1: They are polyphonic instruments. That means they can play multiple notes at the same time. As opposed to something like a flute, only one note at a time. This ties in to the second point:
2: Piano keyboard is the standard for learning music. Even when not at a piano we tend to think in terms of its physical white and black keys and how they are laid out. Even learning guitar the books will show the chords on a piano keyboard often times.
3: Both are easy to play instantly. Many instruments must be assembled, possibly tuned, and then warmed up each time you want to play it. A piano or guitar is ready to go the second you feel like it. I think this is more important than most for why they are popular.
4:Both are *string* instruments. Strings make waveforms (soundwaves) that are closer to the fundamental sine waves that make up sounds. This makes them sound decent when paired or combined with many other things. Extremely versatile is going to naturally be more common right?
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