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

First Inversion Triads

Overview

The use of first inversion triads provides enhanced note choices for bass lines and modifies the sound of chord progressions. First inversion triads occur when melodies appear in the bass (melodic bass), when bass lines are arpeggiated, in nonfunctional passages, and when they are substituted for root position chords.

Melodic Bass and First Inversion Chords

The following example shows how first inversion chords are created by a melodic bass line. The harmony throughout the example is the tonic chord in d minor, but first inversion chords are created when the melody switches to the left hand.

melodic bass and first inversion triads

Bass Arpeggiation and First Inversion Chords

The accompaniments in pieces for piano can include figurations in which the chords are sounded in arpeggiation, and this technique was particularly popular during the Classical period in works by Mozart, Haydn, and others. The following example is taken from the third movement of Mozart’s Piano Sonata in B♭, K. 281. The first note of each measure in the left hand effectively serves as the bass note for each measure because it is on the metrically accented downbeat. These notes are also repeated on successive beats, further contributing to their importance.

Mozart K. 281 example

Alberti Bass

Another technique involving bass arpeggiation is the Alberti bass, named after the composer Domenico Alberti (1710-1740) who used the technique extensively. The Alberti bass is commonly found in the works of Mozart, Haydn, and early Beethoven. The pattern of arpeggiation for the pitches involved is lowest, highest, middle, and highest. This example is taken from the opening of the first movement of Mozart’s Piano Sonata in C major, K. 545. As with the first example, the metrically accented note in each beat serves as the bass note for the entire beat. This example also illustrates how the technique of Alberti bass can be extended to second inversion triads and to seventh chords.

Mozart K. 545 excerpt

Nonfunctional Uses of First Inversion Chords

Passages of nonfunctional first inversion passing chords can be interpolated into a circle of fifths progression to connect chords with stronger harmonic function. The parallel sixth chords used in this manner are not functional because they do not follow the typical circle of fifths progression. This example from the third movement of Beethoven’s Piano Sonata Op. 2 No. 1 beautifully illustrates this concept. The IV chord in measure 59 is connected to the V chord in measure 63 by a stream of nonfunctional first inversion chords.

Beethoven Op. 2 No. 2 excerpt

Function of First Inversion Chords in Substitution

Triads in first inversion are most frequently used as substitutes for root position chords. The inversion does not change that chord’s function within the chart of harmonic progression. A V6 chord, for example, continues to function as a normal V chord whose goal is tonic harmony. Likewise, the ii6 chord continues to function as a subdominant (predominant) chord whose goal is the dominant. The next example shows how first inversion triads can be substituted in an SATB texture. The substituted chords allow a more interesting bass line, the freedom to double notes other than the bass, and generally provide aural relief from the stronger bass motion and sound of root position chords in progression.

substitution of first inversion triads

How to Analyze the Harmonies in Music

At this stage of our studies, we begin to examine music in greater detail and with a deeper focus on excerpts from a broader range of music literature. Musical parameters such as harmony, melody, form, scales, pitch sets, pitch structures, rhythms, timbres, dynamics, texture, and programmatic elements can all be the focus of various analytical techniques developed over the centuries. This text focuses on the analysis of harmonies, melodies, and form, particularly regarding the tonal music of the past four centuries. 

The basic techniques of harmonic analysis can be applied to a diversity of musical textures within the tonal system. For example, some music is homorhythmic, with the supporting lines changing at about the same pace as the rhythm of the melody, while other homophonic pieces feature blocked chords or arpeggiated accompaniments such as the Alberti Bass. Still other pieces are primarily polyphonic in texture and feature two or more relatively independent lines. 

The first step in analyzing harmonies is to determine the harmonic rhythm, which is the speed or rate at which the chords change. Harmonic rhythm is influenced by musical genre, period, composer, meter, tempo, and style. Harmonic rhythm can be very fast, with chords changing every quarter note or even every eighth note, while in other works the harmonic rhythm can be much slower, with chords changing every measure or even less frequently. A good place to start when examining harmonic rhythm is to consider the meter. Chords often change on strong beats within a measure. For example, a passage in common time may feature chord changes on beats one and three.

The second step is to take a pitch class inventory starting with the lowest notes in the texture. The lowest notes – often but not always written in the bass clef – typically serve as the harmonic generator for a passage. After taking the pitch class inventory, find the root of the chord and stack the notes into thirds. Nonchord tones will often be present and are customarily found in the middle to upper voices within a texture because that is where melodies usually occur. We will gain a better understanding of nonchord tones later in this text.

The last step is to use Roman numerals, bass position symbols, and lead-sheet symbols to label the chords, allowing for a clear comprehension of the progression.

First Inversion Part-Writing

Using first inversion chords in SATB part-writing is easier than part-writing using only root position chords because of the increased choices in doubling. The guidelines for doubling were given earlier and are restated here. While some scale degrees such as the tonic, supertonic, subdominant, and dominant are emphasized more than others, essentially any tone except the leading tone can be doubled when part-writing chords in first inversion. 

In first inversion part-writing, the following scale degrees are always good for doubling

  • Scale degrees \(\hat{1}\)\(\hat{2}\)\(\hat{4}\), and \(\hat{5}\), are important in the maintenance of tonality.
  • Scale degrees \(\hat{3}\) and \(\hat{6}\) are modal scale degrees, affecting the tonality of major and minor.
  • For first inversion triads—double scale degrees \(\hat{1}\)\(\hat{2}\)\(\hat{4}\)\(\hat{5}\), then \(\hat{6}\), then \(\hat{3}\), never \(\hat{7}\) (leading tone).

The following are examples with a fixed bass and soprano but with a few different tones chosen for doubling. Playing these examples at the piano will show the subtle differences in sound these changes in doubling make.

first inversion with different doublings

Diminished triads (viio6 and iio6) are usually used in first inversion. When the viio triad is used in root position or in inversion, the third or fifth of the chord must be doubled because the leading tone (root of the chord) cannot be doubled. This may necessitate larger than normal leaps in one voice to avoid parallel octaves if the viiprogresses to the tonic chord with doubled root.

part writing diminished triads in first inversion

The vi6 (VI6) should not be substituted for the root position vi (VI) in a V – vi (VI) deceptive progression because the aural impression is very weak.

avoid first inversions in deceptive cadences

The IV6 (iv6) can be substituted for the vi (VI) chord in a deceptive progression because the ear hears the motion from the dominant note to the submediant note in the bass line. While this is not as common as the V – vi (VI) progression, it is seen with some frequency in the middle of phrases.

substitution in deceptive progression

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