How to Build Piano Chords: Triads, Inversions, Seventh Chords and Chord Symbols

Nearly every chord symbol on a lead sheet, from a plain C to Cø7, describes a stack of 3rds. Learn to measure a 3rd in half steps and you can build any of those chords on any root, spell it with the right letter names, invert it and read its symbol, instead of hunting for a hand shape you once memorized.

This lesson goes in teaching order: triads, the chords of a key, inversions, chord symbols, seventh chords, suspended chords and voicings, then a 10-minute daily routine. Every musical example comes from our free worksheets (the place to start is Triads & their inversions), and many of those sheets have audio.

A triad is two 3rds

A chord is a group of notes sounded together, and the basic one is the triad: three notes stacked in 3rds. In this stacked form the lowest note is the root, the note the chord is named after; above it come the 3rd and the 5th. Stack every other letter and the notes sit line-line-line or space-space-space on the staff. On C, that gives C–E–G.

In chords, 3rds come in two sizes, and the size decides everything. A half step is one move to the very next key, black or white, so count the keys you land on, not the one you start from: C up to E is 4 half steps (C♯, D, D♯, E), a major 3rd; E up to G is 3 (F, F♯, G), a minor 3rd. Major & minor 2nds and 3rds lets you hear both, and our Intervals chart lists every interval up to the octave with its half steps.

That gives you two ways to build a triad on any root. Count up from the root: 4 half steps, then 3 more, makes a major triad. Or stack every other letter name (from a white key, every other white key) and then fix the 3rds. From D, the white keys give D–F–A, but D up to F is only 3 half steps, so that is D minor. For D major, raise F to F♯.

C major and C minor on the keys. Start on one chord tone and count each key you land on, black or white, up to the next one: C major is 4 + 3 half steps, and in C minor the 3rd drops to E♭ (coral), so the counts become 3 + 4.

Four triads, four recipes

Change the sizes of the two 3rds and you get the four triad qualities: major (4 + 3), minor (3 + 4), diminished (3 + 3) and augmented (4 + 4). On C, minor lowers the 3rd to E♭, diminished lowers the 5th to G♭ as well, and augmented raises the 5th to G♯. It is the only quality that raises a note.

The four triads on C, copied from our Augmented triad sheet. Each flat or sharp marks a note that moved away from C major.

They sound as different as they look. Minor is darker than major. Diminished is restless, because its outer notes are 6 half steps apart, the interval called the tritone (The diminished triad). Augmented floats, because its three notes split the octave into three equal parts of 4 half steps (The augmented triad).

The recipes work from any root, but the accidentals change. On D, the major triad needs F♯, the minor triad uses only white keys, diminished needs A♭ and augmented needs F♯ and A♯.

The same four recipes on D. Here the minor triad is the all-white one; the notes that moved away from D major are F, A♭ and A♯.

Spell by letters first, then fix the half steps. Spelled up from the root, a triad's letters always skip one letter, so the 3rd of C minor is E♭, never D♯, and the top of C augmented is G♯, not A♭. They are the same keys, but only E♭ and G♯ make the chord look like stacked 3rds. Our Build the chords exercise gives you twelve roots to build on, and Chord quality review mixes twenty chords to name.

The chords of a key

Build a triad on every note of the C major scale, using only notes of the scale (white keys, in C), and you get the seven chords of the key: C, Dm, Em, F, G, Am and B°. Each takes a Roman numeral for the scale step it stands on: capital for major (I, IV, V), lowercase for minor (ii, iii, vi) and lowercase with a small circle for diminished (vii°). The chords of a key builds them in C, G, F and D major, with audio.

The seven chords of C major, from our Chords of a key sheet, with the numeral of each step below. The numerals carry the quality: three major, three minor, one diminished.

The pattern is the same in every major key: major, minor, minor, major, major, minor, diminished, because every major scale puts its two half steps in the same places. In G major the chords are G, Am, Bm, C, D, Em and F♯°. Name the chords of the key gives you 32 chords to name and build in four keys.

The three major chords, I, IV and V, are the primary chords: C, F and G in C major. The primary chords: I, IV & V calls their loop home, gentle away, tense away and home again, and The Primary Chords in Every Key gives the trio in all 24 keys, with audio.

Minor keys follow a pattern of their own. The natural minor scale gives i, ii°, III, iv, v, VI and VII, but music in minor usually raises the 7th degree, as the harmonic minor scale does, and that makes V major. In C minor, i is C–E♭–G, iv is F–A♭–C and V is G–B–D, with a B natural (The primary chords in minor).

I–IV–V–I in C major and i–iv–V–i in C minor, from our Primary Chords in Every Key sheets. Of the three, only V is major in C minor, thanks to the B natural.

Inversions: the same chord, a new bass note

Any note of a triad can go on the bottom, and the bass note, not the order of the notes above it, names the position. Root position puts the root in the bass (C–E–G), first inversion the 3rd (E–G–C) and second inversion the 5th (G–C–E). In figured bass they are 5/3, 6/3 (usually written just 6) and 6/4, after the intervals above the bass.

C in three positions, from our Triads & their inversions sheet. The notes are always C, E and G; the one in the bass names the position.

To name an inverted triad, look for the gap. Packed as tightly as possible, a root-position triad is a stack of 3rds only, line-line-line or space-space-space, while an inversion has one wider gap, a 4th, and the top note of that 4th is the root. (The augmented triad is the exception: its notes split the octave evenly, so every position looks the same on the keys and only the spelling shows the root.) Identify the triads & inversions drills this with C, F and G in all three positions, and The 6/4 chord shows three jobs that second inversions do in real music.

Inversions matter most under your hand. Play C–F–G–C in root position and the whole hand moves for every chord. Keep the shared note C where it is and the other notes close by instead: F becomes C–F–A, G tucks in underneath as B–D–G, and the hand barely moves.

C–F–G–C in root position and in the nearest shapes, from our Primary Chords in C Major sheet: F appears in second inversion, G in first.

The idea that C–E–G, E–G–C and G–C–E are one chord is old. Writers described the invertible triad in the early 1600s, but the full recognition of a chord and its inversions as one harmony is often credited to Jean-Philippe Rameau's Traité de l'harmonie (Treatise on Harmony), published in Paris in 1722.

The title page of Rameau's Traité de l'harmonie (Paris, 1722), whose second book deals with the nature and properties of chords. Image: public domain, University of Toronto copy via the Internet Archive.

Reading chord symbols

A chord symbol reads left to right: the root letter, then a suffix that changes the chord. Our Chord symbols chart is the reference for every spelling here, all built on C:

• C: a letter alone means a major triad, C–E–G.
• Cm (also Cmin or C−): minor, C–E♭–G.
• C° (also Cdim): diminished, C–E♭–G♭.
• C+ (also Caug): augmented, C–E–G♯.
• C7: a major triad plus a minor 7th, C–E–G–B♭. A 7 on its own means the minor 7th.
• Cmaj7 (also CM7 or CΔ7): a major triad plus a major 7th, C–E–G–B.
• Cm7, Cø7 (also Cm7♭5) and C°7 (also Cdim7): the other seventh chords, below.
• Csus2 and Csus4 (also Csus): the 3rd replaced by a 2nd or a 4th.
• C/E: a slash names the bass note, so this is the C chord with E at the bottom, its first inversion. C/G is the second inversion.

One trap: the m belongs to the triad. In Cm7 the m makes the 3rd minor, and the 7 is still the usual minor 7th. Try one away from C: B♭m7 is the root B♭, a minor triad B♭–D♭–F (3 + 4) and a minor 7th, A♭, a whole step below the root's octave. Reading a lead sheet explains seven symbols, then puts chord symbols to work in a real tune, with audio.

Three questions for any chord symbol: what is the root, what does the suffix change, and is there a slash?

Seventh chords: one more 3rd on top

Stack one more 3rd on a triad and you get a seventh chord: root, 3rd, 5th and 7th, with the letters still skipping (D, F, A, C). There are five common qualities, each a triad plus a 7th:

• maj7: major triad + major 7th, 4 + 3 + 4 half steps.
• 7, the dominant 7th: major triad + minor 7th, 4 + 3 + 3.
• m7: minor triad + minor 7th, 3 + 4 + 3.
• ø7, the half-diminished 7th: diminished triad + minor 7th, 3 + 3 + 4.
• °7, the diminished 7th: diminished triad + diminished 7th, 3 + 3 + 3.

To find the 7th fast, measure down from the root's octave: a major 7th is a half step below it, a minor 7th a whole step below and a diminished 7th a step and a half below.

The five seventh chords on D, from our Minor 7th sheet. Start at Dmaj7 and lower one note a half step at a time: C♯ to C, F♯ to F, A to A♭, then C to C♭. The step from Dm7 to Dø7 lowers the 5th, which is why ø7 is also written m7♭5.

Keeping the letters in 3rds sometimes takes a double flat, which lowers a note two half steps: C°7 is spelled C, E♭, G♭ and B double flat, which you play on the A key, as our Chord symbols chart shows. In the same way, B augmented is B, D♯ and F double sharp, the G key.

In a major key the seventh chords fall into a fixed pattern too: Imaj7, ii7, iii7, IVmaj7, V7, vi7 and viiø7. So every major key has exactly one dominant 7th, built on V: G–B–D–F in C major. Its 3rd and 7th, B and F, are a tritone apart, and both lean. B rises a half step to C and F falls a half step to E, which is why G7 sounds so ready to go home.

G7 to C, and the bare tritone B–F resolving to C–E. The leading tone B rises to C and F falls to E; G holds and D drops out.

Each quality has its own sheet: The major 7th, The minor 7th and The dominant 7th, all with audio, plus The half-diminished 7th and The diminished 7th. Those last two differ by one note: B–D–F–A is Bø7, and lowering the A to A♭ gives B°7. Bø7 is the chord on the 2nd degree of A minor, where it leads to E7 and home to Am: iiø7–V7–i. A diminished 7th has 3 half steps between every pair of neighbors, and its top note is 3 half steps below the root's octave too, so every inversion has the same shape and only three different sets of keys make a diminished 7th.

To practice, name twenty chords in Name the seventh chords, then find the four positions of G7, C7 and D7 in Identify the dominant 7ths & inversions.

Suspended chords: the 3rd replaced

A suspended chord takes the 3rd out and puts a 2nd or a 4th in its place: Csus2 is C–D–G and Csus4 is C–F–G. With no 3rd the chord is neither major nor minor, so Csus4 fits C major and C minor alike. The 4th wants to fall to the 3rd, as Csus4 does when F slips down a half step to E, while a sus2 may rise to the 3rd or simply stay as a color (Suspended chords, with audio). The same sheet has a pop shuffle on D: keep D and A still and let one finger move from F♯ up to G (Dsus4), back to F♯, down to E (Dsus2) and back.

C, Csus2, Csus4 and Csus4 resolving to C, from our Suspended chords sheet. The 3rd, E, gives way to D in Csus2 and to F in Csus4.

Voicing chords at the piano

Building a chord is theory; voicing it is deciding which notes go where. Every chord can arrive blocked, all its notes at once, or broken, one note at a time in any order (Block & Broken Chords). The arpeggio breaks it in order: root, 3rd, 5th and the root an octave up, then back down. In C the right hand plays it with fingers 1-2-3-5 and the left hand with 5-4-2-1 (Arpeggios in Every Key).

Two hands on an upright piano. Photo: Brian Richardson, CC BY 2.0, via Flickr.

A lead sheet gives you a melody with chord symbols over it and leaves the left hand to you. A symbol lasts until the next one. Our lead-sheet worksheets build the left hand in three steps: just the root of each symbol; then a shell, root plus 5th (root plus 7th on a 7 chord); then the chord tones in the closest shapes (a 7 chord can leave out its 5th), so each change moves your fingers as little as possible.

Bars 1–4 of "Amazing Grace" (tune NEW BRITAIN, public domain), realized as in step 3 of our Reading a lead sheet worksheet. Under G7 the left hand plays B–F–G: the 3rd, 7th and root, with no 5th.

Then try it yourself on Realize a lead sheet, which gives you twelve bars of melody to fill in with roots, shells and close chords.

For seventh chords, jazz and pop pianists often use a different shell: the root plus just one color note, the 3rd or the 7th. In maj7, 7 and m7, those two notes decide what kind of chord it is, while the 5th, a perfect 5th in all three, adds no color, though a ø7 needs its lowered 5th (Shell Voicings). In a ii–V–I, alternate the two kinds and the top note holds or slips down a half step while the root jumps.

ii–V–I in C in shells, from our Shell Voicings sheet, each labeled R+3 (root and 3rd) or R+7 (root and 7th). In the first pattern the top notes run F–F–E, in the second C–B–B.

Once these shapes sit under your hands, the next step is putting chords in order, which our guide to common chord progressions in popular music genres picks up.

A 10-minute daily chord routine

Take one root a day and work around the circle of fifths in the order our key-by-key sheets use: C, G, D, A, E, B, G♭, D♭, A♭, E♭, B♭ and F. If you already follow Your Daily Technique Routine, take its key of the week as your root. Give each step two minutes:

1. Four triads: major, minor, diminished and augmented on today's root, saying the half steps out loud.
2. Inversions: the major triad in root position, first and second inversion, each hand, as on Triads & their inversions.
3. The chords of the key: the seven triads of today's major key, up and down, naming each; then I–IV–V–I in the nearest shapes, from The Primary Chords in Every Key.
4. Five sevenths: maj7, 7, m7, ø7 and °7 on today's root, lowering one note at a time, like the ladder on The minor 7th (on some roots the °7 needs a double flat, like the B double flat of C°7).
5. One lead-sheet line: four bars of a tune you know, with roots, then shells, then close chords (Reading a lead sheet).

The routine at a glance: five steps, two minutes each.

Once a week, check yourself on paper with Build the chords or Name the seventh chords; both print their answers upside down at the bottom of the page.

Free worksheets for this lesson

• Triads & their inversions — the triad and its three positions, with audio.
• Major & minor 2nds and 3rds — wide and narrow 2nds and 3rds in half steps, with audio.
• Intervals — every interval to the octave, with half steps.
• The diminished triad — two minor 3rds and the tritone, with audio.
• The augmented triad — two major 3rds; only four exist, with audio.
• Build the chords — twelve triads and sevenths to build.
• Chord quality review — twenty triads and sus chords to name.
• Identify the triads & inversions — C, F and G in every position.
• The 6/4 chord: three jobs — second inversions at work, with audio.
• The chords of a key — seven chords in four major keys, with audio.
• Name the chords of the key — numerals to write and chords to build.
• The primary chords: I, IV & V — the three-chord loop, with audio.
• The Primary Chords in Every Key — the three primary chords in all 24 keys, with audio.
• The primary chords in minor: i, iv & V — why V stays major.
• The major 7th — Cmaj7 and its four positions, with audio.
• The minor 7th — ii7, iii7, vi7 and the ladder on D, with audio.
• The dominant 7th — V7 and its tritone, with audio.
• The half-diminished 7th — Bø7, also written Bm7♭5.
• The diminished 7th — three minor 3rds, three chords.
• Name the seventh chords — twenty sevenths to identify.
• Identify the dominant 7ths & inversions — G7, C7 and D7 in four positions.
• Suspended chords: sus2 and sus4 — the 3rd swapped out, with audio.
• Chord symbols — every common symbol on C, plus five chords in all 12 keys.
• Reading a lead sheet — "Amazing Grace" in three steps, with audio.
• Realize a lead sheet — write the left hand yourself.
• Shell Voicings — root plus 3rd or 7th through the ii–V–I.
• Block & Broken Chords — one chord, two ways to deliver it.
• Arpeggios in Every Key — root position and both inversions, with audio.
• Your Daily Technique Routine — one key a week, with a log.

One root a day

Nearly every chord in this lesson comes from one move: stack 3rds, measure them in half steps and spell them with every other letter. Build the four triads, the chords of the key and the five sevenths on one new root a day, and in twelve days you will have played them on all twelve roots.

If you want someone to listen to your inversions and left-hand voicings, a Tissimo piano teacher can check them in a live lesson and help you choose the next tune to realize.

Sources

• Chord (music) — Wikipedia
• Triad (music) — Wikipedia
• Inversion (music) — Wikipedia
• Root (chord) — Wikipedia
• Traité de l'harmonie réduite à ses principes naturels — Wikipedia
• Traité de l'harmonie (Rameau, Paris 1722), University of Toronto copy — Internet Archive
• Chord notation — Wikipedia
• Seventh chord — Wikipedia
• Suspended chord — Wikipedia