What's Useful About Music Theory
Most Western music divides the octave into 12 evenly spaced notes, a tuning known as 12 equal divisions of the octave (12 EDO). After 12 notes we reach a new octave and the pattern repeats. Many of music theory's concepts are built on this division; below are some of the more useful ones, which depend on neither how the music is notated nor the key it's in.
Intervals
An interval is the distance between 2 notes, and each distance has its own term.
Take the major third interval, starting on 2 different notes:
On the staff they sit on different lines, and one has a sharp (♯) next to it - but to the ear they're the same interval.
Chords
A chord is a stack of intervals, and its term describes that stack. A major chord is a triad, consisting of a major third (4 semitones) with a minor third (3 semitones) on top, from any starting note.
Chord progressions
A chord progression is a sequence of chords, and it's what you recognize when you hear the same song in a different key. The chords below are different, but the progression is the same ii–V–I. The Roman numerals are a handy way to write it down: each one names a chord by its place in the key, not by its letter.
Scales
A scale is a pattern of gaps between notes, and each pattern has its own sound, whatever note it starts on.
Hear it
Recognition comes from hearing, not from reading. Every idea above is a way of describing a sound, and it only really sticks once you can hear it.