A Little Background
Chord inversions are the second thing music students learn about chords, right after how to spell chords over a given root (what the pitches of D Major or F♯ Diminished is). For those who are new to the topic, follow this link.
Chord inversions are mostly taught by looking at chords in the easiest possible manner: as close-position triads or as block chords in simple four-voice chorales. When they are studied like this, students can quickly learn how to identify a chord’s position (either root position or inversion) and assign it a numeric label: 5/3 or 7 for root position, 6 or 6/5 for first inversion, and so forth.
It is much more difficult to apply the concept of inversions to music that doesn’t move in block chords, and in most music, the bass is elaborated in some way, complicating the matter. Sometimes they are ornamented with passing tones and such between “structural” tones, and when a bass line is genuinely florid (as in much classical or jazz music) it becomes very tricky indeed.
So, Why Do They Matter?
Why do we study chord inversions? To many students, it’s tedious busywork to parse the pitches that make up a chord, figure out which is lowest, and assign a numeric label. Some of the point may be to dwell a while on spelling chords. It is also an introduction to the idea of following one note of a chord to the next, which introduces the subject of voice-leading, which is often a primary concern of harmony courses (though that is increasing being considered “old-fashioned”).
The essential reasons for studying chord inversions, though, have to do with genuine sonic effect, both “vertically” (in the moment) and “horizontally” (as a melody underneath the phrase). Inverted chords have a distinctive “color” that adds a weakness, and in some cases, a poignancy to the harmony. One great example is the second inversion A Minor chord that begins the second movement of Beethoven’s Symphony No. 7. Listen to its special fragility here at the beginning of the movement, and compare that to the same chord in root position as Beethoven places it at the end of the movement.
The study of how inverted chords affect voice-leading is also a good practice. One of the principles of good voice-leading is to avoid a series of second inversion chords in a row; as a professor who sees this practice in endless student exercises, I can attest that it’s pretty grating to hear. And ending a musical phrase with a second inversion chord pretty much never happens.
The main feature of chord inversions, however, is that they can be used to create bass melody. Inverted chords carefully interspersed among root position chords can create a musical line in the lowest notes that works as a counterpoint to the treble or vocal melody. It’s true that plenty of great songs use only root position chords, but those that include chord inversions tend to do so to create stepwise connections between the bass notes of chords. Take, for instance, the Billy Joel song Piano Man. Its smoothly descending bass line is a characteristic element of the song. If it only used root position chords. It would sound something like this:
It’s not terrible, but it’s not the Piano Man that made Billy Joel a success.
Inversion Offers Harmonic Options
When I teach the “by-ear” approach to this topic, I like to start by pointing out that any bass note can be harmonized in many different ways. It could be the root of a chord, the third of a chord (that would mean it’s a first inversion chord), the fifth (if it’s a second inversion chord), or even the seventh (if it’s the seventh of a seventh chord). There are other options, too: the bass could be a member of a chord in the key, or of a chord that uses chromatic notes (such as a secondary dominant).
I begin by offering the following bass line, one note at a time; it quickly becomes clear to hipper members of the class that it’s from Procol Harum’s A Whiter Shade of Pale [audio on YouTube].
The exercise is to determine all of the possible chords that these bass notes can support, and then select the one that is actually used in the song. We first consider what chord is most likely to be used at any given point based on several assumptions (if the chord has a “strong” place in the phrase, it is more likely to be in root position; diminished chords are uncommon; mediant chords are uncommon, etc.) and then listen closely to the recording, checking to hear what notes of the chord are present in the melody and accompaniment layers, etc. In the end, we come up with this:
From this we observe that:
- There is a rhythmic aspect to the use of inversions: almost every downbeat of this tune supports strong harmony by using root position chords.
- The “primary triads” (C, F and G: the tonic, subdominant and dominant) are most common: of 17 chords (not counting the last because it belongs to the next phrase), 14 are primary triads.
- Inverted chords allow for a stepwise, melodic bass line.
- Inversion permits the use of primary triads over any scale degree in the bass:
- Tonic harmonies are found over scale degrees 1, 3 and 5 as well as 7 (if it is a seventh chord).
- Dominant harmonies are found over scale degrees 2, 4, 5 and 7.
- Subdominant harmonies are found over scale degrees 1, 4 and 6.
Ways To Describe How Inverted Chords Work In Context: “Bass Functions”
When studying non-chord tones, we learn categorize them as passing tones, neighbor tones, and so forth. Similar descriptions are appropriate for describing how chord inversions affect a bass line. For instance, inverted chords are used:
- To create passing or neighboring bass-motion. The bass notes of chords in inversion often create a stepwise bass melody, either with “passing motion” (the bass notes proceed by step in one direction) or “neighboring motion” (the bass note of the inverted chord moves by step away from a root position chord and back by step to it).
- To create a pedal bass. The bass note of the inverted chord is the same as both that surround it (a “complete” pedal) or the same as just one adjacent bass note (an “incomplete” pedal). Note that repeated chords do not indicate a pedal function – bass motion of this sort is only of interest when a harmony changes while the bass remains steady.
- The cadential 6/4 is a special variety of pedal 6/4 which occurs when scale degree 5 is in the bass and the chord is followed by V; the cadential 6/4 chord is almost always on a metrically stronger part of the measure than the resolution dominant chord.
- To create an arpeggiated bass. The bass note of the inverted chord serves to change inversion without changing the harmony. A bass tone working in this manner may come after a root position chord of the same function (extending or prolonging the previous harmony), may progress to a root position chord of the same function (prolonging the next harmony), or both (arpeggiating through three or four positions of the same chord).
This phrase from a song by Franz Schubert (Die liebe Farbe, from his song-cycle Die schöne Müllerin) demonstrates all of these principles except for the pedal bass [audio on YouTube]:
The next phrase of the song has an example of pedal bass; notice how the low F♯ stays fixed as the harmony changes under it. It works as the root of the F♯ Minor chord, as the seventh of the G♯ half-diminished chord, and finally as the fifth of the B Minor chord.
A Real Emotional Song
Randy Newman’s Real Emotional Girl is a great song to study when learning about inversions. Here’s the sheet music and here is a recording. It is a great classroom piece for many reasons, not least of which being that its simple chordal accompaniment is easy to analyze and it is a heartbreaking pop music example in which the melodic bass helps in a big way to set its mood.
When studying this song, I have students begin by assigning Roman numeral chord-function labels to each chord (my copy of the sheet music leaves out the chord symbols, so they have the figure out the harmonies themselves, including dealing with a few non-chord tones like those in bar 3 and bars 6-9). Then they are asked to describe the function of each bass tone; options are:
- Chord root
- Passing or neighboring bass-tone (may be an incomplete neighbor)
- Arpeggiating bass tone that either initiates a harmony or extends a previous harmony
- Pedal bass-tone (may be an incomplete pedal) or bass of cadential 6/4
What students discover is that Randy Newman has set up a repeating pattern in his accompaniment for the first five bars: a harmony is established (usually with a root position chord) and then weakened through arpeggiation, before leading by stepwise bass to the next harmony. Bar 4 reverses this pattern. Bar 7 demonstrates a tonic 6/4 as a passing harmony between vi and IV, offering an opportunity to discuss the difference between a tonic 6/4 and a cadential 6/4.
Bars 10-13 harmonize a stepwise chromatic bass line, and bar 14 has a pedal I6/4 – V7 that doesn’t lead to a cadence. In a way, the change in approach to using chord inversions (along with the chromatic harmony) sets this phrase apart from the others, establishing a change of mood and intensifying the song’s (real) emotional affect.