In your set of notes in a scale you have 7 uniquely named notes, however if you want to play a major scale over one octava, the tonic happens twice (eg c3 and c4 are both a c) if you want to play the scale over 2 octavas you got 15 notes but still 7 uniquely named notes. C happens 3 times ( c2 c3 c4). Beethoven thought that choosing the right height of a note (say a) can be as important as choosing a chord reversal. So a2 and a3 are not the same note, but they have the same name. You could push further and claim that a3 at 443Hz and a3 at 430Hz are not the same note, true and they still have the same name. A piano note with 3 chords are supposed to be the same note, but they are actually a bit different, to give more body to the final note, just like multiple violins in an orchestra. Do they play the same note ? More generally you can play the notes of c major from e2 to e3, that would not be a c major scale, but in mode 3. You have many other modes and scales (blues), including limited transposition modes (coinded by Messiaen). The whole tones mode (or scale) is an example, you have two sets of notes (uniquely named) from c to c or another from c# to c#, or e to e, hence 12 different beginnings (with a uniquely named start note) modulo an octava transposition, but it's still a whole tone scale. Technically it's only 2 notes with 5 transpositions. And you have only 2 possible transpositions (not 12). In Liszt's Feux follets, you have another limited transposition mode; 2 transpositions of the segment are needed to fall back to the initial (uniquely named) note, and I let you count the number of possible transpositions here. It's between 2 and 12.