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Section 9.4 Harmonic Function

Now we will address non-circle-of-fifths progressions. Notice that we have not included the \(\left.\text{vii}^{\circ}{}\right.\) or \(\left.\text{IV}\right.\) chord in any of the shorter circle of fifths progressions above. However, it is a common axiom that Rock ‘n’ Roll is made up of three chords: \(\left.\text{I}\right.\), \(\left.\text{IV}\right.\), and \(\left.\text{V}\right.\). This is because each of those chords represents a harmonic function. Harmonic function refers to the tendency of certain chords to progress to other chords, or to remain at rest. Many texts on music theory enumerate three harmonic functions. In this text, we will discuss four.

  1. Tonic function (abbreviated “ton.”): The \(\left.\text{I}\right.\) chord has tonic function, which is a state of stability and rest. Tonic chords do not demand progression to other chords.

  2. Dominant function (abbreviated “dom.”): The \(\left.\text{V}\right.\) and \(\left.\text{vii}^{\circ}{}\right.\) (chords containing the leading tone \(\hat{7}\) and supertonic \(\hat{2}\) ) tend to progress to tonic (\(\left.\text{I}\right.\)). Special note: The \(\left.\text{I}\middle/\text{5th}\right.\) chord has dominant function when it resolves to the \(\left.\text{V}\right.\) chord, as in the third chord from the end of the “Star-Spangled Banner.”

    Figure 9.4.1. Key and Smith, “The Star-Spangled Banner”
  3. Pre-dominant function (abbreviated “pre-dom.”): The \(\left.\text{IV}\right.\) and \(\left.\text{ii}\right.\) (chords containing the subdominant \(\hat{4}\) and submediant \(\hat{6}\) ) tend to progress to chords of dominant function.

  4. Tonic prolongation function (abbreviated “ton. prol.”): The \(\left.\text{vi}\right.\) and \(\left.\text{iii}\right.\) (chords that share two common tones with \(\hat{1}\) –\(\hat{3}\) –\(\hat{5}\) from the tonic triad) tend to occur after the tonic chord and progress to chords of pre-dominant function.

Harmonic function is represented on a flowchart in the next section.

Subsection 9.4.1 The Harmonic Flowchart

Harmonic Flowchart in Major
Figure 9.4.2. Harmonic Flowchart in Major

Remember that \(\left.\text{IV}\right.\) goes to \(\left.\text{I}\right.\) in the plagal cadence and \(\left.\text{V}\right.\) goes to \(\left.\text{vi}\right.\) in the deceptive cadence. When \(\left.\text{IV}\right.\) goes to \(\left.\text{I}\right.\), label \(\left.\text{IV}\right.\) as having tonic prolongation function. The plagal cadence and deceptive cadence are exceptions to the harmonic flowchart.

Here is the Harmonic Flowchart in minor. Note the addition of the subtonic \(\left.\text{VII}\right.\) chord, which has one function—to progress to \(\left.\text{III}\right.\).

Harmonic Flowchart in Minor
Figure 9.4.3. Harmonic Flowchart in Minor

The tonic chord \(\left.\text{I}\right.\) can progress directly to a chord of any other function and, in fact, many pieces begin with a \(\left.\text{I}\right.\)–\(\left.\text{V}\right.\)–\(\left.\text{I}\right.\) progression, representing harmonic function of Tonic-Dominant-Tonic.

Subsection 9.4.2 Tonic-Dominant-Tonic Progression

This is the most elemental progression in music, often realized with \(\left.\text{I}\right.\)–\(\left.\text{V}\right.\)–\(\left.\text{I}\right.\).

Figure 9.4.4. Mozart, Piano Sonata, K. 283, I.
Figure 9.4.5. Beethoven, Piano Sonata in C major, Op. 2, No. 3, I.
Figure 9.4.6. Verdi, Rigoletto, “La donna è mobile”
Figure 9.4.7. Lennon-McCartney, “Hey Jude”
Figure 9.4.8. S. Shafer and L. Shafer, “All My Ex’s Live in Texas”

The principle of “Tonic-Dominant-Tonic” could also be represented with \(\left.\text{I}\right.\)–\(\left.\text{vii}^{\circ}{}\right.\)–\(\left.\text{I}\right.\). Even though we learned that “dominant” means “\(\hat{5}\) ” (and also “\(\left.\text{V}\right.\)”) in earlier sections, “dominant function” in terms of harmony means “a chord that progresses to the tonic chord.” We will revisit this concept and other possibilities for “dominant function” later.

Subsection 9.4.3 Tonic-PreDominant-Dominant-Tonic Progression

This sequence of harmonic functions can be realized in four possible ways:

  • \(\left.\text{I}\right.\)–\(\left.\text{ii}\right.\)–\(\left.\text{V}\right.\)–\(\left.\text{I}\right.\)

  • \(\left.\text{I}\right.\)–\(\left.\text{IV}\right.\)–\(\left.\text{V}\right.\)–\(\left.\text{I}\right.\)

  • \(\left.\text{I}\right.\)–\(\left.\text{IV}\right.\)–\(\left.\text{vii}^{\circ}{}\right.\)–\(\left.\text{I}\right.\)

  • \(\left.\text{I}\right.\)–\(\left.\text{ii}\right.\)–\(\left.\text{vii}^{\circ}{}\right.\)–\(\left.\text{I}\right.\)

Here are examples with \(\left.\text{I}\right.\)–\(\left.\text{ii}\right.\)–\(\left.\text{V}\right.\)–\(\left.\text{I}\right.\).

Figure 9.4.9. Bach, J.S., Well-Tempered Clavier, Book I, Prelude 1 in C major BWV 846
Figure 9.4.10. Mozart, Symphony No. 40 in G minor, K. 550, I. (textural reduction)
Figure 9.4.11. Kander and Ebb, “New York, New York”
Figure 9.4.12. Trainor and Kadish, “All About That Bass” (bass line and chord symbols only)

Here are examples with \(\left.\text{I}\right.\)–\(\left.\text{IV}\right.\)–\(\left.\text{V}\right.\)–\(\left.\text{I}\right.\) realizing the Ton-PreDom-Dom-Ton progression.

Figure 9.4.13. Frédéric Chopin, Waltz in A-flat major, Op. 34 No. 1
Figure 9.4.14. Crane, Kauffman, Skloff, Willis, Solem, Wilde, “I'll Be There For You” (bass line and chords only)

Progressions using \(\left.\text{vii}^{\circ}{}\right.\) (\(\left.\text{I}\right.\)–\(\left.\text{IV}\right.\)–\(\left.\text{vii}^{\circ}{}\right.\)–\(\left.\text{I}\right.\) and \(\left.\text{I}\right.\)–\(\left.\text{ii}\right.\)–\(\left.\text{vii}^{\circ}{}\right.\)–\(\left.\text{I}\right.\)) are less common because of the instability of diminished chords.

Subsection 9.4.4 The Tonic-Tonic Prolongation-PreDominant-Dominant Progression

This progression is most commonly realized with \(\left.\text{I}\right.\)–\(\left.\text{vi}\right.\)–\(\left.\text{IV}\right.\)–\(\left.\text{V}\right.\), although in classical music one will often encounter \(\left.\text{I}\right.\)–\(\left.\text{vi}\right.\)–\(\left.\text{ii}\middle/\text{3rd}\right.\)–\(\left.\text{V}\right.\) (mentioned above in the section on \(\left.\text{vi}\right.\)–\(\left.\text{ii}\right.\)–\(\left.\text{V}\right.\)–\(\left.\text{I}\right.\) ).

Notice the bass line starts with descending thirds.

Figure 9.4.15. Compare \(\left.\text{I}\right.\)–\(\left.\text{vi}\right.\)–\(\left.\text{IV}\right.\)–\(\left.\text{V}\right.\) to \(\left.\text{I}\right.\)–\(\left.\text{vi}\right.\)–\(\left.\text{ii}\middle/\text{3rd}\right.\)–\(\left.\text{V}\right.\) (the bass lines are the same)

Here is a musical example with \(\left.\text{I}\right.\)–\(\left.\text{vi}\right.\)–\(\left.\text{ii}\middle/\text{3rd}\right.\)–\(\left.\text{V}\right.\).

Figure 9.4.16. Beethoven, Pathétique Sonata, Op. 13, I

Subsubsection 9.4.4.1 I–vi–IV–V

As mentioned earlier, the progression \(\left.\text{I}\right.\)–\(\left.\text{vi}\right.\)–\(\left.\text{IV}\right.\)–\(\left.\text{V}\right.\) was so prevalent in the 1950s that it is known as the “‘50’s progression” and the “50’s doo-wop progression.”

Listen for this bass line in the following examples.

Figure 9.4.17. \(\left.\text{I}\right.\)–\(\left.\text{vi}\right.\)–\(\left.\text{IV}\right.\)–\(\left.\text{V}\right.\) bass line in C major
  • Carmichael and Loesser, “Heart and Soul” (in C major) (YouTube)

  • Williams, Belvin, Hodge, “Earth Angel” (in A-flat major) (YouTube)

  • Parton, “I Will Always Love You” (in A major) (YouTube)

  • Johnny Ramone, Dee Dee Ramone, Joey Ramone, “Rock ‘n’ Roll High School” (in C major) (YouTube)

In the above examples, the chords have have half-note harmonic rhythm. In the following example, the chords have whole-note harmonic rhythm (4 beats per chord).

  • Stephens and Gad, “All of Me” (in A-flat major) (YouTube)

The \(\left.\text{I}\right.\)–\(\left.\text{vi}\right.\)–\(\left.\text{IV}\right.\)–\(\left.\text{V}\right.\) progression can also be rotated to \(\left.\text{IV}\right.\)–\(\left.\text{V}\right.\)–\(\left.\text{I}\right.\)–\(\left.\text{vi}\right.\), as in the following example.

Figure 9.4.18. Atwey, Messinger, Pellizzer, Spivak, Tanas, “Rude” (bass line and chords only)

You will see more examples of Tonic-Tonic Prolongation-PreDominant-Dominant progressions, including the use of the \(\left.\text{iii}\right.\) chord, in the Practice Exercises and the Homework.

Remember, there are two exceptions in Harmonic Function: \(\left.\text{IV}\right.\) has tonic prolongation function when it progresses to \(\left.\text{I}\right.\), and \(\left.\text{I}\middle/\text{5th}\right.\) has dominant function when it progresses to \(\left.\text{V}\right.\).