There’s nothing terribly special about these pieces musically – they are, in fact, quite formulaic. And as my friend Steve once said to me, I apparently don’t know how to end a song. But they offer a fun little peak into my musical thinking before my undergraduate training, and make for good trivia. You’ll likely not care, but since I went to the trouble of digitizing and archiving them, I thought I might as well share.

If for some incomprehensible reason you’d like to download them, here’s a zip file of the Sketches mp3s complete with metadata and cover art – ready for your iTunes. It’s all licensed CC BY, naturally.

The best recording of this fabulous piece of music is, in my not so humble opinion, John Mauceri leading the London Symphony Orchestra – (previews available from Amazon at Rimsky-Korsakov: Scheherazade). How does this relate to OCW, you ask?

For a number of years there has been an opinion among some in the OCW community that we need (only) one really excellent open version of each of the high enrolling GE courses like English 101. My experience in the car reminded me why several different versions of open courses are necessary. Obviously, a rather talented conductor had led a rather competent orchestra in this recording, and NPR had liked it well enough to play it. But it was truly awful. Painfully so.

In education, as in music, matters of taste matter. No, you won’t learn more or remember longer when the teaching is adapted to your so-called “learning style,” but the experience will be much more pleasant when it is. And who hasn’t sat through a class that made you want to put your head through the desk? I never want to have that excruciating experience again, neither with music nor with learning.

The twelve tone technique is a music composition method generally used for creating atonal music (and is a special, and perhaps the earliest, type of serialism). Using the twelve tone technique, a composer creates a sequencing of the twelve tones of the chromatic scale without repetition, which tends to diffuse any sense of a tonal center in the overall composition. Once the composer arrives at a sequencing of the twelve chromatic tones, these may be manipulated to create a 12 x 12 matrix which can be read left to right, right to left (the retrograde), top to bottom (the inversion), or bottom to top (the retrograde inversion). See this interactive matrix for examples.

While there is much art to everything that comes afterward, arriving at the original sequencing of pitches plays an important role in this type of composition.

Over a decade ago, I was sitting in my room with nothing to do when the thought occurred to me “I wonder if you could use transcendental numbers to create tone rows…” I started with pi. Staring at the number spelled out to several digits, I wondered “how would I even go about this?” The idea occurred to me to choose an arbitrary starting pitch, and then use each digit in pi as a number of half steps to move up from the current pitch. So, taking C as a starting pitch, 3.14 would give a sequence of C, D# (3 half steps up), E (1 half step up), G# (4 half steps up), etc. However, with apologies to my friend Eve, pi just wasn’t cut out for the job – the 10th pitch generated by the digits of pi is a repeat of the first note in the sequence. Oh well, I thought.

In my disappointment, and realizing how amazing it would be if a number could walk the minefield of 12 pitches without landing on a repeat somewhere, I was very pleased to discover that e in fact fits the bill! If we pick an arbitrary starting pitch (E seems like a natural choice), the digits of e give us the next ten pitches without repetition. The 11th digit produces a repetition in the final pitch of the row, but technically we don’t need it – since we already have the first 11 pitches we can determine the final pitch in the row by process of elimination.

So e, it turns out, generates a perfect tone row. Using a value for e of 2.718281828, the matrix based on e looks like this:

Here is a midi statement of the original row, the retrograde, and the inverse. In this recording you’ll hear that the pitch durations are also determined based on the digits of e (a pitch arrived at by going up 2 half steps is twice as long as one arrived at by going up 1 half step).

I’m currently working on two things in connection with this: an actual composition based on the tone sequence, likely a two-part invention or fugue (which I hope to generate completely out of the number itself), and some software to search through the digits of pi, e, and other transcendental numbers in search of digit sequences that will produce tone rows, and therefore matrices, and (hopefully, eventually) inventions, fugues, and other types of music.