4/9 4. Chords and Chord Construction

Chord structure and identity

A chord is a group of at least three different pitch classes sounding together. The two central chord types in this topic are the triad and the seventh chord.

A chord has three features:

• The root is the note on which the chord is built.

• The chord quality describes the intervals above the root.

• The bass note is the lowest-sounding chord member and determines the inversion.

For example, the notes $C\text{–}E\text{–}G$ form a C-major triad. C is the root, E is the third, G is the fifth, and C is also the bass because the chord is in root position.

Takeaway

Identify the root and quality to determine the chord’s identity; then inspect the bass note to determine its position.

Triad qualities and construction

A triad contains a root, third, and fifth. Its quality is determined by the intervals above the root:

• Major: $1\text{–}3\text{–}5$, with a major third and perfect fifth. Example: $C\text{–}E\text{–}G$.

• Minor: $1\text{–}\flat3\text{–}5$, with a minor third and perfect fifth. Example: $C\text{–}E\flat\text{–}G$.

• Diminished: $1\text{–}\flat3\text{–}\flat5$, with a minor third and diminished fifth. Example: $C\text{–}E\flat\text{–}G\flat$.

• Augmented: $1\text{–}3\text{–}\sharp5$, with a major third and augmented fifth. Example: $C\text{–}E\text{–}G\sharp$.

To construct a triad, write the root, add the appropriate third, and then add the appropriate fifth. Preserve the correct letter-name spelling. For example, F-sharp minor is $F\sharp\text{–}A\text{–}C\sharp$, while E diminished is $E\text{–}G\text{–}B\flat$.

The spelling of E diminished must use some form of E, G, and B. Therefore, $E\text{–}G\text{–}B\flat$ is the correct spelling rather than $E\text{–}G\text{–}A\sharp$, even if the final pitches can sound enharmonically equivalent.

Common triad symbols

• A major triad usually uses only the root letter, such as $C$.

• A minor triad uses $m$ or $min$, such as $Cm$.

• A diminished triad uses $dim$ or $\circ$, such as $Cdim$ or $C\circ$.

• An augmented triad uses $aug$ or $+$, such as $Caug$ or $C+$.

Takeaway

Construct every triad from the root, third, and fifth, and use interval quality and correct letter spelling to distinguish the four types.

Triad inversions and slash notation

An inversion occurs when a chord member other than the root is in the bass. Inversion changes the lowest note but does not change the chord’s root or quality.

For a C-major triad:

• Root position: $C\text{–}E\text{–}G$, with C in the bass; figured-bass symbol $5/3$, usually abbreviated to nothing.

• First inversion: $E\text{–}G\text{–}C$, with E in the bass; figured-bass symbol $6/3$, usually abbreviated to $6$.

• Second inversion: $G\text{–}C\text{–}E$, with G in the bass; figured-bass symbol $6/4$.

In lead-sheet notation, the chord name comes first and the bass note follows the slash:

• $C$ means a C-major triad with C in the bass.

• $C/E$ means a C-major triad with E in the bass, or first inversion.

• $C/G$ means a C-major triad with G in the bass, or second inversion.

Thus, $E\text{–}G\text{–}C$ is still a C-major chord even though E is the lowest note. It can be labeled $C/E$ or, in C major, $I^{6}$.

Takeaway

Do not identify a chord solely from its lowest note. Find the root first, then use the bass note to label the inversion.

Seventh-chord qualities and symbols

A seventh chord adds a seventh above the root to a triad. Its members are root, third, fifth, and seventh. The most common qualities are:

• Major seventh: $1\text{–}3\text{–}5\text{–}7$. Example: $C\text{–}E\text{–}G\text{–}B$, written $Cmaj7$.

• Dominant seventh: $1\text{–}3\text{–}5\text{–}\flat7$. Example: $C\text{–}E\text{–}G\text{–}B\flat$, written $C7$.

• Minor seventh: $1\text{–}\flat3\text{–}5\text{–}\flat7$. Example: $C\text{–}E\flat\text{–}G\text{–}B\flat$, written $Cm7$.

• Half-diminished seventh: $1\text{–}\flat3\text{–}\flat5\text{–}\flat7$. Example: $C\text{–}E\flat\text{–}G\flat\text{–}B\flat$, written $C\ø7$ or $Cm7\flat5$.

• Fully diminished seventh: $1\text{–}\flat3\text{–}\flat5\text{–}\flat\flat7$. Example: $C\text{–}E\flat\text{–}G\flat\text{–}B\doubleflat$, written $C\circ7$ or $Cdim7$.

The distinction between $Cmaj7$ and $C7$ is important: $Cmaj7$ contains B, while $C7$ contains B-flat. A plain $7$ after a root letter normally means a dominant seventh, not a major seventh.

Takeaway

Identify the underlying triad first, then determine whether the seventh above the root is major, minor, or diminished.

Seventh-chord inversions

Seventh chords have four positions because each of their four members can be in the bass. Using G7, whose notes are $G\text{–}B\text{–}D\text{–}F$, the positions are:

• Root position: G in the bass, written $G7$; figured-bass symbol $7$.

• First inversion: B in the bass, written $G7/B$; figured-bass symbol $6/5$.

• Second inversion: D in the bass, written $G7/D$; figured-bass symbol $4/3$.

• Third inversion: F in the bass, written $G7/F$; figured-bass symbol $4/2$, often abbreviated to $2$.

These figures describe the intervals above the bass note. The figures $6/5$, $4/3$, and $4/2$ are strongly associated with inverted seventh chords, so the separate $7$ is normally omitted in these forms.

Takeaway

For a seventh chord, the bass member determines whether the chord is in root position, first inversion, second inversion, or third inversion.

Roman numerals and harmonic analysis

Roman-numeral analysis identifies a chord by the scale degree of its root in a key. The case and added symbols communicate quality:

• Uppercase numerals indicate major chords.

• Lowercase numerals indicate minor chords.

• A lowercase numeral with $\circ$ indicates a diminished chord.

• The symbol $+$ indicates an augmented chord.

In C major, the diatonic triads are:

• $I$: $C\text{–}E\text{–}G$, major.

• $ii$: $D\text{–}F\text{–}A$, minor.

• $iii$: $E\text{–}G\text{–}B$, minor.

• $IV$: $F\text{–}A\text{–}C$, major.

• $V$: $G\text{–}B\text{–}D$, major.

• $vi$: $A\text{–}C\text{–}E$, minor.

• $vii\circ$: $B\text{–}D\text{–}F$, diminished.

For seventh chords in C major, $C\text{–}E\text{–}G\text{–}B$ is $Imaj7$, $D\text{–}F\text{–}A\text{–}C$ is $ii7$, $G\text{–}B\text{–}D\text{–}F$ is $V7$, and $B\text{–}D\text{–}F\text{–}A$ is $vii\ø7$.

The inversion figure follows the Roman numeral. For example, G7 with B in the bass is $V^{6}_{5}$, while G7 with D in the bass is $V^{4}_{3}$.

A reliable analysis procedure

1. Collect the sounding notes.

2. Rearrange them mentally into stacked thirds to find the root.

3. Identify the chord quality.

4. Find the root’s scale degree in the stated key.

5. Identify the bass note and add the appropriate inversion figure.

For the notes $B\text{–}D\text{–}F\text{–}G$ in C major, rearrange them as $G\text{–}B\text{–}D\text{–}F$. This is G7, whose root is scale degree five, and B is its third in the bass. The result is $V^{6}_{5}$.

Takeaway

Roman numerals combine root, quality, key, and inversion into one compact label.

A practical identification workflow

Several mistakes can be avoided by separating chord identity from voicing.

• Confusing root and bass: In $E\text{–}G\text{–}C$, E is the bass but C is the root. The chord is C major in first inversion, written $C/E$ or $I^{6}$ in C major.

• Confusing dominant and major seventh: $C7$ is $C\text{–}E\text{–}G\text{–}B\flat$, whereas $Cmaj7$ is $C\text{–}E\text{–}G\text{–}B$.

• Ignoring spelling: A diminished triad must show the correct letter sequence for root, third, and fifth. B diminished is $B\text{–}D\text{–}F$, not $B\text{–}D\text{–}E\sharp$.

• Misreading a slash: In $F/A$, the slash is not a division sign. It means an F chord with A in the bass.

A concise identification workflow is:

1. Rearrange the notes into stacked thirds.

2. Name the root.

3. Compare the third, fifth, and, when present, seventh with the root.

4. Determine the bass note.

5. Write the chord symbol, figured-bass symbol, or Roman-numeral analysis required by the context.

• slash chord