There are multiple definitions of the word octave. Some have to do with frequencies and some have to do with musical scales. Furthermore, no common instrument

There are multiple definitions of the word octave. Some have to do with frequencies and some have to do with musical scales. Furthermore, no common instrument emits a pure tone, there are always overtones and other frequency components (aka timbre). If the 'note' on the instrument is based on the fundamental frequency, there's no guarantee that all of the modes in the timbre are going to re-align at double the frequency of the fundamental. So, basically, we're all talking past each other (again).