Getting Started
So far, you have likely worked with chords built directly on a root, with the root always as the lowest-sounding note. However, music gains significant fluidity and interest by altering which chord member is in the bass. This chapter introduces chord inversions and the historical shorthand system used to notate them, figured bass, which will unlock more sophisticated methods of musical analysis and composition.
What You Should Be Able to Do
After completing this chapter, you will be able to:
Identify the root, quality, and inversion of a chord from both performed and notated music.
Use Roman numerals with appropriate figures to represent the harmony and bass position of chords.
Interpret the Arabic numerals of a figured bass line to identify the intended harmony.
Complete a four-part texture by adding upper voices to a given figured bass line.
Provide a complete Roman numeral analysis for a harmonic progression derived from a figured bass.
Key Concepts & Analysis
This section explores how chords can be inverted and how musicians have historically used a system called figured bass to communicate harmonic structure. We will approach this through the lens of Functional Harmony, where each chord serves a purpose (Tonic, Predominant, Dominant) within a key, and inversions help create smooth and logical connections between these functions.
What is a Chord Inversion?
An inversion describes a chord where a member other than the root is in the lowest-sounding voice, or bass. The identity and quality of the chord remain the same, but its stability and melodic connection to other chords change.
Root Position: The most stable chord formation, where the root of the chord is the lowest note. For a C major triad (C-E-G), C is in the bass.
First Inversion: A less stable formation where the third of the chord is in the bass. This inversion is often used to create a smoother, more melodic bass line. For a C major triad, E is in the bass.
Second Inversion: The least stable formation, where the fifth of the chord is in the bass. This inversion is used in very specific, conventional ways (e.g., at cadences or as part of a passing motion). For a C major triad, G is in the bass.
Introducing Figured Bass
Figured Bass is a notational shorthand, developed in the Baroque era, that uses numbers (figures) below a bass line to indicate the harmonies to be played above it. It provides a blueprint for constructing a full harmonic texture.
The figures represent the generic intervals that should be played above the written bass note. These intervals, combined with the bass note, reveal the full chord.
Root Position Triads: The intervals above the root are a 3rd and a 5th. The full figure is
5/3. By convention, this is considered the default and is usually omitted. A bass note with no figure implies a root position triad.First Inversion Triads: The intervals above the chordal third are a 3rd and a 6th. The full figure is
6/3. This is abbreviated to just6. A6below a bass note indicates a first-inversion triad.Second Inversion Triads: The intervals above the chordal fifth are a 4th and a 6th. The figure is
6/4. This figure is never abbreviated.
Accidentals next to a figure (e.g., ♯, ♭, ♮) apply to that specific interval above the bass. An accidental by itself applies to the third above the bass.
From Figures to Roman Numerals
Analyzing a figured bass line involves a two-step process to determine the correct Roman numeral.
Identify the Chord: Use the bass note and the figures to spell the complete chord and identify its root. For example, in the key of G major, a bass note D with a
6figure means the notes above D are a third (F♯) and a sixth (B). The collection of notes is D-F♯-B. Unstacking these notes reveals the root is B, and the chord is a B minor triad.Determine the Roman Numeral: Find the scale degree of the chord's root and determine its quality (major, minor, etc.). In our example, the root B is scale degree ^3 in G major. The diatonic chord on ^3 is minor. Therefore, the Roman numeral is iii. Since it is in first inversion (as indicated by the
6), the complete analysis is iii6.
Realizing a Figured Bass
Realization is the process of taking a figured bass line and composing the upper voices (typically soprano, alto, and tenor) to create a complete four-part texture. This skill transforms the harmonic blueprint of the figures into a full musical passage. A successful realization follows the principles of good voice leading and respects the underlying harmonic progression implied by the Roman numerals.
Data & Organization Tools
The table below shows the diatonic triads for major and minor keys, along with their typical harmonic functions. Understanding these functions is essential for both analyzing and realizing figured bass, as it provides the logic for why chords progress in a certain order.
| Key | Scale Degree | Roman Numeral | Function |
|---|---|---|---|
| Major | ^1, ^4, ^5 | I, IV, V | Tonic, Predominant, Dominant |
| ^2, ^3, ^6 | ii, iii, vi | Predominant, Tonic, Tonic | |
| ^7 | vii° | Dominant | |
| Minor | ^1, ^4, ^5 | i, iv, V | Tonic, Predominant, Dominant |
| ^2, ^3, ^6 | ii°, III, VI | Predominant, Tonic, Tonic | |
| ^7 | vii° | Dominant |
Note: In minor keys, the leading tone (^7) is often raised, resulting in a major V and diminished vii° chord, which strengthen the dominant function.
Evidence Bank
Root Position: The chordal arrangement where the root is in the bass. Indicated by the absence of a figure or, more formally,
5/3.First Inversion: The chordal arrangement where the third is in the bass. Indicated by the figure
6. Used to create smooth bass lines and connect chords.Second Inversion: The chordal arrangement where the fifth is in the bass. Indicated by the figure
6/4. A highly unstable inversion used in specific contexts.Figured Bass: A notational system using Arabic numerals below a bass line to specify the intervals, and thus the harmony, to be played above.
Figures: The Arabic numerals themselves, which denote the generic intervals above the bass note.
Realization: The act of completing a four-part texture by adding upper voices (soprano, alto, tenor) to a given figured bass line.
Harmonic Progression: A sequence of chords that underlies a piece of music. Figured bass implies a specific harmonic progression.
Bass Note vs. Chord Root: A critical distinction. The bass note is the lowest sounding pitch, while the root is the note upon which the chord is built in its root position. In inversions, these are not the same.
Skill Snapshots
Inversions are not used randomly; they serve functional purposes within a harmonic progression.
Smoother Bass Motion: The progression I – V6 – I in C major creates a bass line of C–B–C (^1–^7–^1). This stepwise motion is much smoother than the leap of C–G–C (^1–^5–^1) that would occur if the V chord were in root position. The function remains Dominant to Tonic.
Connecting Functions: The progression I – ii6 – V – I in F major uses a first-inversion predominant chord. The bass line F–G–C–F (^1–^2–^5–^1) moves smoothly by step from the tonic function (I) to the predominant (ii6) before leaping to the dominant (V).
Prolonging Harmony: The progression i – V6/5 – i in a minor shows how an inverted seventh chord can connect two tonic chords. The bass line A–B–A (^1–^2–^1) creates melodic interest while still fulfilling the essential T–D–T function.
Common Misconceptions & Clarifications
Confusing the Bass Note with the Root: The most common error. Always remember to stack the notes implied by the figures into a root-position triad to find the true root before assigning a Roman numeral.
Figures are Not Specific Notes: The figure
6does not mean "add a G" or "add the 6th scale degree." It means "add the note that is a generic sixth above the written bass note."Quality is Determined by the Root: The quality of the Roman numeral (major, minor, diminished) is based on the triad built on the identified root, not on the quality of the intervals above the bass note.
Inversions Don't Change Function: A V6 chord still has a dominant function, just like a root-position V. Inversions modify the strength and stability of a chord, but not its core harmonic job.
Summary
Chord inversions are a fundamental resource for creating varied and musically compelling compositions. By placing the third or fifth of a chord in the bass, we can create more melodic bass lines and control the relative stability of a harmonic progression. Figured bass provides a precise system for notating these inversions, serving as a blueprint for harmony. The process of interpreting these figures to identify chords, assigning Roman numerals to analyze their function, and realizing them into a full texture are core skills in the study of tonal music. Mastering these concepts allows for a deeper understanding of how music is constructed.