Sunken Monadnock

Shepard tones

I've been struggling for a couple of weeks to decide how to end of this piece. I finally took a "just compose" course and started writing out notes. Soon I realized I was doing something like Shepard tones, so I thought, "Maybe I'll do this for awhile and then end it." Then I went through everything I had written up to this point and timed it. The passage shown below corresponds approximately to the jagged, angular section in the sopranos, beginning around 13:30. It ends about 15:30, but is just beginning to pick up some momentum at that point (haven't filled in everything yet in this picture). I began to realize that this could be the way I build to the end. It's a simple way to gradually layer repeated figures to thicken the texture. The timing is almost perfect. But the best thing about the Shepard tone* is its representation of circularity. Considering the selection of the text with its circular form, and that it will become intelligible as language during this passage, I think this is a bit of serendipity to have happened on the Shepherd tone.

Shepherd.jpeg

*) Of course this isn't a real Shepard tone, but it is a stylized approximation similar to the one found in Ligeti's etude "The Devil's Staircase."

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?


Improvisation and beginnings

I've been playing with the free improvisation group Impulse on Saturdays for the past few months. I'd seen them play many times over the past few years, and I even created a computer program to improvise along with them in 2010, but playing piano with the group has been challenging and rewarding. They haven't had a piano in the past, so it's been interesting figuring out how that instrument fits in with their aesthetic (it's more percussive, less sustaining, and has a much greater range on the low end than the other instruments in the group). The reward for me personally is learning to trust my ear and also to listen to what's happening without trying too hard to force something. I'm hearing incredible sounds and textures that I wouldn't have discovered through my typical compositional processes. I keep catching myself being distracted from the moment, thinking how I can use this sound or that sound in my next piece.

The week before Thanksgiving we had a particularly interesting jam. At one point I was playing fast, steady, chromatic pitches within a one-octave span in the lower third of the keyboard. It was like a broken cluster, but only two notes at a time (one with hand), no patterns, and very rhythmic (regular durations but irregular accents). That evening I decided that's how to begin this dissertation piece.

The idea was hanging suspended in the middle-back of my mind, a bit uneasily because I was thinking of it as a kind of unrelated introduction that would give way to the actual piece. Tonight I finally realized how to make it part of the concept of the piece. The largest of the three sections will be the strings/winds section (joined from time to time by the percussion/piano/guitar group) which, later in the piece, will become engulfed in various circular isorhythms operating independently from one another. But I've always envisioned a very rhythmic and energetic opening that slowly gives way to a more Feldman-like texture. The energy of the "broken cluster" figure will drive the opening section. Occasionally the piano (which will be joined by the electric guitar and percussion here) will suddenly stop, and in the silence, the strings and winds will sustain the cluster's resonance, albeit with different colors. These sustained resonances will have jagged endings, followed by a return of the broken cluster. The rhythmic sections will gradually, and generally, get shorter while the resonances will get longer (although this will likely happen, as always, via a curve that will allow for regression from time to time). As they get longer, they will also begin to accentuate subset harmonies of the cluster resonance (like the held keys in "Filter-Schaukel" from Lachenmann's Ein Kinderspiel). Eventually (after four or five minutes), the rhythmic material will go away and isorhythms will begin to replace the cluster resonances. The textures and harmonies of the interactions of these isorhythmic parts will generate the form of the rest of this (the largest) section of the piece.

The first of the forms

I've been continuing with the vocal parts that enter around 6:00. The previous post explains the order of syllables in each soprano part. I began by writing out the first iteration of the text (i.e. the first column on each spreadsheet above).

First iteration of text in three soprano parts. NB: the notes are

placeholders, not actual pitches yet. Rhythms are precise, however.

I clocked it at about one minute, and then realized that it could take up to 18 minutes to get through each iteration of text if I maintained that pace. That's longer than I had planned, so I began to look more closely at pacing. Eighteen minutes of a linearly progressing pattern is not what I had in mind for this piece (I want to avoid the perception of process music--that's too big an issue to discuss here, though).

The image below shows my notes scribbled along the top of the 1st and 2nd soprano spreadsheets. First, I broke up the part: there's a break between iterations 7 and 8 (big check), and another between 14 and 15 ("railroad tracks"). Iterations 13 and 14 have the letters O and K, which indicate only vowels (O, open) or only consonants (K). I mean "only consonants" literally--just aspirated consonant sounds. The final four iterations contains the culmination of the process that reveals the text as having linguistic meaning.

I feel like this gives the process some shape. It is still goal oriented, but the movement toward the goal is nuanced--sometimes moving linearly, sometimes faster or slower, sometimes hesitating, etc. This is what form does--it gets you from the beginning to the end. Now the vocal parts have an independent, fully operating form, even though in the finished piece these parts will constitute only a portion of the form.

More on the composing out of the vocal parts

Below are the next iterations of the soprano 1 and 2 parts, the text simply written, not notated. Now consonants are coming into the mix. Soprano 1 begins to add consonants to the beginnings of certain syllables while soprano 2 begins to add consonants to the end of certain syllables. The intended effect is that of composite syllables becoming intelligible to the listener. The soprano 3 part will join the other two parts in a similar way--French nonsense and English nonsense being equal after all.

More on the text later...

Distributions

I've noticed that in the past few years I've come to rely more and more on generative systems or algorithms--various devices that output specific pitches and rhythms. It's not that I don't have musical ideas spontaneously arising in my mind, it's that those ideas are usually textural, not thematic. In other words I hears sounds and shapes more often than specific melodies. Dictating a texture directly from the brain has proven a complicated challenge for me, so I've developed intermediary techniques. This is the story of the system I composed on Friday to get the right texture from the vocalists in my dissertation.

I chose the text from Samuel Beckett's

Waiting for Godot

. At the beginning of the second act Vladimir sings a short recursive song that could loop indefinitely. I see this song as a microcosm for the entire play, and think it represents the aesthetic of my dissertation piece quite nicely. Here is the text in French (the original language of the play) and in English (the playwright's native language) from Beckett's translation.

Un chien vint dans l'office
Et prit une andouillette.
Alors à coups de louche
Le chef le mit en miettes.
Les autres chiens ce voyant
Vite vite l'ensevelirent
Au pied d'une croix en bois blanc
Où le passant pouvait lire:
Un chien vint dans l'office
Et prit une andouillette...etc.
A dog came in the kitchen
And stole a piece of bread
And cook up with a ladle
And beat him until he was dead.
Then all the dogs came running
And dug the dog a tomb
And wrote upon the tombstone
For the ages of dogs to come:
A dog came in the kitchen
And stole a piece of bread...etc.

I knew I wanted this text to evolve in a specific way: beginning as vowels, gradually changing to non-sense phonemes, and finally becoming clearly understood as language at the very end of the piece. This process will probably begin around five minutes into the piece and take around 10 minutes or so to work itself out. The trick was to find a logical process by which the text could gradually evolve over that period of time.

I started with the text, then broke it down into syllables. Here's the 56 syllables in the English version:

ə dɒg kem ɪn ðə kɪt tʃən

ænd stol ə pis əv brɛd

ðɛn kʊk əp wɪθ ə le dəl

ænd bit hɪm ən tɪl hi wəz dɛd

ðɛn ɒl ðə dɑgz kem rən nɪŋ

ænd dəg ðə dɒg ə tum

ænd rot ə pɑn ðə tum ston

fɔr ðə edʒ əz əv dɒgz tu kəm

I had to manipulate the French text a little bit to get 56 syllables:

œ᷉ ʃjɛ᷉ vɛ᷉ dɑ᷉ lɔ fis

e pʁi yn ɑ᷉ du ɪ jɛt

a lɔʀ a ku də luʃ

lə ʃɛf lə mi ɑ᷉ mjɛt

le zo tʀ ʃjɛ᷉ sə vwa jɑ᷉

vi tə lɑ᷉ sɛ vɛ li ʀɑ᷉

o pi je dyn kʀwa zɑ᷉ bwa blɑ᷉

u lə pa sɑ᷉ pu vɛ li ʀ

So with each text now divided into 56 syllables and each one labelled 1-56, I could use numbers to effect an even distribution of changes over several iterations of text. I used a random sequence generator to create a the order of syllable for the first iteration of text. I created a different initial sequence for each of three soprano parts. The first two sopranos will sing "toward" the English text and the third sopranos will sing "toward" the French text. Here are the basic distributions for the first two sopranos:

Soprano 1
Soprano 1

Soprano 1

Soprano 2

In the charts above each column represents one sequence of syllables. The first column on the left contains the first

random

 sequence and the last column on the right contains the syllables in original,

text

, sequence. The changes found in each iteration of the text (i.e. each column, top to bottom) are shown, otherwise, the empty squares mean nothing has changed at that position in that sequence. I left most squares empty so that the changes will stand out.

The pattern of changes is mirrored between the two English parts above. In the first, two "correct" syllables enter the sequence on each iteration, beginning at the middle first, then expanding outward. In the second, "correct" syllables enter the sequence at the beginning and ending first, continuing toward the middle. I opted not to move directly from center to ends and

vice versa

 because I felt that with 26 sequences intelligible text patterns would become apparent too early. In other words, if the soprano 1 began to make sense with a string of intelligible words by the third or fourth iteration, that string would simply get longer each time via a simple additive process that would get extremely boring. By reiterating the pattern four times nothing becomes intelligible as language until the final few iterations. There are persistent gaps in the middle.

Soprano 3

For the French text in the third soprano part I doubled up on changes and combined both patterns shown above.

I liked the pacing of this part and began to wonder how to deal with the difference with the pacing in the other two parts. They take 26 iterations to arrive at the original text, while this one only takes 16 (there are some minor errors in the Soprano 3 chart). Since these parts will probably be proportionally notated I didn't need to figure out how to fit 16 into 26--I could just pace it more intuitively.

But then I started wondering if there was a way to speed up the pacing of the other two parts. I have used this method of reiteration with small changes in the past. The third movement of

Septimus

 for string quartet is basically one 10-bar melody that takes 17 iterations to moves from 10 bars of one single pitch to the "original" 10-bar melody at the very end. I like this idea of revealing the original idea at the end. There are pitfalls, the biggest of which is pacing--it can be boring without tweaking along the way. The other major pitfall is creating a sense of linearity. In other words, the sense that the music is progressing directly along a straight path. Without getting into more detail, it's the difference between a straight line and a curve. The music should move along a curve, not a straight line. Straight lines arise from one-to-one relationships. I try to build more complexity into my systems so the outcome doesn't feel too predictable.

So, here are the revisions I made to the first two soprano parts. I've overlapped the iterations of the patterns. I think this will improving on the steady (plodding) pacing and shortening the process and also by increasing the number of changes in each iteration.

Soprano 1, revised

Soprano 2, revised

The process at this point is simply filling in the empty squares with whatever is left of the empty square:

Soprano 1, mid-process

Soprano 1, complete

Soprano 2, mid-process

Soprano 2, complete

Soprano 3, mid- process

Soprano 3, complete

Finally, I used find and replace in Excel to fill in all the syllables in International Phonetic Alphabet symbols.

Footnote--I will begin with vowels alone and gradually add consonants in the piece.

The sunken monadnock

Two weeks ago I didn't know what a monadnock was and now I'm thinking of using it as a guiding principle, if not the title, of my dissertation. In an epic coincidence of web browsing I happened upon something that could generate the music I'm going to compose. It all started when a high school friend posted an article from ESPN on Facebook, which links to City Prints Map Art, a company that makes monochromatic prints of maps with streets like look like veins. Here's a map of Appalachian State University (my undergrad alma mater):

I love minimalist monolithic art (is that a thing?) and I love maps. Add school colors and I would gladly drop $180 to buy this (my wife said no). When I shared this company's website on FB, I got a comment from a Texas friend who shared the online map archive at UT-Austin. After a few hours I got around to looking at the archive and realized they had historical maps from every state, so I clicked on North Carolina, and then found a more complete NC historical map archive and started looking at places I've lived and visited.

It was surreal to see what was missing one hundred years ago. Some towns weren't there. Many roads were dirt. I spent awhile looking at Watuaga County, where I've spent a lot of time over the past 16 years. I was fascinated that highway 194 was the main road from Boone to Avery County, not 105 as it today. Accordingly, the towns along 194 seemed more important on that map. 105 wasn't there, but a dirt road went as far as Shull's Mill. Shull's Mill is no more than a crossroads today, but on that map from the early twentieth century it was so important that, along with Boone, it was featured with an inset street map. One map of Charlotte pointed the way to Blowing Rock, though a dozen larger towns dot the highway to Blowing Rock today.

I spent several hours looking at these maps, becoming engrossed in how much I could tell about what life might have been like from them. At some point I was looking at western Watauga County, noticing that the road today still follows the same path out toward Watauga Lake. Except Watauga Lake wasn't there. I looked it up on Wikipedia and discovered that when the TVA dammed the Watauga River, they flooded the town of Butler, Tennessee. Suddenly images of a sunken town flooded my mind, as did memories of O, Brother Where Art Thouand my wife's phobia of dead bodies in large bodies of water (they got there, she claims, because old graveyards lie at the bottom of lakes). I ordered a book on the history of Butler because it was so intriguing.

That reminded me of some online browsing I had done recently on the geology of Pilot Mountain, a peculiar monadnock I saw every day as a child in my hometown of Pilot Mountain, NC. A monadnock, I learned, is a mountain that rises suddenly and in isolation on a relatively flat plain. Here is the picture (of Pilot Mountain, coincidentally) on the Wikipedia entry:

After several days these two ideas, the sunken town and the monadnock, started to interact with each other in my mind. I began to see a relationship: Both were connected by the flatness of their environments--the surface of the lake and the plain surrounding the mountain. Both deviated from their surroundings in some way--one rising above and one sinking below. The one jutting up, in view for miles and miles, the other completely hidden from view despite the people driving boats and skiing directly above it.

I really liked the inversional, yin-and-yang relationship between these two things and began to think of how this relationship might be abstracted musically. The more I thought about the sunken town, the monadnock, and music the more I started see this in my mind:

Which is an abstraction of this:

Which is a sound wave.

See. Everything has a musical application.

So the title of this blog is a conflation of the two in a way that makes syntactical sense, though semantically it's paradoxical. More on the musical development of this concept next time.

©2017 Joshua Harris