Mnemonics, up and down
Going up: Somewhere Over the Rainbow. The leap on "Some-where" is the most famous octave in recorded music, and for most people it's the only mnemonic this interval ever needs. Singin' in the Rain carries the same jump if Garland isn't in your head but Kelly is.
Going down: Willow Weep for Me drops a full octave on its first two notes. Falling octaves are rarer in melodies than rising ones, which is its own kind of tell: a big drop that lands on "the same note, lower" is almost certainly this.
Jazz keeps its own reference tunes. Mark Levine's interval table fixes the ascending octave to Sam Jones's "Del Sasser" and the descending one to Freddie Hubbard's "Philly Mignon."
On the staff
The same note, higher
Double a string's vibration rate and you get the note an octave up. That 2:1 ratio is the simplest relationship two different pitches can have, and ears treat it as a kind of identity: the two notes blend so completely that a melody doubled in octaves still reads as one voice. Theory formalizes the intuition. Notes an octave apart share a letter name and a pitch class, which is why a piano has eighty-eight keys but only twelve note names.
This is also the everyday experience of singing together. When a room full of mixed voices sings "in unison," the men and women are usually an octave apart and nobody notices. The interval is doing its disappearing act.
Where you'll keep meeting it
Pianists double melodies and bass lines in octaves to make them carry. Orchestras do the same across sections; the brass-and-piccolo opening of The Stars and Stripes Forever is doubled octaves sounding like one enormous instrument. Bass players jump the octave constantly, disco and funk lines especially, because it adds motion without changing the harmony. And every guitar riff played simultaneously on two strings twelve frets apart is leaning on the same trick.
What it gets confused with
Honestly, not much. Once you know the "same note twice" quality, the octave is the giveaway interval, the one learners stop missing first. The major 7th sits one semitone shy, but it's sharply dissonant and leans hard toward resolving, so the two rarely blur. The closest thing to a real confusion is the perfect 5th, the other wide-open interval, but the 5th still sounds like two different notes agreeing, where the octave sounds like one note in two places.
How Aubel handles it
The octave is in the starting pool for every player, with the unison, perfect 4th, and perfect 5th. In those early rounds the work is telling the octave's same-note blend from the 5th's two-note openness, which is the first discrimination most ears solidify. The detail screen leads with Somewhere Over the Rainbow.