Comprehensive Study Notes on Six-Four Chord Progressions and Harmonic Voice Leading and Cadential and Harmonic Analysis

The Nature and Functional Role of Six-Four Chords

Six-four chords ($6/4$) are categorized primarily as ornamental structures within music theory. They are not intended to be the main harmonic attraction; rather, they serve to enhance or ornament the chord that follow them, particularly at a cadence. To achieve maximum ornamental effectiveness and sonic similarity, a six-four chord must share the same bass note as the chord it is ornamenting. This shared foundation allows the ear to perceive the $6/4$ chord as a preparation for the resolution chord.

Credential Six-Four Chords

The credential six-four chord (often colloquially referred to as the "credential 64" in this context) is specifically designed to ornament the final chord of a cadence, such as an imperfect cadence. Because the goal is to be as close to the landing chord as possible, sharing the same bass note is mandatory. In a typical sequence ending on chord $V$, one would use the $I^6_4$ chord because the bass note of the second inversion of $I$ is the same as the root of chord $V$. This results in the progression $1^6_4$ to $5$.

Another variation occurs when ending on a chord $I$. To find a chord that shares the same bass note as the root of chord $I$, one must utilize the second inversion of chord $IV$. This creates an auxiliary-style sequence of $4^6_4$ to $1$. The sequence $1 - 6 - 4 - 5$ is specifically identified as an imperfect cadence. The term "credential" is used specifically for these instances because the chord is functioning as a cadential ornament, rather than a standalone harmonic movement.

Passing Six-Four Chords

Passing six-four chords are characterized by step-wise motion in the bass and are used to transition between different positions of the same chord or between two different chords. There are two primary variations of these progressions. When building these, the bass voice is the most critical element. In solfege, the bass typically follows a $Do$-$Re-$Mi pattern (or $8$-$7-$8).

The first variation involves the progression $I - V^6_4 - I^6$. In this scenario, if the bass is ascending ($Do$-$Re-$Mi), the upper voices should ideally descend ($Mi$-$Re-$Do) to create contrary motion. For a chord $I$ in C major, the voices would include C, E, and G. The passing chord ($V^6_4$) facilitates the movement toward the first inversion ($I^6$). Throughout this process, perfect motion is the goal, often involving step-wise movement and the maintenance of common tones.

A second variation follows the pattern of $IV - I^6_4 - IV^6$. The solfege for the bass in this progression would be $Fa$-$So-$La. This structure requires that one of the horizontal lines in the harmony maintains the step-wise ascending or descending motion, while the other voices fill out the remaining chord tones. Whether the voices are moved around or muddled, the progression remains perfect as long as the ascending/descending steps and common tones are preserved.

Auxiliary Six-Four Chords

An auxiliary six-four chord, also known as a neighboring progression, involves moving from a primary chord to a secondary chord and immediately back to the original chord ($1 - 2 - 1$). This is described as an "up and back down" motion. The auxiliary chord itself is a $6/4$ chord. These progressions are distinct because they occur on weak beats. For example, in a $3/4$ time signature, beat two is a weak beat where a six-four chord would typically be placed.

There are two main examples of this type of progression. The first is $V - I^6_4 - V$. The second is $I - IV^6_4 - I$. In the latter example, if the piece is in C major, the bass note remains a constant C throughout the entire progression. While the bass is static, the upper voices move from the notes of chord $I$ (C, E, G) up to the notes of chord $IV^6_4$ (C, F, A) and then back down to the original positions. This ornamental progression is essentially a cadential six-four with the original chord placed on both sides of the ornament.

Base Arpeggiation

Base arpeggiation (described in the transcript as "base opetiation" and "base arpeggiation") is a technique used when a single chord is held for multiple beats. To keep the listener's ear engaged, the bass voice moves through the various inversions of that chord instead of remaining on the root. This is frequently used in string orchestration.

For example, if a chord $I$ is held for several beats, the bass might move from the root to the second inversion ($6/4$) and then to the first inversion ($6$). Every change in the bass notes must be labeled individually in a harmonic analysis. Even if the harmonic rhythm seems to stay on a single chord, the change in the base determines the inversion (the "number" in the figured bass) and therefore constitutes a change that must be documented. The bass serves as the foundation of the chord, and its movement dictates the analytical label.

Rules for Doubling in First Inversion

A specific rule discussed regarding first inversion chords is that the root of the chord should not be doubled. There are exceptions to this rule: the root may be doubled if the chord is a chord $II$ or a chord $VII$. These exceptions exist because those chords would not be major in those contexts. Outside of these exceptions, doubling the root in a first inversion chord is generally avoided to maintain proper harmonic balance and voice leading standards.

Questions & Discussion

Question: What are the two "credential" six-fours we have? Answer: They are $1 - 4 - 64 - 1$ and $1 - 64 - 5$. The second is an imperfect cadence.

Question: Why do we call it a credential six-four specifically? Answer: Because it is ornamenting the last chord. To be ornamental, it needs to stay as close as possible to the last chord by sharing the same bass note.

Question: Can you explain the auxiliary progression again? Answer: It involves a chord that goes up and then back to the same original chord. It is like a cadential six-four but with the same chord on the other side. A common example is $5 - 164 - 5$ or $1 - 464 - 1$.

Question: Would you cadence with an auxiliary progression? Answer: It depends on the context. In music theory exercises, yes, but in a "conversing" or more natural musical context, it might be perceived as too intense.

Question: Does the base changing mean the harmonic rhythm changes? Answer: The harmonic rhythm is determined by the base because the base is what changes the harmony and inversion. Therefore, even if upper notes are held, a change in the bass note requires a new analytical label.

Practical Application in E major

In a practice assignment set in E major, several specific harmonic requirements must be met. For a passing progression in bar three, a standard sequence like $I - V^6_4 - I^6$ ($1 - 5 - 64 - 16$) is recommended. The bass should follow the solfege pattern of $Do$-$Re-$Mi.

In bar five, a base arpeggiation is required. The progression might move from chord $I$ to $I^6_4$ then to $I^6$, helping to keep the ear engaged before landing on a chord $V$ for the cadence. This helps avoid a static harmony. For the final auxiliary progression, the base note remains on E (the root of chord $I$) while the upper voices move from the tonic triad to the subdominant triad ($4/6/4$) and back to the tonic. During SATV (Soprano, Alto, Tenor, Voice) writing, care should be taken to avoid parallel movements, although they are occasionally acceptable in specific keyboard harmony contexts.