The New Tonality.
It has been more than a century since the inflammatory accusations of a feckless atheistic culture came against the expanding reach of chromatic hearing. The argument, while the rhetoric of a political philosophy, no less contributes to a psychological incapacity to hear structure in contemporary music of the last 100 years. To equate this to an aesthetic prejudice would be dramatic unless expressed within the boundaries of postmodern criticism, and, whether I would adopt Foucault’s , Said’s, or Mbembe’s points on the other as the means to amplify the arbitrariness held within the arguments regarding tonality and atonality, the nuance of these vantage points would focus toward the same result.
All things must be tonal and any complexity that distances itself from a fundamental is still referential. Tonality is a gravitational pull in which all other tones derive hierarchical order. There is no atonal, except that which has been fabricated for political purposes of aesthetic.
Mbembe’s ‘blackness’, or Said’s ‘oriental’ (that by which one orients themselves toward, and thus draws distinctions that present separateness) are all variations on this ‘otherness’ that Foucault and Levinas express as an ontological mirror of the same species. Binary distinctions are politically motivated. Within accordance to that expression, so has a totalitarian misnomer attacked the development of Western music for now over a century. There is only tonality, and tonality governs even the most complex orientation of musical systems.
This orientation-complex does not simply go away when we ignore diatonic functions; those functions available to us under diatonicism will transform when geometrical and intervalic measurements alter course as well. Much music of the so-called atonal era chart these shifts within chromatic voice-leadings, even if the systems that focuses on their preference is still far from establishment theory. It would be prudent to remember that our contemporary attitude toward 18th century practice is a reflective analytical model that originates from German school of analysis of the 19th century. Far more worrisome is the vast majority of social-media promulgation of ‘music theory’ which treats triads and vertical sonorities as synonymous to ‘chords’ and calculates ‘A major’ and "‘G augmented’ as sound objects rather than divisions of octaves into geometrical space.
Diatonicism is inherently natural only as a cultural preference; not a positivistic law which permeates from the intrinsic nature of the sound.
When we are tempted in labeling triadic relationships as non-functional triads, we do so because we assume diatonicism is a normative priori; not the end of an evolution of tempered calculus. The term ‘non-functional’ is little more than a type of sanitizer to dissolve analytical responsibility. I have witnessed credible musicians ignore the tendency of sharps and flats acting as non-harmonic decorations, as though their tendency does not lead; that the very course of 12 equal tempered tones, a system that can only give justification to serialism, is itself impartial to direction. And yet triadic relations that confuse —even undermine— the diatonic model of scale-degrees and their representations as harmonic functions are present from middle period Beethoven; becoming increasingly well worn and even characteristic of the high German schools by the time of Liszt.
It is hard to find any respectable theorist that would argue these works to be atonal, yet many professional educators and performers agitate this promulgation by speaking of a sort of nascent state of atonality in the works of Wagner, Liszt, or Strauss. Yet they offer tonality and atonality to stand on two antipodal mode of a switch; light on/off. Either it’s tonal, or it’s not. Never do they stop to consider how evolution can be present in the face of absence; It is to argue light as a process of evolving dark, rather than the absence of the former.
Therefore it should come as no surprise that what they erroneously label atonality in musical discourse is not the end, or even the return to a chaotic pre-history, but the result of an evolution from triadic diatonicism to the traversal into the larger chromatic universe.
Another confusion must be confronted now as language confounds the understanding of our concept of chromatic. Chromaticism as applied to diatonic rationality refers to scale degrees that have been altered as to change the mode, quality, or outlying structure of the triad. C major(as a tonic), when ^3 is flat creates C minor. To lower ^5 after that would create a diminished triad and call for the status of quality to change to a leading-tone, that is, dominant, function.
Furthermore chromaticism can hide function of diatonic scale degrees. An augmented 6th for instance, inverts a IV and then raises the degree by semitone(represented by #)but the gravity posed by expectation, that #4 appears to sound as b5 which sounds like the dominant of the Phrygian II. When the voice-leading moves outward, b6 and #4 both moving to 5, confirms the former analysis. Expectation is thwarted because of the literary conventions(sharps and flats) converging with the auditory conventions(7ths resolving downward and by step).
This is what we normally think of when we think of Chromaticism. But the chromatic universe contains chromatic triads that are themselves 'diatonic’ within their own self-referential and similar construction. The most common example after major and minor triads is quartal harmony. Even here, a quartal triad can be assumed to exist in the major/minor diatonicism as an elaborated chord; C, G, D can be C major with a suspension on D desiring to resolve to E. But in quartal terms, C, E, G is not a consonant chord. The E is a non-chord tone, and thus, needs resolution to D. Such reciprocity is important for modulations between ‘chromatic triads’ with localized ‘diatonic’ functions.
As triadic harmony increased in the tones available over a fundamental —9th, 11th, 13th chords— inversions gave allusions to other chromatic formations. For instance, a G9 chord, if in inversion with the 7th in the bass would spell F(7), G(1), A(9), B(3). However, it superimposes with the chromatic triad of 2-2(rather than 4-3, the major chord, or its inversion 3-4, the minor). The result is that the G9 chord both belongs to a chromatic triad that we traditionally call a diatonic, major chord, and also to the first 4 scale degrees of a whole-tone collection. If we assume that whole-tone, then the functions change, while the notes stay the same: F(1),G(2),A(3), B(4). This is a concept of chromatic modulation to chromatic triads, and this is responsible for much of the area of play that is encountered in the Romantic literature.
Harmonic ambiguity then becomes a consistent fascination with romantic composers because chromaticism allows multiple functions to converge on singular, once axiomatically autonomous tones. However, for these composers, the lines were clearly delineated to the major/minor system, though perhaps unaware to these composers, the boundaries into other chromatic formations were a potpourri that flavored the traditional diatonic systems.
As example, when Brahms employs Ab, Submediant in C minor, he may proceed by flattening the C to Cb minor, enharmonically B, and at the same time, Ab may be interpreted as G#.
In C Minor, Cb is b1, not 7. It is part of a tonic relationship, not a dominant. Conversely, G# is raised 5 not flat 6. It is diatonically understood as a dominant function, not a predominant. Never the less, Brahms does not indicate the change of function. Both functions are present at once, and what might appear briefly to the discerning ear is the underlying network of tonal connectivity that maps us to a larger aggregate of chromatically operating triads. These diatonic models are superimposed on a larger network, a selection from the chromatic globalism, as it were- but those diatonic mappings reveal pathways, access that smoothly connect from one diatonic collection to another without disruption of function at the local levels. I will briefly mentioned that for Brahms, and his contemporaries, both functions are present at once; but more axiomatically to the point, these functions exist perennially underneath the diatonic model, and in the background, the chromatic superset maps these relationships out logically. That diatonicism is but a focused territory amongst many equally sovereign territories that have been cast into the abyss of atonal insouciance will serve as a main interest to the study of a new conceptualization of tonality.
This type of modulation as the Brahms example reveals the diatonic and ‘chromatic’ models interlining with one another; This is a ‘higher-level’ modulation. By contrast, a diatonic modulation(C major to G major) is merely building a pathway between two innocuous transpositions of the same model collection.
Yet we do not talk about these networks because we do not perceive the gravitational flow through complementary conduits of chromatic partnernship.
Notice that a similar observation can help to elucidate these substructural conduits. The chromatic scale can be unfolded in two presentations; each one contributing to a drastically different aural experience.
The first is to hear each successive semitone, where as the other is to lay them out by 7 semitones each, or, more commonly, the circle of fifths. Playing C, C#, D, D#, E, F, etc is an entirely different sound-spice than playing C, F, Bb, Eb, Ab, Db etc.
Despite the disparity in our aural experience, in each model, the chromatic aggregate is brought to full saturation at exactly the same rate; each note accounted for in the same time. What is different is the ordering and it is that ordering creates our perception of relationship. No one would argue that completing the chromatic aggregate either by semitone or by perfect 5th is alien or unnatural; because our theoretical systems develop attention to the discourse on them.
But so called ‘non-functional’ harmony, and atonality is a dismissive secret-sauce-term designed to make the analysis go down smoothly without heartburn. And it is false. Atonality is a myth.
What this model does call to our perception is the idea of closeness and it’s psychological and analytical discrepancies. Furthermore it reveals the division of melodic formations and harmonic ones; usually presumed to be derived from each other.
Our melodic sensibility and our conventional training in diatonic models would tell us that the chromatic scale, movement by semitone, represents the closest distance between two tones, as, at least in the 12 tone equal-tempered tuning system of Western musical practice. One can not find an interval smaller than a semitone. This would assume that 2 semitones is a bit further, while 7 semitones(perfect 5th) is quite far.
But our harmonic sensibility would say different. Harmonically speaking, roots that are 7 semitones apart represent the closest distance, as each transposition a fifth away alters only one accidental according to its eponymous diatonic collection. Thus, C Major becomes G major when F shifts to F#.
Here, the conception that keys are related by fifth is only the secondary result to the fact that diatonic collections communicate most easily with those transpositions who only displace one element and by semitone. F and F# are nearly identical, and all other tones are transposed into new positions of function. This falls under a rule of IC content with commonalities between pitch class transpositions. Because there are 6 tones that share a IC7=5 between them, C-G, D-A, E-B, F-C, G-D, and A-C, then when T5(the set transposed at IC5) or T7 is enacted, the result is F major, or G major respectively with the result being that only one tone is displaced in the movement. The other movements all map on to tones of the previous collections, so that when C maps on to G, G, maps on to D. Only B will map to F# thus creating a semitonal movement.
This suggests that movement by fifth is the byproduct of smooth voice-leading. To say that functionality is inherently built upon the progression of bass roots by 5th is to confirm that the tail wags the dog.
We walk into the expanse of a globalized tonality blindly when we assume that what lies at the foundation of functional harmony is the circle of fifths. One must only observe the more poignant reason within the diatonic models; voice-leading communication. C major and E minor communicate in the sense that they share two common tones and the notes that are not common(C an B) are a semitone apart. The same is true of E minor and G major except that the difference of tones is a wholetone apart between E and D. G major and B diminished also share two tones, as does D minor and B diminished, D minor and F major and F major and A minor.
Is it not interesting then, that Francesco Galeaszzi in 1796 said that the relation between C major and D minor was ‘wide and weak’, where as C major and E major were’ closely related’, and that e minor and C major were ‘even closer’. Here we have a ‘tonal’ theorist, theorizing during the tonal era, approving two chords we today would state are ‘far-away’ from one another on the circle of fifths(C major-E major) while two chords which function only within C major (C major- D minor), and thus project the unity of exclusive membership are ‘wide and weak.’ Note that these relationships, C major and D minor represent the most important functions to diatonic tonality; Tonic and pre-dominant. Why then, would Galeazzi conclude them to be faraway and weak?
Perhaps we are gauging tonality with different sextants than composers of the assumed tonal era navigated harmonic trajectory and distance?
Two distinctions here then must be made then; our scales are not derived from our harmonic conceptions or vice versa; they are paired. Melodic considerations need close distances to navigate by the voice. Linear, horizontal motion is always in a preferable state when the linear movements are held in close proximity; in steps with occasional leaps. This is as true in so called post-tonal music as it is in Fux.
When this rule is violated, it is done so for two reasons.
1. To emphasize the irregularity and difficulty of the horizontal and vertical obfuscations and thus create a deliberate textural effect, drawing our attention to the abeyance of melody, or…
2. The composer is grasping these coordinations poorly. This consideration is exacerbated by the propagated notion that atonality attempts to avoid tonal implications; ipso facto, literature under this disastrous label has always attempted to confuse a gravitational center for the purpose of teleological freedom; not to be void of internal relationships or functional meaning. Otherwise, why create serialism at all which is a highly regulated system that insists upon its own internal and localized logic? Is that not the raison d'être of the tone row? Furthermore, why did those composers of the second Viennese school spend meticulous thought when crafting the intervalic materials that would give authority to their harmonic and melodic implications in their work? Even Webern’s symmetrical collections may seem to deny progression, but are chosen because the ear would attempt to latch on to the teleological progress that asymmetrical collections evade. In other words, the stasis of Webern was carefully calculated to keep movement distilled; and such a consideration is not outside of the scope of tonal literature. One may consider this just an evolution of the tactic.
In those cases that atonality has been reduced to simply mathematical tiling, I point to the various mathematical structures this essay has hitherto discussed in relation to the ‘old’ tonality. To assume or say that only one equation of mathematics is suitable is to deny the very authority by which tonalists assert the division of ‘musical’ and ‘arbitrary’. Observe the phenomenon of hexatonic cycles. The distance of voice leading between C major and C minor is 1 semitone; to Ab major is one semitone(G-Ab) to Ab minor is one semitone; to E major is one semitone(Ab=G#, C-B); to E minor is one semitone; and from E minor to C major one semitone thus completing the cycle. Notice the Bass movement of such a progression. C G# E, or C Ab E equals a symmetrical augmented chord.
Even within movement around the augmented cycle, a circle of thirds sounds just as convincing as ‘functional’ tonality, despite the fact that the cadences are related in interval sets other than 7 semitones.
Shall we overlook this fascination to promulgate a tired and useless definition of tonality that was not formulated during the time of Mozart and rejected by the composers who populated the era of Wagner’s reign?
My severe retraction from the culture of discourse regarding so-called atonality is that it assumes a binary dialectic. Audiences are convinced that a piece presenting any challenge of complexity is atonal, which is a signifier to mean irrational and without logic or order. On the contrary, much music written in the last century has been every bit tonal as anything in the previous two centuries; what has changed is the aesthetic means, the intellectual apparatus, but not the aim. More unforgivable is those composers, whom, by adopting the erroneous mislabel perpetuating this vacuous approach to the music of our current age, step into the role of chaos, and thus expose their belief that Stravinsky’s Symphony of Psalms, or Thomas Adés Violin Concerto are the result of anti-establishment fist shaking and discursive ink splotting on a score; the result of which is a harmonic happenstance that coincidentally, not the premeditated and focused execution of exploration of harmonic relationships that evolved out of a 300-year-old diatonic predilection.
Triads are not merely arbitrary objects that are inherent to a greater degree in nature than chromatic formations. If we understand the near evenness of triads around Lerdahl’s pitch-space grid, or the understanding that Riemann’s functions, Piston’s Roman numerals, Schoenberg’s structural functions, or Schenker’s Ursätze all point to the same centrality —despite the theoretical aspects that these disparate thinkers situated their arguments around— we can see that the triad’s consonance is an epiphenomenal motivation; the secondary effect of a more basic principle; near evenness is a geometrical occupation of theoretical sound-space. Augmented triads, of course, are the most even, dividing an octave equally into three parts(It must if its a triad), where as the linear dyad, the tritone, comprised of 3 equal wholetones, creates for itself an equality that divides the octave in two. Both Augmented triads and tritones -and for that matter all symmetrical sets of intervalic groupings- are not dissonant as seems to often be employed by unscrupulous composers and reinforced by vacuous university teaching; They are unsettling because of their stability; a fact that they are not susceptible to movement. By displacing the augmented triad by one semitone, for instance if C-E-G# moves G# to G, a displacement of that tone creates a nearly even shape; what we now refer to commonly as a major triad. If we then alter C-E-G to C-Eb-G the minor chord is still displaced from the Augmented triad by one semitone. This time on an Eb Augmented triad, where C moving downward to B would create the augmented triad Eb-G-B. Therefore, Major and Minor chords are invariant, inversional reflections of the same geometric space. This is all to say that the theoretical work compiled over several centuries has focused on consonance as if it were, itself a natural state, causing the erroneous belief that all other states are somehow disfigured. What might be interesting to realize, for purposes of chromatic mapping, and those triads that appear through their interlocking relationships, is that consonance is a semiotic representation of the phenomenon of a geometrical proportion; and after all, proportions are what lead Pythagorus to theorize what sound constituted music. There exists of course, a multitude of chromatic triads that have been in use over the centuries; many even defining the sounds of particular movements, such as the impressionist era and the chromatic triad 2-3 found in much of Debussy’s work.
As for the particular hexatonic cycle, they can be evidenced in works from Haydn and Mozart where these formations govern long term harmonic goals upon which surface harmonies populate the localized functions of 18th century practice. By the time of Brahms the cycles are utilized as sequential material and thus are not distilled by convention.
It was Kofi Agawu that suggested that the most useful aspect of analysis is that it trained the mind what to look for, and the ear how to accept. Milton Babbitt expressed dissatisfaction with writing music that was ‘coherent’ in that for him, to do so meant to write to the level of analytical training of some random, idealized member of the audience, rather than an audience member attempting to understand the work as it worked. I propose we adopt a new analysis that might link the previous centuries to our own as an evolution, and not a separateness of Foulcout’s ‘other’.
My own work is interested in exploring such techniques and is subsumed under the heading metatonality, which creates the bulk of my theoretical and compositional interests.