3.4: Advanced Mixture

30.1 Introduction

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In describing these increasingly chromatic harmonies, we will push our chord-labeling system toward its limit. Roman numerals are a useful, shorthand way of naming chords, identifying their function, and showing their connection to a tonic. Although their primary purpose is to identify diatonic relationships, conventional Roman numerals may be adapted to indicate chromaticism when harmonic practice becomes more complex. Being able to recognize and use such adjustments is essential for analyzing a wide spectrum of music. This chapter will show how we expand Roman numeral conventions to deal with chromatic elements in cases of advanced mixture.

30.2 Roman numerals and simple mixture

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The following example shows several other examples of how Roman numerals may be used to indicate mixture:

Example 30–1.

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Example 30–2.

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You should become familiar enough with the qualities of diatonic chords that you can immediately recognize Roman numerals that indicate chromatic alterations. In the context of a major key, for instance, chords such as i and ii^o should instantly alert you to chromatic alterations.

30.3 Secondary mixture

All of the examples of mixture presented so far have been relatively straightforward. In each case, one or two tones are borrowed from the parallel key to emphasize or intensify certain harmonies. Occasionally, however, you will encounter instances of chromatic alterations that cannot be explained in such simple terms. The following excerpt includes two chromatically-altered harmonies, one in mm. 2–3 and another in m. 7:

Example 30–3. Franz Schubert, “Gondelfahrer” (D.808), mm. 1–13.

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The following example shows another, similar case of secondary mixture:

Example 30–4. Franz Schubert, Piano Sonata No. 17 in D major (D.850), III. Scherzo and Trio, mm. 53–61.

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Despite the chromaticism, we still use Roman numerals to identify the chords described above. The following example illustrates:

Example 30–5.

In instances of secondary mixture the quality of the chord in question is changed, but not through borrowing of tones from the parallel key. The minor quality of the diatonic ii chord becomes major (II) through secondary mixture. Likewise, iii and vi become III and VI, respectively. In each instance, the alteration is indicated by a change in the case (uppercase or lowercase) of the Roman numeral.

The following example shows both simple mixture (bVII) and secondary mixture (II):

Example 30–6. Franz Schubert, Allegro in A minor (D. 947), mm. 87–104.

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Secondary mixture appears in minor keys as well:

Example 30–7.

As shown by Example 30–7, III, VI, and VII in a minor key may be made minor through secondary mixture. In such cases, they are labeled iii, vi, and vii, respectively.

The following example includes a minor vii chord in a minor key:

Example 30–8. Johann Sebastian Bach, Aus tiefer Not schrei ich zu dir (BWV 38), 6. “Aus tiefer Not schrei ich zu dir,” mm. 11–13.

Example 30–8 shows the concluding phrase from a chorale. On the third beat of m. 12, we find a case of secondary mixture. The third of the chord has been lowered to the chromatic Bb, changing what would diatonically be a major VII chord to a minor vii chord.

Activity 30-1

Activity 30–1

Identify each of the following chords in various keys with a Roman numeral. (Note: Each chord is in root position.)

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Exercise 30–1a:

Question

Identify the following chord in Ab major with a Roman numeral:

Hint

Remember to use accidentals to indicate altered roots. The case of the Roman numeral should correspond with the quality of the triad.

Answer

III

Follow-up question

Is this a case of simple or secondary mixture?

Answer

secondary

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Exercise 30–1b:

Question

Identify the following chord in A major with a Roman numeral:

Hint

Remember to use accidentals to indicate altered roots. The case of the Roman numeral should correspond with the quality of the triad.

Answer

bVI

Follow-up question

Is this a case of simple or secondary mixture?

Answer

simple

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Exercise 30–1c:

Question

Identify the following chord in F minor with a Roman numeral:

Hint

Remember to use accidentals to indicate altered roots. The case of the Roman numeral should correspond with the quality of the triad.

Answer

i

Follow-up question

Is this a case of simple or secondary mixture?

Answer

simple

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Exercise 30–1d:

Question

Identify the following chord in C# minor with a Roman numeral:

Hint

Remember to use accidentals to indicate altered roots. The case of the Roman numeral should correspond with the quality of the triad.

Answer

vi

Follow-up question

Is this a case of simple or secondary mixture?

Answer

secondary

30.4 Double mixture

A third type of mixture may be found in the following example, which begins in the key of C minor:

Example 30–9. Franz Schubert, “Die Liebe hat gelogen” (D.751), mm 3–6.

At the beginning of m. 5 we find a clear-cut case of mixture: the E§s in both the voice and the piano change the quality of the tonic triad from minor to major, and C major is then tonicized with an authentic cadence in m. 6. However, in the second half of m. 5, we find an A major triad (#VI). With respect to C minor, all three members of that triad have been raised. This is not a case of simple mixture because C major, the parallel to C minor, does not include C#.

This is a case of double mixture. Double mixture involves changing the quality of a chord derived from simple mixture. In the key of C minor, simple mixture allows for an A-minor triad (#vi). When we encounter an A-major triad (#VI), we may think of it as being a case in which secondary mixture has been applied to a simple mixture chord, hence double mixture.

Once again, we may use Roman numerals to represent these chords. Consider the following cases of double mixture in a major key:

Example 30–10.

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Example 30–11 shows two examples of Roman numeral labeling for double mixture in a minor key:

Example 30–11.

Note again that despite the natural signs altering the roots of these chords, the Roman numerals are preceded by # symbols.

Now consider the following example:

Example 30–12. Claude Debussy, “Beau Soir,” mm. 1-9.

a.

b. reduction

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The sonority in m. 2 (and m. 6) is complicated by the presence of pitch-class B. If the B is heard as a pedal tone—sustained through the framing E-major chords in m. 1 and m. 3—we would consider this another case of double mixture: a simple-mixture bVII with a secondary minor inflection. It is also possible to hear this as a neighboring sonority prolonging the tonic: the D§s are neighbors to the Es, the F§s are neighbors to the Es, and the As are neighbors to the Bs. (Example 30–12b demonstrates this hearing by placing the neighbor tones in parentheses.)

Note: As you can see from the explanation above, discussions involving secondary and double mixture can quickly become quite complicated. Furthermore, faced with such abundant chromaticism, you may have even found it challenging to hear E major as the tonic in Example 30–12. Given the prevalence of chromaticism in such music, one must wonder if the harmonic relationships encountered here are fundamentally different from those found in the tonal music of the high Classical era. Many listeners hear enough of a difference that they consider such music to be, in a way, post-tonal. Indeed, upon hearing the music, one quickly becomes aware that the tonic-dominant relationship forming the foundation of tonal harmony plays a much more peripheral role here.

It follows, then, that one should use caution when employing analytical strategies that were designed for describing a different kind of music. In recent years, music theorists have begun hearing this music on its on terms. According to this new perspective, the relationship heard between, for example, I and biii may be as distinctive and foundational as any authentic cadence. It all depends on the context.

Activity 30-2

Activity 30–2

The following triads exhibit various types of mixture: simple (borrows tones from the parallel key), secondary (alters the quality with pitches not from the parallel key), or double (secondary mixture applied to chords derived through simple mixture). For each exercise, label the triad with the appropriate Roman numeral and identify the type of mixture present:

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Exercise 29–5a:

Question

Provide a Roman numeral for the following triad in G major:

Hint

Remember to match the case of the Roman numerals with the quality of the triad and indicate altered roots with accidentals.

Answer

VI

Follow-up question

What type of mixture is exhibited by this triad?

Answer

secondary

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Exercise 29–5b:

Question

Provide a Roman numeral for the following triad in D minor:

Hint

Remember to match the case of the Roman numerals with the quality of the triad and indicate altered roots with accidentals.

Answer

IV

Follow-up question

What type of mixture is exhibited by this triad?

Answer

simple

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Exercise 29–5c:

Question

Provide a Roman numeral for the following triad in B minor:

Hint

Remember to match the case of the Roman numerals with the quality of the triad and indicate altered roots with accidentals.

Answer

#VI

Follow-up question

What type of mixture is exhibited by this triad?

Answer

double

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Exercise 29–5d:

Question

Provide a Roman numeral for the following triad in Bb major:

Hint

Remember to match the case of the Roman numerals with the quality of the triad and indicate altered roots with accidentals.

Answer

bVI

Follow-up question

What type of mixture is exhibited by this triad?

Answer

simple

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Exercise 29–5e:

Question

Provide a Roman numeral for the following triad in A major:

Hint

Remember to match the case of the Roman numerals with the quality of the triad and indicate altered roots with accidentals.

Answer

biii

Follow-up question

What type of mixture is exhibited by this triad?

Answer

double

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Exercise 29–5f:

Question

Provide a Roman numeral for the following triad Eb major:

Hint

Remember to match the case of the Roman numerals with the quality of the triad and indicate altered roots with accidentals.

Answer

III

Follow-up question

What type of mixture is exhibited by this triad?

Answer

secondary

30.5 Other chromatic chords

A different type of chromatic chord can be seen in the following example:

Example 30–13. Delphine Ugalde, Seule, mm. 1–11.

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Another Neapolitan chord appears in the following example:

Example 30–14. Ludwig van Beethoven, Piano Sonata No. 14 in C# minor [“Moonlight”] (Op. 27, No. 2), I. Adagio sostenuto, mm. 1–5.

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A more detailed discussion of the Neapolitan chord can be found in Chapter 31.

30.6 Summary

Simple mixture consists of borrowing one or more scale degrees from the parallel key to alter the quality of a chord. Other types of mixture also involve changing the quality of a chord, but with chromatic tones that are foreign to both the key at hand as well as its parallel. With secondary mixture, a composer may change the quality of a triad by raising or lowering its root with such a chromatic tone. In cases of double mixture, a composer changes the quality of a simple mixture chord by applying secondary mixture.

Because Roman numerals are able to express both the root and quality of a chord, they are also useful for indicating the three types of mixture. As always, the case of the Roman numerals indicates chord quality. You should become familiar enough with the qualities of diatonic triads that by simply looking at a Roman numeral you are immediately able to recognize the presence of chromatic alterations. Accidentals preceding a Roman numeral signal an altered root: a prefix b indicates a lowered root while # indicates a raised root.