I´m probably just being dense here, but why do "uzman" and "keman" have "ı" suffixes in this sentence?

Uzmanı, bir kemanı kulak yoluyla akort edebilir.

And this is the translation given for it: 

An expert can tune a violin by ear.

The first -ı is possessive suffix, and the second accusative.

Uzmanı = its expert or the expert of it (violin)

So uzmanı means violin expert (more or less).

Edit to add more:

Dropping the first -ı doesn´t sound good. So we need to keep it. Dropping the second -ı may work but we need to change the order:

Uzmanı, kulak yoluyla keman akort edebilir.

The second -ı has "bir" preceeding it. That may sound weird. because you may have seen that -ı acusative suffix is said to be equal to "the" in English. But here it becomes like

bir keman =a violin

bir kemanı = the a violin

So it´s just an approximation and doesn´t work all the time. It´s better to learn what accusative case is and how it works in Turkish.

So, perhaps the idea here is that we are speaking about "the violin" as sort of a concept. The violin in its essence. The violin as a particular instrument. Rather than as "the violin" that I own. Or "the violin" that you own. Or as "a violin" sitting in someone´s music room. Do you know what I mean?

Anyway, thank you very much for the explanation. It was very useful. I doubt I will ever be able to make such distinctions in my own Turkish, but it is good to be able to recognize this sort of construction when I see it.

Tekrar teşekkürler!