Tonality in My Molto Adagio

Estonian Academy of Music and Theatre

Jorge Gómez Rodríguez

Constructing Tonality in Molto Adagio

A Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of

Doctor of Philosophy (Music)

Supervisor: Prof. Mart Humal
Tallinn 2015

Abstract

The focus of this paper is the analysis of the work for string ensemble entitled And

Silence Eternal - Molto Adagio (Molto Adagio for short), written by the author of this

thesis. Its originality lies in the use of a harmonic approach which is referred to as System of Harmonic Classes in this thesis. Owing to the relatively unconventional employment of otherwise traditional harmonic resources in this system, a preliminary theoretical framework needs to be put in place in order to construct an alternative tonal approach that may describe the pitch structure of the Molto Adagio. This will be the aim of Part 1. For this purpose, analytical notions such as symmetric pair, primary

dominant factor, harmonic domain, and harmonic area will be introduced before the

tonal character of the piece (or the extent to which Molto Adagio may be said to be tonal) can be assessed. A detailed description of how the composer envisions and constructs the system will follow, with special consideration to the place the major diatonic scale occupies in relation to it. Part 2 will engage in an analysis of the piece following the analytical directives gathered in Part 1. The concept of modular tonality, which incorporates the notions of harmonic area and harmonic classes, will be put forward as a heuristic term to account for the use of a linear analytical approach.
To my father

Contents

Introduction……………………………………………………………………………i

The System of Harmonic classes (SHC) as the Source of my Compositional Metho d .1

1

1.1 1.2
What is Tonal?...............................................................................................................2 The System of Harmonic Classes ..................................................................................8

1.2.1

Content and Aim of the System of Harmonic Classes.........................................8

Primary Dominant Factor and Harmonic Domain.............................................12 Harmonic Area and Tonal Modules...................................................................17 Harmonic Areas and Vertical Sonoritie s ...........................................................21
1.2.2 1.2.3 1.2.4

1.3

Construction of the SHC..............................................................................................24

1.3.1

Left-Right Symmetry in the Major Diatonic Scale............................................24

2.2.1

Triadic Grid........................................................................................................42

Introduction

In order to guide the analysis of Molto Adagio, the main goal of the present thesis, this paper will offer a description of the compositional method that lies behind it. Briefly put, it consists of a hierarchically organized group of synthetic scales symmetrically constructed upon the major diatonic scale; there is no prioritization of intervals, which means: 1) any type of sonority can be built using any intervallic arrangement possible (seconds, thirds, fourths, and their inversions, whichever the consonant or dissonant quality that these intervals may have), and 2) any combination of scales derived from, and including, the combination of the major scale and its inversion, can constitute a harmonic resource (either in succession or in juxtaposition) without exceeding the restrictions that exist within that method. This method I have labeled the System of Harmonic Classes. Before engaging in a discussion concerning the music, how was it written and what choices were made, the author needs to account for the claim that the work possesses, overall, a tonal orientation and it is guided by tonal principles such as function (the principle that establishes a necessary relation between chords) and hierarchy (the principle that tells us which of these sonorities stands as a primary reference). I am aware that in the context of my own method, which uses musical materials in an organized but, overall, free manner, to claim that a sonority possesses functionality may seem to be stretching this concept too far. And yet, it is my proposal that a given sonority (representing a scale, as I will show), by progressing to another sonority (representative of another scale) at a critical juncture in the music, can be said to resolve onto that subsequent sonority.¹Function, always in the sense Riemann gave to this word,²is perhaps the most telling example of the difficulty to establish a clear-cut division between my system (which informs my compositional practice) and a more rigorous, common, traditional conception of tonality. I understand function as a fluid concept in which a musical object progresses to another musical object providing a

¹Doubtless, in cases such as this other factors are also relevant to bring to the listener an impression of necessity in a musical harmonically consistent flow. These may include dissonance, careful voice leading, and dynamics at structurally significant points. ²“There are only three kinds of tonal functions (significance within the Key), namely, tonic, dominant, and subdominant.” (Riemann 1893, 1900; Introduction).

ii meaningful structural or harmonic relation. Problematic as this may be, it forms the basis of my harmonic thinking and compositional practice, and, I quickly state, it is also limited to it: this means that no theoretical claims of general validity will be made, but only the potential significance or connection, in the context of music theory, of the concepts provided in this thesis. The theoretical premises from where my system is derived require at this point an important precision. Since the early stages of my exploration of harmony as an expressive means, a number of works and a great deal of scholarly research have been drawn to my attention. What appeared to be an old fashioned enquiry into the theory of harmony took all of a sudden a new twist when the work of the neo-Riemannian music theorists, mostly American authors, was introduced to me by Professor Humal of the Estonia Academy of Music. Their research not only put an end to the isolation in which I had been working but promptly made me realize that I had been thinking along the very same lines! Riemann’s theories are nevertheless transformed in the hands of the “neo-Riemannians”,³actively involved in geometrical models and smooth chromatic motions that connect logically almost anything that can be written with the twelve notes onto almost anything else, even to the extent of using computer models to generate analytical results that sometimes contradict cherished theoretical assumptions.⁴Dualism is still problematical in that, by those not acquainted with this specialist field, it still retains the aged aura of Hauptmann and Oettingen acoustic theories or, worse still, Riemann’s speculations about “undertone” series.⁵For me dualism presupposes a symmetric view of musical resources, specifically chords in Riemann and neo-Riemannian accounts, and in that everybody agrees; what I find

³Some of whom do not accept the “dualist” and “neo-Riemannian” labels, but who nonetheless accept gladly their theoretical Riemannian ascendancy. ⁴See R. Cohn (1998), Kopp (2002), D. Tymoczko (2011). I will expand on these authors in due time. ⁵Riemann himself finally dropped this idea (something usually overlooked), although admittedly late

in his career; see Klumpenhouwer, Dualist Tonal Space and Transformation in Nineteenth-Century

Musical Thought (2002) Klumpenhouwer reminds us that dualism is now, at best, an accepted synonym for the hierarchic equivalence of major and minor. See also Rehding: “[…] after 1905, Riemann agreed to do away with arguments based on undertones altogether, provided that overtones were no used either in the arguments of music theory [!]. with this last stage, where acoustical undertones were no longer necessary as a conceptual crutch, Riemann’s theory verged on a new paradigm: the age of psychology was about to supersede the age of acoustics.” (Rehding 2003, 34).

iii missing is an accurate theoretical differentiation between the method based on symmetry and a specific dualistic interpretation of it. Symmetry is to dualism what cogs and wheels to a machine: it could be a bicycle or a grandfather clock, but the function of the purported mechanism is simply to turn. There is a circumstantial connection and that is all it is: circumstantial. Obviously symmetry came first, as an elegant design of things, and then the theories followed. I cannot discern, yet, to what an extent my compositional method connects, or in some manner complements the dualist theories of neo-Riemannian authors. First of all it would be too premature to even suggest that possibility, and second there is still a lot of work to do as regards the consistency of my own system and its applicability outside my own practice. All it can be said with certainty is that, broadly, the system I propose is used in this thesis as a theoretical tool (one that crystallizes my compositional method) and that it appears to move among the same lines as those of the neo-Riemannian authors, although our conclusions are different: for one, I am not convinced that a geometrical account of the connections between chords is an altogether satisfactory approach to “chromatic” music, as it is styled by the neoRiemannian authors mentioned above, and which comprises what it is commonly known as extended common practice. The piece to be analyzed, Molto Adagio, exists in no less than three different versions: as the III movement of a double string quartet (original version), as an additional ensemble arrangement of that movement, whose premiere took place at the Hochschule für Musik und Theater Rostock (HMT)⁶, in Rostock Germany; and finally as part of a string ensemble re-writing of three movements of the double quartet with the title Music for a Mushroom Cloud.⁷This last one is the version I present here for analysis as it has the advantage of being available in audio recording.

***
I would like to thank the professors, composers, teachers, conductors, and staff at the Estonian Academy of Music and Theater, especially Professor Margus Pärtlas for his

⁶Named Rostock Molto Adagio, played by the Ensemble der HMT Rostock, Dir.: Konstantin Heuer.

⁷Whose premiere took place at Mustpeademaja in Tallinn, Estonia, under the direction of Risto Joost,

where Molto Adagio stands as its last movement entitled And Silence Forever

iv determination to see me through, Toivo Tulev for welcoming me back every occasion I drifted, and for taking me hunting, Risto Joost for believing in my music, Professor Mart Humal for supervising my thesis with a true touch of genius, Professor Kristel Pappel for her unending generosity and sympathy (my academic guardian angel), Professors Lippus and Siitan for welcoming an unorthodox student composer in the musicology department (thank you), Helena Tulve for her timely advices, and, last but not least, Professor Kerri Kotta, for positively bringing out, and seeing through, the potential of a work that I myself could have hardly put into words. Thanks, finally, to all the staff at EMTA (IT department guys, my cultural mentor Mr. Koit Pärna, and also the sympathetic library staff) for making this possible. Margit Võsa, thank you for making me a better person with your patience.
1

1 The System of Harmonic classes (SHC) as the Source of my
Compositional Method

No living theorist has had a more profound impact on the field of music theory than Milton Babbitt. But it would be a mistake to separate Babbitt the theorist from Babbitt the composer. Babbitt makes the shift from thinking "about music" to thinking "in music" with integrity, not because his music is "theoretical" but because his theoretical conceptions become aurally cogent. (Cherlin 1986, 75).⁸

Babbit’s example is illustrative of the musical aims of the author of this thesis. The development of the System of Harmonic Classes is the outcome of the particular manner in which I use tonal material in my compositions. What was a personal choice became in time an inquiry into the tenets and propositions of the theory of harmony. The highly idiosyncratic practice and use of harmony by diverse composers throughout history⁹, at least those that influenced my music, made it inevitable to look for a more comprehensive pattern that would include what seemed to me an identical source: the common twelve tones used in Western music. The fact that, say, a C major chord could be used by Wagner with more or less the exact harmonic consequences (constituting a tonic resolution, for instance, or a deceptive cadence) that one could find it in Monteverdi or Bach seemed to me encouraging enough to search the connections; in other words, what connections, differences, or similarities, may be involved. The recourse to music theory in my search for that blueprint, or harmonic

⁸Michael Cherlin, Why We Got into Analysis and What to Get Out of It, Journal Of The Music Theory

Society of New York State vol.11); and it continues shortly after: “It might be correct to say that if Babbitt were not such a powerful thinker in music it would be unlikely that he could be such a powerful thinker about music.” Tymoczko (2011, 25) provides in his book a stern reminder of how far “thinking” can sometimes push the boundaries of communicability by citing Milton Babbitt’s 1958 manifesto “Who Cares if You Listen?”, in which he cheerfully acknowledged that his music was not enjoyed by laypersons, but only by a specialist musical community analogous to the specialist community of professional mathematicians.”

9

For an illustrative account of the changing views and evolution of harmonic practice from the Renaissance up to the Second Viennese School see Diether de la Motte, The Study of Harmony, An Historical Perspective (Dubuque: William C Brown Pub 1991).

2prototype, made it inevitable that part of the technical jargon and open questions I found in theoretical treatises and scholarly research came to form part of the system itself: in other words, at that point my compositional practice began to give way to a “system” of composition, as I began to translate it into technical terms and reorient it into a theoretical investigation running parallel with my composition work.

Both, compositional practice and theoretical inference go hand in hand to the point where the music I present here seems to me sometimes to appeal to a reading audience as much as to a listening one. The system I am about to present is the result of the confluence of theory and practice, faithfully adopting the theoretical results in my compositions.

1.1 What is Tonal?

Diatony therefore does not stem from the so-called Greek or Gregorian modes, but rather from the composing-out process, which is governed by the principle of the fifth. (Schenker 1979, 11-12)

I have always considered myself a tonal composer, with Tymoczko I strive for a “music that brings people together, rather than dividing them”, and with him also I think that “the traditional strategy—writing immediately attractive music that also contains deeper levels of structure—is as potent as it ever was.” (Tymoczko 2011, 26). This traditional strategy, if my reading of his book is accurate, is tonal music with its accompanying musical structures and regularities. And yet, the path from the tonal music I grew up with, the common-practice period, to the one I present in this paper, is not straightforward. Schenker’s quote above stresses a very important point: the synthetic character of musical practice.¹⁰Whether our major diatonic scale is a

¹⁰Brian Hyer’s article in the New Grove Dictionary of Music and Musicians is illustrative enough of the difficulties we encounter when attempting to define tonality. He says, for instance, that “There have also been some basic theoretical disagreements about whether its constituent musical elements are melodies or harmonies: however narrow the definition, the domain of tonal music is so enormous, diverse and complex that one can choose almost any combination of musical phenomena and theoretical principles as a basis for discussion.”. Hyer, Brian. Tonality – The New Grove Dictionary of

3historical product (something Schenker seems to implicitly deny) or a natural phenomena (the overtone series), is not as essential as the results drawn by the composer from the finished product, the major scale. Schenker’s final view of tonality is of major relevance to this paper, if only to stand in contradistinction to that of the present author. He maintains, shortly before the previous quote, that

The same relationship to a fundamental tone prevails also in the foreground: all the foreground diminutions, including the apparent “keys” arising out of the voiceleading transformations, ultimately emanate from the diatony in the background. I

have used the term tonality to include the various illusory effects in the foreground

[emphasis mine]; yet the tonal sparseness of diatony in the background and the fullness of tonality in the foreground are one and the same.

To “flesh in”, as it were, the fundamental diatony of a musical work with “illusory effects” seems to be the work of the “Schenkerian composer”. His view of tonality seems to be marked by what Chua terms a “battle plan”¹¹. Taking the opposite stance one may come across a common criticism of Riemannian functional theory. Referring to De la Motte’s functional views (and his silence over Schenker’s work) Jeffrey Prater says:

The problem ...is essentially the same one found in Piston [,] namely the setting of nearly all harmonic activity at a single fore-ground level. The central deficiency ... is the over determination of most fore-ground (chord to chord) activity and a corresponding inattention to the hierarchical relationships of the harmonies that direct the foreground.¹²

Music and Musicians. Digital Edition. Edited by Stanley Sadie. Here I am only referring to salient common-practice theorists that may offer an eloquent contrast with more recent views, such as those held by Tymoczko, soon to be discussed, or Cohn. For Cohn see Audacious Euphony: Chromaticism