Ta melodia jest spokojna.

Because melodia is a feminine noun.

In Polish, words like this change depending on the gender of the noun:

• ten = masculine
• ta = feminine
• to = neuter

So:

• ta melodia = this melody

Because adjectives in Polish have to agree with the noun they describe.

Since melodia is:

• singular
• feminine

the adjective also has to be:

• singular
• feminine

So you get:

• spokojny = masculine form
• spokojna = feminine form
• spokojne = neuter form

Here, spokojna matches melodia.

It is in the nominative case because it is the subject of the sentence.

In Ta melodia jest spokojna:

• ta melodia = the thing being talked about
• jest spokojna = what is being said about it

The adjective spokojna is also in the nominative here, because it is a predicate adjective after jest.

In a normal, standard sentence like this, yes, jest is the natural form.

• Ta melodia jest spokojna = normal and complete
• Ta melodia spokojna = sounds incomplete, poetic, or very marked

So for everyday neutral Polish, keep jest.

Yes. Polish has no articles like a, an, or the.

That means:

• melodia could mean a melody or the melody, depending on context
• ta melodia specifically means this melody

So ta is not an article — it is a demonstrative word, like this.

Yes. Polish word order is more flexible than English, but the neutral order here is:

• Ta melodia jest spokojna.

Other orders are possible, but they change the emphasis. For example:

• Spokojna jest ta melodia. = emphasizes calm
• Jest spokojna ta melodia. = marked, less neutral

So if you are learning, the safest version is the original one.

A rough English-friendly guide is:

• ta = tah
• melodia = meh-LO-dya
• jest = yest
• spokojna = spo-KOY-na

A full rough pronunciation: tah meh-LO-dya yest spo-KOY-na

Also, Polish stress is usually on the second-to-last syllable, which fits here:

• meLOdia
• spoKOJna

Very often, yes, especially in beginner examples like this one.

In real usage, ten / ta / to can sometimes be translated as:

• this
• that
• sometimes even something closer to the, depending on context

But if you are translating this sentence by itself, this melody is the best choice.

Not exactly.

• melodia = melody, tune
• piosenka = song

So Ta melodia jest spokojna is talking about the tune/melody, not necessarily the whole song.

Usually calm or peaceful here.

For a melody, spokojna suggests something like:

• gentle
• soothing
• not energetic or aggressive

It does not primarily mean quiet in the sense of low volume. For quiet, Polish often uses words like cichy / cicha / ciche.