The Density of Situations

Edgar Varèse (1883 - 1965)

He was a French composer, born right in the heart of Romanticism... but his compositional style definitely is that of a 20th century technician. Imagine being born into a world where all the prominent composers are alive and making amazing music, but everyone is bored out of their fucking minds with the conventional, Western tradition of harmony. Or better yet (and probably more true), the bounds of Western traditional harmony were stretched so far and so wide that innovation in the actual music was hard to come by. Electronic music was at its premature birth with the invention of the Telharmonium in 1897. But other than that, composers in this era sought to find new ways to think about and organize music. I mean, you can't really change the 12 notes that every instrument in traditional harmony can produce, but you have control of pretty much everything else: the note order, the dynamics, the timbre, the arrangement, the articulation. Varèse himself was very much interested in timbre, in how things sounded.

I decided to call my music "organized sound" and myself, not a musician, but a "worker in rhythms, frequencies and intensities." Indeed, to stubbornly conditioned ears, anything new in music has always been called noise. But after all what is music but organized noises? And a composer, like all artists, is an organizer of disparate elements. Subjectively, noise is any sound one doesn't like.

Varese from The Liberation of Sound

I strongly urge everyone reading this to take a gander at Varèse's "Liberation of Sound." He does an excellent job at describing post-tonal nuances and gives the listener an idea of where he's coming from as related to compositional theory.

So to our ears, 20th century music, or new music, sometimes sounds like noise because we are preconditioned to hear a certain way. There are no triads. There are no "real" chords, verses, choruses, or easy signifiers of "keys;" however, other elements of the music, such as dynamic placement, rhythm, form, articulation, timbre, orchestration and instrumentation, register, etc. can give us hints on the content of the piece, or what the composer is trying to accomplish. This brings us into the language of post-tonal harmony, where notes aren't thought of as letters, but as NUMBERS, ala, C = 0, C# = 1, and so forth until B = 11. It's a way to get rid of the harmonic and melodic tendencies our ears are used to hearing in tonality.

i.e.:



I personally find it easier to picture these notes on a clock face.


So where does that leave us? I think Varèse said it best himself: In a world of "liberation from the arbitrary, paralyzing tempered system; the possibility of obtaining any number of cycles or if still desired, subdivisions of the octave, consequently the formation of any desired scale; unsuspected range in low and high registers; new harmonic splendors obtainable from the use of sub-harmonic combinations now impossible; the possibility of obtaining any differentiation of timbre, of sound-combinations; new dynamics far beyond the present human-powered orchestra; a sense of sound-projection in space by means of the emission of sound in any part or in many parts of the hall as may be required by the score; cross rhythms unrelated to each other, treated simultaneously, or to use the old word, "contrapuntally" (since the machine would be able to beat any number of desired notes, any subdivision of them, omission or fraction of them) - all these in a given unit of measure or time which is humanly impossible to attain."

Let's escape into this splendid depth, shall we?

Density 21.5



I started my analysis of Density 21.5 kind of haphazardly. As in, I put my iTunes on shuffle, and it was the first song that played. I was automatically transfixed; all these memories of music school came back to haunt me. I couldn't get passed the first five notes to save my life. Consequently, I have renamed the piece to 60 Measures of "I Don't Know What the Fuck is Going On."

Nonetheless, I started my aural analysis before looking at the score. You can definitely hear a motive (that three note incident in the beginning) and it returns in various forms and transpositions throughout the piece. There are also saturations of pitch interval classes, most notably, tritones, minor thirds, and chromatic steps (and their opposites). Other than that, and the fact that it was written for solo flute in January 1936, at the request of Georges Barrère for the inauguration of his platinum flute (21.5 is the density of platinum), this piece is one big, gigantic, gaping, atonal muleta of a question mark, and I am a confused bull, stagnant in the chutes of dissonance.

Side note: I bought the score at Performer's Music, which is probably the best kept hidden secret in Chicago. If you're ever in the city, definitely check it out. It's in the old Fine Arts building, and you have to take a manual elevator up to the 9th floor to get in. But they seriously have aisles of music- from Bach chorales, to the original printing of X-composer's new percussion trio that came out 2 weeks ago. After buying the sheet music and for the past three-ish weeks, trying to tackle this piece, leaving it, re-visiting it, listening to dissonance for hours on end, and even sketching charts, any conclusions I can make about this piece is merely speculation... which is both enthralling and excruciating at the same time.

In music, expectations are what make the un-expected so momentous. What happens when everything is unexpected? Some would argue that you just leave it- let it be what it is, let it be beautiful. Some would argue that you have to keep listening- listen over and over and over again, until you HEAR the expected. I want to elaborate on the latter. I think that most composers in this period, maybe with the exception of Schoenberg, don't want to abandon the expected; rather, their arrangements and visions redefine the expected, and careful analysis (with a lot of caffeine) can reveal those special moments within the larger-scale of the work. So... let's begin.

Dividing the Octave

Every scale in Western tradition spans within an octave, that is, the twelve half steps between a given note and a note with either half or double its frequency. When we get rid of modal scales, we're just left with twelve notes. Post-tonal composers saw this as an opportunity to create new scales, find different tendencies between notes, arrange notes in a fashion that wasn't so much "chronological" as it was "like putting puzzle pieces together." Once you get over the idea of an ascending scale, the octave pretty much looks like this:

(click)














In order to get Density 21.5's content, you need to understand the Octatonic Scale. It has to do with symmetry in the 12 notes. Basically, if you start with 0 (C), and move three intervals in either direction, you'll eventually get back to 0 (C). Which, makes sense... 12 divided by 3 is 4. You hit four notes before getting back to C. This of course can be transposed to 1 or 2.. starting on C# or D. With equal divisions of the octave, you can only count so far before returning to either 0, 1, or 2. Olivier Messiaen called this a "mode of limited transposition."

Picture: the middle row, equal division of the octave into 4 (3 half steps in either direction)
(click)














Now, if you actually consider the note names for any of these charts, for example, the first cycle in the above picture, you get:

0 = C
3 = Eb
6 = Gb
9 = A

which, in Western traditional harmony, is a diminished 7th chord, starting on C (or Eb, or Gb, or A). That, transposed to start on 1 or 2, will give you a C# diminished 7th chord and a D diminished 7th chord, respectively. In post-tonality, a collection of these pitches occurring in symmetry are called an interval cycle. This particular pitch cycle is notated like this: C30, with "C" referring to cycle, "3" referring to how many intervals are between each note, and "0" referring to the note it's starting on. So, consequently, if we define these tones that occur in equal divisions of the octave, we'll have this:

[0, 3, 6, 9] = C30
[1, 4, 7, 10] = C31
[2, 5, 8, 11] = C32

Any combination of two of the three interval cycles above will make an Octatonic Scale, which, by definition, is an 8-note scale with alternating whole and half step intervals. Pretty cool.

This is KEY to understanding Varèse's musical content. He doesn't use major keys or minor keys; he doesn't imply chordal harmony by melodic expectations; he simply (simply, ha!) uses a saturation of the Octatonic Scale in various combinations, and creates sections of the music by contrasting the three interval cycles against each other.

"So... he pretty much makes music out of a bracket."

Well... yes... but it's not just a bracket. It's a completely different way of thinking about and arranging music: the tendencies of scale degrees aren't there, the harmonic implications definitely are not there, and the performer has limited freedom because of the strict timing, phrasing, and articulation (which is necessary for continuity). In other words, he has deconstructed our ear's expectation, directly connected to how we think about melody and harmony, to create his own permeation of sound moving through time and space- which, essentially, is the mere definition of music.

My Analysis



Here's my analysis of Density 21.5... before I got tired of analyzing it. Let's just take into consideration the first three systems. As you can see, I circled most of the notes that fall into C31, which is the first interval cycle Varèse uses in this piece. Most would ask, how do you know which notes to circle, or which notes are important? I struggled with this for the longest time when analyzing 20th century music, but there are some clues. For example, more important notes are usually held longer. Now this is not to say the F# in measure 1 isn't important; actually, that entire three-note motive is what ties the piece together, melodically. It recurs in various transpositions, inversions, and octaves throughout the piece (my favorite times: in mm. 20-21, fluttertongued in a high octave; m. 50 where it's hidden so well between cycle transitions; and of course, m. 29, in the "B" section of the piece, broken up and retrograded in different registers).

One thing to look at is the DYNAMICS. Knowing that Varèse was a sucker for timbre, he used his dynamics very precisely and intentionally. A flute's dynamics also affect the timbre depending on the register- it's harder to play loud and low than it is to play soft and high. We're pretty much in the range of piano and mezzo-forte (forte only used in crescendos and decrescendos, until you hit the C# in measure 5). So you have all these notes kanoodling around an extremely variant volume, and then we reach a fortissimo in measure 9, after a breath mark (which he uses sparingly), landing on Db, whose enharmonic equivalence is what? C#. Also, if you look at the lowest note and the highest note from measures 1 - 10, in terms of register, they are C#4 and Db5. Which is the same pitch class: 1. Which makes it C31, or [1, 4, 7, 10].

This little melody has three little sections, which are composed thoroughly in their respective order. ie: the first "phrase" is carried out in the first part of the development, the second one in the second part of the development, etc. I'll mark this later when I get a better understanding of the rhythm and its different transpositions (right now I can only hear it.. sorry) BUT the arrival of D in measure 11 is a landmark moment, as we meet a new pitch class outside the C31 interval cycle, underlined by the triple fortissimo. And, Varèse kind of makes it blatantly obvious that we're going into a new interval cycle by writing a bunch of tritones- a stark, biting sound that used to be called the "Devil's interval," and also the interval that divides our cycle in half. aka, it's very prevalent in the C3 cycles, and automatic clue. The D - G#'s and the A - D# kind of gives it away. The combination of those two interval cycles also hint at the Octatonic Scale, starting on P2, which elaborates onto the first development of the motive, marked with a star. The short attacks of C31 and C32 on the last system of the first page build until the climax of the piece, which is also a change in tempo, and marks the arrival of a different interval cycle.

Speaking of tritones, it might be important to note that Varèse moved to New York City when he was 32 and was a total Dadaist. One has to wonder where this guy gets his inspiration. I can just picture him in his Brooklyn apartment, pecking away at his piano with the window open, people talking and screaming an laughing and whistling and sirens going by. If you listen closely, you can hear them around m. 31.

So, I guess if there's anything to be learned from this, it's that musicians had to find new ways to make their weird music not only understandable and explainable by other people, but interesting and accesible too. I think Varèse found an interesting motive that we can grasp onto to make this piece flow and have parts, which in turn, made him take liberty in the staying strictly in the lines of interval class cycles and pitch classes... those things are just there for "structure," anyway, it's what you do with it that is composition. I still haven't completely wrapped my head around it, but I think it's one of those things that'll come to me the more I listen and not think about it. He definitely succeeded in testing the flute to its fullest capabilities and skill. This is not an easy piece to play perfectly. Any electronic instrument would sound completely different from a live performer because of this mild obsession with timbre. But anyway.

Listening to: The Flaming Lips - Embryonic (2009); Spoon - Transference (2010), Against Me! - Searching for a Former Clarity (2005); Edgard Varèse (click play button next to song)