A Summary and Critique of Neo Reimanian Theory as Applied to Post Bop Jazz

Keith Karns

The article “Jazz Harmony After 1960” by Keith Waters and Kent Williams from the 2010 Society for Music Theory journal endeavors to use modern work in Neo-Riemannian theory to describe harmonic gestures indicative of post-bop jazz in the 1960’s. Both Waters and Williams are uniquely qualified for the task and their skills in the field are complimentary. The paper utilizes recent work in Neo-Riemannian theory to analyze harmonic conventions that saw their genesis in the 1960’s.

You can find Waters' and Williams' article in its entirety here

Both Waters and Williams offer unique insight in this field. Waters has a PhD in music theory from the Eastman School and a Master’s Degree in jazz piano from the New England Conservatory. He has been recognized by downbeat magazine for his contributions for jazz scholarship. Waters has also been a frequent presenter at some of the world’s musicological seminars and is well published in the field of music theory. Williams comes out of the Indiana University tradition of interdisciplinary studies in regard to jazz and music theory. He is a frequent contributor to numerous jazz and musicological journals and is known for developing computer applications to facilitate learning advanced harmonic concepts—something that is of upmost use in this article.

Recent work in Neo-Riemannian theory includes offerings by Adrian Childs, Jack Douthett, Peter Steinbach, Edward Gollin and Brian Hyer. These authors have recently applied the initial concepts described by David Lewin as they apply to major and minor triads to seventh chords. Waters and Williams have taken those concepts one step further and applied them to jazz harmonic structures typical of the post bop era of the 1960’s. (Maj9+11, Min9Maj7, Min11 ect.) Their purpose is to better describe the function of traditional harmonic objects in progressions that suppress tonality.

“How do we address harmonic progressions in a way that models harmonic practice?” The problem as seen by the authors is that beginning in the 1960’s many composers began using standard harmonic objects in non-standard ways. (Herbie Hancock, Chick Corea, Wayne Shorter, Joe Henderson ect.) While conventional theory falls short at describing these progressions, the Neo-Riemannian model does not. It should be noted that the article does an excellent job describing the motion of Diatonic, Accoustic, and Hexatonic pitch collections, it leaves the Octatonic as something to be desired, stating only that this pitch collection typically functions as a dominant and so is outside of the purview of their paper.

Waters and Williams classify all harmonic structures in one of four “collections.” (See ex. 1) Using this taxonomy as a starting place they outline strategies for moving through and between each pitch collection while remaining outside traditional harmonic motion. One of the vehicles used to describe this motion is the introduction to the Wayne Shorter composition “Vonetta.”

The harmony in “Vonetta,” moves from the diatonic collection to the hexatonic. (with the exception of the 4th chord, which is addressed in detail later.)

C-9|AbMaj7+5+9 | A maj7 | Eb-7b5 | Dmaj7 | Db-9 |

While all of these objects have seemingly little in common each other, they all maintain at least two common tones with the object preceding it. Waters and Williams depict this through the use of a Tonnetz, which in this case functions as a sort of harmonic tax table to illustrate the preserved pitch classes in each new rotation. Through manipulating a trapezoid over the Tonnetz we can easily grasp the relationships between different pitch collections.

Problems arise in that the Tonnetz seen in ex. 4 does not address anything other than the diatonic and hexatonic pitch collections. Further Tonnetz explore the acoustic and octatonic collections but do not include all pitch collections. As post bop moves through all of these harmonic areas the authors construct a three dimensional Tonnetz to adequately manipulate a trapezoid through all pitch collections. Example 11a. Adequately reflects the relationships between each chord and its pitch collection.

Waters and Williams did an excellent job supporting their argument. While their concepts are baroque in the extreme, the interactive Tonnetz helps to visualize what is being described. This paper is the next logical step when seen from the point of view of Neo-Riemannian scholars such as Adrian Childs, as it applies these concepts to upper structure chords in contemporary jazz. One thing I found particularly interesting was the idea of pitch collections relating to one another through common tones rather than by root movement. This is an immediately recognizable attribute of many contemporary composers and warrants further study.

Where the article falls short is that the process, which the authors describe, is not easy to understand coming from conventional jazz theory. It would be challenging to implement as a jazz methodology because it requires an entirely new harmonic concept in addition to conventional practices. This kind of text tends to alienate many jazz musicians, who advocate, “just play what you hear” without bothering to take the time to train their ears. Even the tune used as an example “Vonetta” is unfamiliar to most jazz musicians and further distances the authors with the primary performing group that would benefit from the article.

Waters and Williams eschew modern pedagogy “…recast the primary focus of jazz pedagogy and theory since at least 1959.” in order to utilize the work of Lewin and Childs and other Neo-Riemmannian writers. As a tool, a new concept works best when nested inside pre existing practice. This paper requires not only a new approach to harmony, but also—at least in the initial stages—the performer to bring the harmonic equivalent of a sextant along to navigate the harmonies of every given tune. (Reconsidering the audience can go a long way in alleviating this problem. This particular article was meant for music theorists, not practicing jazz musicians and no effort was made toward inclusion.)

This paper touches a similar topic as my research, namely non traditional harmonic objects and sequences in post bop jazz. Much of the harmony in Woody Shaw’s music suppresses tonality but I am hesitant to use this paper as a basis for my own analysis. The language of substitution and superimposition as described by David Liebman in "A chromatic approach to jazz harmony and melody" more accurately describes Woody’s music in the lingua franca of jazz. I would have to do more research to be convinced that Neo-Riemmannian harmony would do a better job explaining these harmonic gestures than other conventional sources. To that end, I will continue to study this article and other works sited here, like many good things, this will probably grow on me.

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