A Survey of Music Theory for the College Classroom: Diatonic Harmony

Second Inversion Triads

Overview

The use of second inversion triads augments the chord and bass choices available to composers. Second inversion triads arise when melodies appear in the bass, when accompaniments in pieces for piano are sounded in arpeggiation, when bass lines are arpeggiated over several beats or measures, and as passing, pedal, and cadential chords. 

Bass lines can be arpeggiated over several beats or in multiple measures, as shown in the next example. In a case such as this, the most appropriate way to analyze the passage is as a tonic chord throughout.

six four arpeggiated ass

Functional Six-Four Chords

Second inversion triads that function within the circle of fifths progression include three types – the passing six-four, pedal six-four, and cadential six-four. The first two types – the passing six-four and pedal six-four – are harmonically weak and have a subsidiary and decorative function related to the chords around them. The cadential six-four is a more abundant and much stronger chord that functions as dominant harmony. 

Passing Six-Four

The passing six-four chord occurs when a second inversion triad is used to fill in the gap of a third in a bass line. The passing six-four chord is harmonically weak and serves merely to connect the other two chords. It normally occurs on a weak beat or weak part of a beat. Contrary motion is typical between the bass and soprano, and the bass must be doubled in the passing six-four chord.

passing six four

The opening measures of the first song in Beethoven’s song cycle An Die Ferne GeliebteOp. 98 No. 1 illustrate the passing six-four chord.

Beethoven excerpt of passing six four

Pedal Six-Four

The pedal six-four chord happens when a chord – typically the I or V – is decorated with a six-four chord. The aural effect is like the pedal point (pedal tone) because of the repeated or sustained bass note. Like the passing six-four, the chord usually falls on a weak beat, and the bass must be doubled.

peel six four examples

The following example taken from the closing measures of Schumann’s Wild Rider, Op. 68 No. 8 clearly illustrates a typical use of the pedal six-four chord.

Schumann Wild Rider pedal six four

Cadential Six-Four

The cadential six-four chord is an exceptionally useful companion to the dominant V chord in cadences. Cadences are resting places at the ends of phrases that are described in greater detail later in this text. Cadential six-four chords are very common in western art music and on rare occasions even substitute for the dominant chord in a half-cadence. They have a strong dominant function and serve to heighten the listener’s interest in the expected V(7) chord. They are almost always found on strong beats and like the other functional six-four chords always feature the doubling of the bass note in a four-part texture.

Carefully observe the descent of scale degrees \(\hat{3}\)\(\hat{2}\), and \(\hat{1}\) in the following examples. This descent is often in the soprano, especially when driving to a perfect authentic cadence (PAC), which is discussed in the next chapter. It can also appear in an inner voice if the desired cadence is an imperfect authentic cadence (IAC).

cadential six four examples

The next example is taken from the beginning of the first movement of Mozart’s Piano Sonata in A K. 331. A cadential six-four chord is featured at the ends of both the first and second phrases, which end with a half cadence (HC) and perfect authentic cadence (PAC) respectively.

 

Mozart K. 331 cadential six four

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