- Brazilian Portuguese: often just Pedro, without the article.
Pronunciation is quite different, but the spelling is the same.

So in Brazilian Portuguese everyday speech you’d more often hear:

A música ajuda a acalmar Pedro. (without o)

In European Portuguese, A música ajuda a acalmar o Pedro. is the normal, natural choice.