Possible Harmonic Function—Dominant
The dominant category establishes an intricate family of chord–scale relationships. The dominant category includes four scales: Mixolydian, Mixolydian ♯11, Mixolydian ♭13, and Altered. Figure 8.6 illustrates a chord–scale relationship between dominant modes and corresponding chords.
The only pitch to be avoided is 4. All other notes can freely participate in a chord to project the sound of these dominant-functioning collections. When examining the content of the dominant 7th, 9th, and 13th chords, notice that their pitch content captures the diatonic qualities of the Mixolydian mode. The sound of Mixolydian can also be expressed using two minor upper-structure triads on 5 and 6.
FIGURE 8.6 Dominant Category
The pitch structure of the Mixolydian ♯11 mode approximates the distribution of partials in the overtone series.2 Figure 8.7 illustrates the overtone series, which distributes partials or overtones above the fundamental note, C1. The overtone series illustrates the sonic architecture of fundamental notes as they occur in nature. The distribution of partials above the fundamental note correlates with the location of chord tones and extensions within chords.
Those closer to the fundamental (5ths, 3rds, and 7ths) form chord tones, those further removed from the fundamental (9ths, 11ths, and 13ths) constitute chordal extensions.
FIGURE 8.7 The Overtone Series
The Mixolydian ♭13 mode establishes a chord–scale relationship with the dom7(♯5), dom9(♯5), and dom9(♭13) chords. The mode is typically used in the context of dominant chords occurring in minor keys. Because of the potential spelling discrepancies that might arise in certain chord progressions involving a dom9(♯5) chord, we will implement the syntactically correct dom9(♭13). In the key of C minor, for instance, the ♯5th in G9(♯5) indicates D♯, which does not exist. Although the G9(♯5) spelling preserves the tertian nature of the chord, by referring to ♯5th as ♭13th we avoid making a syntactical error, which is all the more serious because it affects the minor 3rd of the tonic chord, E♭. In addition, the pitch alteration ♯5th becomes the chromatic extension ♭13th in the context of an extended tertian formation, such as a gapped C9(♭13) in Figure 8.6, which includes a perfect 5th as a chord tone.
Even though the dom7(♭5) and dom7(♯5) chords form a relationship with the Altered mode, without the essential chromatic extensions, the Mixolydian ♯11 or Mixolydian ♭13 scales may actually be implied. The five-part chords that establish a chord–scale relationship with the Altered mode in Figure 8.6 have a highly chromatic pitch content and the degree of tension increases with the addition of the ♯9th. There are two major triads (♭5 and ♭6) and two minor triads (♭2 and ♭3) that project the sound of the Altered mode.
In the case of chromatic chords and modes (or even with certain diatonic formations and scales), the issue of providing a unified methodology for labeling extensions is extremely problematic.
As we have observed, extensions can be labeled as pitch alterations and pitch alterations as extensions. Attempting to resolve these discrepancies should give us a good opportunity to think more rigorously about the choice of notation and the implications of those choices.
Suspended Dominant Category
Possible Harmonic Function—Dominant, Predominant, Tonic
In the suspended dominant category there are four modes: Mixolydian, Mixolydian ♭13, Phrygian, and Dorian ♭2. They establish chord–scale relationships with different types of chord: triads, four-, five-, and six-part. The 7sus chord can function as dominant, predominant, or even as tonic in certain types of modal tune.3 Chord–scale theory for this category is rather complex because the 7sus chord can assume different harmonic functions. For instance, a chord–
scale relationship with Phrygian and/or Dorian ♭2 might seem problematic because the major 3rd is not even present in the pitch structure of these modes. We can actually remedy this situation by reinterpreting ♭3 as ♯9th. And since the 7sus chord includes a perfect 4th as an essential chord tone, the absence of the major 3rd from those modes is not too problematic.
Figure 8.8 illustrates chord–scale relationships for this category.
FIGURE 8.8 Suspended Dominant Category
A major triad on ♭7 and a minor triad on 2 are often used to represent the sound of the suspended Mixolydian mode. The Mixolydian ♭13 scale establishes a chord–scale relationship with two chords, dom9(♯5)sus and dom7(♭13)sus, both of which contain a dominant 7th chord on
♭7. In the former, the ♯5th replaces the 5th; in the latter, the ♭13th implies the 5th.
Chords that establish a relationship with the Phrygian mode have an interesting selection of upper structures that can be superimposed over the root of the chord. The 7(♭9)sus chord contains a root position half-diminished 7th chord on 5 (G–B♭–D♭–F); includes an enharmonically spelled root position min7 chord on ♭7 (B♭–D♭–F–G♯); dom7(♯9)sus superimposes an enharmonic major triad with an added major 2nd on ♭3 (D♯–F–G–B♭); and incorporates an enharmonically spelled major tetrachord on ♭3 (D♯–F–G–A♭).
The Dorian ♭2 scale forms a chord–scale relationship with the following formations:
dom7(♭9)sus, dom13(♭9)sus, dom7(♯9)sus, and dom13(♯9)sus. One of the most effective upper
structures that can represent the sound of Dorian ♭2 is an augmented triad on ♭2 over the chordal root.
When comparing the chord–scale relationship between Phrygian and Dorian ♭2 in Figure 8.8, notice that the dom7(♭9)sus and dom7(♯9)sus chords establish a relationship with both modes.
Neither of these chords, however, contains a note that is essential to the corresponding modes:
the dom7(♭9)sus and dom7(♯9)sus chords in Phrygian do not include ♭6, while the dom7(♭9)sus and dom7(♯9)sus chords in Dorian ♭2 do not include major 6. As was the case with other chords that almost captured the sound of particular modes, the missing note from the chord needs to be supplied by the melodic line or assumed aurally. Based on this mutual relationship, we can formulate a basic premise that underlies chord–scale theory: in order to establish the relationship between chords and scales, both musical forces–horizontal and vertical–have to complement and interact with each other in time.