This is usually a very difficult concept to learn, but usually 'a' goes before singular or non-specific nouns. So, this 'hat' is not a specific hat, it is not a hat which you have been talking about in previous sentences, etc. 'the' is used for specific things and can be used for plural nouns as well. So it might be a little confusing but I think piano is regarded as a specific thing, so when you say "piano" it is regarded as a specific type of musical instrument. Saying "a piano" might imply that there were many pianos in one place and that someone was just playing one of them, though you don't know/care about which one. here goes japanese: 基本的に、 a は特定のものの前に使えない。例えば wearing a hat. hat はなんか特定のものじゃないでしょう。piano って言ったら、なんかピアノの種類が関係ない、piano だけでみんなは大体同じイメージがあるんと思う。ピアノという楽器は一つしかないから特定とおもう。まー難しいけどね

About difference of a and the.

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