Modern western music is based on what’s called 12 tone even temper. There are 12 “notes” that repeat, the whole tones (A-F) and the semitones (sharps and flats).
Each 12 tone block is known as an octave. An 88 key piano can play 7 of these octaves. A 76 key piano will play 6 octaves, an 82 key piano will play 6.5 octaves.
This, of course, is the case for a mechanical, acoustic piano.
Digital pianos are a different creature, because they can be whatever they want to be. I have a 2 octave keyboard in my studio that I use for basic composing/transcription and it has an “octave shift” button. This button means that if I want to play low notes, I can shift it down, if I want the upper end, I shift it up. It is in essence a snapshot of the part of the keyboard I want it to be.
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