Learn music theory to analyzing real scores in four months
Four months of daily study — 25 minutes a day on a free interactive site, then a college textbook — gets a musician from "what is a key signature" to writing Roman-numeral analysis of a Bach chorale. Roughly 50 hours total. You will not be a composer. You will be able to read what other musicians are doing and explain why it works.
4 months · ~50 hours · analyze a pop song's chord progression in Roman numerals
1.musictheory.net — Lessons and Exercises
Ricci Adams built this site as a graduate student in 2000 and it is still the cleanest interactive theory primer on the internet, free, no account needed. Work through every lesson in order: notation, intervals, key signatures, scales, triads, seventh chords. Then drill the matching exercises until you can identify any major or minor key signature in under three seconds. The note-identification trainer alone is worth six months of any piano method's reading drills.
Free (the optional Tenuto iOS app is $4 and worth it for daily reps)
musictheory.net →2.Tonal Harmony by Kostka, Payne and Almén
The textbook used at most American conservatories. Buy an older edition used for $25 — the eighth from 2018 is identical for our purposes to the latest. Work through chapters 1–14: the diatonic system, four-part voice leading, cadences, secondary dominants, modulation. Do the workbook exercises and check answers against the included key. By chapter 14 you can write a Roman-numeral analysis of any Common Practice piece. Stop there unless you specifically need post-tonal music.
~$25 used; new editions are $150+ and not worth it
Tonal Harmony →3.Andrew Huang's music theory playlist
The textbook explains tonal Western music. Andrew Huang explains why those rules sound the way they do, and what producers actually use them for. His "Learn music theory in half an hour" video is the single best free overview that exists, and the longer playlist covers modes, voice leading, and chord substitution in pop and electronic music. Watch one video a week as palate cleanser between Tonal Harmony chapters. It will keep you from forgetting why this matters.
Free
Andrew Huang — Production & Music Theory →If you only want to write better songs
Skip Tonal Harmony. After musictheory.net, watch Adam Neely's YouTube channel and read Rikky Rooksby's "How to Write Songs on Guitar" (or "...on Keyboard"). You will not be able to analyze Bach but you will be able to invent a chord progression that is not the same four chords every other song uses. This is the right path for hobbyist songwriters and the wrong path for anyone going to music school.
Why this path
Most theory beginners try to learn from YouTube alone and end up with a scattered vocabulary and no system. Theory is one of the few fields where a textbook still beats every other format — the exercises, the orderly chapters, and the answer key let you self-correct, which YouTube never does. musictheory.net handles the part textbooks are bad at (rote pattern recognition under time pressure). Together they cover what a first-year college course covers, in less time, for $25.