Whew. I have a complete draft! I still need to wait for a few (hopefully minor) edits from a couple people, but the 188 pages and 43,961 words have been provisionally approved by my primary advisor. I spent 7 solid hours on Tuesday manually going thru all those pages checking for different detail things. Very brain fried.
New words for this week include finishing chapter 5:
I have updated a system of labeling for Functional Analysis in hopes of providing a pedagogical tool for the efficient learning of common-practice harmonic analysis. To that end, I have followed the history of functional ideas and their pedagogy, illuminated with many examples the implementation of my updated system of Functional Analysis, and discussed the pedagogical implications that this updated system implies. While I have not added to the theoretical discussion of the specifics of how function works, I never intended to.
The goal was always to update a system of labeling to be as pedagogically friendly as possible, in order to assist students and teachers of harmony to more easily and enjoyably learn, teach, and engage with common-practice-era tonal harmonic practice. Therefore, I included examples of syllabi and assignments, classroom demonstrations or long projects, and carefully discussed each aspect of the labeling as I presented it.
By surveying the history of functional ideas and their evolution, we find that the desire to analyze music for harmonic function is not a new idea, and indeed that this has been a goal of many theorists and harmony teachers for centuries. However, the current methods for instructing in harmonic function still leave students confused or baffled, as they struggle to match functional concepts to labels that don’t exemplify their analytical goals, and to methods that insist on starting from tiny detail instead of beginning from a more complete musical perspective.
The elaboration of each detail of my Functional Analysis system shows how each part of Functional Analysis has been designed to help make harmonic analysis quicker, easier, more intuitive, and more personalized. I have also covered the greater pedagogical implications on a larger scale (involving courses and curriculums), informed by my experience both as a teacher of today’s standard system and from teaching Functional Analysis in the classroom.
These greater curricular concerns lead us to wonder what we should do with music that isn’t perfectly common-practice-era tonal. A few suggestions for extensions and adaptations are provided at the end of Chapters III and IV – by no means a complete look at modern pop music or complex chromaticism, but certainly providing a starting place for further study.
These future avenues for research could include an in depth exploration of how function does and doesn’t apply to late-Romantic-era music, possibly using a hybrid analysis of transformational theory and Functional Analysis to show the inner workings of that type of music. Pieces similar to the Chopin prelude of Section 4.3.2 – those that are tonal on a large scale, but not on a small scale – might be the most fruitful for this type of study. I, for one, previously have written a paper for a class on the aforementioned Chopin prelude involving an in-depth sum class analysis and tracing the journey on the chicken-wire torus. I imagine this type of hybrid analysis would work well, or at least show interesting connections and issues, for many pieces in this era – Liszt, Wagner, and such.
As a highly descriptive (not prescriptive) system, Functional Analysis could help understand what harmonies are present even in very chromatic music, with a little adaptation. Similar to the Dvořák of Example 3.45, music with even distantly related chromatic thirds may still be understood in a functional framework. An analysis of music of this type could lead to interesting discussions of if we hear function in chromatic music at all, how and how strongly we hear that function, and what this sort of analysis tells us about the music. Does having a functional framework help understand any given piece? Does that make the listening experience more rich or enjoyable? Does it help in performance expression? The answers to these questions may be less obvious depending on the level of chromaticism or functional structural strength.
Functional Analysis may also expand into more modern popular music genres. The examples I showed in Sections 3.3.2 and 4.3.3 are admittedly only “non-standard” from a very basic point of view, and there are many examples of more complicated harmonic relationships in modern genres. Functional Analysis might work best where pitch-identity function works in concert with syntax function, since that was how I originally designed Functional Analysis for common-practice-era music. However, I can easily imagine interesting analyses and discussions that use Functional Analysis to highlight where pitch-identity, progression, and syntax types of function are or are not in sync – using the struggle of defining a label for a given chord to describe our hearing of it, much as struggle of deciding which pitches to keep before moving up to the next reductive level in a Schenkerian analysis is the most interesting part of that type of analysis.
At one point, I envisioned expanding this project to include an empirical study with statistics and data to see if one could, in fact, correlate Functional Analysis with faster and better learning outcomes for beginning harmony and aural skills, but I quickly decided that was outside the scope of this dissertation and my research expertise. I would love to see side-by-side trials of Functional Analysis with randomized Roman numeral controls, in addition to more hands-on testing with students to get feedback and keep improving the system as much as possible.
As mentioned in Chapter IV, my goals for the continuation of Functional Analysis lie less in research, but more in teaching application. I hope that Functional Analysis can find a home in various courses throughout the music theory curriculum, whether that be review courses or core curricula. I particularly hope that Functional Analysis can provide musicians of many types new and fruitful ways of looking at harmony to enrich their listening, performing, and teaching of music.
 This paper used a combination of techniques from Richard Cohn, “Square Dances with Cubes,” Journal of Music Theory, Vol. 42 no. 2 and “Maximally Smooth Cycles, Hexatonic Systems, and the Analysis of Late-Romantic Triadic Progressions,” Music Analysis, Vol. 15 no. 1, as well as Jack Douthett and Peter Steinbach, “Parsimonius Graphs: A Study in Parsimony, Contextual Transformations, and Modes of Limited Transposition,” Journal of Music Theory, Vol. 42 no. 2, Brian Hyer,“Reimag(in)ing Riann,” Journal of Music Theory, Vol. 39 no. 1, and Joseph Straus, “Voice Leading in Set-Class Space,” Journal of Music Theory, Vol. 49 no. 1.