Main Body
33 Modulation to closely related keys
Learning goals for Chapter 33
In this chapter, we will learn:
- Key relations (, , , , and )
- How modulations to closely related keys work in context
- How to identify and label a
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 , which are usually 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.
Pivot chord modulations work best when the keys are , 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 . 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
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
This method tells us that F minor, G minor, A major, E major, and B major are closely related to C minor. E major shares the key signature of C minor (3 flats), and F minor and A major (4 flats) and G minor and B 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 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
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
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.
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 , 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 , but not relative, , , and .)
Worksheet example 33‑1. Orchestral reduction of Joseph Bologne, Symphony in G major, op. 11, no. 1, mvt. 2, mm. 9–21[1]
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 . 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
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
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]
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]
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 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 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
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
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]
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.
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
- F major and F minor
- F major and C minor
- G major and D major
- D major and C major
- C minor and E major
- D minor and C major
- E major and E minor
- B major and C major
- F minor and A major
- G major and D major
- B major and F major
- B minor and G major
- B minor and D major
- E major and F major
- E minor and E major
- G major and A major
- A minor and F major
- C minor and E major
- F major and C major
- A major and G major
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 materials for Chapter 33
John Peterson’s chapter on modulation to closely related keys (Open Music Theory)
- Example from https://www.expandingthemusictheorycanon.com/modulation/ ↵
- Example from https://www.expandingthemusictheorycanon.com/modulation/ ↵
- Example from https://musictheoryexamples.com/22MT.html by Timothy Cutler ↵
- "Pièces de clavecin, Livre 1 (Jacquet de La Guerre, Elisabeth)" by Pierre Gouin is licensed under CC BY-NC 4.0 ↵
the relationship between keys that have different tonics but share the same key signature
type of key relationship in which the key signatures differ only up to one sharp or flat
type of key relationship in which the key signatures differ by more than one accidental
the relationship between keys that have the same tonic, but a different key signature
term describing the relationship of notes or chords that sound the same, but are spelled differently
chord that enacts a modulation by possessing one function in the old key and another function in the new key
term referring to notes within a key
any chord that temporarily functions as a dominant to a diatonic major or minor chord that is not tonic
the rate of chord change
non-chord tone that is approached by step and resolved by step in the same direction
process in which a repeating pattern of root motion appears in a harmonic progression
notes that do not belong in a given chord; for example, D would be a non-chord tone in relationship to a C major triad