III. Modulation and Chromatic Harmony

29. Mixture


29.1 Introduction

In Chapter 15 and Chapter 27, we discussed various sorts of chromatic pitches. As we saw, non-diatonic tones may arise as a result of melodic or harmonic embellishment, or as part of an applied chord. This is not the case, however, in the following example:

Example 29–1. Franz Schubert, Die Schöne Müllerin (D. 795), 6. “Der Neugierige,” mm. 23–28.

example_29-1

Notice that in m. 25 scale degree 3 has been lowered from D# to D§. Instead of a major I chord (B major), we hear a minor i chord (B minor). The effect is striking. Why would the composer make such an alteration at this point? Looking at the text of the song, we find the narrator speaking to a brook that led him to a miller’s beautiful daughter. At m. 25, having just asked the brook to tell him whether his heart has mistakenly led him to believe that the maid loves him, he remarks (to the brook), “wie bist du heut’ so stumm!” (“how quiet you are today!”) The observation marks a moment of doubt; a subtle change in mood that the composer intensifies by presenting a minor form of the tonic triad.

This musical phenomenon is referred to as mixture, for it mixes elements of both the major and minor modes of a particular key. In other words, mixture in a major key consists of borrowing chords or tones from the parallel minor, and vice versa. As can be seen in Example 29–1, mixture is particularly effective in music with text. The changes in color, brought about by the borrowed tones, can highlight and intensify certain words or passages. But this is not to say that words are a necessary component. Mixture is equally effective at lending drama to instrumental music.

In this chapter we will first examine the nature and mechanics of mixture. Turning to several examples from the tonal repertoire, we will look at common types of mixture. Finally, we will conclude with a discussion of the large-scale, structural uses of mixture.

29.2 The nature of mixture

To understand mixture, we must consider the differences and similarities between parallel keys. (Refer to Chapter 7 for a more detailed discussion of the minor scale.) As Example 29–2 demonstrates, parallel keys differ at scale degrees 3, 6, and 7 (indicated with arrows in the diagrams below):

In a minor key, scale degrees 3, 6, and 7 are a semitone lower than their parallel major counterparts. Because they constitute the difference between the major and minor modes, these are sometimes referred to as the modal scale degrees. This variation is responsible for the differing qualities of the diatonic chords built on each step of the scale:

As you can see, the difference in scale degrees 3, 6, and 7 affects the quality of every diatonic chord. (Note that the leading tone has not been adjusted for the chords built on scale degrees 5 and 7 in Example 29–3b. We will address this momentarily.)

Instances of mixture—often referred to as borrowed tones or chords—include one or more of the modal scale degrees from the parallel key. In other words, mixture in a major key will lower scale degrees 3, 6, or 7, while mixture in a minor key will raise them. These non-diatonic pitches bring with them all the expressive capabilities of the opposite mode. By incorporating elements of the parallel key in this manner, composers can expand and enhance their creative musical palette.

Activity 29-1

Activity 29–1

For each of the following keys, indicate the three tones that may be borrowed from the parallel major or minor.


Exercise 29–1a:

Question

In the key of A major, what three tones may be borrowed from the parallel minor?

Hint

Remember, the modal scale degrees are 3, 6, and 7.

Answer

C§, F§, and G§


Exercise 29–1b:

Question

In the key of C minor, what three tones may be borrowed from the parallel major?

Hint

Remember, the modal scale degrees are 3, 6, and 7.

Answer

E§, A§, and B§


Exercise 29–1c:

Question

In the key of F major, what three tones may be borrowed from the parallel minor?

Hint

Remember, the modal scale degrees are 3, 6, and 7.

Answer

Ab, Db, and Eb


Exercise 29–1d:

Question

In the key of B minor, what three tones may be borrowed from the parallel major?

Hint

Remember, the modal scale degrees are 3, 6, and 7.

Answer

D#, G#, and A#

29.3 Labeling instances of mixture

Because mixture alters the members and qualities of the affected harmonies, we must address the conventions for labeling borrowed chords. As you know, the case of a Roman numeral indicates the quality of the chord: uppercase for major chords and lowercase for minor and diminished. This should remain consistent in cases of mixture.

Consider the following example:

Example 29–4. Amalie Wilhelmina Koch, Piano Sonata No. 1, mm. 1–14.

example_29-4

The progression in Example 29–4 uses b3 (a lowered scale degree 3; Bb in this case), resulting in a minor triad in m. 8. The Roman numerals are consistent with this change in quality, using lowercase i instead of uppercase I.

Note: You may have previously encountered a different method of labeling with Roman numerals that uses only capital letters. In this system, accidentals appearing after the Roman numeral indicate alterations made to the third of the chord. According to this system, the mixture chord in Example 29–4 would be labeled Ib, the b symbol indicating the lowered third of the chord. Though this method has merits, it will not be used here. Refer to Chapter 30 for a more detailed discussion of advanced Roman numeral usage.

To further accommodate the changes brought about by borrowing from the parallel mode, accidentals are sometimes used in conjunction with Roman numerals. An accidental before a Roman numeral indicates an altered root:

Example 29–5. Isabella Ketterer, “Antoinette March, mm. 13–20.

example_29-5

In the example above, the final chord of m. 18 is built on the lowered sixth scale degree (Ab). The altered root is indicated by the accidental: bVI. Accidentals next to figured bass numerals function as usual, affecting only the indicated pitches.

Note: Occasionally, a borrowed scale degree will negate one of the sharps or flats in the key signature, as in the following example which shows a transposed version of Example 29–5:

Example 29–6. Transposition of Isabella Ketterer, “Antoinette March, mm. 13–20.

example_29-6

Example 29–6 includes a VI chord whose root, F§, negates the F# in the key signature. Nonetheless, it has still been labeled bVI. You may occasionally encounter books that would label this chord §VI. But for the sake of clarity and consistency, we will follow this convention: use a flat for a lowered root and a sharp for a raised root, regardless of the key signature.

Activity 29-2

Activity 29–2

Each of the following exercises shows a chord in a given key with at least one borrowed tone. Label each of the chords according to the conventions outlined above. Be sure to use capital letters for major chords, lowercase for minor, and so on. (Note: All of the chords are in root position, so there is no need to include bass figures.)


Exercise 29–2a:

Question

How should this chord be labeled in the key of E major?

Hint

Remember to use the correct case for indicating the quality of the chord and to place an accidental before the Roman numeral if the root is altered.

Answer

bVI


Exercise 29–2b:

Question

How should this chord be labeled in the key of F minor?

Hint

Remember to use the correct case for indicating the quality of the chord and to place an accidental before the Roman numeral if the root is altered.

Answer

I


Exercise 29–2c:

Question

How should this chord be labeled in the key of B minor?

Hint

Remember to use the correct case for indicating the quality of the chord and to place an accidental before the Roman numeral if the root is altered.

Answer

IV


Exercise 29–2d:

Question

How should this chord be labeled in the key of Bb major?

Hint

Remember to use the correct case for indicating the quality of the chord and to place an accidental before the Roman numeral if the root is altered.

Answer

viio7

29.4 Mixture in major keys

In major keys, instances of mixture usually incorporate b3, b6, or both. (b7 is generally avoided because its presence would subvert the important dominant function of the V and viio chords.)

A lowered scale degree 6 is used to color and intensify chords built on 2 or 4. For example, the presence of b6 will make a IV chord minor (iv) as in the following excerpts:

Example 29–7. Josepha Müllner-Gollenhofer, Danklied, mm. 115-123.

example_29-7

In mm. 120–122, a pair of V7–I progressions echoes the conclusion of the vocal line. The tonic is then is prolonged in m. 122 with a pair of F-minor triads. The Ab, borrowed from the parallel minor, alters the IV chords on beats two and four by making them minor. The Roman numerals are lowercase to reflect the change in chord quality.

Borrowed tones frequently originate as chromatic alterations of diatonic notes. Consider the following example:

Example 29–8. Johann Sebastian Bach, Weihnachtsoratorium (BWV 248), 33. “Ich will dich mit Fleiß bewahren,” mm. 1–3.

example_29-8

Here, b6 appears as a chromatic passing tone in the bass. It occurs with a change of harmony in the upper voices and briefly produces a minor iv chord.

Incorporating a borrowed b6 in a supertonic chord will turn a minor chord into a diminished chord (iio). Seventh chords can likewise be affected by mixture. A ii7 chord, for example, would become half-diminished (iiø7) with the addition of b6.

Example 29–9. Maria Theresia von Paradis, Sicilienne, mm. 1–3.

example_29-9

As in Example 29–7 and Example 29–8, the presence of b6 in m. 1 makes the neighboring iv6/4 chord minor. When an F is added in the next measure it makes a half-diminished chord out of what would have diatonically been a minor seventh.

As discussed in Chapter 20, this kind of borrowing happens routinely in leading-tone seventh chords. Borrowing b6 in a seventh chord built on scale degree 7 will change a half-diminished seventh chord to fully-diminished. The following example borrows an Ab from C minor in m. 14:

Example 29–10. Johann Sebastian Bach, Das wohltemperierte Klavier I, Prelude and Fugue 1 in C major (BWV 846), mm. 11–16.

example_29-10

The Ab in m. 14 changes the quality of the leading-tone seventh chord from half- to fully-diminished.

A lowered scale degree 3 is sometimes used to produce a minor tonic where one would normally expect a major harmony:

In this example, the concluding tonic harmony is made minor by the presence of Eb, borrowed from the parallel minor. The presence of b3 in a tonic harmony can have a surprising and dramatic effect! Consider the following example:

Example 29–12. Franz Schubert, Die Schöne Müllerin (D.795), 4. “Danksagung an den Bach,” mm. 16–28.

example_29-12

Like Example 29–1, this song uses a minor tonic to reflect a change in mood in the song’s text. Following a strong cadence in the key of G major in mm. 17–18, we encounter a minor tonic (i) in m. 22. Again, the effect is startling and intensifies the emotional tension of the moment.

Combining b3 and b6 will result in the bVI chord mentioned above. The bVI chord is one of the most commonly borrowed chords in a major key. When used in a deceptive cadence it increases the dramatic effect by thwarting to an even greater degree the listener’s expectation of tonic harmony. The following example does just this:

Example 29–13. Wolfgang Amadeus Mozart, Don Giovanni, Act I, Scene 5, “Madamina, il catalogo è questo,” mm. 118-127.

example_29-13

Activity 29-3

Activity 29–3

Exercise 29–3:

Question

The ability to recognize and identify instances of mixture is an important skill. In what key is the following excerpt?

Frédéric Chopin, Nocturnes (Op. 32), 2. Lento, mm. 1–4.

activity_29-3

Hint

What chord does the excerpt begin with?

Answer

Ab major

Follow-up question

What Roman numeral should appear at beat four in the first measure (before the Bb in the uppermost voice)?

Hint

Identify the root of the chord to determine the Roman numeral, then adjust the case accordingly to match the quality.

Answer

iv

29.5 Mixture in minor keys

Chapter 4 introduced the concepts of the harmonic and melodic minor composites which feature raised scale degrees 6 and 7. These adjustments can be seen as instances of mixture, where elements of the parallel major are borrowed to suit certain harmonic and melodic contexts. Other than the ubiquitous raising of the leading tone and submediant, mixture is far less common in minor keys than it is in major keys.

Occasionally, composers will incorporate #3 or #6 to lend color to i and iv chords (i becomes I and iv becomes IV with the raising of scale degrees 3 and 6, respectively). The following example incorporates one such borrowed scale degree in m. 3:

Example 29–14. Johann Sebastian Bach, Bisher habt ihr nichts gebeten in meinem Namen (BWV 87), 7. “Muß ich sein betrübet?,” mm. 1–6.

example_29-14

In this example, the chord on the third beat has a B§ in the soprano and then in the tenor. This raised third (scale degree 6) changes the quality of the chord: what would have been minor (iv) is here major (IV). The C# on beat four changes the quality of the following chord to diminished (viio6). Looking at the melody in the soprano part, it is easy to see that both of these alterations are a result of the melodic minor composite which, as described in Chapter 17, is itself a type of mixture.

The following example uses a borrowed scale degree in the final chord:

Example 29–15. Louise Farrenc, 30 Etudes (Op. 26), No. 15, mm. 71–79.

example_29-15

The B# in the final chord of this example makes the tonic major. The raised third of a tonic chord in a minor key is usually referred to as a Picardy third. Composers will commonly employ a Picardy third at the end of a piece in minor, coloring the conclusion with the character of a major tonic.

Activity 29-4

Activity 29–4

Exercise 29–4:

Question

In what key is the following excerpt?

Heinrich Schütz, Di marmo siete voi (SWV 17), mm. 35–36.

activity_29-4

Answer

A minor

Follow-up question

What Roman numeral should appear under the final harmony?

Hint

Identify the root of the chord to determine the Roman numeral, then adjust the case accordingly to match the quality.

Answer

I

Follow-up question

What is the common name for this particular kind of mixture?

Answer

Picardy third

29.6 Mixture and basic interval progressions

Instances of mixture are often the result of adjustments made to the basic interval progressions outlined in Chapter 12. In all of the harmonic progressions considered in this chapter, the voice-leading is governed by the same basic interval progressions whether mixture is present or not. In some cases, however, mixture strengthens the underlying interval progressions.

The motion from a major third to a unison is intensified by altering one of the voices to introduce semitone motion:

The following example puts this into context:

Example 29–17. Johann Sebastian Bach, “Christus, der ist mein Leben” (BWV 281), mm. 5–8.

example_29-17

Whereas typically the motion from a major third to a unison consists of both voices moving by whole tones, moving from a minor third to a unison reduces one voice’s movement to a semitone. The result is similar to the strong semitone/whole tone motion of a major sixth to an octave. Similarly, the motion from a major sixth to a perfect fifth is made stronger by contracting the upper-voice motion to a semitone:

The following example puts this adjustment into context (Example 29–19b provides a reduction of Example 29–19a to clarify the voice-leading):

Example 29–19. Johannes Brahms, 5 Lieder (Op. 105), 1. “Wie Melodien Zieht es mir,” mm 25–28.

a.

example_29-19a

b. reduction

example_29-19b

By lowering the F# to F§, Brahms strengthens the motion to the tonic triad from m. 26 to m. 28.

While mixture often results from such voice-leading, it need not always. Sometimes, mixture is used strictly for purposes of coloration. Consider the following example:

Example 29–20. Wolfgang Amadeus Mozart, Piano Sonata No. 12 in F major (K.332), II. Adagio, mm. 1–8.

example_29-20

In this excerpt from the beginning of a piano sonata movement, we first hear a melody in Bb major. In mm. 5–8 we hear the melody again. This time, however, it is presented in Bb minor to heighten the expressiveness of the music.

29.7 Mixture and modulation

Most of the examples we have looked at so far are relatively small in scale. Composers borrow specific tones from the parallel key to color a chord here or there and thus dramatize the passage. But mixture can affect larger areas of music as well, particularly with regards to modulation.

Consider the following example:

Example 29–21. Maria Theresia von Paradis, 12 Lieder auf ihrer Reise in Musik gesetzt, 9. “Vaterlandslied,” mm. 50–60.

example_29-21

The third verse of the song ends unambiguously in G major (m. 52) followed by a four bar extension of the cadence in the piano. Then, after a short pause, the music shifts directly to G minor, key signature and all.

In the following example, from the same collection of songs as Example 29–25, we find a similar modulation:

Example 29–22. Maria Theresia von Paradis, 12 Lieder auf ihrer Reise in Musik gesetzt, 10. “Da eben seinen Lauf vollbracht,” mm. 21–28.

example_29-22

In m. 24 we hear a perfect authentic cadence in G major. Halfway through the same measure, though, the third of the tonic triad—somewhat hidden in an inner voice—is lowered to Bb. This inflection is initially relegated to the piano part alone. The singer does not sing scale degree 3 until the next measure. Altering the chord in this way smooths the transition between the parallel key areas.

Activity 29-5

Activity 29–5

Exercise 29–5:

Question

The following excerpt begins in A minor but modulates in m. 24. To which key does it modulate?

Wolfgang Amadeus Mozart, Piano Sonata No. 11 in A major (K.331), III. Alla Turca, iii, mm. 1–33.

activity_29-5

Hint

The excerpt modulates to the parallel major.

Answer

A major

Follow-up question

In the tonic key of A minor, what Roman numeral would be used to represent an A major triad?

Hint

The root of an A major triad is the same as the root of the tonic triad in A minor.

Answer

I

In Activity 29–6 we looked at an excerpt from a piano sonata with a modulation from A minor to A major. This modulation involved a change of key signature in the middle of a bar:

Example 29–23. Wolfgang Amadeus Mozart, Piano Sonata No. 11 in A major (K.331), III. Alla Turca, iii, mm. 21–33.

example_29-23

As in Example 29–25, we hear a perfect authentic cadence in the original key followed by a new section of the piece in the parallel key. Once again, scale degree 3 makes the pivotal change, but here it is raised by a semitone to initiate the switch to the parallel major. Despite the mid-measure change of key signature, the listener is unaware of the new key until the downbeat of the following measure where octave C#s are played on the downbeat. (Actually, the first C# we hear is in the grace note arpeggio leading to the downbeat A in the left hand.)

Modulations via mixture are not limited only to the parallel key of the global tonic. The following example in F major modulates to the key of C minor:

Example 29–24. Wolfgang Amadeus Mozart, Piano Sonata No. 12 in F major (K.332), III. Allegro assai, mm. 47–57.

example_29-24

In sonatas such as this one, it is quite common to encounter modulations to the key of the dominant. After a transition section ending in m. 49, we expect just that: a theme in C major. Instead, the melody beginning in m. 50 is clearly in C minor. The result is a move from F major to the rather distantly-related key of C minor through a mixture shift.

29.8 Summary

Mixture consists of the borrowing of elements from the parallel key. Parallel keys differ at scale degrees 3, 6, and 7, so it is at these points that mixture will occur. In both major and minor keys, chords borrowed from the parallel key can intensify the drama of a musical texture.

Some instances of mixture can be seen as a result of strengthening the basic interval progressions governing the voice-leading of a harmonic progression. This is not always the case, however, since some cases of mixture are employed strictly for color, variation, and drama.

Mixture can have an effect on larger spans of music as well. It can initiate modulation to foreign keys via a tonicization of a borrowed chord or by moving directly to a mixture-related key area.

By incorporating chromatic pitches in this manner, composers are able to expand and enrich their options for musical expression. Though common in pieces from across the tonal repertoire, mixture is especially prevalent in music from the Romantic era. Composers in that style period were particularly concerned with the emotional impact of their music and mixture provided an effective means of heightening the level of expression.

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Fundamentals, Function, and Form by Andre Mount is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License, except where otherwise noted.

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