counterpoint

Counterpoint and The Void

"...[A] void exists between musical acoustics and music properly speaking, that it is necessary to fill this void with a science describing sounds, joined to an art of hearing them, and that this hybrid discipline clearly grounds our musical efforts." 
-Pierre Schaeffer


Phenomenology seeks to be this hybrid discipline to fill the void between objectivity (musical acoustics, for example) and subjectivity (music properly speaking). A good musical example of this notion is the difference between frequency and pitch. Frequency is the number of sound waves in a given time; pitch is the way we perceive the frequency. 440 hertz is a frequency; A is the the pitch. Schaeffer's void is the almost ungraspable space between the objective known and the perceived.

It's the space-between that reminds me of counterpoint. Maybe counterpoint is a reflection of the Void, or negative space more generally, and it's the ungraspability of counterpoint that makes it so interesting. Some would argue that it's completely graspable. Indeed, it can be described in great detail. Schenkarian graphs are one example of this description. Species counterpoint captures the essence of a style in order to teach students to emulate that style. But, those examples are akin to the "musical acoustics" of Schaeffer's quotation above. What is less clear is the listener's perception of counterpoint. It's nebulous.



 

Dramatic Counterpoint, Part 1

"Dramatic Counterpoint" is a term used by Paul Lawley in discussing the texture of Beckett's Play.

Play is a play with three characters delivering overlapping monologues on the same story. Not really overlapping--maybe interwoven monologues. Anyway, they don't converse with one another, they just take turns telling bits of their individual perspectives. If one were to parse out the three monologues, three cohesive narratives would emerge, but it's this counterpoint between the three that make it interesting. You can't look at three sides of a statue at the same time, but with Play you get close to simultaneous differing viewpoints--a kind of theatrical cubism. (Another time I might be inclined to think more about the difference in simultaneity versus juxtaposed--maybe they're analogs with harmony and melody. Counterpoint being the space between, of course.)

Anyway, here's an excerpt from a film version of Play from YouTube:

Introductions, part 2: Other Fibonacci applications and accent canons

In the previous post I mentioned that the form of the introduction was based on two Fibonacci series: one a series of thirteen gestures with durations of (in terms of sixteenth notes) 377, 233, 144, 89, ... 2, 1, and the other a series of twelve gestures with durations of 1, 1, 2, 3, ... 144. The first series ends with only one one-sixteenth-note gesture, and what would be the thirteenth gesture of the second series (233) gradually morphs into a new formal section.

I used the Fibonacci series in a few other ways in the piano/percussion/electric guitar texture. As I've described in the previous post, each of the thirteen gestures in this passage is a descent to the bottom of the keyboard. As the gestures get shorter it seemed unreasonable to cover the same interval of 21 semitones from C3 to E-flat1 in each gesture, so I decided to begin gradually lower each time. Here's a table that shows the initial central pitch of each of the thirteen gestures.

Except for the first and last gestures, there is a change in transposition level every two gestures. These changes follow the Fibonacci series (technically, the negafibonacci series). I chose to use the Fibonacci series here because it gives a nice curve to the entire section that mirrors somewhat the descending curve found in each gesture. I did compose the piano's final A0 of this passage outside of the system detailed in the previous post in order to make sure the goal of the lowest possible note was achieved.

I honestly can't remember if this was intentional (it has been a few days), but I find it interesting that the total number of gestures in this passage, 13, is a Fibonacci number, as is the number of semitones between C3 and E-flat1, 21. Not sure if it means anything...

Finally, I used Fibonacci numbers in a way that undermines the recursive nature of the series. I created a row of 81 (unless I miscounted..) Fibonacci numbers based on various simple additive patterns. I used this row to determine where to place accents in the piano, percussion, and electric guitar parts. I broke up the series using additive patterns in order to ensure asymmetry.

The row:

13, 8, 5, 3, 2, 1, 1, 8, 5, 3, 2, 1, 1, 5, 3, 2, 1, 1, 1, 2, 1, 3, 2, 1, 5, 3, 2, 1, 8, 5, 3, 2, 1, 13, 8, 5, 3, 2, 1, 2, 3, 2, 5, 3, 2, 8, 5, 3, 2, 13, 8, 5, 3, 2, 3, 5, 3, 8, 5, 3, 13, 8, 5, 3, 5, 8, 5, 13, 8, 5, 8, 13, 8, 13

Here is the row broken up in sections to show the various patterns.

Each part follows this row, either forward or backward depending on the part, and when it gets to the end it changes direction and traverses it again in the opposite direction. The piano begins at the beginning, the marimba at the end (retrograde), the xylophone begins on the "2" (12th line, lone 2) and moves forward, and the guitar begins on the "1" just before (end of the 11th line) and moves in retrograde. These numbers are time points on a grid of sixteenth notes. Accents fall on the first note, then again after sixteenth notes according to the row. In the end this is just a quick and effective way to ensure some variety and generate patterns in the monotonous sixteenth-note grid. I realize there is some goal-oriented motion embedded here, but this is a canon, of sorts, played by four different instruments (playing in unison or octaves, remember). The interplay among the accents on these instruments will create brief, passing motives, not the sense of direction toward a goal.

Introductions, part 1

Well, there's just one introduction. It's the most unified section of the piece. It will actually have a standard score with a time signature, bar lines, and synchronized parts. I knew the kind of texture I wanted; it came out of an improvisation with Impulse back before the holidays. The primary gesture is based on the physicality of playing the piano in the low register, thumbs together, alternating hands playing "random" notes within a generally fixed range in a fast, regular pattern. The pitches aren't important except in that they should not overly emphasize any particular pitch. Of course, as we know from the history of serial music, it requires some kind of non-intuitive system to make an even distribution of pitches sound just right. In my improvisation a couple months ago I felt like I was getting the right texture intuitively, but when it comes to making decisions about pitches to go down on paper I felt I needed to go to the computer to generate a texture closer to my improvisation. Besides, while my improvisation

felt

 right, without a recording I can't be objective enough about it (not to mention I can't transcribe what I played). Intuition is a dangerous place to spend too much time :)

I went to Max because it's very flexible. I built a very rudimentary patch that outputs MIDI information directly to Sibelius. Here's a picture:

The toggle in the upper left turns on the patch. The metro object bangs the toggle below resulting in alternating 0s and 1s. The 0s go to the "left hand" side of the patch, which generates the left hand notes, and the 1s go to the "right hand" side. Both sides are essentially parallel, generating numbers between 48 (the MIDI number for C3) and 48+6 (or 54, F-sharp3). The left hand side is then lowered 7 semitones, producing the range of F2 to B2. The result is alternating left hand and right hand notes, each hand covering the range of a tritone, which fits very comfortably under the hand.

Once I decided the length of the gestures, I added the objects on the right side of the patch to add a curve to the gesture (more on the length of the gestures below). The center pitch above is MIDI note 48 (C3), or 21 semitones above E-flat1, a tritone above the lowest note on the keyboard (i.e. as low as possible without the left hand running off the keyboard). During my original improvisation I moved gradually to the bottom of the keyboard, and I wanted to recreate that gesture here. I tried to descend by semitone every measure for 21 measures, but found the descent was too regular for my liking. By connecting the

itable

object to the transposition factor (see figure above), I could control the rate of descent. I simply drew the curve that I wanted with my mouse (of course, I had to set the parameter of the

itable

first--in the example above I knew I needed 377 notes, so the x-axis was set to 377). The transposition factor adjusts the center pitch, which is 48 by default, thereby lowering all the pitches proportionally. When the curve reaches the bottom of the

itable

, the transposition is 21 semitones down, for the bottom of the keyboard.

The form of the introduction

The introduction is around 2:20 in length, but it gradually dissipates into the main body of the piece making the ending of this section ambiguous. It represents no more than 10% of the entire work, and probably a little less. I first thought of it as a stand-alone, unrelated section, but now I think of it as crucial to the development of the three component pieces: In the beginning the three are integrated into one gesture, but during the course of this introduction, they begin to foreshadow their distinctive behaviors and come apart from one another. If the idea for the entire work is three separate pieces, the introduction tells the story of how they became separate.

The first 30 seconds or so is an extended reproduction of the improvisatory piano gesture I described above. Percussion and the electric guitar join in unison or octaves, dynamically coloring the piano's timbre. This is notated by 377 sixteenth notes. After one sixteenth rest, the same gesture is played again, but shorter this time--233 sixteenth notes. Then another sixteenth rest precedes a third gesture taking 144 sixteenth notes. There are twelve gestures like this, each getting shorter according to the Fibonacci series down to a one-sixteenth-note gesture. The rests between each gesture (#thevoid) get progressive longer according to the same series.

These rests between each piano/percussion/guitar gesture are filled in by harmonic series chords in the winds, strings, and sopranos. Conceptually, I just wanted static surface texture to contrast with the active sixteenth-note surface. However, as the piano's active texture is colored by the percussion and electric guitar, the static-texture interruption is also elaborated somewhat. The primary static material is found initially in the bassoon and clarinet (though these may change later in the introduction--it's not finished yet). The first static gesture is only one sixteenth note, so in order to avoid it blending too much into the piano/percussion/guitar texture, I orchestrated the event with some higher-frequency resonance. This resonance is found in the flute and string harmonics, and it is sustained somewhat longer than the single sixteenth note played by the bassoon and clarinet. The singers, too, project this idea of resonance with even longer (approximately two measures) passages of unisons and close-voiced harmonies that slowly change.

As the static gestures get longer they come to dominate the surface of the music. From a position of practicality the resonances must either get shorter (because the time between gestures is getting shorter) or begin to wash over the beginning of the next gesture. I will play with this, probably alternating between abrupt changes with no resonance and resonances that become asynchronous with the static event rhythm (think of waves crashing irregularly on a beach). The nature of the soprano parts as harmonically dynamic resonances will begin to change to more static material that will eventually lose prominence to the strings and winds, which will gradually become more active. The sopranos' movement toward stasis will foreshadow the beginning of sopranos' large-scale gesture, which begins quite statically. The winds/strings' growing prominence will signal, by the end of the introduction, the beginning of isorhythmic texture that will dominate those instruments' large-scale gesture. The piano/percussion/guitar part, with its curves in pitch space, foreshadows the tempo curves that will dominate the behavior of those instruments later.

Dissertation Proposal

Introduction

The original composition will be a single-movement work for flute, clarinet, bassoon, violin, cello, electric guitar, piano, two percussionists, and three sopranos. Though it will be a single movement, I think of it conceptually as three overlapping movements, each being independent and distinct. In other words, I will be thinking carefully about experimental approaches to and interpretations of form, not as a simple delineation of linear time, but as counterpoint between contrasting musics.

The impetus for this approach will be discussed in detail in the critical essay. I think of this project as another step in a rich tradition of music, visual art, and prose that explores such concepts as circularity, deferred resolution, stasis, and the void as metaphorical constructs. The critical essay will elaborate on this tradition and make connections between various composers, artists, and writers with my own work.

Overview of the original composition

The original composition for mixed chamber ensemble will focus on formal counterpoint. By formal counterpoint I mean relationships and interactions between temporally discrete sections of music that will be cut, superimposed, merged, and permuted in a variety of ways. Each of three formal sections ("sections" is used loosely since they will overlap with each other temporally) will focus on a single, distinct systematic approach to composition and, to various degrees, on groupings of instruments. The first section will be primarily played by the flute, clarinet, bassoon, violin, cello, and electric guitar. The second section will be primarily played by the piano and two percussionists. The third section will be primarily performed by three sopranos. I have chosen these grouping to achieve a relatively homogenous tone color in each section (although there is obviously variety in the degrees of homogeneity in tone color—the singers being more so, for example, than the winds and strings). Sometimes various instruments may leave their group to join another group or to perform in a secondary section.

Section I (flute, clarinet, bassoon, violin, cello, electric guitar) will focus on isorhythm. I will base all of the parts in this group on four taleae and four colores. There will also likely be taleae based on patterns of accents and dynamics. The taleae will also be permuted by various processes and may migrate among the five instruments.

Section II (piano, percussion) will focus on tempo curves. These tempo curves will be transcribed from click-tracks generated by a computer. The content of these instruments' parts will be single notes or short non-pitched gestures that accelerate or decelerate according to the tempo curves. Not all of the curves will be heard all the time, but they will fade in and out. Other instruments outside this group will be included as the gestures become more pitched. A single audio file will be created to be played along with this group to bolster the texture and to ensure precision with very small tempo variations.

Section III (singers) will be more focused on teleological motion from speech phonemes devoid of linguistic meaning toward clearly discernable, meaningful language. This motion will be imperceptibly slow and follow a complex system with multiple layers of change happening constantly. The text will finally be heard at the end of the composition as the song sung by Vladimir at the beginning of Act 2 of Waiting for Godot by Samuel Beckett. This song summarizes the themes of circularity, stasis, and deferred hope that pervade the play—a verbal analogy for the kind of music explored in this dissertation:

A dog came in the kitchen
And stole a crust of bread.
Then cook up with a ladle
And beat him till he was dead.

Then all the dogs came running
And dug the dog a tomb
And wrote upon the tombstone
For the eyes of dogs to come:

(repeat) A dog came in the kitchen, etc.

The overarching compositional idea governing all these sections is the notion that counterpoint happens on larger levels than traditionally understood by composers. This is merely an extension of the conceptual evolution of counterpoint during the past 100 years. Each of the sections described above will have an independent form that could serve a stand-alone piece of music. The setting of these multiple pieces against one another in counterpoint, however, conveys a different level of meaning to each section.

Overview of the critical essay

I have always thought of composition as being, at its heart, a balancing act between various simultaneously occurring materials. This original composition will be an exaggerated expression of that idea. The critical essay will trace the process of composing this work and analyze the final product, but will also examine the musical and extra-musical influences and precedents for the work. Among the formal and compositional themes influencing the original composition are notions of the Void, stasis, patterns, and non-linearity. Among the many influences for this piece I will focus on a few especially relevant ones: isorhythms and serial procedures in Morton Feldman's Why Patterns?; patterns in Jasper Johns's crosshatch works like Usuyuki; formal counterpoint in Samuel Beckett's Waiting for Godot; and The Void as perceived through a Sufist reading of the late works of Shakir Hassan Al Said.

Below is a proposed outline for the critical essay as well as a list of proposed resources.

Outline of the critical essay

Chapter I. Introduction

Chapter II. Patterns and Systems
    A. Historical precedents
        a. Serialism
        b. Minimalism
        c. Process music
    B. Patterns
        a. Analysis of Why Patterns and Usuyuki
        b. Analysis of the original composition, Section I (isorhythm)
    C. Algorithmic composition
        a. Analysis of the original composition, Section II (tempo curves)

Chapter III. The Void
    A. Notions of the Void
    B. Musical applications of the Void
        a. Negative space (Beethoven)
        b. Evocations of memory (Schubert)
        c. Inversion and other permutations (Webern)
        d. Defamiliarization and recontextualization (Wagner and Lachenmann)
    C. Semiotic networks
        a. How a thing might be emphasized or pointed to by its absence
        b. Sufist reading of Shakir Hassan Al Said's work
        c. Analysis of the original composition, Section III as a process that illuminates emerging signification

Chapter IV. Formal counterpoint
    A. Brief tracing of thought about conterpoint from Bach to Penderecki
    B. Juxtaposition and simultaneity
        a. The problem of non-linearity with respect to music as a temporal art
        b. Formal counterpoint in Beckett
    C. Counterpoint and memory
    D. Analysis of form in the original composition

Chapter V. Conclusion

On counterpoint

I'm almost finished with my dissertation proposal, and it seems fitting that certain themes are rising to the surface without any digging around for them. The concept that pervades the whole concept of this piece is counterpoint, specifically, what I am calling formal counterpoint. I'll post my proposal in a day or two, but this morning as I was working I suddenly had some clarity regarding counterpoint that I thought I should jot down.

Counterpoint is simply a re-contextualizing of material. It's not the same as permutation of material--although that is often crucial to counterpoint--it's taking the material from one situation and putting it into another. Bach placed fugue themes in different voices and different keys and even on different scale degrees within keys so that they would have different tonal functions.

Throughout my musical life I've been fascinated by counterpoint. I took lessons in 16th century and 18th century counterpoint from a mentor as an undergrad. I never felt like I really got it, but it is a pretty dated set of rules (I mean I don't feel like I've internalized the way contemporary composers would have). Since then I've come to realize that it's not the rules of any specific model of counterpoint, but it's the abstract notion of music set against music in some kind of conceptual space. I figured that out in David Sargent's seminar on 20th century counterpoint where we studied, among others, dynamics counterpoint in Ruth Crawford Seeger's string quartet and textural counterpoint in Penderecki's Threnody.

I recently heard a lecture by the composer William Kleinsasser who took the abstraction a bit farther. He talked about pieces being in counterpoint with the memory of other pieces. For him it was kind of a mode of influence. In other words, when he composes he sees the current project as having a contrapuntal relationship with earlier pieces that he has written.

When I heard Kleinsasser's lecture I felt like he hit on something I had been thinking alot about lately--counterpoint between pieces (or between formal sections--formal counterpoint). Except in my concept, the pieces are literally existing and being heard simultaneously. In a sense it's like hearing a fugue answer and countersubject played simultaneously. Both are fully formed, legitimate melodies, but it's in the counterpoint between them that the real musical interest lies. If the melodies move to other places (keys, registers, tonal function, etc.), that is if the composer re-contextualizes the melodies, then the space between also changes. In other words counterpoint focuses on the space between and through various contrapuntal techniques, the composer can manipulate that space.

A couple of tangential ideas:

By placing the "real musical interest" in the space between the two melodies, it also point to a breakdown in the subject-object binary, something I'm also very interested in.

I will need to look at Lachenmann again now. He has been my primary example of re-contextualizing, though I haven't considered his music in terms of counterpoint. If counterpoint is simply a re-contextualizing of music, then his music is likely in counterpoint with something, albeit possibly an unheard something--memory? tradition?


©2017 Joshua Harris