Main Body

33 Modulation to closely related keys

Learning goals for Chapter 33

In this chapter, we will learn:

Modulation to closely related keys

Often composers will change keys within a piece in order to create interest, avoid monotony, and develop tonal tension. The most common way composers do this is through pivot chords, which are usually diatonic and function tonally in both the original key and the new key. A pivot chord thus possesses a double identity and assumes a new tonal function to modulate into the new key. Example 33‑1 demonstrates the use of a pivot chord in a modulation. After the point of the pivot, all chords are labeled in relationship to the new key.

Example 33‑1. Pivot chord modulation

image of chord progression written in four parts on Grand staff in the key of C major: one, six, four, five, one, six, pivot chord symbol used, new key is G major: two, one-six-four, five, one, six, four, five, one

Pivot chord modulations work best when the keys are closely related, which means that the keys either possess the same key signature or have only one flat or sharp different from each other. In Example 33-1 above, C major and G major are closely related keys because their key signatures differ by only one accidental.

Another way to know which keys are closely related to a given tonic key is to identify all the major and minor diatonic chords in that key that can be tonicized with a secondary dominant. A method for finding these five closely related keys is shown below in Figure 33-1 (for major keys) and Figure 33-2 (for minor keys).

Figure 33‑1. Finding closely related keys from a major base key, using a visual model

image

Access a screen-reader friendly .pdf of this figure here: Figure 33.1

Using this method, we find that F major, G major, D minor, A minor, and E minor are closely related to C major. Notice that A minor shares the key signature of C major (no sharps or flats), and F major and D minor (1 flat) and G major and E minor (1 sharp) are only one accidental different from C major.

Figure 33‑2. Finding closely related keys from a minor base key, using a visual model

image

Access a screen-reader friendly .pdf of this figure here: Figure 33.2

This method tells us that F minor, G minor, A\flat major, E\flat major, and B\flat major are closely related to C minor. E\flat major shares the key signature of C minor (3 flats), and F minor and A\flat major (4 flats) and G minor and B\flat major (2 flats) are only one accidental different from C minor.

Pivot-chord modulation in a musical context

Example 33‑2 shows a swift pivot-chord modulation from E minor to its relative major, G major. This key relationship is not only a closely related key, but also the relative relationship, meaning the two key areas share the same key signature. The pivot chord occurs in m. 6, which in E minor is the subdominant (iv6) chord and in G major is the supertonic (ii6) chord.

Example 33‑2. Franz Joseph Haydn, Sonata in E minor for piano, Hob. XVI:34, mvt. 3, mm. 1–8

image of score

Listen to the full track, performed by pianist Markus Becker, on Spotify.

Learn about Franz Joseph Haydn (1732–1809) by reading this Oxford Music Online article, written by Georg Feder and James Webster.

Video: T60 Modulation to closely related key areas (10:25)

This video introduces the concept of modulation to closely related keys. In this video, we learn what pivot chords and closely related keys are, then explore pivot-chord modulation in a piano sonata by Haydn (Example 33-2).

Access the slideshow here: Modulation to closely related keys slides

EXERCISE 33-1 Finding closely related keys

EXERCISE 33-1 Finding closely related keys

Given the tonic keys in each problem below, complete the rest of each chart to show all of the keys closely related to the given tonic.

image of six problems where tonic is given and five spaces remain for labeling the remaining closely related keys. (1) tonic is F major, (2) tonic is F-sharp minor, (3) tonic is D-flat major, (4) tonic is B-flat major, (5) tonic is F minor, and (6) tonic is B minor.

Access a printer-friendly .pdf of the exercise here: Ex33.1 Finding closely related keys

EXERCISE 33-2 Analysis with modulation

EXERCISE 33-2 Analysis with modulation

Study and listen to each Worksheet example. Then complete the following tasks for each:

  • Identify the starting and ending keys.
  • Determine the harmonic rhythm, and provide a Roman numeral analysis beneath the staff. Include a pivot chord to show where the modulations take place.
  • Answer the question(s) regarding each excerpt.

Question for Worksheet example 33‑1: What term best describes the relationship between the two keys in this excerpt? (Choices include relative, closely related but not relative, distantly related, parallel, and enharmonic.)

Worksheet example 33‑1. Orchestral reduction of Joseph Bologne, Symphony in G major, op. 11, no. 1, mvt. 2, mm. 9–21[1]

image

Listen to the full track, performed by the Tafelmusik Baroque Orchestra, on Spotify.

Learn about Joseph Bologne (1745–1799) by reading this Oxford Music Online article, written by Gabriel Banat.

Note for Worksheet example 33‑2: Don’t get too caught up in chord inversion and position in this excerpt, as the cello part continually moves by step, thus changing chord inversion and infusing the texture with a lot of passing tones. It is more important to identify Roman numerals and pivot chord placement than to label chord inversion in this excerpt.

Questions for Worksheet example 33‑2:

  • This section modulates twice. What term best describes the relationship between the two key areas that are used in this excerpt?
  • What kind of cadence occurs in mm. 3–4?
  • What kind of cadence occurs in mm. 7–8?
  • What kind of cadence occurs in mm. 11–12?
  • What kind of cadence occurs in mm. 15–16?
  • What term(s) best describe the form of mm. 9–16?

Worksheet example 33‑2. Franz Joseph Haydn, String Quartet in D major, op. 20, no. 4, mvt. 3, trio section

image of score

Listen to the full track on Spotify.

Learn about Franz Joseph Haydn (1732–1809) by reading this Oxford Music Online article, written by Georg Feder and James Webster.

Questions for Worksheet example 33‑3:

  • What term best describes the relationship between the opening and ending keys?
  • What kind of cadence occurs in mm. 7–8?
  • What kind of cadence occurs in mm. 11–12?
  • What term(s) best describe the form of this excerpt?

Worksheet example 33‑3. Robert Schumann, Myrthen, op. 25, “Hochländers Abschied,” mm. 1–12

image of score

Listen to the full track, performed by lyric tenor Ian Partridge, on Spotify.

Learn about German composer Robert Schumann (1810–1856) by reading this Oxford Music Online article, written by John Daverio and Eric Sams.

Questions for Worksheet example 33‑4:

  • What term best describes the relationship between the opening and ending keys of this excerpt?
  • What kind of cadence occurs in m. 4?
  • What kind of cadence occurs at the end of this excerpt?
  • Based on this cadence structure, what is the best term(s) to describe the form of the excerpt?

Worksheet example 33‑4. Cécile Chaminade, Gavotte from Album des Enfants, op. 123, mm. 1–8[2]

image of score

Listen to the full track, performed by pianist Anna Caterina Binda, on Spotify.

Learn about French composer Cécile Chaminade (1857–1944) by reading this Oxford Music Online article, written by Marcia J. Citron.

Note for Worksheet example 33‑5: Assume a harmonic rhythm of one chord per bar.

Question for Worksheet example 33‑5: What term best describes the relationship between the two key areas of this example?

Worksheet example 33‑5. Antonio Vivaldi, Violin Concerto in E minor, RV 277 (“Il Favorito”), mvt. 2, mm. 8–15[3]

image of score

Listen to the full track, performed by violinist Giuliano Carmignola and Sonatori de la Gioiosa Marca, on Spotify.

Learn about Antonio Vivaldi (1678–1741) by reading this Oxford Music Online article, written by Michael Talbot and revised by Nicholas Lockey.

Questions for Worksheet example 33‑6:

  • What term best describes the relationship between the opening and ending keys of this excerpt?
  • Describe the root motion of the harmonic sequence that starts in m. 2.
  • Describe the root motion of the harmonic sequence that starts in m. 3.
  • Describe the root motion of the harmonic sequence that starts in m. 4.
  • What kind of non-chord tone is used in m. 1?
  • What kind of non-chord tone is used in mm. 4–5?

Worksheet example 33‑6. J. S. Bach, Well Tempered Clavier Bk. 1, Prelude 6, mm. 1–6

image of score

Listen to the full track, performed by pianist Enrica Cavallo, on Spotify.

Learn about German composer Johann Sebastian Bach (1685–1750) by reading this Oxford Music Online article, written by Christoph Wolff and Walter Emery.

Questions for Worksheet example 33‑7:

  • What term best describes the relationship between the opening and ending keys?
  • What kind of cadence occurs in m. 2?
  • What kind of cadence occurs in m. 4?
  • What kind of cadence occurs in m. 6?
  • What kind of cadence occurs in m. 8?
  • What term(s) best describe the form of mm. 1–4?
  • What term(s) best describe the form of mm. 5–8?

Worksheet example 33‑7. Ludwig van Beethoven, Piano Sonata no. 10, op. 14, no. 2, mvt. 2, mm. 1–8

image of score

Listen to the full track, performed by Gerhard Oppitz, on Spotify.

Learn about German composer Ludwig van Beethoven (1770–1827) by reading this Oxford Music Online article, written by Joseph Kerman and others.

Note for Worksheet example 33‑8: For this excerpt, there is no need to label all implied chords beneath the staff. Instead, simply identify the opening and ending keys, and identify the best place for a pivot chord and provide a label showing the function in both keys.

Questions for Worksheet example 33‑8:

  • What term best describes the relationship between the opening and ending keys of this excerpt?
  • What kind of cadence occurs at the end of this excerpt?

Worksheet example 33‑8. Elisabeth Jacquet de La Guerre, Suite in F major, Allemande, mm. 1–7[4]

image of score

Listen to the full track, performed by harpsichordist Elizabeth Farr, on Spotify.

Learn about French harpsichordist and composer Elisabeth Jacquet de La Guerre (1665–1729) by reading this Oxford Music Online article, written by Catherine Cessac.

Access a printer-friendly .pdf of the exercise here: Ex33.2 Analysis with modulation
Listen to the audio examples featured in this exercise here: Spotify playlist for modulation to closely related keys

EXERCISE 33-3 Key relations

EXERCISE 33-3 Key relations

Study each of the key relationships below and label it as one of the following:

C = Closely related (but not relative)

R = Relative

P = Parallel

D = Distantly related or foreign (but not parallel)

E = Enharmonic

  1. F\sharp major and F\sharp minor
  2. F major and C minor
  3. G major and D major
  4. D\flat major and C\sharp major
  5. C\sharp minor and E major
  6. D minor and C major
  7. E\flat major and E\flat minor
  8. B major and C\flat major
  9. F minor and A major
  10. G\flat major and D\flat major
  11. B\flat major and F major
  12. B minor and G major
  13. B\flat minor and D\flat major
  14. E\flat major and F major
  15. E minor and E major
  16. G major and A\flat major
  17. A minor and F major
  18. C minor and E\flat major
  19. F\sharp major and C\sharp major
  20. A major and G major
Access a printer-friendly .pdf of the exercise here: Ex33.3 Key relations

Video: S35 Sight singing a modulating melody (5:47)

This interactive video walks you through the steps needed to sing a modulating melody from the Berkowitz et al. collection titled A New Approach to Sight Singing. We begin by analyzing the melodic structure and implied key areas, identify appropriate notes to pivot solfege syllables, practice reading the rhythm aloud by chanting the solfege syllables while conducting, and finally sing the melody.

Self-quiz on pivot chord thinking problems

Supplemental resources

Supplemental resources for Chapter 33

John Peterson’s chapter on modulation to closely related keys (Open Music Theory)

  1. Example from https://www.expandingthemusictheorycanon.com/modulation/ ↵
  2. Example from  https://www.expandingthemusictheorycanon.com/modulation/ ↵
  3. Example from https://musictheoryexamples.com/22MT.html by Timothy Cutler (accessed July 6, 2020). Website no longer available; the author's examples now appear in an anthology published by W.W. Norton. ↵
  4. "Pièces de clavecin, Livre 1 (Jacquet de La Guerre, Elisabeth)" by Pierre Gouin is licensed under CC BY-NC 4.0 ↵
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