This is a follow-up question to What's the point of keys other than C and Am?
After going through that question, I wrote down the key general facts:
- The C major and A minor keys have the simplest key signatures.
- Music is not about the individual notes but the relationships between them (intervals).
- Music can be transposed to a different key. For example, vocalists music all the time to match their vocal range.
- Keys are only identical on equal-tempered instruments
- The chosen key is often constrained within the limits of the range of the chosen instrument.
My question is about the specific case of the piano, where I see that the points about just intonation and instrument range do not apply. Also, all the notes of the C major (C) and A minor (Am) scales are white notes on the piano.
For example, in this video of the Tetris theme tune being played on the piano in different keys, I would not have been able to guess which of them is the original or correct key. The piano seems to be an instrument where changing the key does not change much.
However, Western piano composers, old and contemporary, have not composed all their music in C or Am, or at least started there if they intend to change the key later (modulation). For example, Moonlight Sonata is in C-sharp minor.
If music sounds similar in each key, why would a piano composer choose a key over another? Why not just start composing a song in the simplest key for piano?