Archive for May, 2010

Fun little math problem

Monday, May 17th, 2010

I love math and logic puzzles that seem like they could require a lot of thinking but turn out to be answerable in 30 seconds if you think about them the right way. Here’s one Jake Wildstrom recently posed that I liked:

Take a random permutation of the n integers from 1 to n. On average (that is, we’re asking for the mean), how many elements will be in their “correct positions” (e.g,. 3 in the third slot)?

2010 US Chess Championship

Saturday, May 15th, 2010

This year’s US Chess Championship is currently being played in Saint Louis; it started yesterday and runs through May 24. The reason I bring it up here is that I think that the organizers are doing a good job of making it accessible and interesting for casual chess players, one of which may be you. The live coverage in particular is very nice; it’s hosted by Grandmaster Maurice Ashley and Woman Grandmaster (don’t get me started on that title) Jennifer Shahade, who are both really good at making the game exciting for people who are already a little interested in chess. They’re not trying to “jazz it up” for people who don’t care at chess at all; they assume you already know a bit about the game and are inherently excited by, say, someone sacrificing a rook for a knight, or pushing a pawn closer to queening.

There are also a bunch of different types of players, ranging in age from 15 to 50+, with a variety of personalities and styles, so it’s not hard to find someone to root for if you like that sort of thing. If you already have a casual interest in chess but don’t know much about high-level tournament play, I recommend checking it out and seeing if it grabs you. (If you don’t, never mind this post!) The games run about 2pm-8pm Central Time every day.

Hilary Mantel: Wolf Hall

Saturday, May 15th, 2010

This novel takes the all-too-familiar career of Thomas Cromwell and turns it inside out, revealing an unexpectedly thoughtful and empathetic character. What’s that, you’re not familiar at all with the career of Thomas Cromwell? Well, neither was I, and I suspect that that made my reading of it much different from the intended one, as I ended up reading it purely as a historical novel and not as some great reimagining. But it was a really good historical novel.

Thomas Cromwell was born a commoner and rose to become one of the must trusted advisors to Henry VIII (the one with the six wives — we just get the first two of them here). He seems to be regarded by history mostly as a villain, largely based on his standing as the chief nemesis of Thomas More, who opposed the king’s declaring himself the head of the church. Mantel turns Cromwell into a real person, who is not perfect but is generally always trying to do the right thing.

Her writing style here is intriguing; it’s very restrained, avoiding much emotion or florid description, and you get the feeling that it is meant to reflect Cromwell’s own character. Cromwell himself, although present in every scene (as far as I can remember), is hardly ever mentioned explicitly by name, but is just called “he” unless it is really necessary to distinguish him from another man in the scene. There is pretty much no “As you know, Bob” exposition; the characters talk to each other as if they already know the subject they’re discussing, which can make it a little hard for the reader to catch up, but is rewarding once you do, making it feel a bit like you’re in on a secret.

The plot moves fairly slowly, and I think I might have been happier with it at 400 pages instead of 550, but it remained very interesting all the way through. I imagine that part of the slowness for me was that Mantel wanted to visit and reinterpret a number of important historical incidents, none of which meant much to me.

So I feel like I didn’t get everything out of it that the author put in; it’s sort of like hearing a cover of a song without knowing the original and thus not being able to hear what original aspects of the song the new performer kept or discarded or reworked. If you are already familiar with 16th century English history this book is probably revelatory (and in fact it has won all sorts of prizes); if you’re not, it’s still an excellent read.

Cardiacs: musical vocabulary

Sunday, May 9th, 2010

It’s been a while since I first posted about Cardiacs but I’ve been fitfully taking some notes and doing some transcribing, and I should post some of it before I forget about it entirely. If I list a song here without a video link you can probably find it in the previous post.

Although a lot of the music of Tim Smith (leader and main songwriter of Cardiacs) might seem pretty random, he has a pretty consistent vocabulary that makes it easier to get a handle on his songs after you’ve heard a few of them. Going through his oeuvre, here are the things that stand out to me:

Melodic movement by whole tones. One common consequence is the use of chord sequences involving I, ♭­VII, and ♭­VI (think “All Along the Watchtower” for one classic example). Even more common is the next item:

Use of the Lydian scale. That’s a scale on the white notes if you start on F. Its distinguishing characteristic is that it starts with three whole-tone steps (F-G-A-B) rather than two whole-tone steps followed by a semitone (F-G-A-B♭­). Smith really loves that sharp fourth and it shows up all over the place in his music.

v – I and ♭­III – v – I cadences. These are sort of related to whole-tone melodic movement as well. If you play a normal V – I cadence (say, B major to E major) but use a flatted seventh instead of a leading tone (D♮ instead of D♯ in this case), so that you’re moving by a whole step instead of a semitone to get to the tonic note, you get a v – I cadence instead (B minor to E major), which has a much more ambiguous quality. In Cardiacs songs, this frequently comes in the context of the progression ♭­III – v – I (e.g., G – Bm – E), which has quite an unstable feel. Often the ♭­III has been heavily tonicized, which can make the sudden shift feel like the rug is being pulled out from under you; when repeated, it can also create the impression of shifting back and forth between two tonics, never fully coming to rest on one or the other. “Odd Even”, for example, is fundamentally based on a G – Bm – E progression, and it’s hard to decide whether to take G or E as the key of the song. The coda of “Dirty Boy” is another classic example that just repeats this progression over and over.

Quick-changing chords, often every other beat and accompanied by their dominants. The harmonies can often move at a dizzying pace, but because Smith usually precedes or follows a chord with one a fifth away, you get a little more stability and each chord at least has a bit of context to it. “Anything I Can’t Eat” is a classic example (sorry about the bad recording).

Hemiolas and other rhythmic ambiguity. A hemiola is when you take a six-beat-long phrase and go back and forth between treating it as two groups of three and three groups of two, creating a sort of rhythmic pun that throws the listener off. Smith uses explicit hemiolas (“Gibber and Twitch” and “Too Many Irons in the Fire” both switch from 3/4 to 6/8 mid-chorus) but is also happy to use any other technique he can to disturb the perceived meter of the song.

Tempo shifts, particularly a slow last chorus. It’s astonishing how effective this is, given its relative crudity — just shift down a gear entering the final chorus and have everybody sing along, and the majesty of the song doubles. There are probably ten Cardiacs songs that do this, though it never seems to get old; the classic example to me is “Big Ship”.

I am probably the first person to ever compare Tim Smith to the classical composer Olivier Messiaen, but one thing they do have in common is a very personal musical vocabulary (in Messaien’s case, it’s things like birdsong and harmonies built on top of palindromic modes). In both cases, initial experiences can be rather befuddling, but once you start hearing the common building blocks from piece to piece, the broader context helps in making sense of each one.

Next up, a case study of one Cardiacs song.