system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: How are two notes that are an octave apart "the same note" if they have different frequencies.

I get that notes that are octave apart aren't really the same exact note, but how can you play a piece an octave higher and it still sounds the same?
gpt
notes one octave higher have exactly twice the frequency and have the same "sound" to humans.

One of the earliest diatonic scales (similar to the modern do re mi....) have notes generated by using frequency ratio of 3/2  for each fifth note. (a fifth note to musicians is the interval between C and G for example) by multiplying this ratio repeatedly you can generate a circle of fifths (all the tones and semitones) Modern tuning adjusts this a bit to be less discordant so that you can transpose music from one key to another and yet sound fairly harmonious. 

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