Home

Geeky

Not Dead Yet

Thu, 01/14/2010 - 1:08pm — Nathan

Apologies once again for the long silence. Fortunately, I'm doing much better than I was when I wrote my last post, both emotionally and musically. In fact, I am putting the finishing touches on a 15-minute work for concert band, tentatively titled Siren Fantasy. I started right around Thanksgiving, arrived at a double bar a few days ago, and will be editing like mad shortly. I hope to get it wrapped up by the end of the month, and if I'm lucky, get a performance by the end of the semester. After having made many abortive attempts at writing for band, I'm very excited to have this one under my belt.

But for now, I am too busy to savor that feeling. I have been gearing up for the MIT Mystery Hunt, which starts tomorrow, and today I have a lot of packing to do. Puzzles are perhaps my greatest vice, and the Mystery Hunt is a weekend-long all-you-can-solve buffet of 100 or more delightfully difficult puzzles, perfect for a junkie like me. My team, Just for the Halibut, is in no danger of winning -- rather fortunately, as the winning team must then write the next year's Hunt -- but we have a lot of fun nonetheless.

The puzzles at the Mystery Hunt run the gamut from crosswords to logic puzzles to trivia to everything in between, including a fair number of music-related puzzles. Most music puzzles are centered around pop song identification, which I leave to my teammates, but there have been a few puzzles that skewed more towards my areas of expertise:

  • Go Bye-Bye, Whinging Muchacha! is a neat little puzzle from 2002, the year before I started Hunting. It hinges on recognizing a particular thing, but that thing is reasonably well known in the classical music world. The answer to this puzzle is a single word.
  • Stairway to Heaven is a puzzle from 2003 which draws on a good deal of musical trivia. The final solution -- which is not a word but an object or image -- hinges on knowledge of the MIT campus, but the relevant information can be found from within this virtual tour.
  • Having Fun, from 2004, is the only jazz-themed puzzle that I can think of. I single-handedly nailed that one, making my team one of only three to get it. I will say that I found the clue phrase very frustrating and misleading -- at one point the organizers informed me that the last word of the clue should be "TITLE," instead of what was given -- but the two-word answer is certainly apropos for the title.
  • Concerto Delle Oche Volanti eluded me in 2005 -- I assumed the puzzle involved much more sophisticated musical knowledge than was actually required. I have an unfortunate tendency to overthink puzzles with simpler mechanics sometimes.

If I ever get to help write the Mystery Hunt, I have some ideas for music-related puzzles I'd like to try, but I have to show some restraint. While I could easily write a 12-tone composition which encodes the letters of the answer in the different row operations, I can't imagine that being fun to solve for most teams. But I have other tricks up my sleeve...

In any event, I should go finish packing. And don't be surprised if I wind up gushing about the Mystery Hunt sometime next week. And yes, I will try to write about music, too.

Contra Affair

Tue, 07/08/2008 - 3:36pm — Nathan

It's been over a month since I last made a Shell Script post; I moved to a new apartment last month, and that took up much of my energy from late May through much of June. Hopefully, I'll be able to stay more current now that things have settled down.

At the end of June, I spent the weekend at a large geek gathering in the middle of nowhere. We camped on the top of a mountain, and indulged in all sorts of geeky off-line entertainments, from liquid nitrogen ice cream to aerial silks to contra dancing. The contra dancing intrigued me somewhat: I didn't dance, but I was curious about the music. I was sufficiently interested that I asked the caller what the parameters of contra dance music were, and offered to write a contra tune. I was initially hoping that I might be able to write a tune quickly enough that the small band -- two violins, bass clarinet, and mandolin -- could play it later that night, but I decided to actively watch the dancers and listen to the band, rather than tuning them out to write my own music. Nevertheless, I'm still interested in writing a contra tune or two.

One of the things that I find most appealing about writing a tune for contra dancing is that it would take me out of some of my comfort zones. Most significantly, I would be writing music with a specific social function. For most geeks, music performance is almost always imbued with some sort of social function. In addition to the contra dancing, there were planned and unplanned singalongs at the weekend gathering, and elsewhere, concerts by geek-oriented musicians such as Paul and Storm and Jonathan Coulton are typically communal, audience-inclusive events. In contrast, classical music concerts, especially in the academic branch of contemporary music that I have been accustomed to, tend to be divorced from any social function whatsoever. All the music that I have written to this point was meant to be experienced on a personal basis, independent of other listeners. Since I do fancy myself a geek, and feel more at home in the geek community than the contemporary classical music community, I have been concerned with this discrepancy. If I wish to present my music to a primarily geeky audience, I think it will be helpful for me to try working in some of the modes of presentation normally associated with my audience.

The second challenge that contra music presents to me is more technical, though it certainly pertains to the function of the music. Contra tunes, like most music for social dancing, are very circumscribed in rhythm and structure. In this case, the tune must be in duple meter (i.e., two beats per bar) at around 120 beats per minute, and take up exactly 32 bars. Usually the tune will break down further into 8-bar phrases in something like an AABB structure. This is a far cry from most of the music that I have written. Of all the pieces I've written, I can think of only three or four that stay in one time signature throughout; in fact, I've written more pieces that have sections with no time signature at all. And of those three or four songs that have a steady time signature, only one of them breaks down into any sort of consistent phrase structure. Even the pieces that I call "dances" (Trinkle Dance, "Repose" from Song and Dance: Panic and Repose) have irregular rhythms and phrase lengths. Also, the perpetuum mobile style of most contra melodies is something that I find difficult to work with. I like my music to breathe, and favor the push and pull that comes from rhythmic variety in both the melody and the underlying time signatures. Also, I'm a trombonist at heart, and the nonstop eighth-note melodies which suit fiddlers just fine are simply not in my idiom. But I certainly relish the challenge.

In the spirit of contra dancing, I leave you with one of my favorite reels, Percy Grainger's arrangement of Molly on the Shore.

Luciano Berio meets Jim Henson

Sat, 05/31/2008 - 1:25am — Nathan

So, there's this composer, Luciano Berio. He wrote a lot of great music, as some compoers are wont to do, and died in 2003 (Wow, was it really that long ago? It feels more recent to me, like he and Ligeti both died a short time apart, in the last couple of years. I guess memory can really distort one's sense of time.). One of his most widely-known works is his Sinfonia for eight voices and orchestra, written in 1968 for the 125th anniversary of the New York Philharmonic.

The third movement of the Sinfonia is particularly notorious among music students, for its unusual collage construction. For the base layer of this collage, Berio started with the scherzo from Mahler's second symphony, which you can listen to here. On top of this scherzo, which runs continuously throughout the third movement of the Sinfonia, Berio adds a number of shorter musical quotations from other composers, ranging from old masters like Monteverdi and J. S. Bach to Berio's contemporaries, including Stockhausen and Boulez. Additionally, the eight vocalists make their own contributions to this medley, with spoken lines taken from Beckett and other sources. The end result of this collage can be heard in two parts, here and here. Go ahead, take a listen.

Fun stuff, isn't it? You might recognize some of the quotations, you might not. I certainly can't name them all. But it certainly sounds like a collage. Snatches of music which clearly come from disparate sources fade in and out like radio signals, and the underlying Mahler scherzo, though often obscured, still runs through it all, like a river which periodically disappears behind trees and hills. Charles Ives used a similar collage technique in his symphonies and other works some fifty years earlier, but not to the full extent that Berio did in Sinfonia: Ives would often slightly alter the melody of a hymn tune or patriotic song in order to better fit the musical texture, and used original material to harmonize these quotations and tie them together, while I believe every note of the third movement of Sinfonia (though not necessarily every word) can be directly tied to a pre-existing source. This doesn't mean that Berio's collage is better or worse than those of Ives; the two composers used similar techniques for similar but slightly different evocative purposes, and they both succeeded in realizing their intents effectively.

Once upon a time, a couple years ago, I read a post on some composer's blog -- I want to say it was Lawrence Dillon's blog at Sequenza21 (which, incidentally, takes its name from a series of solo works by Berio) but failed to find the post after a cursory search -- about the Sinfonia. In reference to the third movement, the author said something to the effect of, "At last! Somebody's written a piece that sounds like what goes on in my head all the time!" And many other musicians commented on that post, agreeing with the sentiment. I, too, concur; I have a mishmash of heard and unheard music running through my head almost constantly. But while Berio's collage limits its musical sources to the European "classical" tradition, my mind often casts its net in much wider waters, whether I like it or no.

Recently, my roommate has gotten me hooked on Fraggle Rock, and we have been working our way through the second season on DVD. I had only vague memories of Fraggle Rock from my childhood, as it aired on HBO, and the only place I was able to watch it was at my maternal grandmother's house, which I visited maybe twice a year. But now I can watch it at my leisure, and it's good. It also has songs. Fun songs, happy songs, silly songs. One of the episodes we watched tonight included the song "Shine On Me," which you can watch here. In case you're interested the full episode yourself, I won't say much about the context of the song -- though plenty of context is hinted at in the clip itself -- except to say that the song was a total letdown from my perspective. I was expecting something more substantial, and got... that... but it is catchy, if you're in the right mood. And I guess I was in the right mood, because it stuck in my head for a while afterward.

But not long thereafter, my head started making impromptu mashups, as it is wont to do. The chorus, as disappointing as it is, pretty clearly resembles, both lyrically and musically, the chorus to "Instant Karma", so that went in the mix. And for the verse, I was, for some reason, reminded of, um..."Barbie Girl". "What did you saywrite? I can hardly hearread you!" Okay, fine. "Barbie Girl". Running through my head, I've got "Shine On Me", "Instant Karma", and "Barbie Girl"! I don't have the technical chops to actually realize this mashup, and you should probably be thankful for that. But maybe you can try to imagine it, and get it stuck in your head, too.

Mr. Berio, I'll see your Samuel Beckett, Gustav Mahler, and Karlheinz Stockhausen, and raise you Jim Henson, John Lennon, and Aqua.

Head go 'splode

Wed, 05/07/2008 - 10:22pm — Nathan

The past couple of weeks, I've been putting a lot of work into this site, and I still have plenty more to do before I'm ready to unveil it to the public. I enjoy working on the site for the most part, but it's also occasionally stressful. Diving headfirst into web design, barely knowing HTML and having no prior experience with CSS, PHP, SQL, and other related acronyms is a bit of a challenge, even when I have a great set of tools to work with. So, to clear my head, I thought I'd work on composing for a little bit.

For a while, I've been intrigued by just intonation, and I'm finally dipping my toe into the water. Let me say up front that just intonation (JI) is one of the most mathematically fertile areas in music. You get number theory: JI is all about the comparison of various products and ratios of whole numbers, and the reason why we historically had to make compromises in our tuning systems in the first place is tied to the Fundamental Turkey of Arithmetic. You get group theory: some tunings can be constructed to be isomorphic to the free abelian group on n elements, with a set of relations. You get linear algebra: that same tuning is also isomorphic to a set of n-dimensional lattice points bordered by some hyperparallelepiped. You get topology: either way, when you're actually looking at where that group or lattice lies in the pitch continuum, you homomorphicaly map it to the unit circle. It's possible to do a lot of music without every dirtying your hands with mathematics, but not if you're a modern composer working in JI.

Basically, just intonation is the practice of tuning musical intervals according to (preferably small) whole number ratios like 3/2, 4/3, 5/4, and the like. Most musical instruments today, and consequently most music today, is tuned according to the idea that every half-step -- the distance between two immediately adjacent notes on a piano keyboard -- should be of equal size, and this results in every half-step having a ratio of the 12th root of 2, which is irrational. So in order to perform music in just intonation, contemporary musicians have a limited range of options:

1) Make their own instruments, specifically constructed to be in tune in some variety of JI. This is the route most famously followed by Harry Partch, and was at first the only option JI composers had.

2) Compose for synthesizers, or other electronic instruments whose pitch can be absolutely controlled. In terms of available pitch inventory, this is the most versatile option, though obviously a more recent development

3) Use or adapt existing musical instruments to produce pitches in JI. This method can be implemented with varying degrees of success. Fretless stringed instruments have the ability to produce notes across the entire pitch continuum; all the performer needs to learn is where to put their fingers. Keyboard instruments can be retuned, but this is a major undertaking, and the instrument is essentially limited to playing in a single 12-pitch JI scale indefinitely. Nonetheless, some notable works have been written for justly-retuned piano, most notably The Well-Tuned Piano by La Monte Young. Woodwind instruments can approximate JI pitches with nonstandard fingerings and embouchure adjustments, but the performer must learn a new fingering and adjustment for each note. For brass instruments, it is possible to get a certain set of JI scales by properly tuning the individual valves on a trumpet, horn, or tuba, and the trombone, like the strings, can play any desired pitch with little difficulty. It's difficult for an individual keyed brass player to change their scale in the midst of a piece, but with, say, a brass quintet, it's possible for the different players to achieve a variety of related tunings between them.

That last bit is the route I'm taking. I've got a good idea of a tuning that works for any individual instrument, and by using instruments which are naturally pitched in different keys -- one trumpet in C, the other in Bb, a double horn in F and Bb, a trombone which can play anything but most naturally gravitates toward Bb -- I can get multiple overlapping scales for a good bit of harmonic variety. And I think that the tuba, with longer tuning slides, might have enough leeway for me to give it a slightly different tuning. I'd have to try it out with an actual tubist to be sure. Also, different tuba players favor instruments in a surprising variety of keys -- Bb, C, Eb, and F -- so I should probably nail down a particular brass quintet and find out which key their tuba is in, before commiting too much to paper.

In the meantime, I've been doing some preliminary exercises, to get myself used to working in JI. The first order of business is notation. Actually, that's the second order of business, but I already took care of the first -- figuring out a JI scheme for (most of) the instruments. But while I know what pitches I can get from each instrument, it isn't as clear to me, from the start, what available harmonies I will have spanning disparate tunings, and one way for me to figure that out is to get everything written out on paper. After all, it's a little easier for me to deal with the notes B, C, and D than it is to deal with the ratios 15:16:18.

Now, just intonation uses a different set of pitches than equal temperament, so some notational changes are necessary. However, our modern equal temperament, and its concomitant notational system of naturals, sharps, and flats, evolved in steps from older tunings based on whole-number ratios -- just intonation is not merely a recent innovation. Accordingly, the system I am using, devised by Ben Johnston, is in some ways merely an extension of traditional notation.

The first step is to define the natural pitches, those without accidentals. In Johnston's notation, the chords C-E-G, F-A-C, and G-B-D are all tuned as perfect major triads, in the ratio 4:5:6. If you work out all the pairwise intervals involved, you see that F-C, C-G, G-D, A-E, and E-B all form perfect fifths in the ratio 3:2, as one might expect from looking at the keyboard and counting semitones (each of those intervals is 7 semitones wide). However, D-A, which also looks like it should be a perfect fifth, is decidedly not -- those notes are in the ratio 40:27, which is in fact a pretty severe dissonance. So, right from the start, some of our assumptions are shaken up. But we're only just beginning!

Next, we have to define the accidentals, and there are a lot of them. We do have sharps and flats, though. We said that C-E-G was a 4:5:6 major triad; can we make C-Eb-G a minor triad? Sure! A purely tuned minor triad has ratios of 1/6:1/5:1/4, or 10:12:15. Now, that means that, if the frequency of Eb is 12/10=6/5 times that of C, and the frequency of E is 5/4 times that of C, then the frequency of Eb is (6/5)/(5/4) times that of E, or 24/25. So a flat sign (b) lowers a pitch, any pitch, by a factor of 24:25. Conversely, a sharp (#) raises a pitch by an interval of 25/24. To deal with the fact that D-A wasn't a perfect fifth, we use the symbols + and - to indicate altering a pitch by 81/80 and 80/81, respectively. To get pitches relating to the seventh harmonic of the overtone series, we use 7 to lower a pitch by the interval 35/36, and L (an upside-down 7) to raise the pitch by the interval 36/35. There are also accidental symbols incorporating numbers with factors of 11 and 13, but they don't come into play in the tuning system I'm using, so I won't go into them. Any of these symbols can be combined -- compared to C, a Bb7 is 3/2 (C-G) x5/4 (G-B) x24/25 (b) x35/36 (7) = 7/4, which is precisely the seventh harmonic of C (two octaves removed, but we tend to ignore octaves -- or powers of two, from a mathematical perspective -- when comparing intervals). We can even repeat accidentals on a single note, just like the occasional double-sharps and double-flats in traditional notation. We have lots and lots of accidentals!

Now, in my case, I can't just go around writing #s and +s and Ls willy-nilly. I have a very definite set of pitches that I can work with, and I have to make the accidentals work with what I got. Since the JI notation is centered around the key of C, I started out with the C trumpet. I worked out all the ratios I was going to get in a single partial, applied those ratios to the available harmonics in the overtone series, and for each resulting ratio, factored it into a product of the appropriate accidentals. But I'm going to be working in Finale, so I have to define a bunch of expressions to attach to notes for the weird accidentals. But I don't just have to define +, -, 7, and L. I want to be able to hear the resulting pitches and intervals accurately, and since these pitches are not covered by the equal-tempered scales, I have to define pitch adjustments. Usually, intervals in general -- JI, equal-tempered, and anything in between -- are measured in cents. There are 100 cents in a semitone, and 1200 cents in an octave. However, Finale defines microtonal pitch adjustments in terms of the pitchwheel, and after some experimentation, I was able to determine that there were 8192 equally-spaced pitchwheel divisions in an octave, at least as my computer played it back. But wait, there's more. Since the naturals in Johnston's JI notation are not the same as their equal-tempered counterparts, I have to define separate accidentals, with separate pitch adjustments, for each note. The difference between JI C#L and equal-tempered C# is different from the difference between F#L and equal-tempered F#, so they need to be different Ls. I even need to make invisible markings to apply to the diatonic pitches, to make sure they're in tune. For every note in my desired scale, I had to go back to the ratio, look it up in Kyle Gann's Anatomy of an Octave, use Google's built-in calculator to convert from cents to pitchwheel increments, and define an accidental just for that pitch, complete with a description telling me which pitch it's defined for. Sounds like a lot of work? It is. Fortunately, I can save all my JI accidentals in a library, so it'll get easier as I go along.

Now, that was for the trumpet in C. Other instruments have the same overall shape of their scale, but built on different starting pitches. Also, some of these instruments -- the Bb trumpet and horn -- are transposing instruments, which means that the notes on the page are a certain transposition away from the actual sounding notes. Working in equal temperament, this isn't a big deal at all -- I got used to reading most of the standard transpositions in high school, due to my general interest in band music. In JI, or at least my current flavor of JI, it wreaks havoc on the system. I have a different set of pitches, some of which overlap with the pitches of the trumpet. They're certainly related to the trumpet's pitches -- in fact, if I'm working on the F side of the horn, they're just the same pitches as the C trumpet, transposed down a perfect fifth. But because of the transposition, the written notes, including accidentals, are the same as the trumpet. When the actual pitches do coincide with some of the C trumpet's, I can reuse the already defined markings -- after all, the same pitches are going to have the same pitch adjustments. Except that sometimes the actual written accidentals aren't the same: the pitch that was a B in the trumpet is not an F# in the horn, but an F#+ -- again going back to the fact that some of the "fifths" in the diatonic JI collection were not actually perfect fifths. Similarly, when defining new pitches, I have to not only do all of the above calculations and lookups, but I also have to keep reminding asking myself, "was this a written A+ but a sounding D, or a written A and a sounding D-?" It's almost enough to make my head go 'splode. And I haven't even gotten to the Bb side (technically the Bb- side, if you're being JI-precise about it) of the horn yet. I'm half afraid that that will make my head go 'splode.

Maybe I should go unwind, and work on debugging the online store.

Syndicate content