An octave is simply an interval created by the use of the factor 2 instead - e.g. if we started with our 100Hz note again, and we wanted to go up an octave, we would double the frequency, taking us to 200Hz. If we wanted to go down an octave, we'd halve it, taking us to 50Hz. Why is this factor of 2 so special?
It makes me wonder if the 12-semitone octave sounded good before the advent of "music as we know it" or if it is something of an acquired taste, in which case alternative breakdowns of the octave could be adapted to, like in the case of western vs indian vs east asian music.
Why are there twelve notes in an octave? - Music: Practice & Theory ...
Was the term “octave” coined after the development of early music theory? No. As shown below, it was already in use by the 11th century to denote the musical interval (although the principal name for the interval at that time seems still to have been diapason). What system was in use in medieval Europe when the term octave arose, and what did the term octave refer to? I'm a little hazy on ...
tuning - Was the term "octave" coined after the development of early ...
40 First, let's be clear that the standard (major) musical scale divides the octave into seven parts, not eight. The word "octave" comes from eight, because a unison (two notes sounding at the same frequency) is considered to be a "prime" or kind of a "one" in the system, rather than zero.