Combinaciones de negocios y plusvalía

In jazz, the relationship between chords and scales is explained using chord–scale theory.

Chord–scale theory relates certain harmonies to melodies and melodies to harmonies. It also illustrates what kinds of harmony and chord progression can be derived from particular scales or modes. The terms “scale” and “mode” will be used interchangeably. By extension, chord–scale theory measures the harmonic identity of improvised lines and examines melodies for their harmonic clarity. Finally, chord–scale theory allows us to formulate rules of voice leading that govern the behavior of harmonic progressions and melodic lines. In short, the relationship between scales and chords can be summarized with the following statement: any melodic line can be represented by a chord and/or harmonic progression and, conversely, any chord or harmonic progression can be horizontalized with a melodic line.

Since we will combine four- and five-part chords (as well as triads and extended tertian sonorities) that add up to some 49 harmonic formations, chord–scale relationships will involve many-to-one ratios. This means that certain scales can accommodate more than a single chord and certain chords can establish a chord–scale relationship with more than a single mode.

The possibility that many chords can form a relationship with a single scale is of great importance to the improviser. A proper understanding of this relationship can influence our decisions in finding the most fitting harmonic match for a single scale or vice versa. Even though certain chords might not contain all the essential notes from a given mode, they can still form a convincing chord–scale relationship with that mode.

CHORD–SCALE RELATIONSHIPS

A chord built entirely of thirds, so-called tertian formation, has seven notes that can be arranged

in the form of a scale.¹ The notes within the scale, however, have very different melodic and harmonic behaviors. Any vertical or linear combination of notes derived from the scale has the potential to convey the sound of that scale. In order to express such a sound, the selection of pitches in a chord has to be very specific. Figure 8.1 illustrates a chord–scale relationship between CMaj^13(♯11) and the Lydian mode.

There are two ways of explaining the chord–scale relationship between CMaj^13(♯11) and Lydian.

First, an extended tertian structure, CMaj^13(♯11), can be horizontalized as the Lydian mode.

Second, Lydian can be verticalized as the CMaj^13(♯11) harmony. To project the Lydian sound, however, we do not necessarily need a complete seven-note chord; as few as three pitches, major 3rd, major 7th, and ♯11th (or ♭5th), may be used. The relationship between CMaj^13(♯11) and Lydian means that the vertical and horizontal dimensions exhibit the same voice-leading behaviors and one can be used to represent and/or complement the other. Just as the structure of CMaj^13(♯11) is representative of Lydian, so is the structure of other chords representative of other scales. Figure 8.2 represents the CMaj^13(♯11) chord as a melodic phrase with characteristic modal features.

FIGURE 8.1 CMaj^13(♯11) and Lydian Mode

FIGURE 8.2 Lydian Phrase

In this figure, the Lydian mode has a very distinct sound. The melodic line prioritizes chord tones and the beauty mark ♯11th, avoids a perfect 5th, highlights a major triad on D, and uses successive fourths at the end of the phrase. The bottom stave projects the Lydian sound through the use of quartal harmonies or structures (that is, chords built in stacked fourths). These contain the most active notes derived from the Lydian mode. The interplay between the melodic line and the underlying harmonies unifies both musical dimensions. Not only does chord–scale theory control the relationship between lines and chords, but it also suggests a particular melodic and harmonic vocabulary derived from the structure of specific chords and scales.

Major Category

Possible Harmonic Function—Tonic and Predominant

In the forthcoming discussion, modes and chords are placed in the familiar functional categories. Each figure provides an analysis of the mode’s pitch content in terms of chord tones and extensions along with a selection of chords and upper structures. The term “upper structure” refers to a triad or four-part chord that contains extensions or chord tones (excluding the root) of an extended harmonic formation.

The major category includes three scales: Ionian, Lydian, and Lydian Augmented. They establish a chord–scale relationship with different types of major chord. Figure 8.3 illustrates the pitch structure of these modes along with the corresponding chords.

Note that in the Ionian mode, the 6, Maj7, ^6/9, Maj⁹, and CMaj¹³ chords include the most important chord tones and extensions from the scale. The six-part CMaj¹³ is an example of the so-called gapped formation. Gapped formations interrupt the underlying pattern of introducing pitches from the scale in order to prevent excessive doubling. This creates more interesting voicings, or–as is the case in this example–avoids a note that does not fit the content of a fully extended chord. Two triads, major on 5 and minor on 3, summarize the chord–scale relationship using limited harmonic means. Scale degree four is typically employed as a metrically unstressed passing or neighbor tone. In more advanced harmonic settings, however, the avoid note can also participate in the projection of a mode. For instance, harmonic structures such as C(add4) or CMaj7(add4) convey the sound of Ionian, but these structures require a different set of voice-leading rules and specific voicings to make them sound convincing.

FIGURE 8.3 Major Category

In Lydian, the ♯11th is a pitch that flavors the mode in a highly recognizable manner. The chord–

scale relationship in Lydian illustrates one of many spelling discrepancies that we will try to untangle. The ♯11th functions as an extension in extended tertian formations, such as in CMaj^13(♯11). The ♯11th, then, assumes the presence of the perfect 5th. In four-and five-part chords such as CMaj7^(♭5) and CMaj^9(♭5), the alternate spelling ♭5th is used for the same pitch in order to preserve the tertian nature of their respective structures. A major upper-structure triad on 2 and a minor upper-structure triad on 7 convey the character of the Lydian collection using limited harmonic means.

In Lydian Augmented, the ♯5 is a pitch that injects the characteristic augmented sound into the framework of the mode or chords. The Maj7^(♯5) and Maj^9(♯5) chords delineate the sound of the scale. The most common triad within this mode is the one built on 3 and has a major quality. The major 13th functions as an extension in the context of a complete tertian formation, as in

. Otherwise it functions as a passing or neighbor tone.

Minor Category

Possible Harmonic Function—Tonic and Predominant

Possible Harmonic Function—Tonic and Predominant

The minor category includes three modes: Melodic Minor, Aeolian, and Dorian. Figure 8.4 establishes a chord–scale relationship for this category.

The first four chords, min6, min^(♯7), min^6/9, and min^9(♯7) constitute the familiar four- and five-part formations and form a strong chord–scale relationship with Melodic Minor. The remaining ones, min^11(♯7) and min^13(♯7), feature extended tertian structures that incorporate six and seven notes from the scale, respectively. A major upper-structure triad on 5 captures the sound of Melodic Minor using limited triadic means.

Similarly, all the notes from the Aeolian mode can be implemented in a chord. Among the four formations from Figure 8.4, the min^9(♭6) and min^11(♭13) chords admit both the chord tones and the beauty mark into their structure. The first two, min7 and min⁹, can represent the scale too, provided that the beauty mark occurs somewhere in the melodic line. In this particular context, the min7 and min9 chords assume the presence of ♭6th or ♭13th in the melodic dimension.

The complementary relationship between chords and lines constitutes an important feature of chord–scale theory.

The Dorian mode is an interesting collection with equally interesting chord–scale relationships.

The dual harmonic function of Dorian–tonic and predominant–slightly complicates these relationships. The Dorian mode is a symmetrical scale that features two adjacent minor tetrachords. In theory, Dorian can admit all the notes from the scale into the structure of a chord. In practice, though, the selection of notes for a melodic line or a chord is entirely predicated on the context in which the Dorian mode appears. All the chords from Figure 8.4 establish a chord–scale relationship with Dorian and can potentially function as tonic formations. Yet, only min7, min⁹, and min¹¹ function exclusively as predominant chords.

Therefore, the role of the beauty mark decreases in predominant-type chords and increases in tonic formations. We can also emphasize these two different functional associations of Dorian by using specific upper-structure triads. In the tonic formation, we can use a minor triad on 2; in the predominant Dorian, a major triad on ♭7.

FIGURE 8.4 Minor Category