harrison, daniel. 2002. dissonant tonics and post-tonality tonality

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Slightly modified version of a paper read at the Music Theory Society of New York State, April 28, 2002.

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Harrison, Dissonant Tonics, MTSNYS 4/28/021 Dissonant Tonics and Post-Tonal Tonality (MTSNYS Presentation Version) A red thread running through my work on harmonic theory is an interest in back-of-the-book topics, those issues that appear in the later chapters of our standard harmony texts. Ive often felt that the typical plot of tonal- music instruction, as read in these texts, amounts to little more than this: the story of a brave beginning of theoretical rigor and explanatory power that becomes, by the end, an exercise of lever-pulling, wheel-whirling, huffing and puffing, all in the hopes of keeping Toto away from the curtain. This is to say that the final chapters of many of our standard undergraduate harmony texts offer a grab-bag of explanations of only apparently local use. When approaching techniques that have been associated with problems in the later history of tonalityequal division of the octave, extreme chromaticism and enharmonicism, not to mention questions of large-scale structuretheir tone often becomes tentative and even apologetic. My contributions so far to harmonic theory try to convey a sense of how these topics may be presented less as signs of tonal dissolution than as signs of tonal development and enlargement. And it is in this spirit that I speak today. I want to deal witha matter of theory, frequently propounded early in instruction and with some authority, that is certainly at least partly responsible for the problems of back-of-the-book harmony, including the embarrassed agonies of any final chapters that attempt to treat post common-practice harmony. The topic is a large one, and I am able today only to outline the issues, do a little infilling, and point out connections with the work of other theorists as well as suggest directions for making those connections stronger. One of the fundamentals of tonal music, in both practice and theory, is that only a consonant triad can stand as a tonic chord of a key. This is why the keys of C major and C minor exist, for example, but not C diminished. For Rameau and, later, Riemann, consonance and tonic are related symmetrically, which is to say that tonics are consonant and consonances are tonics are equally true. Both theorists built out extensively from this relationship in their music theories.1 Rameau, in comments about the authentic cadence that concludes a composition, noted that the consonance of the final chordthe tonicdistinguishes it from all other chords. Were the dominant chord also fundamentally consonant, the mind, not desiring anything more after such a chord, would be uncertain upon which of the two sounds to rest. Dissonance seems needed here in order that its harshness should make the listener desire the rest which follows.2 (David Cohen glosses this and related passages in his recent article on musical perfections in MTS.) In this way, the tonic alone was fundamentally consonant (i.e., a Harrison, Dissonant Tonics, MTSNYS 4/28/022 major or minor triad); the dominant, in its true and characteristic form, was a dissonant major minor-seventh chord. Riemann later identified the major added-sixth chord as the characteristic subdominant dissonance. For both Rameau and Riemann, dominants and subdominants, even those appearing in triadic forms, were understood theoretically as representatives of underlying dissonant, tetradic structures. The tonic triad, incontrast, was both consonant and complete.We may no longer appeal in our harmony classes to things like fundamental categories of chords or characteristic dissonances, but we nonetheless speak about tonic and key in ways that are completely consonant with these old- fashioned ideas. In fact, from species counterpoint to Schenkerian analysisthe gamut of technical knowledge generally taught concerning tonal musicthe tonic-consonance fundamental is an unquestioned given. But we are also well aware of pieces and even entire repertories in which a traditionally dissonant chord projects tonic. And these tonic chords can and often do have the same phenomenological attributes possessed by consonant-triad tonics. Example 1 shows some easy-to-recall cases from semi-classical repertory, reminding us also that the technique is Gerswhins as well as Debussys. So heres the problem: how can we square Debussy and Gerswhin with the still worthwhile concepts from Rameau and Riemann? The starting point has to be discussion on the compositional discovery about chordal statics made towards the latter part of the nineteenth century: consonance could be relativized without damaging the tonal-system environment. In other words, tonics could be made from chords that were more consonant relative to non-tonics, but not necessarily triads. This accomplishment, of course, goes hand-in- glove with the well-known increase in dissonant chordal formations during the nineteenth century; increasing levels of dissonance allow a higher setting of the consonance band to maintain the same rough absolute distance between imperfect, non-tonic and perfect, tonic sonorities, the perfection of the latter, in essence, being defined down. Maintaining both the distinction between these two categories and the construction of progressions that highlight this distinction suggests an analytic method that Paul Hindemith, in the 1930s, identified as harmonic fluctuation.3 My interest in this paper is partly in the dynamic conditions of musical structure that allow for dissonant tonics, but mostly in the types of static structures (chords) that are used when the dynamic conditions allow. There is already some literature on tonal structure that focuses on dynamics almost exclusivelyIm thinking here of the 1960s work of Roy Travis and Saul Novack, as well as of Robert Morgans well-known article on dissonant prolongation. But the sonorities proffered as tonics in these studies invariably fail to give the same phenomenological experience as do traditional tonicsHarrison, Dissonant Tonics, MTSNYS 4/28/023 they dont sound or feel like tonal- music tonics in the same was as those in Example 1. Im interested primarily in those structures that do sound and feel like tonal- music tonics, which is a matter of chordal statics. But since there is no context- free musical situation in which tonics exist, there can be no satisfactory theoretical opposite to a purely dynamic, contextual view of tonicthat is, a pure statics of tonic. So, I will sketch a few dynamic influences. Here is a familiar meaningful unit of chord grammar: IV7, V7I. Although only two chord types are used here, they are formed as antimetabole, as two phrases of the same two words but in reverse grammatical order. In the first phrase, tonic is subject and the dominant seventh predicate, if you will. But the dominant is dissonant and hence both imperfect and incapable of being an ending product. In the second phrase, tonic is consonant and predicated by imperfect-to-perfect succession from a chordal-dynamics point of view. In addition, the predication is underscored by the completion of chordal-succession and phrase symmetries. In this way, the wild, phrase-concluding C+7 chord of Example 1(a) receives a strong tonic accent and, therefore, sounds perfectly appropriate, even withstanding a change in the otherwise strict Tp4 relationship between antecedent and consequent. The same grammatical archetype is composed out in Example 1(b), although the dominant is expressed in this case through a ninth and not a seventh chord. Note that the Tp2 antecedent-consequent relationship is preserved by the dissonant tonic chord. In these two examples, at least, end position is a strong indicator of tonic and is indifferent to both absolute, triadic consonance and the products of motivic activity. Examples 1(c) and (d) instance another grammatical unit: TSDT, a single bilateral exploration of functional relations working out a StartDepartReturnArrival paradigm.4 The concluding C6 chord benefits from the same perfecting circumstances as in (a) and (b), but the starting chord benefits from another rhetorical conventionweaker than the firstthat associates structural beginnings with tonics, allowing (c), the opening added-sixth chord, to act tonically. The tonic-beginnings convention is also at work in the antecedent phrase of Example 1(a), where little fuss ensues about the vocal D, a free-standing ninth against the C-chord accompaniment (perhaps it does resolve to C at the end of m. 2). The convention of tonic beginnings assimilates the D as a chord tone, rendering the acoustically consonant E a dissonant escape tone.5 At the start of Mackie Messer, the added sixth, A, slips in easily and over the course of the phrase will prove to be, essentially, the reciting tone of the tune. Harmonic activitythe TSDT processseems to take place underneath and without much notice from the A-obsessed tune, which only responds autonomically with a whole-step lowering of the motives pickup notes. Harrison, Dissonant Tonics, MTSNYS 4/28/024 Example 2 presents a more substantial situation involving concluding-tonic rhetoric. Excerpted from the closing measures of Maurice DuruflsRequiem, op. 9 (1947), the passage is based on a cantus firmus, In Paradisum, that appears in the top staff. This antiphon is in F mixolydian, with a key signature of five sharps; that this signature is the same as that of B major will prove to be significant in the following discussion. PLAY EXAMPLE Underlaying the chant are a pedal on F and a haze of chordsmostly conventional seventh- and ninth-chordsthat, after reaching a nadir in reh. 101+2, gradually ascend until the uppermost note reaches F5 at reh. 102+2. At this very point the haze and the pedal clear away, revealing a simple B-minor triad, the first triad heard in the movement. It is not immediately certain what kind of tonal cue this triad gives. A diminuendo having started two measures before and the chant having reached its final, a conclusion seems imminent. But upon what to