Learn Hardcore German: Der Musiker stimmt seine Geige, während die Musikerin am Klavier ruhig die ersten Töne spielt. - The musician tunes his violin while the female musician calmly plays the first notes on the piano.

The suffix -in is a very common way to form a feminine profession or role:
- der Lehrer → die Lehrerin (teacher)
- der Arzt → die Ärztin (doctor)
The article also changes:
- masculine singular: der Musiker
- feminine singular: die Musikerin

So the sentence literally contrasts a male musician (der Musiker) with a female musician (die Musikerin).

What does stimmt mean in Der Musiker stimmt seine Geige? I thought stimmen meant “to be right / to be correct”.

stimmen has several meanings, and context decides which one is meant.

In music, stimmen = to tune (an instrument):
- Der Musiker stimmt seine Geige.
  → The musician is tuning his violin.
- Kannst du bitte die Gitarre stimmen?
  → Can you tune the guitar, please?
In statements, stimmen = to be correct / to be true:
- Das stimmt.
  → That’s right / That’s true.
In politics, stimmen can mean to vote:
- Ich stimme für den Vorschlag.
  → I vote for the proposal.

In your sentence, because we have seine Geige (his violin), the musical meaning “to tune” is the natural one.

Why is it seine Geige and not sein Geige or seiner Geige?

seine is a possessive determiner that must agree in gender, number, and case with the noun it describes (Geige), and it must reflect the gender of the owner (the musician).

The owner is der Musiker (masculine), so we use the sein- stem (his).
Geige is:
- feminine (die Geige),
- singular,
- in the accusative case (direct object of stimmen).

Feminine singular accusative with a possessive gets the ending -e:

ich – meine Geige
du – deine Geige
er – seine Geige
sie (she) – ihre Geige

So the correct form is seine Geige (“his violin”) in the accusative.
sein Geige is wrong, and seiner Geige would be dative/genitive, which does not fit here.

Why does the sentence need a comma before während, and why is spielt at the end of the second part?

während is used here as a subordinating conjunction (“while”). Subordinating conjunctions:

Introduce a subordinate clause.
Are preceded by a comma.
Send the conjugated verb to the end of that clause.

So the structure is:

Main clause (verb in 2nd position):
Der Musiker – stimmt – seine Geige, …
Subordinate clause with während (verb at the end):
während – die Musikerin am Klavier ruhig die ersten Töne – spielt.

Other subordinating conjunctions that work the same way:

weil (because):
…, weil er müde ist.
obwohl (although):
…, obwohl es spät ist.

Can während also be a preposition? Does it change the case?

Yes. während can be:

A subordinating conjunction (as in your sentence), introducing a clause:
- …, während die Musikerin … spielt.
  (no case issue; it just changes word order)
A preposition that normally takes the genitive:
- während des Konzerts = during the concert
- während der Pause = during the break

So:

In your sentence, während is a conjunction, not a preposition.
When you see während + noun, expect the genitive:
während des Tages, während der Nacht, etc.

What exactly does am Klavier mean? Why not just Klavier or auf dem Klavier?

am Klavier is a fixed and very common phrase meaning “at the piano” (often: positioned at it, playing it).

am = contraction of an dem (at the).
am Klavier: physically at the piano, usually implying playing:
- Sie sitzt am Klavier. → She is sitting at the piano.
- Er übt am Klavier. → He is practicing at the piano.

Other options:

Klavier spielen (without article):
Sie spielt Klavier. → She plays the piano (general ability/habit).
auf dem Klavier (literally “on the piano”) usually refers to the surface:
Die Blumen stehen auf dem Klavier.

In your sentence, am Klavier nicely suggests her position at the instrument while she plays.

Does ruhig here mean “quiet” or “calm”? How is it functioning in the sentence?

In ruhig die ersten Töne spielt, ruhig is an adverb, modifying the way she plays.

It can mean:
- calmly / in a composed way, or
- quietly / softly, depending on context.

Here, both ideas are compatible: she starts the piece in a calm, gentle manner, not loudly or nervously.

Grammar-wise:

Adjective: ein ruhiger Abend (a quiet evening)
Adverb: Sie spielt ruhig. (She plays calmly/quietly.)

German often uses the same form for adjective and adverb; the role is decided by context.

Why is it die ersten Töne and not die erste Töne or die ersten Tonen?

Several things are happening at once:

Plural of Ton:
- singular: der Ton
- plural: die Töne (with umlaut + -e)
The phrase is in the accusative plural (direct object of spielt):
- Sie spielt die ersten Töne. → She plays the first notes.
With a definite article (die) and a plural noun in the accusative, the adjective (erste-) gets the ending -en:
- die ersten Töne
- die schönen Lieder
- Ich sehe die roten Autos.

So:

die erste Töne → wrong (adjective ending doesn’t match plural accusative).
Tonen → wrong plural; it must be Töne.
Correct: die ersten Töne.

Why is the word order ruhig die ersten Töne spielt and not die ersten Töne ruhig spielt? Can I change it?

Both orders are grammatically possible, but the usual and most neutral order is:

ruhig die ersten Töne spielt

General tendencies:

In the “middle field” of a German clause, the order often goes:
- adverbs (manner, place, time)
- then objects (like die ersten Töne)
Adverb before object is very natural:
- Sie spielt ruhig die ersten Töne.
- Er liest laut das Buch.

If you say die ersten Töne ruhig spielt, you’re putting a bit more emphasis on die ersten Töne and then qualifying them with ruhig. It’s not wrong, but it sounds slightly marked or stylistic.

In normal prose, ruhig die ersten Töne spielt is the default and matches textbook word order.

German uses the simple present stimmt and spielt, but English says “is tuning / is playing”. Is this always allowed in German?

German has no separate present progressive tense. The Präsens (simple present) typically covers both:

present facts or habits, and
actions happening right now.

So:

Der Musiker stimmt seine Geige.
→ The musician tunes his violin.
→ The musician is tuning his violin.
Die Musikerin spielt die ersten Töne.
→ The musician plays the first notes.
→ The musician is playing the first notes.

Context tells the listener whether this is a general habit or something happening at the moment. In your sentence, because of the scene described, the natural English translation is progressive, but in German you just use the normal present.

Why is Geige feminine (die Geige) and Klavier neuter (das Klavier)? Is there any rule?

For most nouns, grammatical gender in German is largely arbitrary and must be learned with the noun.

die Geige (feminine)
das Klavier (neuter)
die Gitarre (feminine)
die Trompete (feminine)
das Cello (neuter)

There are some patterns (e.g. many nouns ending in -e are feminine, foreign words ending in -ier are often neuter), but there are enough exceptions that you should always learn the article with the word:

die Geige
das Klavier

That’s also why we get:

seine Geige (feminine object of a male owner)
am Klavier (neuter noun in the dative after an dem → am).

Could I move am Klavier and ruhig around? For example: während die Musikerin ruhig am Klavier die ersten Töne spielt?

Yes. German word order in the “middle field” is relatively flexible. All of these are grammatical, with only slight shifts in emphasis:

während die Musikerin am Klavier ruhig die ersten Töne spielt (original)
während die Musikerin ruhig am Klavier die ersten Töne spielt
während die Musikerin ruhig die ersten Töne am Klavier spielt

Nuances:

ruhig am Klavier draws a bit more attention to her calm presence at the piano.
ruhig die ersten Töne focuses more on the calmness of the first notes themselves.
The most standard-sounding version is very close to your original; but all three would be understood without any problem.