Dissertation Diary 2015-11-19

I finished up some lingering edits in chapter 3 and did some more finessing on chapter 2, thanks to edits from advisors. As it stands, I now have 12k some words and 50 pages in chapter 2, for total current document length of 123 pages and 28k words. One more chapter next quarter, and then I’ll be on to intro/conclusion/formatting!

Here’s the opening of chapter 2 as it stands:


            “In the beginning was the Tonic” would be a promising opening for the gospel of tonality. Though the tonic pitch may be the origin and goal of harmonic progression, in itself offers no diversity, no motion.[1]


It is difficult to pinpoint the beginnings of functional harmonic ideas. Should we go back to modal ficta and examine why tendency tones were performed a certain way in the middle ages? Or should we start with the codification of the triad, with Lippius and Zarlino? Do we need to wade into the battle of primacy of melody versus harmony? At what point in history is music mostly or entirely written in a Common Practice Period tonality – before or after composers and theorists are cognizant of the difference between major-minor tonality and modes?

I have chosen to start with Rameau. The purpose of this historical discussion is to trace functional ideas as they wend through different formats and relevancies, showing the historical precedence for Functional Analysis and looking at the various guises functional language has worn. From Rameau we move to the Thoroughbass of his contemporaries, then to Stufentheorie, and then to Riemann and related authors, and finally to Schenker. In each case, these historical scholars have used functional ideas with evolving language that shows the contemporary analytical concerns.

This historical investigation will also provide some of the background on the historical emergence of Roman numerals as well, which I find shows that Roman numerals were always intended to be functional as it was understood at the time. In fact, some of the primary precedents of Roman numerals are also important antecedents to Functionstheorie and Functional Analysis.

            2.1.1 Rameau

While Rameau’s treatises are written firmly in the Enlightenment era, more than a century after the more or less accepted beginning of tonality, he is often proclaimed as the first true harmonic theorist,[2] and it is definitely true that “since the appearance of his Traite de l’harmonie in 1722, both the conceptualization and the pedagogy of tonal music have been profoundly altered.”[3]

Jean-Phillipe Rameau (1683-1764) is recognized as the first theorist to demonstrate the understanding that all the elements of music, whether they be triads, bass foundations, counterpoint, root generation, directed harmonic motion towards a cadence, interaction of diatonic scales and chromaticism, harmony, or rhythm and meter all work together to create a sense of tonality.[4] His concept of a Fundamental Bass underlying harmonic progression spread widely and quickly.[5] As with any theorist, Rameau did build on the work of his predecessors, and much of his work consists of reformulating and combining previous theories,[6] the most obvious and contemporary of which is the idea of thoroughbass which I will come to shortly in Section 2.1.2.

The primary idea behind Functional Analysis is the tension between dominant and tonic. This can be articulated in multiple ways, including referencing the desire for dominant to resolve to tonic, or the pull of the leading-tone, but no matter the phrasing, dominant represents motion and tonic represents rest. Rameau’s thoughts on dissonance and the seventh chord translate into dissonance propelling harmony from dominant to tonic,[7] and in his theories all non-tonic harmonies are compelled to return to the tonic,[8] heralding the beginnings of functional harmonic thought.

Some of the lesser functional ideas of Rameau’s that are still in use in Functional Analysis include his preference of bass movement by third and fifth[9] – which resembles the relationships between functions and their substitutes [Section 3.1.2], double emploi (“double employment,” which is based in part on his desire for thirds in the bass instead of steps)[10] – and is cited as the idea behind the P6 [See Example 3.20], and the idea of a subdominant – which was not previously common.[11] These last two ideas are introduced in Rameau’s later treatise Nouve système (1726), and both are essential to the treatise Generation harmonique (1737).[12]

The main drive behind Rameau’s description of these harmonic phenomena was his concern with providing scientific proof of musical ideas he knew were common. Functional Analysis is less concerned with proving the rationality of any given phenomenon and more with describing it in a useful way to analysts. Thus, Functional Analysis simply recognizes the commonness of chord relationships and progressions by thirds and fifths without the necessity of answering why they came to be. And while Rameau’s original purpose behind theorizing double employment is unnecessary in a descriptive system, the idea that ii6 and IV are somewhat equivalent and mostly interchangeable remains.

Generation harmonique is the first treatise in which Rameau writes on the topic of a tonic surrounded by fifths on either side, with subdominant below and dominant above.[13] This is the sort of idea that will later influence dualist writers like Hauptmann and Öttingen, and Rameau is often listed as one of the intellectual forbearers of Riemann.[14] Dualism is still an important forerunner to Functional Analysis, even if it has been discredited in many ways.

While Rameau is considered the inventor of harmony, a very vertical concept, Christensen argues that Rameau is also a melodic and horizontal thinker, noting that all his analyses are time-based and unfolding:

… the central claim of the Traite remained unaltered and unchallenged: music is a coherent and intelligible succession of directed harmonies over real time that can be both defined by and modeled with the fundamental bass.[15]

This is not surprising, as the most linear, horizontal theories of modern times, those of Schenker, can also be traced back to Rameau through Stufentheorie.[16] Functional Analysis also seeks to strike a balance between vertical and horizontal.

[1] David Damschroder, Thinking About Harmony, 105.

[2] Thomas Christensen, Rameau and Musical Thought in the Enlightenment, 26.

[3] Christensen, Rameau and Musical Thought, 1.

[4] Joel Lester, “Rameau and eighteenth-century harmonic theory,” The Cambridge History of Western Music Theory, 753.

[5] Lester, “Rameau,” 772.

[6] Lester, “Rameau,” 753.

[7] Lester, “Rameau,” 761; Christensen, Rameau and Musical Thought, 120.

[8] Christensen, Rameau and Musical Thought, 129.

[9] Lester, “Rameau,” 763.

[10] Lester, “Rameau,” 766.

[11] Lester, “Rameau,” 768.

[12] Lester, “Rameau,” 768.

[13] Lester, “Rameau,” 768.

[14] Lester, “Rameau,” 774.

[15] Christensen, Rameau and Musical Thought, 132.

[16] More on Schenker in section 2.3 and more on Stufentheorie in Section 2.1.3.

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