Learn German: Der Dirigent hält den Takt nicht, geschweige denn den richtigen Rhythmus. - The conductor does not keep the beat, let alone the right rhythm.

The connector geschweige denn translates to "let alone" or "not to mention". It is almost always preceded by a negative statement, which is why we have nicht in the first half of the sentence. It emphasizes that since the first, more basic expectation (keeping the beat) isn't being met, the second, more complex one (keeping the rhythm) is completely out of the question.

Why is it den richtigen Rhythmus in the accusative case?

The connector geschweige denn links two parallel elements. Because it is comparing the second noun directly to the first noun (den Takt), they must share the same case. Since the verb halten requires a direct object in the accusative case, both masculine nouns take the accusative article den.

Why is nicht placed after den Takt instead of before it?

When you negate an entire action or the verb itself, nicht usually goes at the end of the clause (right before the comma here). It negates the whole idea of keeping the beat. If you placed nicht directly before den Takt, it would mean he keeps something else, just not the beat, which wouldn't make logical sense with the geschweige denn follow-up.

Where does the word geschweige come from?