Music Theory

I.  My interests are varied, perhaps to point of being unfocussed.  This is because so many things fascinate me.  I am very immersed in 20th-century music, particularly music between the World Wars.  Within this interest lies a fascination with the recurring use among many composers of Golden Section (GS), or proportional formal design.  This is much in evidence in the mature works of Debussy, Hindemith, and Bartók.  It appears to be employed to a greater or lesser degree among other composers, for example Ravel, the group of French composers informally referee to as Les Six, Stockhausen, Xenakis and others.


Viewed by many scholars to be a naturalistic alternative to exhausted (perhaps desiccate?) tonal formal plans, GS is used in a multiplicity of ways in the ordering of many post-tonal (post-common practice) compositions.  The usual method is to employ one of a number of commonly known summation series, such as Fibonacci, Lucas, the “Evangelist” series and, in some cases, any whole number summation ordering.  The ratio between adjacent pairs yields the so-called “Golden Section” Proportion.

These series may be mapped out in measure delineations, more often they are orderings of pulse values.  Intricate interweaving of different series often occur, creating nested values of multiple series within the same span of music.  In my own research of the music of Paul Hindemith, these organizational techniques permeate the entire composition from large-scale segmentation by GS values down through (at times) constructivist control of the thematic sub-phrase.


Some composers use summation series values as clock-time in formal layouts, yielding GS proportions chronometrically.  Stockhausen’s Sirius appears to use this technique.  I have observed GS use in Achorripsis by Iannis Xenakis. This is not surprising, considering he studied mathematics under Le Corbusier.


Although I cannot prove the following assertion (and I would rather be thought wrong than take the time and trouble to prove myself right) it is my belief that the final volume of Hindemith’s Craft of Musical Composition, left unfinished at his death, and intended to be a theory of rhythm, would have been  a thorough explication of GS technique as exemplified in his own creative output.


In some quarters, this technique (or in some cases phenomenon) is derided and dismissed as some sort of musical voodoo.  From an ontological viewpoint in art and aesthetics, there is no doubt that GS and its attendant constructions have been intellectually abused. This usually takes the form of the Proselyte wingeing on about the supernatural aspects of GS as phenomenology or, antithetically, the Doubting Thomas who will usually attempt to debunk the presence of GS by asking some sort of question along the lines of, “Did the composer ‘mean’ to do this?” For me, it does occur with enough frequency to justify investigation and recognition of its use in conflationary analytical results, if no other.


II.  I am very interested in theory pedagogy.  I am currently assembling an aural skills manual, Dicta Musica, that is intended to present systematically the ear-training techniques that I have absorbed and developed over many years in the classroom.  This method is procedural and employs “process” teaching (rather than merely rote drill and/or accompanied singing), instilling in the students acquired sets of tools and tactics that proffer solution-based procedures for the development of musicianship and aural skills.


More directly stated, I use specialized drills and exercises that the student will learn by rote initially, but will rapidly employ as gradient solutions for a multiplicity of aural skills tasks.


In the study of harmony (as I teach it at the undergraduate level), I follow the more traditional Conservatory approach (as opposed to the “Literature and Materials” approach).  This term is often maligned and misinterpreted by those who don’t (or recalcitrantly refuse) to understand it.  It simply means that one explores the language of music by emulating the compositional style of any given composer from some historical/compositional style period.  One learns tonal harmony by writing (initially) in the contrapuntal-harmonic style.


The emphasis is upon the linear (contrapuntal) aspects of composition rather than merely upon the vertical (chordal) aspects.


III. I am a mild Schenker disciple.  I do believe that the approach to the analysis of tonal compositions as exemplified by the reductive graphing techniques invented by Heinrich Schenker over a lifetime of study offer an elegant view of tonal practice.  This epistemological hintergründ (forgive the pun) has had a profound effect upon how I perceive music and how I express analytical processes to students of Harmony.


It has become fashionable in recent years to abandon 18th-century contrapuntal-harmonic examples for analysis (the Chorale style) in favor of Fuxian Species counterpoint as the initial introduction to harmony for students.  I perceive that this trend has two-fold origins: (a) Schenkerian precepts are presented “under the radar,” since the ultimate focus of reductive graphs are two-voice Species One Counterpoint, and: (b) it is an attempt to orient the student toward the pre-tonal era in a theoretical/historical context.


This is an error in theory pedagogy and an untenable position.  Species Counterpoint as exemplified in Fux’s Gradus is too far removed culturally for the vast majority of undergraduate music theory students to accurately perceive and understand from an aural and intellectual point of view, and the Gradus is a misrepresentation of the style of Palestrina anyway: Fux’s solutions are more “tonal” than modal in their general shape, contour, and sense of expectation.


For me, the fact that the exercises were employed by Hadyn and Mozart (pére et fils), learned by Beethoven under the strokes of Albrechtberger’s whip, and extrapolated to Marxian theoretical tenets in 19th-century German theory are irrelevancies when attempting to inculcate the fundamentals of tonal composition into the 18 year-old mind.


Fux (or better still, Arthur Tillman Merritt) comes later.


So, I employ the 371 Chorales and 69 Chorale Melodies of Sebastian Bach, edited by Albert Riemannschneider, the only worthy edition.  For my purposes in Harmony, they are discreet compositions of exceeding elegance and grace, they are contrapuntal in their aspect, while displaying harmonic tenets of common tonal practice, and they force the student to “account for every pitch.”


As I tell my students, “if you understand fully the Chorales then you understand tonal music with the exception of the expansion of chromaticism and upper dominant discords/non-dominant upper extensions, as exemplified in late 18th and 19th-century composition.”  It is simply the most efficient way (for me) to have students attain a complete and comprehensive understanding of common-practice tonality.  Thus we progress forward through the Dissolution of Tonality and and subsequent post-tonal practices, and then we cast back to the Modal Era to examine representative music and how it evolved by degrees into tonal practice.



IV. Another deep and abiding interest is Jazz improvisation, or “spontaneous composition,” and Jazz Pedagogy.  In its pure form, fairly rare nowadays, true improvisation is the ultimate expression of the Jazz creative imperative, the sine qua non (thanks Dr. Bad!) that defines Jazz as an Art music.  Usually this is only thought of as melodic (melodo-rhythmic) improvisation: I view the process not only as melodic invention, but as a much more complex set of spontaneous collective compositional constructs.  In a truly aesthetically integrated collective of responsive Jazz musicians, this becomes (for lack of a better term) Structural Improvisation.  Very complex sets of musical (melodic/harmonic/rhythmic), as well as semiotic signs contribute to the overall collective composition, and permeate the complete texture of any given Jazz performance. There is no experience that compares to this when it happens, and no experience worse than when the collective does not communicate properly.


Contemporary Jazz pedagogy has unfortunately, in my view, degenerated into an extremely limited and fixed repertoire of scalar extrapolations of given harmonies.  This “chord/scale equivalency” (and its attendant related topics of study) has become the tail that wags the dog in Jazz improvisation. I believe this has become so in order to (a) have a fixed, “measurable” curriculum in Jazz education; (b) create a common “lingua franca” in Jazz that appeals to the lowest common denominator in terms of music and musicians, and; (c) “legitimize” Jazz in the predominantly “classical” music world within academia.


My comments here seem heretical and negative:  this is not so.  I believe in the efficacy of these techniques as technical training methods and exercises pursuant to the study of Jazz.  But at some point, equating these fixed musical responses with the creative act of composition is “paint by numbers,” not music.  I have also observed that, as a result of this sort of thinking, there is a critical disconnect between the creative compositional act and merely delivering pre-extant or pre-conceived patterns.  The results that I have observed are stultifying.


When I teach Jazz, it is from (big surprise) a theoretical perspective.  I have always felt that the great Master Jazz players combined their intuitive genius with a personalized (rather than strictly academic) theoretical approach to improvisation. I have often attempted to rectify the results of this (as it has been handed down to successive generations of Jazz players as a “separate” Jazz-specific theory of music) with traditional theory as it evolved in late 19th- and 20th-century music.  The object is to prove that the language is identical: there are merely different dialects and stylistic attributes.


V. While researching materials and potential methods of analysis for my Master’s thesis, I became fascinated by the notion of applying Piaget Structuralist tenets to the analysis of music.  At the time, I found this a potentially fascinating precept, but I could not contrive an analytical symbology suitable to the task.  This degenerated into alliterative analysis (supported by examples) that paled in comparison to Tovey or, better still, Rosen.