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 1 The System of Harmonic classes (SHC) as the Source of my Compositional Method . 1 1.1 What is Tonal? ............................................................................................................... 2 1.2 The System of Harmonic Classes .................................................................................. 8 1.2.1 Content and Aim of the System of Harmonic Classes ......................................... 8 1.2.2 Primary Dominant Factor and Harmonic Domain............................................. 12 1.2.3 Harmonic Area and Tonal Modules ................................................................... 17 1.2.4 Harmonic Areas and Vertical Sonorities ........................................................... 21 1.3 Construction of the SHC .............................................................................................. 24 1.3.1 Left-Right Symmetry in the Major Diatonic Scale ............................................ 24 1.3.2 Modal Layers ..................................................................................................... 25 1.3.3 Modal Interchange ............................................................................................. 27 1.3.4 Harmonic Classes............................................................................................... 31 1.4 The Major Diatonic Scale as a Harmonic Class .......................................................... 35 2 Analysis of Molto Adagio ............................................................................................ 37 2.1 Compositional Background ......................................................................................... 40 2.2 Musical form, harmonic and motivic material ............................................................. 41 2.2.1 Triadic Grid ........................................................................................................ 42 2.2.2 Motivic Material ................................................................................................ 44 2.2.3 Harmonic Material ............................................................................................. 47 2.2.4 Linear Approach ................................................................................................ 50 2.3 Tonal layers in Molto Adagio and their analytical representation ............................... 65 3 Conclusion ................................................................................................................... 67 4 Bibliography ................................................................................................................ 74 5 Töö lühikokkuvõte ....................................................................................................... 76 6 Appendix: And Silence Eternal .................................................................................. 80 i 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.1 Function, always in the sense Riemann gave to this word,2 is 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 1 Doubtless, 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”,3 actively 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.4 Dualism 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.5 For 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 3 Some of whom do not accept the “dualist” and “neo-Riemannian” labels, but who nonetheless accept gladly their theoretical Riemannian ascendancy. 4 See R. Cohn (1998), Kopp (2002), D. Tymoczko (2011). I will expand on these authors in due time. 5 Riemann 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