1. Harmonic Expansions
G. DeBenedetti

2. Chapter 8: Expanding the Dominant and the Initial Tonic 8
Chapter 8: Expanding the Dominant and the Initial Tonic 8.1 Expanding the Dominant with the Cadential 6/4

3. Chords or Nonharmonic Tones?
In Chapter 7 the fundamental harmonic progression was expanded with just a few nonharmonic tones--usually in the soprano only.

4. Chords or Nonharmonic Tones?
In Chapter 7 the fundamental harmonic progression was expanded with just a few nonharmonic tones--usually in the soprano only.
In contrast, in Chapter 8 this progression will be expanded with at least two simultaneous nonharmonic tones.

5. Chords or Nonharmonic Tones?
In Chapter 7 the fundamental harmonic progression was expanded with just a few nonharmonic tones--usually in the soprano only.
In contrast, in Chapter 8 this progression will be expanded with at least two simultaneous nonharmonic tones.
These combinations of notes often sound like chords.

6. Chords or Nonharmonic Tones?
In Chapter 7 the fundamental harmonic progression was expanded with just a few nonharmonic tones--usually in the soprano only.
In contrast, in Chapter 8 this progression will be expanded with at least two simultaneous nonharmonic tones.
These combinations of notes often sound like chords.
Many factors related to the musical context and the individual listener influence whether they are heard as nonharmonic tones or chords…

7. Chords or Nonharmonic Tones?
In Chapter 7 the fundamental harmonic progression was expanded with just a few nonharmonic tones--usually in the soprano only.
In contrast, in Chapter 8 this progression will be expanded with at least two simultaneous nonharmonic tones.
These combinations of notes often sound like chords.
Many factors related to the musical context and the individual listener influence whether they are heard as nonharmonic tones or chords…
And what we end up calling them depends on what level of analysis we use.

8. In these illustrations, nonharmonic tones expand V in the fundamental harmonic progression, as in Chapter 7.

9. In these illustrations, nonharmonic tones expand V in the fundamental harmonic progression, as in Chapter 7.
Three common basses are shown under the dominant.

10. Three common basses are shown under the dominant.
In these illustrations, nonharmonic tones expand V in the fundamental harmonic progression, as in Chapter 7.
Three common basses are shown under the dominant.
The underlying melodies in the soprano are scale degrees:
1, 7, 1 in Example 1
1, 2, 1 in Example 2
3, 2, 1 in Example 3

11. Three common basses are shown under the dominant.
In these illustrations, nonharmonic tones expand V in the fundamental harmonic progression, as in Chapter 7.
Three common basses are shown under the dominant.
The underlying melodies in the soprano are scale degrees:
1, 7, 1 in Example 1
1, 2, 1 in Example 2
3, 2, 1 in Example 3
The last few chords of a phrase are called the cadence.

12. The previous examples are now shown with added nonharmonic tones.

13. The previous examples are now shown with added nonharmonic tones.
The new Arabic numerals, , reflect the changed notes.

14. The previous examples are now shown with added nonharmonic tones.
The new Arabic numerals, , reflect the changed notes.
The chord above the 6/4 is called a cadential 6/4.

15. The previous examples are now shown with added nonharmonic tones.
The new Arabic numerals, , reflect the changed notes.
The chord above the 6/4 is called a cadential 6/4.
The 6th above the bass is not normally dissonant, and is not normally a nonharmonic tone…

16. The previous examples are now shown with added nonharmonic tones.
The new Arabic numerals, , reflect the changed notes.
The chord above the 6/4 is called a cadential 6/4.
The 6th above the bass is not normally dissonant, and is not normally a nonharmonic tone…
But in this case, with a strong dominant in the bass, and with the phrase coming to a close on the tonic, there is a sense of resolution as the 6th moves to a 5th.

17. Closer inspection shows that the cadential 6/4 is a second inversion tonic chord.

18. Closer inspection shows that the cadential 6/4 is a second inversion tonic chord.
The new Arabic and Roman numerals below the staff, I6/4, now reflect this new root.

19. Closer inspection shows that the cadential 6/4 is a second inversion tonic chord.
The new Arabic and Roman numerals below the staff, I6/4, now reflect this new root.
Yet the nonharmonic labels remain, reflecting this chord's instability with respect to V.

20. So which is it? Is the cadential 6/4…
Closer inspection shows that the cadential 6/4 is a second inversion tonic chord.
The new Arabic and Roman numerals below the staff, I6/4, now reflect this new root.
Yet the nonharmonic labels remain, reflecting this chord's instability with respect to V.
So which is it? Is the cadential 6/4…
a I6/4 chord moving to V… OR…
a V chord altered by two nonharmonic tones??

21. In fact, the second chord in these examples is both a tonic 6/4 and an altered V chord .

22. In fact, the second chord in these examples is both a tonic 6/4 and an altered V chord .
This ambiguity is reflected in the above illustration by a second level of analysis under the brackets.

23. In fact, the second chord in these examples is both a tonic 6/4 and an altered V chord .
This ambiguity is reflected in the above illustration by a second level of analysis under the brackets.
When looking strictly vertically the chord is a tonic 6/4.

24. In fact, the second chord in these examples is both a tonic 6/4 and an altered V chord .
This ambiguity is reflected in the above illustration by a second level of analysis under the brackets.
When looking strictly vertically the chord is a tonic 6/4.
When looking more broadly the chord is an altered V.

25. In fact, the second chord in these examples is both a tonic 6/4 and an altered V chord .
This ambiguity is reflected in the above illustration by a second level of analysis under the brackets.
When looking strictly vertically the chord is a tonic 6/4.
When looking more broadly the chord is an altered V.
Music theorists encourage students to look at scores broadly, but an initial analysis might quite correctly involve vertical sonorities only.

26. The concept of analytical levels is a powerful one and can be extended to include the "birth" of the fundamental progression I V I from the "primordial tonic" (Chapter 6).

27. The concept of analytical levels is a powerful one and can be extended to include the "birth" of the fundamental progression I V I from the "primordial tonic" (Chapter 6).
The illustration above shows this relationship in Level 3.

28. The concept of analytical levels is a powerful one and can be extended to include the "birth" of the fundamental progression I V I from the "primordial tonic" (Chapter 6).
The illustration above shows this relationship in Level 3.
In the following sections of Chapter 8, other ambiguities will result from simultaneous nonharmonic tones.

29. The concept of analytical levels is a powerful one and can be extended to include the "birth" of the fundamental progression I V I from the "primordial tonic" (Chapter 6).
The illustration above shows this relationship in Level 3.
In the following sections of Chapter 8, other ambiguities will result from simultaneous nonharmonic tones.
They will be explained, like the cadential 6/4, by two levels of analysis.

30. But first, an excerpt from "real" music: here is an example of a cadential 6/4 in the introduction to Schubert's Erlkönig.

31. Your Turn!
Review the Fundamental Harmonic Progression and Consonant Skips from Chapter 6 with some dictation exercises.
DOWNLOAD an answer sheet for you to write on.
LISTEN to the mp3 files specified in the instructions.
WRITE the soprano of the progressions you will hear.
DOWNLOAD the solutions page and CHECK your work.