28. Modulation

Ivette Herryman Rodriguez; Andre Mount; Jerod Sommerfeldt

28. Modulation

Closely Related Keys

Keys are considered to be “closely related” if their signatures differ by no more than one accidental. Identify the keys that are closely related to each of the tonics listed below. For each closely related key, write in the name of the key and its relation to the given home key. Then, write in the corresponding key signature on the staff above. (Use natural symbols to cancel out key signatures when needed.)

Key Relationships

In the table below, the first column lists the home keys of a series of hypothetical compositions. The second column lists a modulatory destination. Consider the relationships between each pair of keys, then put a check mark in the appropriate box to indicate if the two keys are distantly or closely related. If the two keys are closely related, specify the name of the new key in relation to the home key.

home key	secondary key	relationship
C major	G major	dominant
A minor	Bb major	n/a
A major	G major	n/a
Ab major	Bb minor	supertonic
Eb major	Ab major	subdominant
F# major	C major	n/a
G major	E minor	submediant (relative)
B minor	F# minor	dominant
C major	Db major	n/a
E minor	B major	n/a
G major	D major	dominant
D minor	F major	mediant (relative)
F major	C minor	n/a
A major	C# minor	mediant
E minor	C major	submediant
Eb major	Ab minor	n/a
F major	B major	n/a
D minor	G minor	subdominant
C major	Ab major	n/a

Pivot Chords

Each of the exercises below specifies a pair of keys: a home key listed first (with its signature shown on the staff) and a closely related secondary key below it. Identify the chords that may be used as pivots between each key pair. Write each chord on the staff and indicate the Roman numerals used to label it in each key. Finally, identify the relationship of the secondary key to the given tonic on the blank line below.

Relation of secondary key to given tonic:
dominant

Relation of secondary key to given tonic:

dominant

Relation of secondary key to given tonic:

mediant/relative major

Relation of secondary key to given tonic:

submediant

Relation of secondary key to given tonic:

dominant

Relation of secondary key to given tonic:

subdominant

Relation of secondary key to given tonic:

submediant

SATB Part-Writing

Complete each of the exercises below, following standard voice-leading conventions as closely as possible. For more detailed instructions, strategies, and proofreading tips, consult the part-writing guide found at the beginning of this book.

Figured Bass Realization

Write the Roman numerals that correspond with each figured bass note on the lines provided. Then, complete the progression by filling in the upper voices.

Note that each of these exercises modulates. For chords that belong to the original key, write the Roman numeral above the blank line provided. For chords that belong to the secondary key, write the Roman numeral below the blank line provided. For pivot chords, add Roman numerals both above and below the line and separate them with an asymmetrical bracket. Don’t forget to write the name of the new key with a colon where the lower set of Roman numerals begin. (See the following activity for an example.)

Roman Numeral Realization

Complete the progression according to the given key and Roman numerals by filling in all four voices. The first chord of each progression has been provided for you.

Note that each exercise modulates and chords that belong to the secondary key are labeled on a lower line of Roman numerals. Pivot chords are labeled with two Roman numerals—one in each key—and asymmetrical brackets are used to separte the two sets of Roman numerals.

Melody Harmonization

Write the scale degree numbers of each note in the soprano melody on the lines above the staff. Then, select a suitable chord progression which incorporates the harmonies covered in this chapter to harmonize the melody and write the appropriate Roman numerals on the lines below the staff. Finally, complete the progression by filling in the remaining voices.

Modulate to the dominant in each exercise, using a pivot chord at the specified location. Write scale degrees for the new key below the given lines.

Composing with Pivot-Chord Modulations to the Dominant

For each of the exercises below, write a pivot chord modulation in SATB format. The home key, destination key, and meter are provided in each case. Follow these steps as you plan your progression:

Begin each progression with a tonic prolongation to establish the home key (e.g., I–V4/2–I6 or I–IV6–V6–I or I–ii6–V–I)
Select a pivot chord that can perform a pre-dominant function in the new key (e.g., C: vi6 = G: ii6 or C: I = G: IV)
Reinforce the modulation with a dominant chord (e.g., V or V7) or dominant prolongation (e.g., V–I or V4/2–I6 or V–V6–V7) in the new key immediately after the pivot
Conclude the progression by confirming the new tonic with a cadence (e.g., PAC, IAC, PC) using pre-dominant or cadential 64 chords at your discretion

The following sample bass lines show several possibilities:

Home key: D major
Destination key: A major

Home key: F major
Destination key: C major

Composing with Pivot-Chord Modulations to the Sub-Dominant

For each of the exercises below, write a pivot chord modulation in SATB format. The home key, destination key, and meter are provided in each case. Follow these steps as you plan your progression:

Begin each progression with a tonic prolongation to establish the home key (e.g., I–V4/2–I6 or I–IV6–V6–I or I–ii6–V–I)
Select a pivot chord that can perform a tonic function in the new key (e.g., C: ii6 = F: vi6 or C: IV = F: I)
Reinforce the modulation with a pre-dominant chord (e.g., IV or ii6) in the new key immediately after the pivot
Conclude the progression with a dominant-tonic progression in the new key (e.g., V8-7–I or V6-4/5-3–I)

The following sample bass lines show several possibilities:

Home key: Bb major
Destination key: Eb major

Home key: G major
Destination key: C major

Composing with Pivot-Chord Modulations with Sequences

For each of the exercises below, write a pivot chord modulation with a sequence in SATB format. The home key, destination key, and meter are provided in each case. Follow these steps as you plan your progression:

Begin each progression with a tonic prolongation to establish the home key (e.g., I–V4/2–I6 or I–IV6–V6–I or I–ii6–V–I)
Write a descending-fifths sequences that starts on vi and ends on a chord with tonic function in the home key (e.g., I or iii or vi)
Write a pivot chord that can perform a tonic function in the new key
Reinforce the modulation with a pre-dominant chord (e.g., IV or ii6) in the new key immediately after the pivot
Conclude the progression with a dominant-tonic progression in the new key (e.g., V8-7–I or V6-4/5-3–I)

The following sample bass line shows one possibility:

Home key: C major
Destination key: G major

Home key: A major
Destination key: D major

Analysis (major keys)

Analyze each of the following excerpts by adding a Roman numeral to each of the lines below the lower staff. Don’t forget to match your Roman numeral case (upper or lower) to the quality of the chord and use extra symbols (like ^o) where needed. Use bass figures to indicate inversions.

Note that each of these excerpts modulates. For chords that belong to the original key, write the Roman numeral above the blank line provided. For chords that belong to the secondary key, write the Roman numeral below the blank line provided. For pivot chords, add Roman numerals both above and below the line and separate them with an asymmetrical bracket. Don’t forget to write the name of the new key with a colon where the lower set of Roman numerals begin. (See activity IV above for an example.)

In cases of direct modulations, you may simply write all of the Roman numerals above the blank lines, making sure to specify the name of the new key when it first appears.

Maria Hester Park, A Waltz, mm. 19-26

Maria Frances Parke, Piano Sonata in D major (Op. 1, No. 3), II. Largo, mm. 1-8

Chiquinha Gonzaga, “Manhã de amor,” mm. 34-65

Sophia Dussek, The New German Waltz, mm. 1-8

Louise Farrenc, 20 Etudes de moyenne Difficulté pour Piano (Op. 42), No. 7 in D major, mm. 1-8

Maria Theresia von Paradis, 12 Lieder auf ihrer Reise in Musik gesetzt, 10. “Da eben seinen Lauf vollbracht,” mm. 1-16

Françoise Desfossez, Sonata in E major (Op. 3, No. 2), III. Rondo—Graziozo, mm. 1-12

Sabine Hitzelberger, Für fülende Seelen am Klavier, 8. “Einladung zur Brunnen-Kur,” mm. 1-8

Analysis (minor keys)

Analyze each of the following excerpts by adding a Roman numeral to each of the lines below the lower staff. Don’t forget to match your Roman numeral case (upper or lower) to the quality of the chord and use extra symbols (like ^o) where needed. Use bass figures to indicate inversions.

Note that each of these excerpts modulates. For chords that belong to the original key, write the Roman numeral above the blank line provided. For chords that belong to the secondary key, write the Roman numeral below the blank line provided. For pivot chords, add Roman numerals both above and below the line and separate them with an asymmetrical bracket. Don’t forget to write the name of the new key with a colon where the lower set of Roman numerals begin. (See activity IV above for an example.)

In cases of direct modulations, you may simply write all of the Roman numerals above the blank lines, making sure to specify the name of the new key when it first appears.

Louise Farrenc, Violin Sonata No. 2 (Op. 39), II. Scherzo—Allegro, mm. 1-12

Marie-Thérèse-Louise Benaut, Recueil d’airs avec variations (Op. 4), “Le novice de la Trappe,” mm. 42-49

Louise Farrenc, 25 Etudes faciles (Op. 50), No. 2 in A minor, mm. 1-8

Louise Farrenc, 12 Etudes de dextérité (Op. 41), No. 8 in C minor, mm. 1-6

Analysis (modulations to less common destinations)

Analyze each of the following excerpts by adding a Roman numeral to each of the lines below the lower staff. Don’t forget to match your Roman numeral case (upper or lower) to the quality of the chord and use extra symbols (like ^o) where needed. Use bass figures to indicate inversions.

Note that each of these excerpts modulates. For chords that belong to the original key, write the Roman numeral above the blank line provided. For chords that belong to the secondary key, write the Roman numeral below the blank line provided. For pivot chords, add Roman numerals both above and below the line and separate them with an asymmetrical bracket. Don’t forget to write the name of the new key with a colon where the lower set of Roman numerals begin. (See activity IV above for an example.)

In cases of direct modulations, you may simply write all of the Roman numerals above the blank lines, making sure to specify the name of the new key when it first appears.

Fanny Hensel, Walzer, mm. 1-16