Jazz Transformations of the ii⁷–V⁷–I Progression

Dariusz Terefenko

Introduction

Jazz syntax features a variety of chordal formations, intervallic structures, idiomatic harmonic progressions, and contrapuntal procedures that—in comparison to common practice and other kinds of music—constitutes a distinctive musical language. [1] Not only is the surface level of jazz music susceptible to its own grammar rules, but more importantly, so is the deeper level, governed by idiomatic voice leading procedures, an assortment of harmonic progressions and contrapuntal behaviors. Given the uniqueness of jazz harmony and a number of historically significant transformations that have had a lasting influence on its syntax, jazz scholars have proposed numerous theories enabling examination of various aspects of jazz music and strategies for advancing jazz improvisation. [2] Among many publications on the subject of jazz theory, the contributions by Waters (1996), [3] Martin (1996), [4] Larson (1998), [5] and others, stand out as truly exceptional, and by now, have entered the canon of scholarly publications on jazz. [6] They have helped advance the status of jazz in academia and put jazz scholarship on the par with other “legitimate” types of writings about music.

Nowhere is the uniqueness of jazz harmonic syntax more evident and its grammar rules more explicit than in the structure and behavior of the ii⁷–V⁷–I progression. [7] Broadly speaking, the function of the progression includes cadential confirmations, local tonicizations, and harmonic substitutions. Its syntactical origins are rooted in the fundamental V⁷–I motion. The structure of the progression and its behavior are ultimately related to the conventions of various performance practice traditions exemplified by particular jazz styles. Although we will discuss the behavior of the ii⁷–V⁷–I progression in a number of historically significant contexts, its manifestation in early jazz, which was closely linked with the early blues, was often disguised by a much more idiomatic V⁷–I progression—the structural backbone of the ii⁷–V⁷–I progression.

The concept of jazz transformations or reharmonization has been intimately related to jazz theory and (especially) practice. [8] Whether one intends to realize a lead sheet or provide substitute changes, the ability to reharmonize the ii⁷–V⁷–I progression constitutes an important starting point in that process.

Note: This article uses interactive musical notation produced using Sibelius notation software. The Sibelius Scorch plug-in allows for musical notation to be displayed as well as heard. Transcriptions are notated at concert pitch. The play button starts playback from the beginning. Clicking on any point in the notation starts the playback from that point. Key and tempo can be changed by the user. If you do not see the score, get the Scorch plug-in here.

Theory

Example 1 shows a four-measure ii⁷–V⁷–I progression that will undergo a number of harmonic transformations.

First, let us examine the harmonic structure and contrapuntal behavior of the progression. Note that the 3rd and 7th (6th) constitute the essential members of the progression. They form two independently moving melodic strands, also known as guide-tone lines: one starting on the 7th and the other on the 3rd of Dmi⁷. The unfolding of the progression results from the voice leading forces engaging the chords’ most potent members and their natural directional propensities: the 7th of a chord descends down to the 3rd of the next, the 3rd of a chord becomes the 7th, and the 7th of the tonic moves downwards to a more stable 6th. Not only does the guide-tone line determine the functionality and typology of a chord, but, more importantly, its members have the potential of being reinterpreted as chord tones or chordal extensions of various substitute formations.

Figure 1 shows a typical chord progression from the repertory of standard tunes. [9]

What is particularly striking—and generally true about the harmonic design of the majority of standard tunes as well—is the sheer number of ii⁷–V⁷–I progressions controlling the harmonic structure in Figure 1. A close analysis reveals a variety of contextual and hierarchical manifestations of the progression as well as its different rhetorical layouts. The function of the progression includes cadential confirmations and local tonicizations, and its rhetorical layout—complete and incomplete—further qualifies and determines the status and functionality of the progression. Given the tonic of the piece, A♭, the ii⁷–V⁷–I progression in mm. 33–35 is hierarchically more significant than other ii⁷–V⁷–I’s. Its role is to confirm the arrival of the tonic key. Other ii⁷–V⁷–I’s, such as in mm. 6 or 14, function as mere tonicizations of the secondary key areas, C major and E♭ major, respectively. Still others, as in m. 30, are incomplete and offer a sense of harmonic departure from the underlying framework expanding its diatonic structure.

Having discussed the basic properties of the ii⁷–V⁷–I progression and the kinetic forces governing its behavior, let us now turn to the specific harmonic techniques that can transform the structure of V⁷–I.

Early Jazz Harmonic Transformations

Example 2a illustrates a typical V⁷–I progression from the early jazz period; its relationship to the ii⁷–V⁷–I progression is shown in Example 2b.

The comparison of the two progressions shows a fleeting similarity between the design of bass lines and the supporting harmonies: it is true that the presence of the D in the bass of Example 2a can be justified as an arpeggiation of the dominant (G) harmony, yet, that D has the potential of being transformed into a predominant ii⁷.

Example 3 demonstrates yet another version of the progression embellished with an assortment of chordal inversions—another trademark of early jazz harmony.

Examples 4a, 4b, and 4c illustrate further substitutions of the V⁷–I progression that originated during the swing period.

The diminished seventh chord plays an important role in transforming the V⁷–I framework; it adds welcomed chromaticism and “improves” the voice leading between the participating chords. The use of upper and lower chromatic neighbors as well as passing and double passing chords is not only idiomatic, but greatly enhances the structure of the progression. Note that the structural V⁷–I progression becomes heavily disguised and the result of such elaborations yields very interesting harmonic outcomes. In Example 4a, for instance, the use of lower chromatic neighbor of ^2 creates a tritone relationship with the root of the dominant. The chromatic passing, D°⁷, between Dmi and C/E in Example 4b adds a much more interesting chromatic bass line to the otherwise diatonic framework. The use of two consecutive diminished seventh chords, A°⁷ and A♯°⁷, in Example 4c further transforms and enhances the diatonic V⁷–I progression. What becomes apparent from Examples 4a, 4b, and 4c is that the use of diminished seventh chord has boundless potential for transforming the V⁷–I progression.

Modern Jazz Transformations

During the bebop and post bop periods, the ii⁷–V⁷–I became subject to a number of harmonic transformations. The structure of the progression was greatly transformed through a number of idiomatic substitutions (tritone substitutions and symmetrical root movements) intimately associated with the bebop and post bop periods.

Example 5 illustrates a tritone substitute change at the dominant level.

Note that the tritone of the dominant remains invariant, with chord tones, the 3rd and the 7th, swapping their functional roles: the 3rd of G⁷ becomes the enharmonic 7th of D♭⁷ and the 7th of G⁷ becomes the 3rd of D♭⁷. When used musically and always in support of the melodic layer, this substitution has a potential to “improve” a diatonic progression and make voice leading—on the account of a chromatic descent from ^♭2 to ^1—parsimonious.

Another substitution of the diatonic ii⁷–V⁷–I includes the use of the secondary dominant seventh in place of the predominant as shown in Example 6.

The use of the secondary dominant creates a directed motion toward the point of repose. The “guide-tone” line features chromatically altered notes that make the arrival of the tonic more forceful and inevitable. Note that the behavior of the chromatic note, F♯—which does not get to resolve (up to G)—does not fulfill the rules of common-practice voice leading and causes motion where there was no motion before! The F♯ replaces an F which would have been a common tone between Dmi⁷ and G⁷.

Given the premise that any local dominant seventh formation can be transformed via tritone substitution, and that both diatonic dominants and their tritone replacements can be paired in a variety of creative ways to accelerate harmonic rhythm and enhance the harmonic progression, one can generate an impressive number of possible substitutions of the ii⁷–V⁷–I progression. Examples 7a, 7b, and 7c include a number of idiomatic transformations combining diatonic and tritone substitution dominant formations.

One of the most effective jazz reharmonization techniques is the expansion of the dominant seventh (either diatonic or chromatic) into a local incomplete ii⁷–V⁷ progression. Based on that premise, the tritone substitution of the diatonic V becomes an incomplete chromatic ii⁷–V⁷ as shown in Example 8.

Following the same logic of dominant expansion into an incomplete ii⁷–V⁷, A♭⁷ can be expanded into E♭mi⁷–A♭⁷ enhancing the structure of the diatonic progression and further departing from the diatonic environment. Example 9 illustrates this possibility.

Ever since the bebop period, the ii⁷–V⁷–I progression has become a fixture of tonal jazz. Jazz players in the post bop period have searched for new ways of transforming the progression either through the use of symmetrical cycles or chromatic expansions. Example 10 shows John Coltrane’s transformation of the ii⁷–V⁷–I progression using a symmetrical major-third cycle.

John Coltrane’s recording of “Giant Steps” in 1959 corresponded to the period of the artist’s harmonic explorations, most notably symmetrical cycles. His recording of “Countdown,” which constitutes a “harmonic" contrafact on Miles Davis’s “Tune Up,” illustrates the use of the so-called Coltrane Substitutions. At the core of that substitution lies the projection of a major-third cycle generated from the governing tonic with each local major chord tonicized by its dominant. In the context of the Dmi⁷–G⁷–Cma⁷ progression (provided in Example 10), the A♭ma⁷ harmony is accessed through its dominant, E♭⁷, following the predominant, Dmi⁷. The next member of the third cycle, Ema⁷, is preceded by its dominant, B⁷, before completing the progression with the diatonic G⁷ resolving to the tonic.

Since the tritone divides the octave into equal parts and since the tritone, in the context of the dominant seventh, is intimately related to the half-whole collection, other symmetrical partitions such as the minor-third cycle can participate in harmonic transformations of the ii⁷–V⁷–I progression. The minor-third cycle in the context of the dominant chord corresponds to the half-whole collection and, therefore, dominant formations a minor third apart can be used as viable substitutions of the diatonic dominant seventh. Example 11a and 11b shows the relationship between the half-whole scale and the dominant seventh chords, respectively.

The half-whole collection contains major chordal extensions: ♭9, ♯9, ♯11, and 13. Given the symmetrical nature of the collection—its intervallic invariance in a minor-third cycle—these chordal extensions are also present in the dominant formations shown in Example 11b.

The use of various minor third substitutions, ensuing voice leading, and the hierarchy among them are illustrated in Example 12a, 12b, and 12c.

What becomes clear from Examples 12a, 12b, and 12c is that in musical practice, the relationship between voice leading and melody influences a particular substitution. In the context of five-part texture and without reference to any specific melody, it is quite difficult to choose between different substitutions. Based on the hierarchy of usage in jazz literature, the tritone substitution is the most common; a minor third up substitution—with its blues-like flavor on the account of the ♭VII^♭7 harmony—is also quite effective; and a minor third down is probably least desirable given its relative scarcity and practicality of use. Once we begin to consider the design of the melodic structure—an ultimate determinant for launching any harmonic transformations—our substitute choices become more manifest.

Practical Demonstration

Figure 2 shows mm. 1–16 of “All of Me” by Seymour Simons and Gerald Marks.

Examples 13a and 13b illustrate two basic transformations of the original progression: diatonic with complete and incomplete ii⁷–V⁷’s, and chromatic with various tritone substitutions.

Example 13a utilizes a basic reharmonization technique that expands an underlying local dominant seventh into an incomplete ii⁷–V⁷ progression. These particular substitutions speed up the harmonic rhythm of the progression and convincingly support the melodic content.

Example 13b provides a number of tritone substitutions creating a variety of interesting melodic/harmonic relationships, not all of which work effectively. In m.4 the use of B♭⁷ nicely supports the E in the melody and so does D♭⁷ in the last measure harmonizing the note B. The use of E♭⁷ in m. 6 and A♭⁷ in m.14 is not as effective. The melodic content in the former emphasizes upper chromatic extensions: the E being ♭9 and the A being ♯11; in the latter, the pitch succession: A, D, B functions as ♭9, ♯11, and ♯9, respectively. Such a use of tritone substitutions renders the melody too chromatic.

Examples 14a, 14b, and 14c show three different melodic phrases derived from the repertory of standard tunes with their possible substitutions derived from the minor-third cycle.

The tritone substitution change works quite successfully: the melodic note, B, which in the original chord progression functions as a major 3rd of the underlying dominant seventh, becomes a minor 3rd of A♭mi⁷ and later a minor 7th of D♭⁷. The incomplete A♭mi¹¹–D♭^7(♯9) progression expands the diatonic G⁷ which is momentarily inserted on beat 3 to chromatically render the diatonic members of the A♭mi¹¹, the D♭ and E♭, as ♯11 and ♭13, respectively.

In the original chord progression, the melodic motion E♭–F in the penultimate measure is supported with the diatonic ii⁷–V⁷ progression. A minor third up substitution is plausible on account of melodic reinterpretation of the E♭ and F as a perfect 5th and a major 3rd of the A♭mi⁷–D♭⁹ progression. Note that the outer voice counterpoint between the penultimate and last chords features an effective contrary relationship.

In this instance, the harmonic reinterpretation of the melodic pitch, G, is more daring, yet within the parameters established earlier. In the original harmony, the G functions as a major 9th and major 13th of the Fmi⁷–B♭⁷ progression; upon a minor third down substitution, it becomes a natural 11th of Dmi¹¹ and the root of G^7(♯5). The choice of the alternate progression renders the melodic note G “more inside.” Another set of transformations of the ii⁷–V⁷–I progression that involves the use of the major third cycle through the projection of the augmented triad can further modify the diatonic framework. Examples 15a and 15b demonstrate the use of the major-third cycle up and down from the predominant ii⁷, respectively.

Not only does a major third up ii⁷–V⁷ substitution—provided that it agrees with the melodic content as is does in Example 15a—add an interesting chromatic flavor to the diatonic progression, but it also anticipates the arrival of the final tonic in a parsimonious manner along with a compelling outer voice counterpoint. The melodic descent: E–D–C concluding the phrase is reinterpreted as the 11th of Bmi¹¹, the 7th of E⁹ and the 5th of Fma⁷.

The harmonic reinterpretation of the F in m. 33 as a major 9th and major 13th of the chromatic E♭mi⁹ and A♭⁹, respectively, fulfils the conditions for the use of that particular substitution and also prepares the arrival of Gmi⁹ in m. 34 in an effective manner satisfying the rules of voice leading.

Conclusion

Given a plethora of transformational possibilities that can enhance the structure of the ii⁷–V⁷–I progression, jazz theory offers a fascinating subject to be studied and researched. While this paper sought to explore the harmonic possibilities of the ii⁷–V⁷–I progression with emphasis on some important substitute techniques, in my future research I will examine the progression’s contrapuntal ramifications and propose a number of linear improvisational techniques that enable horizontal navigation of the progression and its substitute variants.

Bibliography

• Dobbins, Bill. A Creative Approach to Jazz Piano Harmony. Rottenburg N, Germany: Advance Music, 1991.
• Forte, Allan. “Harmonic Relations: American Popular Harmonies (1925–1950) and Their European Kin.” Contemporary Music Review 19.1 (2000).
• Larson, Steven. “Schenkerian Analysis of Modern Jazz: Questions About Method.” Music Theory Spectrum 20.2 (1998).
• Levine, Mark. The Jazz Piano Book. Petaluma, CA: Sher Music Co., 1989.
• Levine, Mark. The Jazz Theory Book. Petaluma, CA: Sher Music Co, 1995.
• Martin, Henry. “Exempli Gratia: As You Like it (Chord Substitution in Ellington’s ‘Satin Doll’).” In Theory Only 1 (1975).
• Martin, Henry. “Jazz Harmony: A Syntactic Background.” Annual Review of Jazz Studies 4 (1988).
• Martin, Henry. Charlie Parker and Thematic Improvisation. Lanham, MD: Scarecrow Press, 1996.
• Owens, Thomas. “Charlie Parker: Techniques of Improvisation,” 2 Vols. Ph.D. dissertation, University of California-Los Angeles, 1974.
• Stewart, Milton. "Structural Development in the Jazz Improvisational Technique of Clifford Brown.” Jazzforschung/Jazz Research 6/7 (1975).
• Strunk, Steven. “The Harmony of Early Bop: A Layered Approach.” Journal of Jazz Studies 6 (1979).
• Terefenko, Dariusz. Keith Jarrett’s Transformation of Standard Tunes. Theory, Analysis and Pedagogy. VDM Verlag Dr. Müller, 2009.
• Waters, Keith. “Motivic and Formal Improvisation in the Miles Davis Quintet 1965–1968.” Tijdschrift voor Muziektheorie 8.1 (2003).
• Waters, Keith. “Blurring the Barline: Metric Displacement in the Piano Solos of Herbie Hancock.” Annual Review of Jazz Studies 8 (1996).

Notes

[1] By common practice music, I mean music between circa 1675 and late 19th century.

[2] Thomas Owens, “Charlie Parker: Techniques of Improvisation,” 2 Vols. (Ph.D. dissertation, University of California, 1974); Milton Stewart, “Structural Development in the Jazz Improvisational Technique of Clifford Brown,” Jazzforschung/Jazz Research 6/7 (1975): 141–273; Steven Strunk, “The Harmony of Early Bop: A Layered Approach,” Journal of Jazz Studies 6 (1979): 4–53; Henry Martin, “Jazz Harmony: A Syntactic Background,” Annual Review of Jazz Studies 4 (1988): 9–30; Allan Forte, “Harmonic Relations: American Popular Harmonies (1925–1950) and Their European Kin,” Contemporary Music Review 19.1 (2000): 5–36; Keith Waters, “Motivic and Formal Improvisation in the Miles Davis Quintet 1965–1968,” Tijdschrift voor Muziektheorie 8.1 (2003): 25–39.

[3] Keith Waters, “Blurring the Barline: Metric Displacement in the Piano Solos of Herbie Hancock,” Annual Review of Jazz Studies 8 (1996): 19–37.

[4] Henry Martin, Charlie Parker and Thematic Improvisation (Lanham, MD: Scarecrow Press, 1996).

[5] Steven Larson, “Schenkerian Analysis of Modern Jazz: Questions About Method,” Music Theory Spectrum 20.2 (1998): 209–41.

[6] For more bibliographical sources visit: http://music.uncg.edu:2001/

[7] Since (analytical) chord symbols in jazz writing feature a variety of shortcuts that are largely understood by jazz practitioners and theorists, the tonic “I” in the ii⁷–V⁷–I progression stands for either Imaj⁷ or I⁶ depending on the context.

[8] Bill Dobbins, A Creative Approach to Jazz Piano Harmony (Rottenburg N, Germany: Advance Music, 1991); Henry Martin, “Exempli Gratia: As You Like it (Chord Substitution in Ellington’s ‘Satin Doll’),” In Theory Only 1 (1975): 371; Mark Levine, The Jazz Piano Book (Petaluma, CA: Sher Music Co., 1989); Mark Levine, The Jazz Theory Book (Petaluma, CA: Sher Music Co, 1995).

[9] The term “standards” refers to primarily American “popular” tunes performed frequently by countless musicians.

Author Information: 
is Assistant Professor of Jazz and Contemporary Media at the Eastman School of Music, University of Rochester. He teaches courses on jazz theory, jazz improvisation, and jazz history. He is also a jazz pianist.

Abstract: 
The ii⁷–V⁷–I progression is an essential part of jazz and over the course of the music’s development, transformations of this progression have enriched the harmonic language of jazz. This article explores the harmonic possibilities of the ii⁷–V⁷–I progression with emphasis on some important substitute techniques.

Keywords:
jazz, harmony, chord progressions

How to cite this article:

• Chicago 15th ed.: Terefenko, Dariusz. “Jazz Transformations of the ii⁷–V⁷–I Progression.” Current Research in Jazz 1, (2009).
• MLA 6th ed.: Terefenko, Dariusz. “Jazz Transformations of the ii⁷–V⁷–I Progression.” Current Research in Jazz 1 (2009).
• APA 5th ed.: Terefenko, D. (2009). Jazz transformations of the ii⁷–V⁷–I progression. Current Research in Jazz, 1