Ntuple Indemnity

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.

As some readers may have noticed – and whoever they are, I admire their persistence in providing return traffic in the face of abject futility, however motivated by ennui it may be – this alleged weblog has been less than rife with recent activity of late. As pleasurable as it is to thumb my virtual nose at virtual people in this besotted cyber-realm with only words as my weapon, I must admit it has not in contemporaneous times been my first and foremost love.

Advance Wars: Dual Strike is not my first and foremost love either, but it is most of what I have been galvanizing to fill the few extant temporal vacuums that betray the character of the astute hobbyist. It is, in short, probably the most enthralling video game I’ve played on any system this calendar year – the dream strategy title for those who prefer patient and methodical turn-based analysis to the rapid improvisation of an RTS, but can spare neither the time or the commitment to get mired in late-game micromanagement. For a crude associative description: think of it as a Sid Meier game with everything removed except combat and cold, hard cash. As a result it moves a lot faster, but has just enough depth to open the possibility of dragging out a battle to be settled by attrition – and you will sit through the ordeal without realizing how many hours are going by outside your soap bubble of virtual warfare.

In a way, the various incarnations of Advance Wars – and this one in particular, given the tangible manipulation of pieces offered by its supplementary touchscreen control scheme – mark the natural evolution of the tabletop board game, with all the conveniences of the digital age as their selected adaptations: interchangeable and editable board layouts, automated calculations in the place of twenty-sided dice, and artificial intelligence robust enough to provide competent opposition when there exist no other DS owners within a radius of thirty feet. I almost wish Dual Strike were released with support for Nintendo’s global Wi-Fi network to launch in November, but it already provides a bountiful playing experience as it is; besides, the scale of multiplayer matchups it makes possible have a tendency to result in disconnections and dead batteries.

And now for something completely different. As you may know, Disneyland celebrated its 50th anniversary this summer after a year of renovations and refurbishments – and boy, was it worth it. I’ve had the good fortune of visiting the resort on numerous occasions, and it’s never looked so good. The original rides are now decorated with gold-plated anniversary cars (or horses, or teacups, or whatever applies). There’s a museum of Disneyland memorabilia with such exhibits as blueprints and schematic artwork, every variety of admission ticket from every era, and a cheesy but insightful doc short hosted by Steve Martin and Donald Duck.

Classic Disney scenes are on display throughout the park in the form of photo collages assembled from the visages of animators, staffers and guests, each of them consisting of two to ten thousand images. As you enter Main Street, there is a grandiose two-level monochrome collage where these photographs congeal into the faces of the men and women who were with Uncle Walt’s empire when it began, which in turn compose a still from “Steamboat Willie”. I’ve found an online archive of these exhibits, and the one I just spoke of is here, but a mere JPEG does not capture the sheer ambition of the monument. Nor does a photograph show you that the Haunted Mansion collage glows in the dark. There are wonders to behold at this happy place, and this is just one of them. There are others.

The fireworks, for instance. Nowadays, we are so accustomed to pyrotechnics that it’s easy to be disenchanted at how fireworks, while still magnificent once you delve into the constructed choreography of a given display, all look and feel the same. Sure, the last decade or so have brought us the odd laser projection every so often, but we are fundamentally looking at the same old centrifugal fractal patterns set to Tchaikovsky, right?

Well, since 17 July, Disneyland has restored genuine spectacle to the ancient art of synchronized rocketry. The proverbial magic is back. Sparks fly over the repainted Sleeping Beauty Castle to the tune of “When You Wish Upon a Star” like the opening titles of a feature film, but live and right in front of you. Tinker Bell zips around the parapets. And it’s all narrated by Mary Poppins – that is to say, Julie Andrews.

Then the display becomes a sort of interpretive dance of light and sound, a whirlwind tour of Disneyland attractions representing each of its sectors (though “It’s A Small World” is noticeably absent, and the New Orleans sector is underscored by Joplin’s “Maple Leaf Rag” played, not surprisingly, too fast). There’s a broadside battle waged right over the heads of the audience for “Pirates of the Caribbean”, and if you sit close enough you can see the Jolly Roger aglow on the Matterhorn’s peak like a distant Bat-Signal. “Star Tours” has laser cannons and explosions of green flame that light up the night set to John Williams’ end credits to Episode IV. The Frontierland shooting gallery features ducks with targets on them projected on the castle itself, which move about and seemingly get shot down one by one. And so on.

I’ve never seen anything like it. Chances are you haven’t either, unless you paid the House that Walt Built a visit of your own in the last seven or eight weeks.

If you plan to visit Disneyland anytime in the near future, or if you’ve never been there – make it so and make it soon. The “Happiest Homecoming on Earth” celebration is supposed to last until September 2006, according to the five-part golden anniversary retrospective that was posted at Jim Hill Media the same week I was in Anaheim, though by next summer’s end the top-billed novelty may have tapered off somewhat.

You really do have to see those fireworks show. My description does it about as much justice as a Klingon court-martial.

I haven’t devoted any of my recent blog-writing to what’s going on in wide-release cinema, in spite of having seen a passable, if less-than-usual quantity of major films of the ones that hit theatres between May and August, that quantity being eleven and a half. (The English dub of Howl’s Moving Castle is the half.) I attribute this to two causes. The first is that July and the better (or in this case, worse) part of August were for all intents and purposes dead, and all rumours of a box-office slump are for once both patently true and justified. The second is that the big films of May and June that were any good, a surprising number of them, turned out to be phenomenal; simply praising these achievements is a monotonous and redundant activity, and critiquing them intelligently takes too long.

Perhaps I will at some point offer a synoptic assessment that gathers and dispenses with the lot, but not today. For now, just go see the most satisfying film of the past few weeks, and certainly one of the best of the year. It’s called The Constant Gardener and it stars Lord Voldemort.

It’s Dave Wiegand in five. Going into the best-of-five ESPN final, it couldn’t have been closer by much – Wiegand stood at 21-7, +1074, while World Champion Panupol Sujjayakorn snagged the second spot with the same victory count and a +1000 spread.

Panupol took Game 1 with a calculated bingo-out, the 86-point SABERING – final score, 467-388. An early lead propelled him to another huge win, 463-349, in Game 2. Both were great games, the first in particular: I’m sure heads turned when Panupol closed up and grabbed a triple with DUPER in Move #10, instead of opening wide with the bingo UPREARED. A miss, or an example of inscrutable n-ply genius? I don’t know, but THERMOS was one hot-looking play.

Then Dave pulled a threepeat. Check out the beautiful find in Move #5 of Game 3, EULACHON on a double-double – the best of only two possible bingo words and a very limited number of positions to play them. (Actually, play through all the games if you can – there’s some overtly championship-level Scrabble on display from both sides of the board. Not many would spot all the minute strategic considerations at work, but the obscurity of the word-slinging is a sight to behold.)

I found Game 4 to be the most interesting, in part because it was the closest battle yet – step through it, and look at how the two players leapfrog each other in seventy-point bounds, both stopping only to dump and reload their racks. There’s a dramatic moment in Move #17 when Panupol, holding ILORTT?, sees the unplayable seven – TRIOLeT – and, according to the commentary, lays it on the board before pulling it back, realizing it made the SOWPODS-only TE#. How much of a strategic advantage it provided Wiegand, I’m not in a position to know, but the Oregonian held a lead to the end.

That was more of an evenly matched deciding game than Game 5, which was a huge run of luck for Dave; with two blanks and three bingos in his first four moves – LENSMEn, REENTERs and PARTING, all he had to do was shut down the lanes and grab the bonus squares, which he did in style. 539-331 and the 2005 National Scrabble Championship go to Dave Wiegand, though apparently the players scored it as a 529 without a recount (as clearly, none was necessary).

I’m wondering how much of the final will make it into the ESPN broadcast; last year’s matchup between Trey Wright and Dave Gibson only went to three, and I hear a good chunk of it was trimmed to make it into an hour with commercials. Here’s hoping Game 4 is the one they show in full, although I’m looking forward to seeing any of those televised should I manage to do so here in ESPN-less Canada, so as to get a sense of the pacing in this incredible series.

Subtract one or two divisions, and this is my life. It’s also an excellent Wall Street Journal piece by Scrabble’s patron journalist Stefan Fatsis. He captures the travails of losing game after game in Division 3 far better than this guy did in the same category last year when he, too, plummeted faster than a coyote in an Acme bat-suit. But for him, the real punishment came on Days 3 and 4 of the tournament, whilst Stefan is holding up well – breaking even at 9-9, +229 and ranked 59th of 135. He needs to be a lot further in the black to keep his rating, but if he doesn’t, more’s the chance I’ll get to play him come 2006 – that is, if I dig myself out of the hole without being too terribly befuddled by the gargantuan lexical overhaul that is moving in over the next few months.

In other news, this was a terrific story while it lasted, but I found the ending to be a little anticlimactic. I suppose we’re all in the mood for a melody. I’ve also been told that Billy Joel’s “Piano Man” is the most frequently requested cocktail piano tune, which is a reasonable hypothesis, but one that I have yet to test on a sufficiently large data set to substantiate with experimental observation.

As possible as it remains that I will be eating some fresh-plucked import crow from the Village of Fowl Devotees two months from now, I’m going to place some chips on the table: I can say with almost total conviction that Book the Twelfth will be entitled The Nameless Novel.

Those of you who haven’t read the Lemony Snicket series should do so immediately. Those of you who have know by now that at the end of every volume is a teaser for the next, which always hints at some of the objects and locations to appear and includes the alliterative title for the volume to come; all except the piecemeal fragments at the end of The Grim Grotto, which revealed no succeeding title at all. It would be very much in keeping with the self-referential nature of the books, and the fictitious scenario that the author is an elusive man on the run who sends his editor the manuscripts telling of the Baudelaire children’s misfortunes by a host of unconventional means (coupled with his failure to send the editor a new title), if the absence of a title was played upon.

Last month, HarperCollins unveiled an activity website, The Nameless Novel, designed to market the book by presenting a day-by-day calendar of puzzles that fall into the theme of discovering the title of the twelfth book. The assembled solutions so far have revealed a full page from the book and a handful of new Helquist illustrations; the latter “investigation” is, at the time of this writing, still ongoing. That leaves time for a third set of clues beginning in mid-September, with the book’s publication due 18 October.

That seems like an awfully short lead time to announce the title to the general public, and The Nameless Novel is such a perfect fit that – given the little we know – it’s hard to imagine that it is only the moniker for a promotional website that only a fraction of all readers will actually visit. (Yes, J.K. Rowling revealed the title of The Half-Blood Prince via a website puzzle as well, but that’s quite a different scenario – and besides, it was well before the book went to press.)

The lack of a new title to follow The Grim Grotto can’t simply be leveraged towards this limited a purpose; I see it as significant enough that its resolution will be projected at the readership in its entirety. What I’m saying is that the launch of this website was itself the title announcement, albeit one that fell right into the meta-fiction of the Snicketverse. Keen observers will also note that each title alliterates a different letter, and ‘N’ is not yet taken.

In the end, this isn’t that substantive a matter to be speculating about. It is nonetheless exciting enough that such a phenomenal series – largely an exercise in style, but with a progressively meatier plot – is pulling up to its conclusion.

And now, for something completely different: you might have noticed that my finding the time to post this is probably a good indicator that I’m not fatigued out of my mind in the middle of Nevada right now, which would be the case if I were playing in this year’s National Scrabble Championship in Reno.

Call me a vicarious spectator, and an elated one. It’s two days and fourteen rounds into the premier Scrabble competition in North America, and Calgary’s very own Paul Sidorsky – former club co-director and developer of LAMPWords – is in fifth place of eighty-seven in Division 1. Not bad for the eighty-fifth seed. His 10-4, +458 record makes him the top-ranked Canadian halfway into the event, and puts him sandwiched right between Wiegand and Cappelletto.

This is, to don my verbal scuba gear and dive into the vernacular, freakin’ awesome. I’ve hardly played at the Calgary club for the past year for geographical reasons, the result being that my word knowledge is declining faster than your run-of-the-mill British sea power, but back when it was a weekly stop for me, Paul was always a challenging and humbling opponent – that is, whenever I earned a spot on the ladder high enough to face him. The first time I played him, he landed five bingos to my one and racked up 594 points, the most anybody has scored against me to date as the tile gods have mercifully spared me from the thunderous bludgeoning inflicted by the Mjollnir that is the 600-point Scrabble game.

I’ve since won a few games against Paul, but it’s been an uphill battle every time. This is a game where you come to appreciate the uphill battles, because they teach you a thing or two by way of glorious negative reinforcement. Downhill tumbles are not so fun. What you come to realize, though, is that even the toughest opponents are mortal when you draw all the blanks, though mortality makes little difference when not knowing how to deploy decent tiles is about as effective as clubbing someone with the blunt end of a very sharp pencil. And deification is one of many things called into question when you see one of your mentors ranked among and above the gods of the game, the characters you hear about in books and documentaries.

This is my way of sending a remote congratulations and wishing Paul the best of luck in the second half of the tournament – where, after all, anything is mutable. May he cleaneth the proverbial house.

Currently in first place with a 13-1, +653 record is 2003 World Champion Panupol Sujjayakorn from Thailand, who bears an age equivalent to mine and a vocabulary greater by several orders of magnitude. I have a clipping of a prominent newsprint congratulations offered him by the Bangkok papers months after his victory. If he stays on track, this will be his best performance yet under the North American dictionary, though he was already one of the undisputed luminaries of the game to begin with.

No announcement about the OWL2 yet, but I expect it will drop in very, very soon.

Now, excuse me while I go back to two-stepping through the playable live coverage on the tournament website. My board vision is rustier than the Tin Woodman; if it only had a heart.