No not always at all. The piece will generally end on the tonic harmony (say a c major chord) of the key the piece is in. But it can start on any note at all. And that is just older tonal "classical" music (and most pop music which is far more akin to older "classical" than modern "classical"). Modern music does away with the concept of tonality completely in many cases. But even in "classical" you will often find pieces beginning on the fourth fifth seventh. Anything. It will generally start with the tonic chord in the harmony though. A famous story: Schubert (I think) and friends were playing songs one night and they stopped on the dominant chord of the key and left it unresolved. They then all went to bed. Schubert tossed and turned until the early morning when he eventually got up and went downstairs to the piano and played the cadence's resolution. He then went back to bed and slept like a lamb. Kinda like doing shave and a haircut without the Two Bits. :) NB I have used "classical" to indicate what is commonly called classical i.e. orchestral music etc which includes Baroque, Rococo , Romantic, Modern etc, as true "Classical" music is a short period about 1750-1800.