How Chords Are Built

Every chord StrumAndKey documents, across all three instruments and every quality from a plain major triad to a fully extended 13th chord, is built the same way: starting from a root note, stack notes a 3rd apart on top of it. That single rule — stacked 3rds — is the foundation this entire site's chord data is computed from, and understanding it is the fastest way to stop seeing chord names as arbitrary labels to memorize and start seeing them as a predictable, generative system.

A 3rd is the interval spanning three letter names (C to E is a 3rd, skipping D; D to F is a 3rd, skipping E), and it comes in two sizes: a major 3rd (4 semitones) and a minor 3rd (3 semitones). Which size 3rd you stack, and in what order, is what actually determines a chord's quality. Stack a major 3rd on the root, then a minor 3rd on top of that, and you get a major triad (root, major 3rd, perfect 5th — the perfect 5th being the sum of those two stacked 3rds, 7 semitones from the root). Reverse the order — minor 3rd first, then major 3rd — and you get a minor triad instead. The outer interval (root to 5th) is identical in both cases; only the middle note, and therefore which size 3rd comes first, changes.

Diminished and augmented triads extend this same logic to its two remaining possibilities: stack two minor 3rds in a row and you get a diminished triad (a flattened, unstable 5th as the natural result of two small intervals stacked together); stack two major 3rds in a row and you get an augmented triad (a sharpened 5th as the result of two large intervals stacked together). Every one of the four possible triad qualities — major, minor, diminished, augmented — is fully explained by just these two choices (which 3rd comes first, which 3rd comes second), with nothing else needed.

Adding a fourth note continues the exact same stacking process one more 3rd up: a major triad plus a major 3rd on top produces a major 7th chord; a major triad plus a minor 3rd on top produces a dominant 7th chord; a minor triad plus a minor 3rd on top produces a minor 7th chord. This is why 7th chords are so often introduced as "a triad with one more note" rather than as a wholly separate category — structurally, that's exactly what they are, and the same 3rd-stacking rule that built the triad just continues one layer further.

Extended chords (9ths, 11ths, 13ths) keep stacking past the 7th using the identical logic, each new note landing a 3rd above the previous one. Because these notes eventually exceed a single octave's worth of range, they're renamed relative to the octave they land in — a 9th is really the 2nd scale degree an octave higher, an 11th is really the 4th degree an octave higher, and a 13th is really the 6th degree an octave higher — but the underlying construction process (keep stacking 3rds) never changes. Chord Extensions covers what happens once these stacks get long enough that real players start omitting notes for practical voicing reasons.

Two chord families deliberately break this stacked-3rds pattern, and it's worth naming them here rather than treating them as unexplained exceptions. Suspended chords replace the 3rd — the very interval this whole system is built from — with a 2nd or 4th instead, which is exactly why they carry neither major nor minor quality (Suspended Chords Explained covers this in full). Power chords go further and remove the 3rd from a triad entirely, leaving just a root and a 5th with no 3rd-based quality at all (Power Chords Explained). Both are best understood not as violations of the stacked-3rds rule but as deliberate, specific departures from it, chosen for a specific sonic reason.

Once this system clicks, the rest of StrumAndKey's chord vocabulary stops looking like hundreds of unrelated shapes to memorize and starts looking like one small rule (stack 3rds, choose major or minor at each step) applied consistently across 12 roots and 21 qualities. Major Scale Formula is the natural next stop — it explains where those major and minor 3rds actually come from in the first place, by building outward from a scale rather than a chord.

It's worth being explicit about why "3rds" specifically, and not some other interval, is the building block of Western tonal harmony. A stacked 3rd produces the widest spacing between adjacent chord tones that's still achievable without skipping over any letter names in the musical alphabet — C, E, G each occupy every other letter, C-D-E-F-G, which spreads the three notes of a triad out enough to sound genuinely full and resonant rather than clustered. Stack a 2nd instead (C, D, E) and the notes sit so close together that the result reads as a tone cluster rather than a chord in the traditional sense; stack a 4th instead (C, F, Bb) and you get a real, distinct harmonic system called quartal harmony, used deliberately in some jazz and 20th-century classical writing, but a genuinely different sound from the triadic system this whole site's chord vocabulary is built on.

The interval math behind each individual chord quality is worth stating explicitly rather than left implicit, since it's the actual computation StrumAndKey's chord pages are generated from. A major triad: root, +4 semitones (major 3rd), +7 semitones (perfect 5th). A minor triad: root, +3, +7. A diminished triad: root, +3, +6. An augmented triad: root, +4, +8. Extending each of these by one more 3rd (major = +4, minor = +3) produces every 7th-chord quality: major 7th is a major triad plus another major 3rd (+11 total); dominant 7th is a major triad plus a minor 3rd on top (+10 total); minor 7th is a minor triad plus a minor 3rd on top (+10 total, landing on the identical semitone count as dominant 7th's 7th, just built from a different triad underneath); half-diminished (m7b5) is a diminished triad plus a minor 3rd on top (+10); fully diminished 7th is a diminished triad plus one more minor 3rd (+9, the diminished 7th interval, enharmonically a major 6th).

This stacked-3rd logic also explains something that trips up a lot of players moving from triads to 7th chords for the first time: why dominant 7th gets the "plain" 7 symbol (just "C7") while major 7th needs the extra "maj" (Cmaj7). Historically, dominant 7th chords (built from a major triad plus a minor 3rd) entered common harmonic practice earlier and more centrally than major 7th chords did, largely because of the dominant 7th's strong pull toward resolution (covered in Chord Progressions and Chord Function) — an asymmetry in how tonal harmony actually developed, not an arbitrary naming choice, and StrumAndKey's chord symbols throughout the site follow that same long-standing convention.

Every one of the 21 chord qualities in StrumAndKey's guitar roster (and the narrower piano and ukulele subsets) reduces to exactly this same stacked-3rds process, just carried out to different lengths and with different choices of major/minor 3rd at each step. Learning the system once, rather than memorizing 21 unrelated quality names, is genuinely the more efficient path — and it's the reason src/lib/theory's chord-computation engine can generate every chord on this site from just two small tables (the 12 chromatic notes, and each quality's list of semitone offsets) rather than needing 576 individually hand-entered note lists.

The practical payoff of understanding stacked 3rds shows up the moment a player encounters an unfamiliar chord symbol on a chart. A symbol like "Fm7b5" stops being a shape to look up and becomes a shape to derive: start on F, stack a minor 3rd (Ab), stack another minor 3rd on top of that (Cb, enharmonically B), stack a minor 3rd on top of that (Ebb, enharmonically D) — a diminished triad (F-Ab-Cb) plus a minor 7th on top, exactly matching the half-diminished formula above. That derivation takes seconds once the underlying system is internalized, and it works identically for any root and any of this site's 21 documented qualities, which is the real, durable skill this topic exists to build.

Teachers introducing this system to beginners often find it lands better demonstrated at an instrument than described on paper — play a plain C major triad, then slide the middle note down a fret or a key to hear it become C minor, then flatten the top note as well to hear the diminished triad emerge. Feeling those single-note changes happen under the fingers, rather than only reading the semitone counts, is frequently what makes the stacked-3rds system click as an intuitive, physical fact about the instrument rather than an abstract rule to recall from memory — a genuinely more durable kind of understanding than memorized interval numbers alone, and one worth returning to any time a new chord quality feels unfamiliar rather than starting the memorization process over from scratch each time.