Ntuple Indemnity

If the rigorous movie analyses and Scrabble game logs at this establishment are the scrumptious sushi selections on the menu, posts like the one you are about to read would be the assorted tempura.

There isn’t much on my Christmas wishlist this year, but on it is the 1950-1952 volume of The Complete Peanuts, which is already on shelves. Schulz’s early work that sprung off his Lil’ Folks panels, when the characters were even younger than how we have come to know them, has in the past seen very little in the way of publication. Now is as opportune a time as any to start collecting the entire run of Peanuts in tandem with this project.

Geoff Pullum picks on Dan Brown again, and as always, echoes my own feelings in a far more eloquent manner. “The great thing about filming Dan Brown’s novels,” he says, “will be that it will get rid of his execrable expository prose.”

On some of their vintage DVD releases, Warner Brothers includes a feature entitled Warner Night at the Movies, which attempts to re-create the way movies used to be presented; the main feature is preceded by a trailer, newsreel, animated short, and live short, all selected from the same year as the film’s release. It’s a commendable mode of presentation, and film buffs should appreciate such classics as The Adventures of Robin Hood and Yankee Doodle Dandy being given such a respectful treatment.

I mention this because local readers may find some amusement in this tidbit: on the DVD of The Treasure of the Sierra Madre, the included newsreel features one segment on a fire-eater delighting the kids of one Edmonton, Alberta. The footage is brief and contains nothing that identifies the city in a way one could distinguish today, but it’s there.

The next set of films to get the Warner Night at the Movies treatment is the Warner Gangsters Collection to be released in January. It’s hard to get a hold of these pre-Maltese Falcon pictures where Bogart is in his early phase as a supporting hoodlum while Cagney is in his first-billed prime, so these restorations are much appreciated.

Speaking of box sets, put this on my Christmas list as well: the Criterion Collection Akira Kurosawa: Four Samurai Classics (The Seven Samurai, The Hidden Fortress, Yojimbo and Sanjuro). So many DVDs, so little time.

Today I saw Happnin’, the U of A Jazz Choir, perform their Fall Concert. To put it succinctly, I would see them again, and so should you; there are more performances to come next year, including their Spring Concert (2 April) and an appearance at the Rocky Mountain Music Festival in Banff (14-17 April).

David Yates is as good as confirmed to be sitting in the director’s chair for Harry Potter and the Order of the Phoenix. Personally, I think Jeunet shouldn’t have turned it down, but he would have been better for one of the early films anyhow. And it’s a shame nobody caught on to just how perfect Terry Gilliam is for this particular chapter in the Potter saga, but with both The Brothers Grimm and Tideland on his plate, it hardly fits into his schedule anyhow.

On a final note, my television is tuned to a channel emulating a fireplace and playing easy-listening music. Weird.

This is less a marriage of music and mathematics than a summer fling of sorts, but I’ll let the pi10k experiment speak for itself:

This experiment attempts to convert the first 10,000 digits of pi into a musical sequence.

Select ten notes, and your corresponding selection translates into an integer. The first note you select will equal “1”, the second “2”, and so on. As your computer cycles through the digits of pi, the corresponding notes will “play.”

Those of you who can make heads or tails of a basic keyboard layout should try it out.

A few comments: First of all, I think the experiment would be on the whole far more interesting if you introduced a number of other factors. The first is that this would be a whole lot more interesting if prior to iterating over the digits of pi, you first converted everybody’s favourite transcendental circumference-diameter ratio into base 12 (0 through 9, A and B), and proceeded to assign notes from there covering the entire twelve-note octave. It would make for some variety, to say the least. Perhaps it would produce the same brand of atonality as what one would expect from, say, Schoenberg’s twelve-tone technique.

The next thing I did was plug in a C blues scale to see what kind of a jazz-me-up solo you can do with pi. This reminded me of two things: first, sitting on the same chord and the same key for more than a few bars at a time is boring. Maybe if it was automatically transposed up to F and G blues scales in accordance with the prototypical twelve-bar progression, it would be a whole lot more interesting. Second, pi (as it is implemented in that particular experiment) could do with some rhythm. Maybe if each of the digits were assigned a relative rhythmic value, the band would be swingin’.

This got me thinking about the iterability of musical sequences, and whether or not there is a systematic way to generate traditional consonance-dissonance tensions by formula without having to resort to an atonal result like the one we have here. Let’s go back to fundamentals here, and examine the circle of fifths. It occurred to me that if you cycle through these, as you do in the traditional vi-ii-V-I cadence back to the tonic, you begin to see that this particular foundation of music theory is a cyclic algebraic group of order 12. (Consider the V-I to be the “operation” in question, thus making the IV-I the “inverse.”)

Now that you have the roots of the chord progression in place, what remains is to map it to a harmonic pattern – your basic major, minor and diminished triads, or the more interesting texture you get when you add a major or minor seventh up top. If you look at the bridge to Gershwin’s “I Got Rhythm” – in B-flat rhythm changes, it goes D7-G7-C7-F7 – the iteration is done entirely over the dominant seventh. This is by itself not very interesting until you add some substitutions, say an alternation with changes every two beats instead of four: Am7-D7-Dm7-G7-Gm7-C7-Cm7-F7. Maybe throw in some tritone substitutions to boot, inverting the third and the seventh of the dominant chords, which is a common substitution trick that translates into some fancy bass lines.

But what does such a series have to do with something as random as pi? How can you generate tonality out of that randomness?

Well, the answer to that is, take advantage of the fact that pi isn’t all that random, and use a numerical approximation algorithm. Euler’s isn’t of much use here, unless you figure out a way to assign arctangents to chords, but if you take something simpler like Newton’s recursive expansion, you’re in business.

In fact, you can try something like this with any infinite series – geometric, Taylor, MacLaurin, what have you. All it takes is to find an analogous operation that moves from chord to chord or note to note (or better yet, manipulates the push-and-pull of time in a systematic rubato) and assign it to the operations the series uses to generate each successive term.

I’ll end with a fun fact that hardly anybody knows (until now): back in high school, I won $25 in a St. Patrick’s Day limerick contest, wherein I did a few stanzas on pi. I had to take a bit of a liberty in rhyming “Euler” with “ruler” (it’s actually pronounced “Oiler,” as in that local hockey franchise), but nobody noticed.