Eers nadat altstemme toonlere geneurie het, begin ons.

Here eers means something like only, not until then, or only once.

So Eers nadat ... begin ons means:

• Only after ... do we begin
• We begin only after ...

This is a very common Afrikaans way to emphasize that one thing happens later, after another action is completed.

Nadat means after in the sense of after something has happened.

It introduces a subordinate clause:

• nadat altstemme toonlere geneurie het

That whole part means after alto voices have hummed scales.

Compare:

• voordat = before
• nadat = after

So the structure is:

• Eers nadat X gebeur het, begin ons.
• Only after X has happened do we begin.

Because the clause after nadat is a subordinate clause, and Afrikaans changes the word order there.

In a normal main clause, you often get:

• Die altstemme het toonlere geneurie.

But in a subordinate clause introduced by nadat, the finite verb usually moves to the end, and with the perfect tense you get:

• ... nadat altstemme toonlere geneurie het

So:

• geneurie = past participle
• het = auxiliary verb

This end-position of the verb is very typical in Afrikaans subordinate clauses.

This is because Afrikaans is a verb-second language in main clauses.

The first position in the sentence is taken by the whole fronted phrase:

• Eers nadat altstemme toonlere geneurie het

Once that long phrase comes first, the finite verb of the main clause must come next:

• begin ons

So the pattern is:

• [Fronted element], [verb], [subject]

Compare:

• Ons begin.
• Vandag begin ons.
• Eers nadat hulle klaar is, begin ons.

So begin ons is completely normal here.

Yes. Begin here is present tense: we begin.

The sentence combines:

• a completed earlier action: geneurie het = have hummed
• a present/main action that follows from it: begin ons = we begin

Afrikaans often uses the present tense in places where English also uses the present in this kind of statement.

Altstemme is the plural of altstem.

It is a compound word:

• alt = alto
• stem = voice
• altstemme = alto voices

Afrikaans forms compounds very freely, so it is normal to join these into one word.

Depending on context, altstemme could refer to:

• the alto section in a choir
• singers with alto voices

Toonlere is the plural of toonleer, meaning scale in the musical sense.

So:

• toonleer = scale
• toonlere = scales

In this sentence, toonlere geneurie means to hum scales.

This is musical vocabulary, so it may look unfamiliar if you only know everyday Afrikaans.

Geneurie comes from the verb neurie, which means to hum.

So:

• neurie = hum
• geneurie = hummed / hum

In the perfect tense, Afrikaans usually uses ge- with the past participle:

• neurie → geneurie

So toonlere geneurie het means have hummed scales.

Afrikaans often leaves out articles where English might also leave them out, especially with plural nouns used in a general sense.

Here the sentence is talking about alto voices and scales in a fairly general way:

• altstemme
• toonlere

You could sometimes make things more specific in other contexts, for example:

• die altstemme = the alto voices
• die toonlere = the scales

But in this sentence, the article is not necessary.

The comma separates the fronted subordinate clause from the main clause.

Structure:

• Eers nadat altstemme toonlere geneurie het, = subordinate clause
• begin ons. = main clause

This comma makes the sentence easier to read and clearly shows where the first clause ends.

Yes. A less fronted version would be:

• Ons begin eers nadat altstemme toonlere geneurie het.

That means the same thing.

The original version:

• Eers nadat altstemme toonlere geneurie het, begin ons.

sounds a bit more formal or emphatic, because it puts the time condition first. It highlights the idea of only after that.