Here’s the proposal I turned in yesterday. The footnotes worked this time! It feels good to reach this hurdle.
In this dissertation, I aim to establish an updated system of Functional Analysis. This system will be based in part on Hugo Riemann’s Funktionstheorie, borrowing many of the functional ideas but focusing very little on the transformational ideas associated with neo-Riemannian theory. In this way, my system of Functional Analysis resembles the type of analysis currently in use in Germany, but I have translated and adjusted it for English speakers to maximize easy implementation. Additionally, I have adapted Functional Analysis to flow smoothly into Schenkerian-type reductive ideas. The focus of Functional Analysis is common-practice-period music/tonality, but I will also show ways in which Functional Analysis can apply to more modern music, including later Romantic chromatic music and modal or pop music.
I aim not only to define and demonstrate Functional Analysis, but also to also present the historical, pedagogical, and practical reasons for adopting it. Many historical theories supported a functional view of harmony, even before the word “function” was used in music theory or analysis; I will explore the functional aspects of Thoroughbass, Fundamental Bass, and Stufentheorie below. Recent pedagogical ideas trend toward using analysis to show function. For example, even a quick overview of the table of contents of two leading texts (Clendinning and Marvin’s Musician’s Guide and Laitz’s Complete Musician) indicate tonic and dominant as “tonal pillars” and “Defining the Phrase Model,” or explicitly mention predominant function. Additionally, master pedagogues suggest functional ideas to help students learn better and faster, which I will expand more on later. On this count, I can offer first-hand experience from teaching Functional Analysis a year ago.
I have designed Functional Analysis such that it can often provide new insights into common-practice tonality more quickly than current methods, principally by encouraging a combination of short and long term thinking to more quickly identify interesting harmonic occurrences. This could prove a boon to performers and musicians who mistakenly see music theory as forbidding and difficult. I want performers and musicians of all types to be able to use theory to their advantage, to find theory undaunting, and maybe even fun. Since many of us still deal with common-practice-period functional tonality (and those who don’t still are often in dialogue with the common practice period), I believe that making this music easier to understand on a deeper level could help many musicians of many different types.
What is Functional Analysis?
Functional Analysis is a harmonic analysis system that focuses on roots from a bass-oriented perspective. It is triad-based, but does not rigidly demand stacks of thirds when determining roots, preferring to privilege function and bass rather than only building chords out of thirds. It can also be used to provide insight into voice-leading when using detailed analysis, and insight into phrasing and larger forms, through connections with other types of analysis, particularly formal analysis and Schenkerian analysis.
An introduction to Functional Analysis begins with the concept of cadence, which defines the three primary functions (Tonic, Dominant, and Predominant). Since cadences in turn define phrases, this means that students get a chance to understand and analyze phrase structure, even if only at a surface level, right away. This then leads to a functional outline of typical harmonic progressions before focusing in on harmonic details. The exploration of harmonic details unfolds naturally into discussion of voice-leading, while the larger-scale focus of phrasing progresses to form and large-scale reductive techniques.
The basic cadences in a major and minor key can be described thus: in C major, the primary predominant is the F major triad (F A C), followed by the dominant of G major (G B D), and finally tonic of C major (C E G). In A minor, predominant is D minor (D F A), dominant is E major (E G# B), and tonic is A minor (A C E). The following examples show this on a staff.
In my dissertation I will explain how to identify various chords in different contexts as they relate to these primary functions. One additional important aspect of Functional Analysis is use of superscripts and subscripts. Unlike Roman numerals, bass lines and upper voices are separated out into two different places in the label. Pitches of the bass line that have changed from the primary function are shown separately from those that have changed in other voices, seen below with a C major triad with a third in the bass followed by a B♭triad with a sixth above the bass in the alto line, and a C dominant seventh chord with the seventh in the soprano:
This system has significant pedagogical implications and motivations. In my experience as a teacher, I have seen the need for analytical 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. Depending on context, aural attention, and other factors, different performers may wish to bring out different aspects of a piece of music. There are many ways in which notes may look the same while having more than one potential meaning, but the simplest is the example of the Tonic Relative versus the Predominant Variant. Because the chord in the following example has two pitches in common with the tonic triad of C major (C and E), some may hear this chord as a relative of the C major triad. However, in another context, the ear may focus on the pitches in common with the predominant triad of F major (A and C), and in that case we may hear it as more closely linked with the F major triad.
One of the principal performer-directed aspects is the flexibility of levels; different levels of analysis may be appropriate for different levels of performer (or amount of time till performance). If there is not enough time to perform a detailed analysis, Functional Analysis trains musicians to start on a larger level of analysis and then later zoom into details. While it is definitely possible to decide to use Roman numerals in a similar fashion for different levels – all detail or only structural chords – the very vertical nature of Roman numerals makes it harder to do so. Also, as Roman numerals are usually conceived on a detailed level and then later zoomed out, this leads students of Roman numeral analysis to begin small and only later look at bigger structures. However, Functional Analysis is designed to start on the bigger structure level and then later zoom in. 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 Roman numeral analysis, I have found it leads to new or different understandings of harmony. Tonic and Dominant functions are already fairly commonly used, but secondary functions (replacements of the primary functions) are more challenging to talk about with current labels, because Roman numerals are based on pitch membership of a chord and do not allow multiple labels for the different functions of the same notes (as noted above). Also, predominants are acknowledged to be the most flexible and flavorful category in harmonic analysis – this is where interesting chromatic chords such as Augmented Sixths and Neapolitans occur. Functional Analysis draws connections between different flavors of predominant and helps both to show their similarities and to remember their differences, reminding analysts that these sometimes confusing altered chords are just that, simple alterations of the primary predominant function (or one of its substitutes), and that these alterations follow the voice-leading principles we are familiar with.
Finally, for both students and performers of all types, the aural grounding, the flexibility, the simplicity, and the emphasis on multiple levels of Functional Analysis lead to much faster analysis. Aural grounding with flexibility provide a quick, easy connection to each musician’s own musical reality. Functional Analysis encourages using the least complicated label and has a few levels of removal from that reality as possible. By having an emphasis on learning larger chord chunks by understanding harmonic rhythm and phrase motion before concerning ourselves with the details, the analytical process of chunking into larger structural functions can lead to more expressive phrasing in performance and faster memorization. Students may learn to be fast with current methods; with Functional Analysis speed is much more inherent.
History of Functional Thought
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 thoroughbass is not only one of the first codifications of tonality, but that it is also a harmonic theory in the 19th-century German sense, as an explanation of how keys and chords work or function – 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 describes the 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 some 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 Riemann’s teaching is Scheinkonsonanz, feigning consonance, which is similar to a concept that I use to explain structural versus decorative harmonies. Alexander Rehding’s 2003 book, Hugo Riemann and the Birth of Modern Musical Thought explores Riemann’s philosophical background and motivations, and reframes Riemann in terms more approachable by modern thinking. Rehding clarifies many concepts and elucidates the philosophical context in which Riemann was working, and even points out that sometimes Riemann himself is unclear on how he is using his terminology: “…equivocation between chords and their interpretation is a constant source of tension in Riemann’s theory of harmonic function.” 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 and evolution from Riemann’s original to today’s modern German usage are outlined in a book by Renate Imig from 1970.
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 surveyed practical teaching manuals. The texts I surveyed ranged from a 19th-century 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 despite the title), to the primary Harmony works by Schoenberg, 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 teaching – and specifically harmony – 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 it may even be better), and I also believe 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, he 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 the most essential elements of tonality itself.” Function helps provide that sense of harmonic motion in a tonal context, by efficiently describing and encapsulating the musical motion through the phrase, driving from one functional area to the next and highlighting unexpected harmonic occurrences by identifying the mundane.
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 – depending on context, chords can mean something other than their notes originally suggest. 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’s 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 Notley has written in the Journal of the American Musicological Society about how dualistic concepts can explain some types of late-nineteenth-century harmony, but is again drawing from Riemann’s ideas predominantly without using function. Scholars like Eytan Agmon look directly at how we hear function, exploring prototype theory. While I have made good use of Agmon’s work in exploring non-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.
Functional Concepts in non-Common-Practice-Period Music
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 often more important because of the prevalence of the ii-V-I traditional cadence. Nicole Biamonte, using Agmon’s prototypes, explores dominants other than V in pentatonic and modal pop music (often IV, VI, and VII); these might seem counterintuitive, but they are concept I strongly believe in. David Temperley is also interested in non-V dominants, such as 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 magnetism) 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 Riemann’s concepts of function and dualism can help explain late Romantic music.
Functional Analysis in the Classroom
During the winter quarter of 2014, I had an opportunity to test-drive Functional Analysis with undergrad students. Ranging from non-music majors to senior majors, we covered everything from basic functions through tonicization and chromatic chords (mode mixture and augmented sixths) in ten weeks.
Throughout the course we worked with concrete examples from the music literature, finding functional pillars before describing their elaborations. Advanced students were also asked to write some progressions to consider how function affects voice-leading. One of the favorite homework assignments was one comparing various iterations of the chordal pattern of the Bach Chaconne from the D minor Partita for Unaccompanied Violin. A similar exercise was attempted with different versions of famous Bach Chorales (Herzlich tut mich verlangen) and with Functional Analysis it was quite easy to analyze and track the changes to the functional pillars of the phrase.
Student feedback was overwhelmingly positive, with comments [edited for grammar] such as:
- “I appreciated the opportunity to shed more light on how music ticks. I loved that I could apply this even without a great deal of music theory analysis experience.”
- “It helped give perspective to functional/structural aspects of music. Rather than trying to look at I and vi or ii6 and IV as separate things, it helps me to understand these as variations of a function.
Helped me to put chord progressions in perspective, and helped me in my ear-training by listening first for functionality, rather than specific chord-types.”
- “It shows a much faster analysis of a piece of music.”
Some new ways of looking at things were challenging at first (different conceptualizations of sixth chords and relations in minor, for example), but by the end of the quarter, all students wrote papers on a piece of their choosing, using FA to help them uncover something new (to them) about the piece.
In my own personal practice and analysis, I find that using Functional Analysis for harmonic analysis instead of Roman numerals helps me get to the graphing step of Schenkerian analysis quicker. Additionally, functional thinking allows me to memorize music for performance, something I have personally struggled with. In my teaching, presenting Aural Skills materials to freshmen from a functional perspective has them nodding their heads enthusiastically instead of staring at me with a glazed look.
The impact of Functional Analysis is not always readily apparent to experienced theorists who have already internalized Roman numeral analysis. However, Functional Analysis can make theory and analysis more user-friendly for students and musicians who otherwise may not use theory, to help them gain perspective and insight on both unfamiliar and well-loved musics, to ease memorizing, and serve as a gateway to other theories and types of analyses by making theory more approachable.
My dissertation will contain three large chapters: 1) Historical Background, exploring the historical roots of functional thought and outlining the trends that have brought current tonal analysis practices where they stand, 2) Implementation: describing in detail the system and providing numerous practical examples; providing possible homework assignments and syllabi, and 3) Hybrids and Adaptations, detailing how function is applicable in diatonic modal music and slightly-functional chromatic music, as well as how to use Functional Analysis in conjunction with other types of analysis (such as Schenkerian Analysis or neo-Rie
 Steven Laitz, The Complete Musician, (Oxford: Oxford University Press, 2008), vi.
 Jane Piper Clendinning and Elizabeth West Marvin, The Musician’s Guide to Theory and Analysis, 2nd ed., (New York: W.W. Norton and Co, 2011), xiii.
 Laitz, vii; Clendinning and Marvin, xiii.
 Joel Lester, Compositional Theory in the Eighteenth Century (Cambridge: Harvard University Press, 1992).
 Lester, 72.
 Ludwig Holtmeier, “Heinichen, Rameau, and the Italian Thoroughbass Tradition: Concepts of Tonality and Chord in the Rule of the Octave,” Journal of Music Theory 51:1 (Spring 2007), 5-49.
 Holtmeier, 11-12.
 Thomas Christensen, Rameau and Musical Thought in the Enlightenment, (Cambridge: Cambridge University Press, 1993).
 Christensen, 1.
 Janna Saslaw, “Weber, (Jacob) Gottfried,” Grove Music Online, Oxford Music Online, (Oxford: Oxford University Press, accessed January 7, 2015), http://www.oxfordmusiconline.com/subscriber/article/grove/music/29983.
 Hugo Riemann, Harmony Simplified, trans, (London: Augener Ltd, 1896?), 9.
 Riemann, 22.
 Alexander Rehding, Hugo Riemann and the Birth of Modern Musical Thought, (Cambridge: Cambridge University Press, 2003).
 Rehding, 58.
 Renate Imig, Systeme der Funktionsbezeichnungen zeit Hugo Riemann, (Kassel: Bärenreiter, 1970).
 Ernst Richter, Manual of Harmony, Trans. JCD Parker, 8th ed., (Boston: Oliver Ditson Company, 1873).
Francis L. York, Harmony Simplified. A Practical Introduction to Composition, 4th ed. (Boston: Oliver Ditson Company, 1909).
Walter Piston, Harmony, 1st ed., (New York: W.W. Norton and Co, 1941).
Paul Hindemith, Traditional Harmony, (London: Schott and Co, 1943).
Arnold Schoenberg, Structural Functions of Harmony, ed. Leonard Stein, (New York: W.W. Norton and Co, 1969).
Allen Forte, Tonal Harmony in Concept and Practice, 3rd ed., (New York: Holt, Rinehart and Winston, 1979).
Ralph Turek, Elements of Music, (New York: McGraw-Hill, 1996).
Diether de la Motte, Harmonielehre, 14th ed., (Kassel: Bärenreiter, 2007).
Stephan Kostka and Dorothy Payne, Tonal Harmony, (New York: McGraw-Hill, 2009).
Jane Piper Clendinning and Elizabeth West Marvin, Musician’s Guide to Theory and Analysis, 2nd ed., (New York: W.W. Norton and Co, 2011).
Edward Aldwell, Carl Schachter, and Allen Cadwallader, Harmony and Voice Leading, 4th ed., (Boston: Schirmer, 2011).
 David Kulma and Meghan Naxer, “Beyond Partwriting: Modernizing the Curriculum,” Engaging Students Vol. 2 (2014). http://www.flipcamp.org/engagingstudents2/essays/kulmaNaxer.html
 Michael Rogers, Teaching Approaches in Music Theory, (Carbondale: Southern Illinois University Press, 2008).
Gary Karpinski, Aural Skills Acquisition, (Oxford: Oxford University Press, 2000).
 Rogers, 44-46.
 Karpinski, 120, 180.
 Heinrich Schenker, Harmony, ed. Oswald Jonas, trans. Elisabeth Mann Borgese, (Chicago: University of Chicago Press, 1954).
 Schenker, 138-139.
 Milo Fultz, May 10, 2014.
Whether or not teachers try to teach RN as vertical or with a more linear approach to harmony, the mechanisms for determining RNs often force students into a more vertical perspective.
 Steven Rings, Tonality and Transformation, (Oxford: Oxford University Press, 2011).
 Margaret Notley, “Plagal Harmony as Other: Asymmetrical Dualism and Instrumental Music by Brahms,” The Journal of Musicology Vol. 22, No. 1 (Winter 2005), pp. 90-130.
 Eytan Agmon, “Functional Harmony Revisited: A Prototype-Theoretic Approach,” Music Theory Spectrum Vol. 17, No. 2 (Autumn, 1995), pp. 196-214.
 John Rothgeb, “Re: Eyan Agmon on Functional Theory,” Music Theory Online vol 2.1 (1996).
 James McGowan, “Riemann’s Functional Framework for Extended Jazz Harmony,” Intégral Vol. 24, (2010), pp. 115-133.
 Nicole Biamonte, “Triadic Modal and Pentatonic Patterns in Rock Music,” Music Theory Spectrum Vol. 32, No. 2 (Fall 2010), pp. 95-110.
 David Temperley, “The Cadential IV in Rock,” Music Theory Online vol 17.1 (2011).
 Steve Larson, Musical Forces, (Bloomington: Indiana University Press, 2012).
 Daniel Harrison, Harmonic Function in Chromatic Music: A Renewed Dualist Theory and an Account of Its Precedents, (Chicago: University of Chicago Press, 1994).
 I documented my course with a blog: https://functionalanalysis.wordpress.com/2013/12/12/syllabus-and-schedule/
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