I am aware that there are kind of music which are not based on normal octaves (e.g. Bohlen-Pierce).
Of course, the middle C and the one octave higher C are not the "same note", although they do differ by an integer number of octaves, so in octave-based music they are related in this way which is the kind of music that it is. It is called "same note" because it is both called "C" due to being based on octave-based system (such as 12-TET), and the style of music which is based on it is such that many cases can be considered as a "same note".
What I did not know is that octave-based music is uncommon in some places.
