Dr. Kit Music

I got back helpful comments on my first draft of my proposal, and even got some editing in! I’m hoping to have another draft ready to send in before the Thanksgiving holiday.

I still need to fix the intro, and the end is about the class that started this blog, but here’s a chunk from the middle of the proposal:

This system has significant pedagogical implications and motivations. In my experience as a teacher, I have seen the need for analysis tools that are easy to use and remember. I have designed Functional Analysis to facilitate easy use. Additionally, to meet that goal of ease, I have designed Functional Analysis from an aural basis – what your hear is what you label – and with performers in mind. Functional Analysis is adaptable for personalized analysis, acknowledging that different people hear the same music in different ways.

One of the principal performer-directed aspects is the flexibility of levels; different levels/depths of analysis may be appropriate for different levels of performer (or amount of time till performance). Levels are also useful as a pedagogical tool for theorists who wish to continue on to Schenkerian Analysis.

While on the surface Functional Analysis may not look all that different from current harmonic analysis, I have found it leads to new or different understandings harmony. Tonic and Dominant functions are already fairly widely used, but secondary functions (relatives and variants) are more challenging to talk about with current labels. Predominants are acknowledged to be the most flexible and flavorful category in harmonic analysis; Functional Analysis draws connections between different flavors of predominant and helps both show their similarities and remember their differences.

Finally, for both students and performers of all types, the aural grounding, the simplicity, and the flexibility with and emphasis on multiple levels leads to much faster analysis. Students can learn to be fast with current methods; with Functional Analysis speed is much more inherent, with a directive to learn larger chord chunks by understanding harmonic rhythm and phrase motion before dithering over details. This process of chunking can lead to more expressive phrasing and faster memorization.

Throughout the history of music theory, scholars have been talking about function with the terminology available to them. Some of the earliest examples of functional ideas are explored in Joel Lester’s Compositional Theory in the 18th Century, where he discusses the different approaches to thoroughbass practice and Fundamental bass theory. There he points out that the rule of the octave shows a move towards tonal thinking because “the règle promoted recognition of the manner in which harmony expresses a key.” Another look at thoroughbass traditions and their relationship to Rameau is provided by Ludwig Holtmeier. He argues that thorough bass is not only one of the first codifications of tonality, but that it is also a harmonic theory in the 19th century German sense (in addition to Rameau’s Fundamental Bass), saying “The basse fondamentale constitutes the inner ‘essence’ of harmony, the Rule of the Octave its outward appearance.” Thomas Christensen’s Rameau and Musical Thought in the Enlightenment provides some context of the prevailing scholarly climate at the time. Rameau is an important predecessor to Riemann, functional thinking, and indeed to all modern musical scholars, as Christensen points out: “Since the appearance of his Traite de l’harmonie in 1722, both the conceptualization and the pedagogy of tonal music have been profoundly altered.”

Early Roman numeral/Stufen theorists, such as Gottfried Weber, also try to explain harmony functionally with the resources at their disposal. Weber made adjustments to Georg Vogler’s original usage of Roman numerals to describe the Stufen in a scale, but more importantly he was one of the first conceptualize modulation and tonicization. Our current understanding of applied chords and pivot modulations are descended from Weber.

The obvious predecessor to Functional Analysis is Hugo Riemann. His best known treatise, Vereinfachte Harmonielehre (Harmony Simplified) lays out his concept of chord and of function. Another idea that features prominently in Reimann’s teaching is Scheinkonsonanz, feigning consonance, which is similar to a concept that I use to explain structural versus decorative harmonies. Understanding Riemann’s philosophical background and motivations, and reframing Riemann in terms more understandable by modern thinking, are explored in Alexander Rehding’s 2003 book. However, my current usage of Functional Analysis is more closely based on modern German trends, which I encountered in Berlin in 2008. The differences between Riemann’s original and today’s modern German usage are outlined in a book by Renate Imig.

One may wonder why I would like to implement a whole new system, instead of just adapting current methodologies to my purposes. My dissatisfaction with Roman numerals mostly stems from a square-peg-round-hole problem. It seems to me that Roman numerals do not fit the job we are asking them to do, and attempting to further adapt them only makes them more confusing, not less.

After digging into the theoretical history, I performed a survey of practical teaching manuals. The texts I surveyed ranged from the translation of Ernst Richter’s Manual of Harmony (closely based on Weber), to a 1909 volume titled Harmony Simplified (by Francis York, which bears no relation to Riemann’s work), to the primary Harmony works by Schönberg, Hindemith, and Piston, to modern American texts, and even the Harmonielehre I became acquainted with in Berlin. These texts seem to indicate that the two main goals of music theory – and specifically harmony – teaching are voice-leading and harmonic progression. I maintain that Functional Analysis can meet the goal of harmonic analysis better than current practices, and that Roman numerals are not quite designed to show harmonic progression optimally. There are arguments for using figured bass or counterpoint to teach voice-leading, but I don’t think Functional Analysis is severely deficient in this area (and perhaps even better), and that modern students need a more flexible approach to voice-leading than dry figured bass exercises, as argued in a recent article in an online journal by David Kulma and Meghan Naxer.

Functional ideas are also used in many pedagogical resources, such as Michael Rogers’s Teaching approaches in Music Theory and Gary Karpinski’s Aural Skills Acquisition. Rogers argues that students should never use Roman numerals without understanding their function, wanting to avoid mere labeling, exhorting “These relationships, not the chords themselves, are responsible for our sensations of tonal centers and the establishing of keys.” Karpinski doesn’t necessarily use the word ‘function’ but after discussing how to use bass lines to hear harmonic motion and improve performance, underscores that “… musically convincing and satisfying performances of tonal music depend heavily on performers’ ability to think and act harmonically. Performance without a sense of harmonic motion are lifeless and uninteresting, devoid of of the most essential elements of tonality itself.” Function helps provide that sense of harmonic motion in a tonal context.

Aside from teaching, current harmonic analysis is often in service to linear, Schenkerian analysis. Schenker’s own work Harmony contains functional ideas, especially if considering the functional orientation of Thoroughbass practice and Stufen theory. Additionally, Schenker’s insistence that not every triad is counted as a scale step resembles Riemann’s idea of Scheinkonsonanz – that chords can mean something other than their notes originally suggest out of context. My application of Functional Analysis is influenced by reductive analysis, and I have heard from students that they feel it would be easier to learn Schenker if they didn’t have to unlearn vertical, slice-based, Roman numeral ideas. Other current harmonic trends might be based on/influenced by other aspects of Riemann’s theories, such as Steven Rings Tonality and Transformation which delves into the interactions between transformational theory and functional diatonic music, but his work is focused more on the transformation and less on the function. Margaret Notely has written in JAMS about how dualistic concepts can explain some types of late nineteenth century harmony, but is again drawing from Riemann’s ideas without using function. Scholars like Eton Agmon look directly at how we hear function, exploring prototype theory. While I have made good use of Agmon’s work in exploring post-CPP tonality, John Rothgeb writes an interesting critique of his prototypes. The divide between these two authors seems to be whether to focus on the function or the root, but I hope that Functional Analysis can do both.

While functional tonality is usually considered the domain of the Common Practice Period, there are many instances in which I feel Functional Analysis can help us understand or provide insight into different, less traditionally “tonal” musics. The use of collections other than V as dominant is prevalent in jazz and pop music, but the dominant pull is still present. For example James McGowan looks at Jazz music where different collections provide each functional sound (T D or P) and where predominant function is more important because of the ii-V-I traditional cadence. Nicole Biamonte, using Agmon’s prototypes, explores dominants other than V in pentatonic and modal pop music; these might seem counterintuitive, but they are concept I strongly believe in. David Temperley is interested in the blues-derived phenomenon of the IV as a primary pre-tonic chord. I also find Steve Larson’s concept of Musical Forces (gravity, inertia, and magnetistm) helpful when I am considering non-CPP musics.

Another intersection of Functional Analysis and less functional music is late Romantic music. I have personally looked into hybridizing Transformational theory and Functional Analysis/Schenker to understand Chopin’s E minor prelude op 28 no. 4. Daniel Harrison’s book Harmonic Function in Chromatic Music considers how Reimann’s concepts of function and dualism can help explain late Romantic music.

{sorry all the footnotes disappeared}