in music theory and also some other places an octave is a fancy name for 2 notes that sound kind of the same but not really for an example sing along or alone to somewhere over the rainbow and then you yourself can feel how the second note (where) is both higher than the first note (some) but also not a totally different note when you hear it

in just intonation we represent an octave as a 2 to 1 frequency ratio which means that the higher note's sound has twice as many vibrations per second in its waves as the lower note

just intonation is based on the harmonic series which contains intervals like 2 to 1 (the octave) and 3 to 2 (perfect fifth) and 4 to 3 (perfect fourth) and 5 to 4 (major third) and 6 to 5 (minor third) and also 13 to 11 and 1117 to 61

7 to 4 gives you a harmonic seventh (or a septimal seventh if you know the lingo) and it is bluesy great for barbershop singers locking and ringing and chord-worshipping barbershop chords

and! there are so many more fraction options than just the above 7 to 6 gives you a very bluesy minor third and 13 to 8 can elicit dire feelings when death is near and so on and so forth

every single prime number (all infinitely many of them) offers something unique sonically that no other prime ever can (see ancient greece for a proof of why there are infinitely many prime numbers it is actually so cute and clever) so in just intonation the possibilities are unironically and fully literally endless

in just intonation you do not a priori say please give me 12 or 24 or 72 or 10000 notes per octave you say something like ooh i like that interval that goes nicely with my chord yay

unlike temperament which divides the octave into mathematically irrational (think square root and cube root and 12th root and logarithms and all that jazz) equal and or unequal parts just intonation uses whole integer ratios (never decimals) resulting in chords that are stably resonant regardless of so called consonance and or dissonance

click a link to read and then please listen to some just intonation music since it is the fastest way to unlearn and then start learning anew