Chapter 23

Spelling and Modulating, enharmonically

By

Robert Fleisher, Northern Illinois University

We learn in this chapter that notes, chords, and keys can all be spelled enharmonically. The notes F# and Gb (and E double-sharp), and the chords and keys of F# major and Gb major all have the identical sound; they are merely spelled differently (as are all the pitches in their equivalent key signatures). Enharmonicism requires special care, since the spelling of chords often obscures their true function.¹ Composers have different reasons for enharmonic spellings, but whatever the reason, you cannot hear this difference. However, anyone with a "good ear" may notice an enharmonic modulation—these are often striking musical events.²

We've also learned that any (primary or secondary) dominant seventh chord is enharmonically equivalent to a Ger+6 (in another key), permitting this sonority (however spelled) to function as a pivot.³ In resolutions to a cadential six-four in major keys, the Ger+6 is commonly spelled enharmonically, as in Ex. 22-13c (p. 376): #2 (ri) replaces b3 (me). In such cases, ri resolves to mi; (in minor keys, me is a common tone with the cadential six-four).⁴ Now listen to Self-Test 22-1, C.5. (p. 386): the first chord in m. 105 is spelled (and it resolves) as a Ger+6, but when the same sound recurs in the next measure, its new spelling, position, and resolution reveal its reinterpretation as a V42/N6 (tonicizing N6 in the same measure). This passage never leaves B minor, but the conditions for an enharmonic modulation to C major are fully present; the only remaining requirement is a progression confirming the new tonic.

Compare the tritone-related dominant seventh chords, Bb7 and E7, at the piano; in jazz, these sonorities are considered similar enough to be interchangeable ("tritone substitutes"). Although not enharmonically equivalent, they share two common tones. What interval do these tones form? What role (i.e., root, 3rd, 5th, 7th) do they occupy in these chords? How does this help explain why a Bb7 can substitute for E7 (V7) in the key of A major? In a PAC employing such a substitution in this key, how do you suppose the 7th of the Bb7 would be respelled, and why? What category of augmented sixth chord discussed in Chapter 22 would best describe this hypothetical example?⁵

The "enharmonic terminologies" of jazz and classical music also provide different names for many of the same sounds: e.g., Kostka and Payne observe that the chord labeled "Bb7(b5)" in Ex. 22-9 (p. 375) is a Fr+6 by another name. In Chapter 23 (p. 394), they mention that the Fr+6 can also serve as an enharmonic pivot. Compare the tritone-related and enharmonically equivalent "altered dominant seventh" chords E7b5 and Bb7b5 at the piano. As enharmonic equivalents, they can naturally substitute for one another in two different keys. But think about this: these two (enharmonically equivalent) seventh chords are also enharmonically equivalent to two (enharmonically equivalent) Fr+6 chords that can serve as enharmonic pivots!⁶

Diminished seventh chords are amazing: they divide the octave into four equal divisions (of minor 3rds), and are therefore symmetrical in structure. And you can invert them all you like (on paper): like a freshly starched shirt, this chord never loses it shape! As a pivot, this chord has ready access to more keys than any other. Play the four leading-tone diminished seventh chords and their resolutions in Ex. 23-8 (p. 397). These chords all sound the same, but they are spelled four different ways consistent with the keys shown in the example.⁷

Like diminished seventh chords, augmented triads divide the octave equally (into three divisions of major 3rds) and their inversions also sound the same, even if they look different on paper. After studying what is arguably the most common usage of this sonority in Chapter 24—as V+ (a dominant triad with raised 5th)—you will better understand how this chord can be a pivot in an enharmonic modulation.⁸

Notes
¹ There is a real enharmonic puzzle toward the final cadence of Chopin's Op. 28 Prelude 4 in E minor (in Burkhart); listen to this brief, memorable work. What's the "C7" chord doing in m. 23? It's neither tonicizing nor modulating to the key of the Neapolitan (F major): the only remaining sound in this piece a PAC (V with a 4-3 suspension resolving to tonic)! Try re-spelling: this "C7" functions as a Ger+6 in an irregular position (with #4 in the bass) and it is spelled enharmonically (i.e., #4 as b5). Some texts prefer to call this a "diminished third" chord because the +6 interval has been inverted. See "Other Bass Positions" in Chapter 22 and Ex. 22-18 (p. 380). 
² The spelling of enharmonic pivots often contradicts their function, since these may be reinterpreted (i.e., re-thought) in the new key without being respelled by the composer. It is the resolution of the pivot, above all, that reveals its true function.
³ It is helpful to consider the key relationships involved in such modulations: V7 in C (major or minor) is enharmonically equivalent to the Ger+6 in B (major or minor); we confirm this by reinterpreting the minor 7th (G-F) as the +6 interval (G-E#) that normally resolves to the dominant in the new key. So, if a V7 is reinterpreted as a Ger+6, the modulation is down by half step; if a Ger+6 (e.g., in B minor) is reinterpreted as V7, the modulation will be up by half step (to C). Naturally, if secondary V7 chords are involved, the variety of key relations will significantly increase.
⁴ Some texts call this a doubly-augmented fourth chord since the P5 (formed by le and me) is replaced by a doubly-augmented 4th (between le and ri, Eb and A# in the example). 
⁵ See Ex. 22-22 (p. 382). 
⁶ Respell these as Fr+6 chords and resolve them conventionally to dominant and then tonic. What interval separates the two keys that would be linked by such a pivot, and why? 
⁷ Because each chord member can serve as the root of this leading-tone seventh chord, the keys that can be linked by such an enharmonic pivot must also be related by minor third (a half step higher): in this example the keys are Ab, f, d, and b-for which parallel (major or minor) keys can also be substituted. Naturally, this pivot just as easily permits modulation between keys a tritone (two minor thirds) apart; e.g., Ab and d. Just as with the V7=Ger+6 pivot, the number of possible key relationships significantly increases if secondary functions are involved.
⁸ See p. 411. We don't often encounter augmented triads as enharmonic pivots, probably since we don't generally encounter augmented triads in tonal music.