Ntuple Indemnity

I can’t seem to mention my favourite developing country without saying a few words about the musical compositions of its presiding Philosopher King, so perhaps I’ll take a moment to devote an entire post to the subject. For those of you who are new to the show: do familiarize yourself with the Rama IX Art Museum Foundation’s comprehensive online exhibit, which I’ve only just had the pleasure to discover myself. It comprises a biographical overview of His Majesty King Bhumibol Adulyadej’s musical background, audio samples of forty of his songs, historical notes on specific compositions, and even lead sheets of the melodies and chords.

And if you want to hear something exceptionally cool: there’s always a lot of talk about how the King once played alongside America’s own King of Swing, Benny Goodman (indeed, that’s the subject of the photograph atop the musical archive’s introductory page), but now I’ve found some aural proof—samples from Benny Goodman’s 1955 concert in Bangkok, in which he plays several of the King’s signature compositions, including the Thai Royal Anthem. I’ve linked to my personal favourite, “Sai Fon” (“Falling Rain”); the song is written as a waltz, but the band plays it in 4/4.

My own interest in King Bhumibol’s music originates from my first visit to his realm in December 2003, when I first heard that he was a noted saxophonist and big band composer in addition to everything else he did (painting, translating Economist articles, ending military coups with a single command, and so on). It wasn’t until after the adventure that I actually listened to some of his music and fell in love with a number of the tunes. But this time around, I went to Thailand prepared—and after traipsing around the country for nearly three weeks, I can absolutely confirm that the King’s music is as ubiquitous as the documents about it claim.

I also returned with a handful of compact discs, all of which I will discuss below.

Continued »

I have a fascination with sculptures inspired by fictitious characters, like that of Sherlock Holmes outside the Baker Street tube station in London, or the bronze Eleanor Rigby seated on a bench in Liverpool underneath a dedication “to all the lonely people.” Today I learned that in Madrid, there is a monument to Cervantes that comprises a stone sculpture of Dulcinea del Toboso. If you know your Quixote, you know why this is interesting: how, exactly, does one visualize a fiction within a fiction?

I may or may not have had a point there.

Somebody important to me got married today, and I wish her all the best.

There’s nothing quite like a musician’s wedding, because the musical programme is bound to be exquisite. Today’s ceremony featured a live string quartet that ran the whole gamut of tearjerking Italian opera before the Bach processional, among their selections the Intermezzo from Mascagni’s Cavalleria rusticana (which you might recognize from the film Raging Bull) and “O mio babbino caro” from Puccini’s Gianni Schicchi (itself notable in Peanuts lore as the aria that Peppermint Patty skates to in the television special She’s a Good Skate, Charlie Brown). The recessional was Gardel’s Por una cabeza, which is the tango of choice in too many films to count, one of which concerned the Holocaust and also had a critical scene featuring Bach.

It was all very pretty and perfect, and I’ve come to the conclusion that wedding ceremonies just aren’t the same without live music. And I’m not just saying that as an egotist who once took a Catholic wedding as an excuse to play selections from The Legend of Zelda: A Link to the Past.

Then again, as a Lutheran service, the proceedings were musical through and through. Hymns have a way of pushing you a bit higher than you can go, but I always appreciate the reinstatement of music as an activity of the community, which you see so rarely these days aside from jazz jams and the national anthems before a hockey game. In some cases, it may be for the best. I never did figure out the melody to “Ring out a cheer for our Alberta”, and I blame the fact that I don’t think anybody else did either.

What you don’t see every day, though, is a surprise sermon preceding the vows that doubles as a chemistry experiment involving fish tanks, food colouring and Barbie dolls. It was scripturally over the head of this here heathen, but engrossing all the same.

Some time ago I made an observation about wedding music that I’m surprised I never posted here. It took less than a century for Wagner’s Lohengrin (“Here comes the bride”) and Mendelssohn’s “Wedding March” to become wedding pieces standard to the point of being cliché. Given sufficient momentum, there’s nothing to say that in less than a hundred years, the same can’t happen to John Williams’ celebration march at the end of Star Wars, complete with Chewie not getting a medal. I, for one, will do my part.

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.

I’m to play a number of pieces at a wedding that is taking place on Canada Day, and the task of preparing them is my first serious return to the rigour of practicing small-C classical piano for the sake of performance since completing my Royal Conservatory ARCT three years ago. Skill at a musical instrument is something that atrophies quickly, but comes back with the kind of whoosh that brings to mind Stephen Chow, eyes shut and enlightened, reawakening to his repressed Shaolin or Buddhist Palm powers or what have you. It seems that if you spend a nontrivial proportion of your adolescence perfecting a tricky Liszt cadenza, it’s programmed into your fingers for life. The power that courses through your digits upon its return is a release of energeia so magnificent, you are led to think you can harness it to fry a rack of bacon. You would be wrong, but never mind those mortal limitations.

For this event, I was given a list of requests at a few weeks’ notice, with instructions to throw in any other favourites I deemed appropriate should the guests be taking inordinately long to seat themselves. Naturally, in addition to the standard corpus of the pretty Chopin waltzes nobody ever thinks of because they can’t remember the indices, I entertained the notion of sneaking in “Han and the Princess” from The Empire Strikes Back for good measure. “Across the Stars” is the more relevant cue in a wedding scenario, but playing it by ear is not a straightforward initiative, not because the compound rhythm is hard to pin down on first listen (it’s simple once you figure out which beat to think of as your anchor), but because Williams introduces a very subtle modulation with each iteration of the theme: the key you finish in is a whole tone lower than your key of origin. So you can take it for as long as you want, hitting five other keys before you loop back to where you started; the subsequent transpositions generate a cyclic group modulo 6. Whenever it comes up in the score to Attack of the Clones, a meandering transition escapes the cycle after only about two iterations at a time, and it’s a hard one to capture without having some sheet music as a guide.

The requests were an item of interest, though – and two of them in particular, both by that most temperamental of legendary German folk, Ludwig van Beethoven. They had two things in common: everybody knows them, yet after over a decade with the instrument, I’d never learnt them.

The first is “Für Elise”. Its popularity is unfathomable. I sometimes wonder what Beethoven would say should he return from the grave to discover that this innocent little Bagatelle in A minor he wrote for some chick is not only the default ringtone on the biggest overnight hit in the technological history of mankind, the mobile phone, but is – no joke – played by Taiwanese garbage trucks to signal their presence, like how ice cream cars over here use Joplin’s “The Entertainer”. It’s not a very spectacular composition – a simple ABACA with no modulations except for brief jaunts into the relative major a few bars at a time, and only meagre hints of Ludwig’s trademark tantrums – and one wonders if it is the phenomenon it has become because of its technical simplicity. It’s very easy for a beginning pianist to pick it up and woodshed it, and at the same time rewarding, because it has just enough musical elegance to not sound as dinky as a lot of early piano repertoire is wont to be.

The second piece to which I refer is the First Movement of the Sonata quasi una fantasia in C-sharp minor, perhaps better known as the “Moonlight Sonata”. I’m pointing out the obvious here, but like “Für Elise”, this composition is, to borrow what John Lennon said of the Beatles, bigger than Jesus. It was significant enough to be the namesake of an infamous German bombing operation – indeed, the source of one of Winston Churchill’s most controversial wartime gambits, a classic game-theoretical case study. Again, I have very little idea why it has penetrated the cultural consciousness so deeply, to the layman it bears on synecdoche for what classical piano sounds like. It is said that on the sonata’s popularity, Beethoven once wrote Carl Czerny with the remark, “Surely I’ve written better things.” And if we speak of quality in terms of the intricacy and range of his manoeuvres in the dimensions of harmony, melody and rhythm, he’d be right. But maybe the simplicity of the piece – long pedal points that change up in broad strokes under the controlled pianissimo of periodic triplets overhead – is what attracts the casual listener.

More to the point, in both of these selections, Beethoven doesn’t go very far, but what he does is sit on universals. Now, the musically literate may harp on this idea of universals as good old-fashioned Western European paternalism, but the precept that makes Beethoven tick – the very property of Mozart that makes babies smarter – is the binary relationship of tension and resolution that occurs when you frame music as consonance punctuated by dissonance. “Für Elise” and the First Movement of the “Moonlight” are similar in this respect: they are, fundamentally, grounded in minor-key consonances that are broken and arpeggiated, thinned out so the listener can in effect capture everything. And for the performer, as I am discovering firsthand, these ideal patterns spin a safety net of technical comfort.

I would deem it likely that it is because of this property of traditional forms underlying a proto-Romantic versatility of expression that they persist, while in the latter half of the twentieth century, the experiments to dissolve the binaristic “othering” of dissonance in opposition to consonance (or in the case of John Cage, silence to sound) led the methodical compositions of art music down a path that an untrained listener would consider highly esoteric. Yet the divergent rise of popular music in the 1950s with the emergence of doo-wop and rock-and-roll went in the opposite direction – back to simple harmonies and catchy melodic constructions.

The implication is that there is a disposition present in all of us, and arguably not something merely constructed, to be receptive to consonant harmonies and furthermore, retain them not in their harmonic form, but in terms of the melodic variations built on top of them. It is like how we feel the push and pull of a conflict in a dramatic setting, but we don’t remember the different kinds of conflict in terms of their categoric labels. On the contrary, we retain instances: Hamlet and Claudius, Rhett and Scarlett, Linus and Lucy. In primary school some talk about conflict as a 3-vector of man against man, himself and nature, but even that is demonstrated by example, and remembered by example. Like melody over harmony, it is not a relation of part to whole, but of building to foundations.

There’s a much bigger question that comes out of all this, one that strikes out at what it is we acquire that one equates with a heightened cultural literacy. For the sake of not obfuscating the above with interminable length, this is a thread I will leave hanging for now.

As some of you know, I played a banquet Saturday night (that being the National Debating Championships formal), accompanying Happnin’ alto and fellow debater Maria Chen. Word is that we survived the dinner performance in spite of a horribly out-of-tune B natural above middle C that forced us to work around the charts we set to sharp keys, and the precarious decision to situate my personal decorative glass of red wine on the grand when the wheels were not locked in. I can’t speak to any of this myself, as I wasn’t listening.

Later in the evening, as I took a break for dinner, some random attendee who had earlier attempted to run off with my precious Hal Leonard “Little” commandeered the piano in my place, approaching it in much the same way as Draco Malfoy would treat a Hippogryph. Now, he was hardly without skill, though a brief conversation on technique I had with him about Gershwin’s changes in “Let’s Call The Whole Thing Off” revealed him to be new to substitution. But one should remember that skill is very different from finesse, and while some finesse is bound to be lacking even for the relatively seasoned improviser – I’ll freely admit that I somewhat butchered Koji Kondo’s “athletic” Donut Plains theme from Super Mario World – there is really little excuse to throw it out the window for cheap tricks when it comes to playing something fully composed.

There is a very simple litmus test for rooting out rank amateurs who try to show off at the keys with little respect for the music they are performing, especially when that music is ragtime. This performer I speak of, whom I have yet to identify, committed the crime of trying to play “Maple Leaf Rag” as fast as he could.

I don’t see why people insist on butchering “Maple Leaf Rag” the way they do. It’s marked Tempo di marcia, but there is no end of piano hacks who play it not as a march so much as a hundred-horse cavalry charge. Well, the guns of Aqaba may face the sea, but anyone who has ever bothered to take Scott Joplin, ragtime and stride seriously is not so inattentive, and knows that ragtime is never played fast.

Observe the following tempo markings. “Elite Syncopations”: Not fast. “The Easy Winners”: Not fast. “The Entertainer” – yes, that “Entertainer”: Not fast. Joplin’s sheets to “Fig Leaf” and “Sugar Cane” carry a little box on Page 1 akin to a Surgeon General’s warning: “NOTE – Do not play this piece fast. It is never right to play ‘Ragtime’ fast.”

“Maple Leaf Rag”: For the love of all that be Good and Holy, dare I invoketh the honoured rolls of Tin Pan Alley and Preservation Hall, do not ever play this piece fast, you simple-minded irreverent blasphemous fool. Or, in other words, Tempo di marcia.

It is especially appalling that even performers who are otherwise professionals of a calibre well beyond that of my own still drag “Maple Leaf” through the mud at tempos befitting the Autobahn for a spurt of cheap amateur showmanship. Over the summer, I saw the keyboard player in a band performing on as prestigious a jazz-tourist destination as the Mississippi steamship Natchez do the exact same thing. Technically, he was a talented performer with a good sense of syncopated rhythm who had huge hands that graced progressive tenths with ease. I think he was blind, too, but I’m not sure. But for goodness’ sake, that is not by any means a license to play ragtime as fast as you can.

Maybe it comes of how most people are exposed to ragtime in the form of ice cream delivery vehicle jingles and cellular telephone ringtones, but I do not presume to know the origin of this tragically widespread interpretation. Now, I’m not one to commit the intentional fallacy and say that ragtime shouldn’t be played fast because Joplin said so, but I am one to say that to a literate musician, it sounds like ass. There are pieces that you can play as fast as you can to show off to your friends – “burner” swings like Ellington’s “Take the ‘A’ Train” and Kondo’s “athletic” Donut Plains theme from Super Mario World. “Maple Leaf Rag” is not one of these pieces.

The tournament itself was fantastically run by the organizers behind the curtains, and they have really done the club proud. After adjudicating one round I was pulled into a swing team (which, in debate lingo, is a placeholder team to even out odd numbers) with Dan Sirbu, who had never done a Canadian Parliamentary tournament before. After cleaning up in the first two rounds, we dropped like rocks in the other four. I think it was a positive experience for my partner, though; it’s not every day that a complete novice gets the beneficial learning experience of being creamed, eviscerated, and totally wiped out by Jo Nairn and Ren in the later bracketed rounds of a competition. And I say that in earnest, as nothing drives you to improve so much as being done in by the best of the lot.

Congratulations to Mike Kotrly and Rahool Agarwal, who won the tournament this year after a second-place finish apiece in the last two Nationals. Mikey I’ve talked about, but Rahool was also someone I was quite glad to see win. Yesterday, he definitely slowed down from the rapid-fire rhetoric he used to display, but he remained as analytically thorough as ever. Rahool was on his way out of Alberta in my novice year, and much of the values and debating philosophies to which I subscribe bear traces of his influence. For such an accomplished orator who was well aware of the distinction between good and bad debate and never hesitated to point it out, he was always eager to train us newcomers. It’s been a long road to the title, but he earned it.