Triads and Inversions: Root Position, Sixth, Six-Four

Three notes can sit in any vertical order, yet harmony treats the arrangements differently. Triads and inversions are the study of which chord member stands in the bass and why that choice changes the weight, the direction, and the manners of the harmony above it.

#Root position and its two inversions

A C major triad contains C, E, and G. Put C in the bass and the chord is in root position, stable and declarative. Put E in the bass and it is in first inversion, lighter and more mobile. Put G in the bass and it is in second inversion, the least stable of the three, which needs careful handling.

All three sonorities above contain the same pitch classes. The bass decides the name: C means root position, E means first inversion, G means second inversion. Upper-voice order, spacing, and doubling change the color but never the inversion.

Hear them as bass steps under a held upper structure. The harmony stays C major while the foundation moves.

That block repeats one voicing for reference. Real inversion practice moves the bass while the upper voices adjust by step, which the next section demonstrates with the standard voice-leading patterns from four-part voice leading.

#First inversion: the working inversion

First-inversion triads do most of the connective labor in tonal music. They appear between root-position chords to fill bass gaps, under passing melodic tones, and at phrase openings where full root-position weight would sound too final too soon.

The voice leading into first inversion follows small habits. Double the root or the fifth rather than the bass note, since the bass already carries the chord third and doubling it thickens the color unevenly. Approach the inverted bass by step where possible; the smoothness is the reason for choosing the inversion.

Parallel first-inversion triads moving together, called fauxbourdon when the pattern extends through a whole passage, create a gliding texture composers use for sequences and transitions. Fauré and Debussy stretched the device into whole paragraphs, letting the parallel sixths wash away the sense of root motion entirely.

One caution: a first-inversion tonic at a final cadence weakens the close. The bass sits on the third instead of driving 5 to 1, so the arrival sounds provisional. Student exercises often end phrases on I6 by accident and wonder why the period refuses to conclude.

#Second inversion: handle with a label

Second-inversion triads, with the fifth in the bass, sound unstable because the bass forms a fourth against an upper voice. Tonal practice allows them only in four recognized situations, and every six-four chord in an analysis should carry one of these labels.

Cadential six-four. The I6/4 before V at a cadence, where the bass already holds scale degree 5. It delays the dominant and carries the melodic descent. This is the most common six-four in the repertoire and the only one that regularly takes an accent.

Passing six-four. A bass passing between two stable positions, harmonized with a triad whose fifth happens to sit in the bass. The classic case fills the gap between I and I6, or connects IV to IV6. The chord earns its place through bass motion, not harmonic function.

Neighbor six-four. A bass that steps away from a stable chord and returns, with the excursion harmonized in second inversion. The neighboring sonority decorates rather than progresses.

Arpeggiated six-four. A bass that outlines one harmony by leaping through its chord tones. Fanfares and Alberti-style accompaniments produce these constantly; the six-four is an echo of the prevailing root-position harmony.

Any second-inversion triad that fits none of these roles is probably misanalyzed or misspelled. When in doubt, check whether the bass note belongs to the prevailing harmony as a nonchord tone before inventing a new six-four license.

#Figures and how to read them

Figured bass compresses inversion into numbers written under the bass line. Root position usually carries no figure. First inversion is marked 6, shorthand for the sixth and third sounding above the bass. Second inversion is 6/4, naming both intervals.

Chromatic alterations attach accidentals to the figures: 6 with a sharp raises the sixth above the bass. The complete shorthand, including seventh-chord figures, belongs to figured bass, the Baroque notation that turned these numbers into a performing art.

Modern lead sheets ignore most of this machinery and write C/E for a C triad over E. The slash says exactly what the figure said: chord above, bass below. Classical analysis keeps the figures because they encode voice-leading expectations the slash leaves out, especially the special treatment of 6/4 chords.

Roman numerals combine with the figures to name both function and position. In C major, I6 is a tonic triad in first inversion, V6/4 is a cadential six-four, and IV6 is a subdominant over its third. That compact label tells a trained reader the root, the quality, the bass, and the expected behavior at once.

#Where inversions mislead people

Beginners often identify inversions from the top note or from the spacing rather than from the bass. A widely spaced chord with the fifth on top is still in root position if the bass holds the root. Only the lowest sounding pitch matters, which is why analysis starts by circling bass notes before naming anything.

A second error treats all inversions as interchangeable color. Substituting I6 for I at a structural arrival changes the phrase shape, and replacing a passing six-four with a root-position chord breaks the bass line it was smoothing. Inversion is a functional choice with audible consequences for line and closure.

Guitar voicings add confusion because the lowest string is not always the musical bass in a band texture. A guitarist playing an E-shape chord while the bassist holds G produces a first-inversion sonority no matter what the guitar diagram claims. Inversion describes the sounding result across the whole ensemble.

#What to do with it

Take any Bach chorale phrase and label every chord with a Roman numeral plus inversion figures. Count how many six-four chords appear and assign each one of the four licenses. Most phrases contain exactly one, sitting at the cadence, which shows how sparingly the style spends its least stable resource.

At the keyboard, play a I IV V I progression in root position, then replay it with a stepping bass: C D E F or its mirror. The inversions the smooth bass forces are the natural habitat of first-inversion triads. Practice until the figures feel like bass fingerings rather than arithmetic.

Finish by harmonizing a simple stepwise bass (C D E F G) four ways, each time choosing different inversions above it. Some choices will sound inevitable and others awkward; the awkward ones violate doubling or six-four rules the ear detects before the textbook names them. Functional harmony then explains why the good choices work as progressions, not just as isolated voicings.

Questions

What are the inversions of a triad?

Root position puts the chord root in the bass, first inversion puts the third in the bass, and second inversion puts the fifth in the bass. The upper voices can sit in any order; only the bass note decides the inversion.

How do you tell which inversion a triad is in?

Find the root by stacking the notes in thirds, then look at the bass. If the bass holds the root, the chord is in root position. If it holds the third or fifth, the chord is in first or second inversion.

Why invert chords instead of using root position everywhere?

Inversions smooth the bass line, soften arrivals, and let the same harmony support different melodic situations. A chain of root-position triads sounds blocky because the bass leaps with every root; inversions let it walk.

What do the numbers 6 and 6/4 mean under a bass note?

They are figured-bass shorthand for the intervals above the bass. A 6 means first inversion (a sixth and a third above the bass), and 6/4 means second inversion (a sixth and a fourth). No figure normally means root position.