Ptolemaic pianocentrism

Saturday, 10 September 2005 — 5:09pm | Classical, Jazz, Music, Pianism

If you were expecting a post on the applicability of “Turtle Talk with Crush” as a superstructural blueprint for the Turing Test, precursory omens of why high-definition post-DVD storage media are doomed to failure in the general consumer market, secret schematics of the Nintendo Revolution controller or more invective hilarity induced by a certain undeservedly bestselling author, come back later. This is not the post for you.

What’s better than one blog unlocking the mysteries of music theory? That’s right – two blogs unlocking the mysteries of music theory. Below I respond to Guillaume‘s criticism of the elevation of middle C in the Western European musical tradition, and while I may get on a slightly technical bent, it is my hope that this post will not be wholly inaccessible.

You should read Guillaume’s statements before proceeding, as he presents a concise historical overview of the familiar A to G tonal system as well as a rundown of what he considers to be a problem: that C, and the major and minor keys built upon it as a tonic, is an arbitrarily-selected tonal centre of gravity that is presently overemphasized and overrepresented. Those who are at all familiar with the rhetoric of Marxist or postcolonial literature should at once recognize the tropic structure of his argument, which is the age-old attack on an instance of reification. It runs thus: a) the governing establishment (in this case, a cultural bourgeoisie of tonality) presents an artificial construction (C as the organizing epicentre) as a normative and natural entity; b) the foundations of this construction are arbitrary; therefore, 3) the constructed norm, now revealed, must be disestablished.

Being a neo-imperialistic bourgeois know-it-all, I feel inclined to reject the conclusion that the C “mythology” (to borrow Barthes’ sense of the word), once properly exposed, should necessarily be subjected to demotion. Certainly, I concede that C is an overelevated focal point (and will attempt to explicate it with additional reasons that may ease Mr. Laroche’s bewilderment); and certainly, as a musician, I see the pedagogical value in exposing both students of music and the public at large to the undiscovered country beyond the major-minor system, though I do not envision such instruction as concurrent.

But the battle cry for change is a case of overstated alarmism, and the bizarre suggestion that A would be a suitable alternative makes hardly sense at all. Where it is not based on a circular rationale to do with the order of the Latin alphabet, for crying out loud, it refers to 440Hz as “a nice number, easily divisible into a number of smaller parts.” Here, the menace of the constructed norm rears its ugly head in the other direction. 440Hz was never standardized as the standard acoustic tuning frequency until the ISO 16 specification, dated 1955 and renewed 1975; prior to that, Guillaume’s assumption of a “properly-made tuning fork” was far from a proper existence, as proprietary conventions hovered all over the place.

Furthermore, if we are going to talk about divisibility as a theoretician’s convenience, we must also remember that these numbers are founded on a unit of measurement that is also not a natural entity. The hertz is the inverse of the second, and the authority of the second has no relevance to music in its unquantified form. Now, as soon as you quantify music, the second becomes important – not just in terms of frequency, but also in the dimension of tempo when it comes to variables like prescribed metronome markings – but these are every bit arbitrary conventions in no worse a way than C is a convention. To justify a mathematical convenience with itself is patently tautological.

A system built upon twelve well-tempered semitones to the octave derives its tonality from ratios of resonant frequencies, and the important thing to remember about ratios is that they are relative. Like the Kelvin scale (that would be a scale of temperature, not music), the only absolute is zero. Outside the realm of the theoretical, relative intervalic distances are sufficient.

In sum, arbitrariness is unavoidable. That said, C has a far better claim to its present position as the Ptolemaic do of the solfege in elementary instruction. Yes, this claim is one part retrospective and another part descriptivist, but at least it’s based on something practical, which is more than one can say for Guillaume’s argument for A to take its place. A is no more the sun of western music than C is the Earth.

So let’s examine some possible causes for the prominence of C. I attribute it first and foremost to notation. C Major has no sharps or flats. It tends to be very readable in any clef (and I hasten to point out that the thriving clefs, treble and bass, are founded on G and F respectively). This presumes the authority of the Ionian mode, but it also permits the definition and instruction of other scales in terms of how they differ from it; scales are easier learnt from identifying distinguishing accidentals than from note-to-note intervalic distances.

But, one might object, even if you accept the Ionian as the organizing mode of western music, you could establish it on any scale – and the readability of C Major doesn’t correspond to the ease of its playability on a given instrument. So how is it that C-oriented musical notation set foot in composition and performance?

Answer: keyboards.

The keyboard configuration of black keys and white keys is a direct visual isomorphism of musical notation, a representational mapping from sight to sound – albeit not a lossless one, due to the limitation that enharmonic equivalences like A# and Bb (or more tellingly, B# and C) are indistinguishable. Middle C is easier to grasp than, say, a hypothetical middle A, because only hitting the white keys with C as the tonic delivers an entire major tonality, just as hitting only the black keys delivers a pentatonic spectrum.

This isn’t something to be prescribed to the serious aspiring pianist, as it has the potential to lead to fingering habits that are undesirable in the long run as the keyboardist progresses to more complex pieces; Chopin famously trained his piano students starting with the B Major scale to avoid exactly that pitfall. But basic keyboard literacy is nowadays fundamental to any performer, and familiarity with the black-and-white layout is often a requirement for intermediate musical studies in any instrument. For them, keyboard technique is a secondary consideration, ranking behind the layout’s usefulness as a theoretical aid.

I’ve coined what I think is a clever word for this phenomenon, which I do not believe has been employed in a theoretical context: pianocentrism.

The continued entrenchment of C as a de facto “starting note” since the fifteenth century is a pianocentric result; the black-and-white alternation first emerged in exactly that period. The keyboard has historically been, and persists to be, the reinforcing mechanism for what Philip Tagg, in his paper on the semiotics of popular music, refers to notational centricity. Any way you swing it, notation has restricted much of our tonal cognition to a discrete twelve-step cycle, when pitch in the abstract is a continuous domain. Fred Lerdahl’s work on formal grammars of music outlines this conception in a generalized framework; the pianocentric orbit around C Major that I am here identifying is a specific, if popular case.

There exists a solid objection to this, and it is one that Guillaume implicitly posits when he defends his preference for A based on its suitability to the Aeolian mode – that is to say, the natural minor on the sharpless and flatless staff, executable on white keys alone. The idea is that if we reverted to an A-oriented model, which brings us back to how A-to-G notation was alphabetized in the first place, natural minors and not majors would be the new point of origin in a coordinate system that remains diatonic.

In other words, the dominance of C is a direct product of the dominance of the major scale. The utility of teaching the major scale first is what leads us to a descriptivist argument: simply put, it permits the beginning performer easy access to what we now call small-c classical music as well as a plentiful repository of nursery rhymes. In the dungeons of tonality, the major scale is the Big Key.

Is it limiting that the major-minor system – and as a result, C Major – indoctrinates society with traditional prejudices of consonance and dissonance? Yes, in the same way that the limitations of Euclidean geometry are prejudiced against hyperbolic surfaces. Yes, in the same way that the limitations of Newtonian physics make no allowances for wave-particle duality on the atomic level. It is no coincidence that Arnold Schoenberg (and every time I mention him, I just know Guillaume is going to jump all over my flagrant misunderstandings of serialism) described his twelve-tone system as being to music what relativity was to classical physics.

By this I mean that tonal prejudices, reified as they are, hold for a reason. Like the postulates of Euclid and Newton – although a better analogy would be to Northrop Frye’s theory of archetypes in English literature – tonality defined around the major scale is a theoretical approximation that only works under certain assumptions, but its utility is sufficiently justified by the breadth of observable phenomena it envelops.

Of course, music performance is one thing, and composition is quite a different matter; in that regard, it has been some time now that composers have dispensed with pianocentricity in the key of C, not to mention every other rudiment in the unwritten classical rulebook. This is by no means confined to atonal experimentation, nor has it failed to elicit popular consumption.

Think Leonard Bernstein. Or, for that matter, Danny Elfman’s title theme to The Simpsons. Or John Williams, probably the most popular symphonic composer of modern times. Although a good many of his lavish and bombastic leitmotifs that are now as firm a part of the cultural fabric as Wagner was a century ago are strongly major or minor, much of his work is not: the contrapuntal dialogue between keyboard and spaceship in Close Encounters of the Third Kind is the exemplary cue, but consider the echoes of Stravinsky in The Empire Strikes Back (both its incidental music and the thunderous “Imperial March”), the “Scherzo for Motorcycle and Orchestra” in Indiana Jones and the Last Crusade, and a good chunk of Jaws. In video games, the Japanese RPG music of composers like Nobuo Uematsu and Yasunori Mitsuda was heavily modal (particularly in the Aeolian and Dorian); notice the frequency with which they resolve cadences from minor dominant chords, putting a whole tone of space between the leading note and the tonic.

Guillaume also makes an interesting observation that I feel should be quoted directly:

The reason kids don’t appreciate Messiaen’s sense of tonality (he argues that it’s there in his Technique de mon language musical, I tend to agree based on my definition of what tonality should be…) is partially because from the beginning we have them play nice little pieces in C+ that shy away from dissonance. We teach them that dissonance is bad because these cute little pieces alternate between the chords of I, IV and V, and anything outside that is a minor chord and thus to be avoided. If a minor chord is to be avoided, how are we supposed to appreciate the beauty of an augmented chord with a minor 9th added on top? Even on the other side of the musical learning, that thing called jazz, most books teach the chords and progressions and techniques from a base of C. How unoriginal.

(“Aha!” sayeth Nick as he espies a mention of his own personal field of quasi-expertise, “a chance for Faramir, Captain of Gondor, to show his quality!”)

This is an interesting passage, partly because jazz harmony is almost exclusively founded on 9th, 11th and 13th extensions when it is not busy mucking about with overlapping inversions and funky pedal points. In fact, I speculate that is precisely why illustrations of leadsheet chord symbols are presented by example with C as the root: the accidentals on the staff explicitly signify how these harmonies fit into or differ from the diatonic sequence of the major scale.

In practice, the situation is quite different. Chord substitution and voicing revolve around emphasizing the traditionally discouraged tritone, often using it as a diametric pivot across the circle of fifths. Melodic improvisation is one big exercise in the convergence of modes and blues scales. New syntheses of these scales with the vocabulary of underlying extended chords are happening all the time, and complete conversions to a modal framework are old news; Miles Davis was doing it half a century ago in “So What”.

In my own experience, C is not the most comfortable of keys for the jazz pianist, as the white-key correspondence to the diatonic major becomes almost a hindrance and a distraction once one has found tactile comfort in a roughly equal proportion of black and white landings. I much prefer Eb, as the proximities surrounding it lend themselves to some very interesting progressions that feel a lot more natural to the fingers.

The ideal standard of performance in any genre, of course, is equal and balanced proficiency starting on any note. But for most purposes, C is as good a place to start as any.

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