Atonal Accessibility? - Perle's Sinfonietta II

Although we've dealt with very few hardcore atonal works here at Unsung Symphonies so far, there does exist a (somewhat sporadic) thread of symphony writing among composers of a...less-than-tonal persuasion. The founding trinity of mainstream atonality, Schoenberg, Berg, and Webern, all composed multi-movement orchestral works -- some symphs in all but name (Berg's 3 Orchestral Pieces), others in barely anything other than name (Webern's Symphony Op. 21). I venture that their ambivalence towards the genre stems from conflicting urges for 1) non-repetition and the abandonment of set forms and 2) a certain penchant for familiar containers with a lot of cultural cachet to ground their experimental impulses.

One composer who felt this atonal ambivalence with special acuteness was the American George Perle (1915-2009). Enraptured with the wide open possibilities of Viennese atonality from an early age, Perle nevertheless felt Schoenberg left behind an unfinished project. Perle believed that Schoenberg's 12-Tone Method (also known as serialism) was a partial and unsatisfactory way for dealing with these new resources. As prominent a music theorist as he was a composer, Perle set out to discover a more musical basis for picking this note over that. In a series of influential books and articles, he ended up formulating what he called "Twelve Tone Tonality," a system that allowed for many of the gestures of traditional music -- cadences, "mode" and "keys", and most importantly a real sense of directed chord progression -- without any of the trappings of tonal pitch selection or syntax.[1] Perle wrote the majority of his own music according to this system. But rather than existing simply to validate his music theoretically, Perle's special brand of "Tonality" was deeply committed to accessibility.

Someone suspicious of atonality and its reputation of ugliness and difficulty would do well to give Perle's Sinfonietta II a listen. He composed this in the fall of 1990 during his three year tenure as the San Francisco Symphony's composer-in-residence. It was performed in February of the next year under the baton of Herbert Blomstedt. Newspaper reviews were quite lavish with their praise, and especially quick to emphasize how enjoyable, or in the words of Sacramento Bee reviewer William Glackin, how "happy" a work it was.[2] The San Francisco Examiner called the Sinfonietta "disarmingly communicative" (expecting something else?), while the San Jose Mercury News basically dubbed Perle the spiritual successor of France's "Les Six": "Nothing is trite; nothing is a rerun; nothing panders to popular taste."

Like the duration (a fleeting 16 minutes), the orchestra of Perle's Sinfonietta II is quite small, save for the percussion section, which keeps its four performers busy with thirteen colorful instruments in strategic reserve. The outer movements, labelled Scherzo I and Scherzo II, are siblings in terms of structure and ethos, both playful romps with a clear ABA form. Orchestration is usually tidy and open, the opposite of Berg and Schoenberg's dense-thicket approach, closer in spirit to Webern's crystal lattices. But that's basically where the Webern similarities end, because Perle projects a sense of fun and extroversion completely alien to that more rarefied style. Melodies and motifs crop up repeatedly, meaning that Perle keeps the listener from worrying about where they are in the piece. The attention span of these ideas is quite short, leading to a manic, scurrying quality that persists throughout -- at several times, especially in the second Scherzo, there is a strong suggestion of cartoon music!

The first Scherzo sets off with a handful of tricks: first a climb up an arpeggiated diminished seventh (I mean, err, presentation of the interval-3 cycle mode-1...), then a harmonized flute phrase, a pair of cello interrogations followed by more arpeggios, and a set of strident but not-too-dissonant string chords:



The harmonic materials, the play of rhythms, and the quickly alternating orchestral colors are characteristic of the whole movement. The B-section "trio" introduces a nervous triplet pattern for strings, over which the flute and piccolo rush in a panic, soothed and egged on at intervals by vibraphone and brass whole-tone arpeggios.

To me, the second Scherzo is the funnier of the two. There is right off the bat a strong contrast between annoyed insistence (the strings' upward bounding, dissonant theme) and mellow sheepishness (the wind and pizzicato answers). After each urgent string statement, a corresponding gesture of deflation seems to follow. Particularly striking are the unvarnished clarinet major thirds and the short passages of honest-to-goodness jazz scoring for brass and percussion -- what better way to puncture an insecure atonal phrase's sense of angsty importance?!:



I have no doubt this work's pitch design is rigorously organized, but the impression is the exact opposite of what you'd expect coming from a theorist of 12-tone quasi-mathematical structure: this is academic atonality, thoroughly defanged.

The heart of this short work is the second movement, "Chorales and Diversions." Hearing it on Pandora (on my Nørgård channel, no less) first made me interested in Perle's Sinfonietta, and it is the movement I find myself returning to the most. A rondo in form, the movement sandwiches some eerie passages of rather Bergian sound between statements of a lyrical chorale melody, given almost exclusively to a solo bucket-muted bass trombone. The theme respires in and out like a Bach chorale glimpsed in the dusk, and is harmonized homophonically with some truly lush lower string writing. Here is the entire first section of this nocturnal movement:



George Perle may be the only composer of resolutely "atonal" music for whom I've noticed the label "conservative" repeatedly applied. Sometimes this is in reference to his choice of musical forms. But elsewhere it seems "conservative" is the only word we have for composers who attempt to eschew abstraction for its own sake, and instead choose to ground their music in a consistent and accessible system like traditional tonality. Ultimately, it's as unsatisfyingly simplistic a label as would be "progressive." Better to take Perle at his own word:

"There's this mystique that there's an elite of specialists for whom contemporary music is written. I don't write up or down to anyone. I'm just doing what composers have always done. Some people have written about me as though I were a composer of inaccessible music. But my experience has been that people who listen to my music are amazed by how accessible they find it." [3]

--Frank Lehman

-------
1: The foundations of Perle's theory are two interlocking organizational parameters. The first is the inversional array, which relates notes of the chromatic scale to stable pitch axes (often about a tritone) - this hinge is his equivalent to "key." The second is the interval cycle, which selects a number of pitches based on some symmetrical partition of the scale, such as minor thirds or major seconds - this furnishes the sense of "mode." Both are prominent aspects of the styles of not just Berg and co., but of Bartok, Debussy, and even composers further back into the 19th Century. In compositional practice (and Perle's analyses) the interactions of these two factors can become exceedingly complex, but the important point is that they help produce points of reference and stability that keep the listener from ever becoming too lost.
2: Reviews excerpted at GeorgePerle.net (not surprising that they are so positive!)
3: Quoted in For the Love of Music: Invitations to Listening (Steinberg and Rothe, 147)

Master of the Infinite Series - Nørgård’s Second Symphony

Per Nørgård (1932-) has been Denmark’s leading modernist composer since the 1960s. His fertile musical imagination has led to the creation of seven symphonies over the course of fifty years, the most recent premiering as recently as 2006. Nørgård's music is rigorously constructed but surprisingly approachable, in some cases even ecstatically enjoyable. 

Among the deeds Nørgård (pronounced "Ner-gore") is known for is the planning of large scale compositions around the same principles that would eventually be formalized in the idea of the “fractal” was even coined. The key to his prescient anticipation of fractals is his use of a specific music-composition device that he (and he alone) invented. Since 1959, a great deal of Nørgård's music has been based on what he called the “infinite series.” (alternatively "infinity series"). His Second Symphony, a one movement work lasting about one half hour, is among his first and most rigorous applications of this tool. Here’s how it works:

Nørgård’s infinite series is actually an integer sequence produced by a relatively simple algorithm that “unpacks” a single musical interval. A single interval is all you need to generate an unstoppable Nørgård sequence. Say you want to begin a piece with the melody G - A. Let’s assume just white notes (diatonic) are in use. From this melody, Nørgård would extract an essential piece of info, the ascending +1 “go up by one” interval between G and A. Then, he composes out that interval, using its inverted form as instructions on what the next pitch shall be: go -1 away from G. Thus, the 3rd note in the sequence is 1 below G, or F. He does the same for A, only with the original interval, so that the 4th note in the series is +1 from A, or B. We’ve got a nice little tune, already fanning away from G! The instructions we’re following are essentially: take each new interval that appears in the sequence starting at the front, and go that far (in inversion) from the second to last note in sequence, and then go that far (uninverted) from the last note in the sequence.

Infinity Series Algorithm for Initial Interval +1 (white-note) step. Click to expand.

This diagram shows the process for two iterations, the first (+1 interval) and the second (+2), producing six notes from the original two. As you get further into the sequence, the new intervals get increasingly far away from the pitches they are “producing” at the other end. This is not a barrier to understanding, however; no one expects you to hear how specific notes are being chosen, because the effect is one of carefully tuned chaos – totally dependent on the initial condition (the +1 interval), seemingly random but thoroughly determined.¹

Continue generating the melody,² and you’ll begin seeing notes slightly further away from the starting point. But not by much – a fairly (statistically) tight grip around the starting range is always retained, and big leaps tend to be followed by leaps in the opposite direction. The resulting succession of pitches is what mathematicians call non-monotonic. No, they’re not referring to its lack of a clearly defined central pitch! Rather, it’s the tendency to avoid continuous motion in the same direction; the iterative process Nørgård uses produces unstable melodies, constantly flopping up and down, locally unpredictable but globally secure.

Pick any sample slice of this pitch sequence and it’ll likely look pretty similar to any other given slice. But in order to take advantage of the more rarefied property of self-similarity, these resemblances must show up on multiple levels. Cue Nørgård’s truly recursive compositional process in the Second Symphony.

The clearest fractal property at work in this piece is the use of a single G-to-A-flat based infinite series at several time-scales. The strict sequential orderings of pitches can be difficult to discern aurally, but you can easily tell that there are multiple orchestral strata doing different but related things. At measure 60, the orchestra splits into three streams. Woodwinds trade sprightly runs in constant eighth notes, buzzing in the vicinity of G. Brass operate at a more leisurely pace, generally 4x slower (half-notes), while the entire string section explores pyramidal figures at a *much* slower rate – roughly one change every 30 measures, or 1/120th the speed of the metronomic winds. Around halfway through the piece, these three main temporal roles suddenly begin alternating, shifting between players.

Sounds good in theory, but how does it all come out sounding? At times, Nørgård’s procedures produce truly dazzling passages. Here’s a clip (and, for the curious/masochistic, a score excerpt) of the initiation of the woodwind stream. The recording is from Segerstam's glittering performance with the Danish National Symphony orchestra.


Woodwind Stream:

[Score Example: Measure 60]

A great deal of the symphony sounds like this, with some stratum chugging away at their 8th-note pitch sequence while the rest of the orchestra slowly shifts in hue. Because pitch, as determined by the sequence, is usually so tightly wound around a certain range, our attention drifts to other matters, especially tone color, and Nørgård’s imagination for orchestral combinations is impressive. There are no catchy themes, but little shards of melodies do phase in and out of focus, and various ideas do come back. One is the throbbing unison pulses from brass at several form defining moments, celebrating the arrival at an important member of the infinite series with bizarre fanfare.

Brass Fanfare:


This is the kind of piece you can only write once, and Nørgård’s subsequent output, while equally ingenuous, tends to treat his infinite series less as the structuring principle as here, and more as a jumping off point. Which is not to say his Second Symphony isn’t successful. There is a hypnotic quality to this music quite unlike anything from the minimalists. And a sense of yawning expanse that pushes beyond much of the “sonorist” work from the 60s. Whether he beat chaos-theorists to the punch with his unpredictable, recursive music or not, Per Nørgård certainly created the bar and then raised it ridiculously high for anyone wishing to write a “fractal symphony.”

— Frank Lehman

---

1. This pretty extraordinary website has tons info on (and can play back!) any integer sequence you can dream up, including several from and inspired by Nørgård. For example the following functions specify the "infinite series" sequence beginning with 0-1: [pitch(starting place) = 0 ; pitch (2n places) = - pitch(n places ; pitch (2n + 1 places) = pitch(n places) + 1]

2. A “fun” exercise, if you’d like to try yourself. Check with the website above to see if you’re right, or consult Kullberg, “Beyond Infinity” in The Music of Per Nørgård in Fourteen Interpretive Essays.