The "Paradoxical Complexity" of Sound Masses

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Written By Jason Noble

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My title, Simplicity out of Complexity out of Simplicity, names a compositional goal that I admire. Beginning with simple elements of sound, composers can use their expertise to craft compositional systems that may be enormously complex and far beyond the comprehension of most listeners. But by the end, I think it is a magical thing if it comes around to become perceptually simple again: a musical organism with processes, gestures, and gestalts that are readily appreciated and comprehended even by listeners who do not know anything about the underlying system. This was my goal in the piece I am presenting today, fantaisie harmonique for guitar double-orchestra; you may judge whether or not I succeeded. What you see in this figures is a page of the score, which many people have told me looks complex and even intimidating. The process of composing it was certainly very complex and demanding for me. But as I hope to show, the materials from which the piece is constructed are relatively simple, and the musical effects perceived by the listener may be relatively simple as well. 

Module Outline

Part 1

Theoretical Background: Complexity and Simplicity

Complexity and simplicity are the kinds of terms I find the most problematic in scholarship: words that everyone knows and uses in many contexts on a regular basis. It is much more difficult to define terms like these precisely, because they come with all the baggage of everyday connotations. They are also highly polysemic terms, with many different shades of meaning that vary depending on context. To attempt to provide definitions of complexity and simplicity that will hold for all relevant musical situations seems doomed to failure. I will instead look at a number of relevant examples of these concepts in music history and scholarship, and then discuss them in relation to my own work. In taking this approach, I assume that everybody has an intuitive understanding of what complexity and simplicity are, accepting the high degree of subjectivity and probable differences of interpretation. But I believe that as with many other big concepts, including music itself, the absence of a universally accepted definition should not stop us from diving in.

Complexity in polyphony

The first specific instance of musical complexity I would like to mention is polyphony. As a general rule, polyphony is more complex than other textures such as monophony or homophony because of its multiplicity of concurrent parts and their contrapuntal independence. Polyphonic complexity has traditionally been an esteemed musical value, identified with the “learned style” or “high style,” and with superlative associations such as elevation, sublimity, sophistication, prestige, and so forth. Counterpoint has long been a foundational component of Western music education, and great admiration is afforded to historical composers such as Palestrina and Bach who mastered the complexities of contrapuntal writing. The individual musical lines are not necessarily very complex in and of themselves in polyphonic music: indeed, simplicity of lines can be seen as a virtue, as it can help the performers to execute them reliably and the audience to follow them. But the virtuosic craftsmanship involved in combining simple lines into complex textures has long been a high value in Western musical practice and scholarship. This is a prime example of what I mean by complexity built out of simplicity.

Perceptual Limits of Polyphonic Complexity

But musical textures cannot be infinitely complex: there are limits to the degree of musical complexity that listeners are able to parse and appreciate, beginning with the sheer number of contrapuntal lines. Although there are many fugues nominally with four, five, six, or more voices, that does not mean that all of these voices are active at any given time: there are moments when some voices drop out, or function with attenuated rhythmic activity such as pedal tones, or divide a single line between two voices in a hocket-style pattern, and so forth.  As music psychologist David Huron notes, “Listeners do not have an unbounded capacity to track multiple concurrent lines of sound.” In a perceptual study, he found that even expert listeners are much more likely to make tracking errors and to underestimate the number of voices present when there are more than three. He also found, in a corpus analysis of the contrapuntal works of Bach, that most pieces gravitate towards three active voices at any given time, regardless of the nominal number of voices in the work. Huron interprets these findings to support a general “un, deux, trois, beaucoup” pattern in perception, and uses this to derive a Principle of Limited Density: 

“If a composer intends to write music in which independent parts are easily distinguished, then the number of concurrent voices or parts ought to be kept to three or fewer.”

 

“Listeners do not have an unbounded capacity to track multiple concurrent lines of sound” (David Huron, 2001, “Tone and Voice: A Derivation of the Rules of Voice-Leading from Perceptual Principles”)

 

Huron also draws on many studies in music perception to ground the canonical rules of voice leading in tonal and modal counterpoint, such as preference for steps and common tones over leaps, avoiding part crossing, avoiding parallel perfect fifths and octaves, and so forth, demonstrating that these rules allow listeners to follow independent lines.  

Complexity in Serialism

Those rules, of course, were rejected by many composers of the twentieth century, notably in the practice of serialism, which is the next example of musical complexity I will mention. Many serial composers maintained respect for the value of polyphonic complexity in their music, developing ever-more elaborate contrapuntal constructions in their works while also writing more complex individual lines full of disjunct leaps, part crossing, unrestrained use of dissonance,, and other such deviations from the practices of the past. All of this led to the well-known criticism that the complexity of this music exceeds the aural comprehension of most listeners. This critique was succinctly stated by composer Iannis Xenakis:

“Linear polyphony destroys itself by its very complexity; what one hears is really nothing but a mass of notes in various registers. The enormous complexity prevents the audience from following the intertwining of the lines and has as its macroscopic effect an irrational and fortuitous dispersion of sounds over the whole extent of the sonic spectrum. There is consequently a contradiction between the polyphonic linear system and the heard result, which is surface or mass.” (Iannis Xenakis, 1955/1971, Formalized Music)

Responses to Serial Complexity

Descendants of the serial tradition responded to the contradiction Xenakis names in several ways.

Some composers, notably in the Minimalist tradition, rejected excessive complexity and embraced an intentionally simplified musical vocabulary.

Some composers, notably in the New Complexity tradition, embraced excessive complexity as an aesthetic ethos, pushing the limits of musical notation and performance practice.

And some composers, notably in the Sound Mass tradition, exploited the contradiction itself, composing massed sonorities that deliberately overwhelm the listener’s perceptual analysis, turning attention away from the individual events or lines and onto the mass itself, which suddenly appears as a simple sonic entity.

That is to say, a simple perception emerges out of a complex musical texture that itself emerged out of simple musical lines: simplicity out of complexity out of simplicity.

Paradoxical Complexity

This is an instance of what composer and musicologist Lasse Thoresen calls “paradoxical complexity”:

“we now find a category in which the very complex and the very simple meet in a paradoxical, ambivalent union. We shall call this form-element paradoxical complexity—a specific case of the classical coincidentia oppositorum, the unity of opposites. It applies to objects with myriad details, but with a perceptually simple overall character.” (Lasse Thoresen, and Andreas Hedman, 2015, Emergent Musical Forms)

Composers have achieved this effect of self-canceling complexity resulting in perceptual simplicity in many ways.

 

(Lasse Thoresen, and Andreas Hedman, 2015, Emergent Musical Forms)

 

I detail some of them in my paper “Sound Mass, Auditory Perception, and ‘Post-Tone’ Music,” with reference to the perceptual principles listed by David Huron which I mentioned earlier. Most obviously, the Principle of Limited Density, which states that listeners are most likely to follow contrapuntal lines if there are three or fewer active at a time, can be overwhelmed by adding more voices, in some cases many more. This was demonstrated forcefully in compositions in the 1950s and 1960s such as Metastaseis and Pithoprakta by Xenakis, Atmosphères and Lontano by György Ligeti, and Polymorphia and Threnody to the Victims of Hiroshima by Krzysztof Penderecki. In these pieces, the orchestra is divided into dozens of lines, sometimes with each individual string instrument given a separate part, vastly exceeding the listener’s ability to follow them as individual voices. As I detail in my paper, there are many other ways sound mass assimilation has been affected by composers, including exploiting registral extremes where our sensitivity to pitch is less precise, voicing chords so closely that auditory masking makes individual notes difficult or impossible to hear out, using semblant or otherwise coherent motion to cause the parts to group into a single gestalt, and so forth.

Sound Mass and Metaphor

Sound mass composers describe their aims through many vivid and evocative metaphors: clouds, galaxies, the edifice of a cathedral viewed from afar, with many details that are not visible from that distance but that nevertheless contribute to the overall impression of the whole. One particularly beautiful analogy drawn by György Ligeti is the way simple colours in perception are the product of complex molecular structures:      

“I can perhaps make this clearer through a comparison with painting...the effect of each colour is the result of the chemical combination of certain dyes. As far as the picture itself is concerned, the chemical composition of the dye is of no immediate relevance...the effect ‘white’ is produced by a certain arrangement of lead and oxygen atoms or of zinc and oxygen atoms, but in regard to the picture it is only the effect ‘white’ that is significant, not the question whether the dye contains atoms of zinc or lead. In place of zinc and lead atoms one could speak of crystal lattices, electron orbits, light absorption, and so on—each plane has another plane beneath it—but I am painting directly with white and only indirectly with crystal lattices.” (György Ligeti, 1983, Ligeti in Conversation).

 

György Ligeti, excerpt from Atmosphères (1961)

 

Empirical Research: Fusion, Density, Complexity, Homogeneity

Several years ago in the Music Perception and Cognition Lab at McGill University, I conducted a perceptual experiment to explore how metaphors work in sound mass music, under the supervision of Stephen McAdams. The experiment aimed to provide a better understanding of sound mass perception, and the semantic associations listeners may have with sound masses. Listeners heard 40 short excerpts of contemporary music, and rated them on about two dozen semantic scales. Four of those scales are Fusion, Density, Complexity, and Homogeneity, which were chosen because the terms come up often in published literature on sound mass. So listeners heard excerpts of music, and had to rate how fused they felt the excerpt was, how dense it was, and so forth. They were instructed to consider Fusion to be synonymous with sound mass. Based on the way the terms Density, Complexity, and Homogeneity are used in the literature, I expected all three to correlate strongly with fusion, as all three are described by many authors as conditions of sound mass perception. But to our surprise, while Homogeneity and Density correlated positively with sound mass Fusion, Complexity showed a strong negative correlation with sound mass Fusion, meaning that the more complex listeners found an excerpt to be, the less fused they found it to be. This was the first discovery in my research that led me to consider the paradox described by Thoresen, the contradiction between acoustical and perceptual complexity. It led me to offer the following definition of sound mass: 

Defining Sound Mass

Sound Mass: A perceptually homogeneous and dense auditory unit integrating multiple sound events or components while retaining an impression of multiplicity. Although their acoustical correlates may be highly complex, sound masses are perceptually simple because they resist perceptual segregation in one or more parameters (e.g., pitch, rhythm, timbre).

I’ve taken some time to explain this theoretical background, because these ideas have influenced me greatly as a composer. I think this will become obvious in the main piece I will be presenting in Part 3, fantaisie harmonique for two guitar orchestras. But before we get there, I would like to share with you my first composition for guitar, Shadow Prism, because many of the ideas in fantaisie harmonique grow directly out of it. Part 2 begins with a score-following video of it, which runs just under 6 minutes long.

Part 2

Shadow Prism

Shadow Prism was my first piece for guitar, and at the time I had very limited experience with the instrument. I could play some basic chords, and that was about it. I felt like I barely knew what I was doing when I was composing it, but to my surprise it has become one of my most successful pieces. The score is now published by les Productions d’Oz, recordings appear on two albums by different guitarists, and it has been performed dozens of times by many different guitarists around the world. I owe a lot of gratitude for this success to Steve Cowan, for whom the piece was composed, and who championed it many times in concerts and around the classical guitar world.

 
 

The guitar can be an intimidating instrument for non-guitarist composers. It is a polyphonic instrument, but visualizing how polyphonic patterns will work can be quite difficult. Most notes exist in multiple positions, and non-guitarist composers have no reliable way to visualize the fingerings and physical movements required to execute them. So in composing Shadow Prism, I decided to focus on natural harmonics, both because I love the sound of them and because they present a way to avoid these challenges of visualizing fingering. The left hand need only touch the node at the moment of attack, and is instantly freed to move to the next position, unlike fretted pitches in which the string must be depressed for the full duration of the note. I also decided to give the player some freedom in terms of timing, note sequences, and so forth, in the hopes of avoiding unintentionally writing music that is excessively awkward, difficult, or unpleasant to perform.

Tuning System in Shadow Prism

The piece uses only natural harmonics and open strings. To make things more interesting, I devised a new tuning system that combines elements of equal temperament and just intonation. I lowered three of the strings by a semitone, so that instead of E-A-D-G-B-E, it would be Eb-A-C#-G-Bb-E. This tuning gives a combination of an Eb major triad and an A major triad, which is a transposition of the Petruschka chord. I further made each of these triads just-intoned by instructing the guitarist to tune the third strings (G and C#) to the fifth harmonics of the root strings (Eb and A). Accordingly, the G and C# strings, and all of their natural harmonics, are lowered slightly with respect to equal temperament, resulting in a microtonal tuning system grounded in triadic harmony but based on a nonfunctional tritone relation between fundamentals. I charted this system out by writing out the first seven partials for each string, and then grouping the partials that approximately corresponded with each equal-tempered pitch class. From there I planned out the scales and harmonic structures that make up the piece.

 

The piece uses only natural harmonics and open strings.

 

Geometrical notation in Shadow Prism

In much of the piece, I thought of the harmonic structures not as precise series of notes but as global fields with the order and density of events left to the free choice of the performer. The approach is comparable to granular synthesis.

For example, in this image of a spectrograph from Barry Truax’s Riverrun, the distribution of grains follows a readily apparent geometrical plan over the course of the piece, but the grains themselves are distributed with stochastic procedures rather than being individually specified by the composer. The effect is also comparable to things like windchimes and Aeolian bells, and to naturally occurring sound masses like flocks of birds and rustling leaves. There is a certain charm in the freedom and spontaneity that such systems exhibit: in some ways they are closely controlled and predictable, but in other ways there is subtle variation and potential for new discovery on every encounter. Many composers have called for such effects by writing a set of elements on a normal staff and providing the instruction.

 

Spectrograph from Barry Truax’s Riverrun

 

I have adopted a flowchart-like geometrical notation that presents more explicitly the many pathways between a given set of elements without prioritizing any particular orderings. Here is the opening system of Shadow Prism, which begins with a network of two nodes, then expands to three, then four, then five, with pacing left to the free choice of the performer. The bottom staff indicates playing position and the top staff indicates sounding pitch. The only rule in terms of event order is that any two consecutive harmonics must be played on different strings, in order to maximize resonance. This is why some arrows between nodes are missing: those nodes contain harmonics on the same string

 

The opening system of Shadow Prism

 

Later in the piece, this concept is expanded to include networks of networks, recursively expanding the piece’s nonlinear organization. Additionally, feathered beam symbols are provided to indicate accel, decel, accel-decel, or decel-accel rhythmic contours. Geometrical networks are interspersed with more conventionally notated sections, whose event order is specified. I’ve loved hearing different guitarists interpret this piece: there really are striking individual differences, even as it remains unmistakeably the same piece.

 

Networks of networks

 

Part 3

fantaisie harmonique

Several years later, and after composing much more for the guitar, I was commissioned to compose a piece for an orchestra of classical guitars and an orchestra of electric guitars, which would be premiered at a conference in Ottawa called “The 21st Century Guitar.” The concert was in a church with a dome roof, and featured 3D projection art by German light artist Kurt Laurenz Theinert, which you see in the image at the top of the page. The orchestras were assembled from conference attendees and community members. The premiere was a success, but due to limited rehearsal time, many nuances and details in the score were not fully realized in the performance. Steve Cowan expressed interest in doing a one-man orchestra multitrack recording of the piece, which we produced over the last few months, and which we will show publicly for the first time at the end of this presentation.

Our Team

We received funding from the ACTOR Strategic Project Fund to create this recording, so we were able to hire recording engineer Denis Martin and recording assistants Nick Pelletier and Will Sylvain to produce a recording in 3D audio. We were also able to hire Kurt Laurenz Theinert to adapt his projection art from the premiere into a video and, eventually, a virtual reality experience, and Simon Rouhier, a member of the Université de Montréal community, to do additional work on animation and visuals. Our collaborators overseeing the project are Caroline Traube at Université de Montréal, and Martha de Francisco at McGill University. We currently have a 2D video with a stereo mix of the recording; future deliverables will include 3D renderings, a virtual reality experience, an installation version, and a concert version for live performance. Before I show the video, I will discuss several aspects of the composition that I hope will demonstrate the idea of simplicity out of complexity out of simplicity: its tuning system, its notation, its perceptually-grounded orchestration, and its spatialization-as-orchestration.

I. Instrument-Specific Tuning System

 
 

By instrument-specific, I mean that this tuning system is meant to work idiomatically for the guitar, and is not necessarily transferable to other instruments. It may be possible for other instruments to produce all of the same pitches, but the system is designed as a complex scordatura for six-stringed instruments with the standard tuning of the guitar, and realizes the pitches with the open strings and natural harmonics available within that scordatura. Additionally, the timbre of the guitar’s natural harmonics is at the heart of the concept of both the tuning system and the composition. It would therefore be very difficult or impossible to reorchestrate this piece for any other ensemble without changing the tuning system, and therefore reconceptualizing the piece.

I had been encouraged by the results of Shadow Prism, and by the response it had received, and wondered if I could expand the concept to orchestral proportions. Recall that its scordatura retuned the strings to a just-intoned Eb major and a just-intoned A major triad. I wondered if it would be possible to devise a tuning system that would cover all twelve major triads in a similar way, by dividing the orchestra into six groups with the open strings of each group covering two triads.

I worked out the tuning system shown in this table, which achieves that goal while keeping the amount any strings are retuned as limited as possible. I ran all of these tunings by Steve to make sure they would be OK for the guitar. The biggest retunings are a minor third down in Group 1 low E string and the Group 5 D string; all others are within a tone of standard tuning, and usually lowered rather than raised to avoid placing excessive tension on the instrument. All triads are in root position, in that the root of the chord is always the lowest-sounding string. The arrows in parentheses indicate third strings, which are just-intoned to the roots as in Shadow Prism. An interesting result of this system is that no two groups have exactly the same tuning for any string.

 
 

Whereas Shadow Prism used harmonics up to the seventh, I decided to limit the palette in fantaisie harmonique to the first five partials (the open string and the first four natural harmonics), which are the easiest and most reliable to produce. This resulted in a total collection of 30 pitches per group, or 180 pitches altogether, and 60 single-position major triads (i.e., a triad that can be produced by one guitar group with partials of the same harmonic rank on three strings). This system is vastly larger than the one from Shadow Prism and it was too much to work with by hand, so I did something I never imagined I would do and used a Microsoft Excel spreadsheet as a compositional tool. This allowed me to order them all as a continuous scale, or to group all of the ones with the same pitch class, or to sort them by harmonic rank, and so forth, which was very useful.

Melodic Hocket

For example, there is an extended hocketing section in which smooth, microtonal melodic lines are divided between the guitars. This was much easier to do with a spreadsheet than it would have been to go hunting for the pitches “by hand.” To make the overall organization clear in the score, I put a pitch reduction on the top staff, which is reproduced in all of the parts so that both the conductor and the performers can see clearly how all the parts fit together.

 
 

Triadic Hocket

In an earlier part of the same section, a similar passage is constructed using single-position triads. Various other pitch constructions are used throughout the piece, including microtonal saturation over an octave span, various polychordal combinations, a “thickening” of E major to include all tones plus or minus a semitone of each of its chord members, and so forth. In such a rich tuning system, there is no way that a single piece could exhaust all of the interesting possibilities. I felt that the best I could hope to do was to choose a few ideas to work with, and explore their potential to the best of my ability, but I found it humbling to consider how many more possibilities there are within this system that I have not even imagined.

 
 

II. Nonlinear Notation

 
 

The main ideas of nonlinear notation in fantaisie harmonique were already discussed in relation to Shadow Prism, with a few small differences. 

I realized that rather than having the performer be on the lookout for missing arrows between nodes, it is more economical to group all the harmonics on a single string within the same node, so that the performer can choose one before moving to the next. In the example in this figure, there are five nodes representing five of the six strings, and each node has between one and four harmonics from which to choose. Once the performer gets used to the appearance of this notation, I believe it is easier to read than some of the larger polygons in Shadow Prism. 

A key difference between the two pieces is that with many more instruments, I had the option of multiple simultaneous types of temporal organization. So the unordered geometrical networks in some voices are superimposed on ordered repeat cells in others, as you see in the page of the score below. 

Metrical vs. Ametrical

Additionally, in some sections of the piece, synchronized, metrical patterns in one orchestra are offset against ametrical material in the other. The original plan in the premiere was to have two conductors; I emulated this in the click track we used for the recording by including a beat pattern only where needed for metrical synchronization, and just including duration markers otherwise.

III. Perceptually Grounded Orchestration

 
 

The third aspect of the piece I would like to mention is perceptually grounded orchestration, which requires a little explanation. Stephen McAdams and his colleagues in the ACTOR project are doing a great deal of work on the multidisciplinary study of orchestration, which has traditionally been an underrepresented area of music scholarship. One particular focus is developing a theory of orchestration, which does not really exist at the moment in any way comparable to theories of harmony and pitch structure, for example. To be sure, there are many orchestration guides and treatises, but these usually consist of series of examples from the canonical repertoire, and recipe-like instructions for the kinds of instrumental combinations that work well. McAdams wants to bring orchestration scholarship to the next level by categorizing such combinations with a taxonomy of orchestral effects that describes their perceptual results. 

The diagram you see on this slide summarizes this taxonomy in three hierarchical tiers: simultaneity, which describes how concurrent timbres combine or separate in the formation of musical events, sequentiality, which describes how events combine or separate in the formation of musical streams or layers, and segmentation, which describes how streams or layers combine or separate in the formation of larger-scale musical units such as phrases or sections. McAdams and his team have catalogued many examples of all of these effects from the orchestral repertoire, but to date this has mostly focused on the symphony orchestra with its heterogeneous combination of instruments. But as I hope to demonstrate here, the same principles are operative in orchestration for homogeneous ensembles such as guitar orchestras. I consciously applied them in composing this piece, and they are a very useful aid in naming the simple perceptual outcome of a complex compositional process. I’ll demonstrate with a fairly detailed discussion of perceptually grounded orchestral effects in the opening section of the piece, and briefly mention a few other examples from later.

Blend

One concurrent effect that I expect everybody is familiar with is blend, in which different sound sources fuse into a more or less unified auditory event. McAdams’ taxonomy differentiates between timbral augmentation, in which there is one dominant timbre that is embellished, highlighted, or reinforced by one or more other sound sources, and timbral emergence, in which there is no one dominant timbre but a new timbre emerges from the fusion of more than one sound source. An example of timbral emergence is found early in fantaisie harmonique, in the orchestra of electric guitars. The notes are all synchronized but have niente attacks, followed by hairpin dynamics. As more and more notes are added in the different groups, the harmony thickens, and a new, transforming timbre emerges. 

 
 

Surface Texture Integration

At the same time, the classical guitar orchestra has unordered aleatoric patterns of the same notes as the corresponding groups in the electric guitars. Because these notes are not synchronized, they do not blend as such, but rather are integrated into a texture that becomes richer and richer as more notes are added into the mix.

 
 

Stratification

Because of their different timbral and rhythmic profiles, the two orchestras form two distinct musical layers, even though their pitch contents are globally identical

 
 

Gradual Addition

Neither layer is static, but each is continually transforming through the addition of new pitches and the corresponding change in timbre. As the spectralists have noted, the difference between harmony and timbre is blurry at best, and in addition we may note that timbre covaries with pitch. Therefore, although traditional types of analysis might focus on the changing pitch structure over the course of this section, I would argue that the timbre changes through a process of spectral filling as well, and this was my deliberate focus in composing it. Each orchestral layer individually undergoes a process of gradual addition, and their parallel unfolding unifies the whole ensemble into a single coherent gesture even as the layers remain distinct.

 
 

Sectional Contrast

After a long process of addition, there is an abrupt section contrast with fortissimo dynamics, the addition of distortion to the electric guitars, and sul ponticello plucking in the classical guitars. The repeated figures in each orchestra lose their distinct profiles and become identical, causing the whole ensemble to function as a single layer for the first time. There is then another process of transformation, a gradual reduction of timbral intensity, dynamic level, and rhythmic activity, thinning the whole out until only one part remains, splitting off from the global layer as a distinct auditory stream.

This section is presented in a sound example, so you can hear all of these things playing out. At this point my two fantastic visual artists have been producing exciting ideas, and I have two very different versions of animated videos. In time we will produce a unified final version, but we haven’t had time to do that just yet, so for this presentation I will showcase each artist’s work individually. In this excerpt I’ll show the work of Simon Rouhier.

 
 

Textural Integration -> Punctuation Blend

Later in the piece, a different kind of process unfolds. As explained in this table, which appears in the performance notes for the piece, the process is of different degrees of synchronization of strum patterns. At first, the notes are very diffuse over a wide interval of time, with just a slight accel-decel pattern indicating the location of the downbeat. The coordination then becomes greater, with a slow rolled chord, then a faster rolled chord, which are fast enough to be perceived as a rhythmic unit as opposed to a diffuse texture. By the end of the process, the strums are so fast and synchronized that they are perceived as single, fused events, with the near-perfect synchrony of the onsets causing all of the notes to group together perceptually; this is an instance of what McAdams calls “punctuation blend.” Although I notated this process with the four distinct symbols pictured here, as shown in the excerpted staff at the bottom of the figure, I ask the performers to think of it like a continuous process. I picture it as a statistical distribution around a mean, with the bell curve getting narrower and narrower. There are many other examples of perceptually grounded orchestration effects in this piece, but hopefully that should be enough to give you a sense of what is meant by that term.

IV. Spatialization as Orchestration

 
 

The last concept I would like to touch on before presenting the video is spatialization as orchestration. 

Although we have exciting new technology to work with today, this is in fact an ancient idea, with precedents such as antiphonal and processional choral music. 

More recently, 20th and 21st century composers, including in the sound mass tradition, have been very interested in musical space. 

In compositions such as Lontano, which translates to “far away,” Ligeti was expressly concerned with creating the illusion of movement in virtual space. 

The architect Xenakis sometimes used physical space as a compositional parameter, as in Terretektorrh in which the musicians are dispersed among the audience, and their listening experience is position-dependent. 

And although I do not know the piece, a colleague recently informed me of a Canadian example, Stereophony by Harry Somers. 

In his treatise On Sonic Art, composer Trevor Wishart also laid out a theoretical foundation for spatialization in electroacoustic music. 

For me, the idea of spatialization as orchestration is that the distribution or movement of sound sources in space adds a new layer of aesthetic interest to the composition, and provides new grouping cues that influence the perception of concurrent, sequential, and segmental orchestrational effects. These can interact with other orchestrational cues, either reinforcing them or contradicting them in interesting ways. These spatial effects are most effective in a 3D audio rendering, which we have produced but which is unfortunately not available at this point in an online format. In the stereo mix, they might be only subtly present, or you might not be able to hear them at all. I will nevertheless take a few minutes to talk about the spatial design and its role in the piece’s orchestration.

Spatialization in the Hocketing Section

On the other hand, in the hocketing section, we used spatial orchestration and timbral orchestration at cross-purposes. This seemed a logical extension of the spatialization already implied in the tuning system, which divides a smooth microtonal scale between six different instruments. We gave each of the six instruments a stationary spatial position around the listener, with no added animation. The result is that the timbral homogeneity and smoothness of the microtonal melodic lines strongly imply stream integration, while the spatial dispersion of the sound sources strongly implies stream segregation, creating an interesting perceptual ambiguity that I believe enhances the listening experience.

 
 

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Jason Noble https://jasonnoble.ca/
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