Abstract
While serial music is a mainstay of college instruction in both music theory and music history courses, many people still struggle to find a human connection to the compositional practice. This article explores metaphorical connections between serialism and three other fields of human endeavor. With respect to language study, serial works are compared to auxiliary (i.e., invented) languages, and it becomes clear that very similar impulses underlie creativity in these fields. Serialism also relates especially well to contemporaneous developments in visual arts, in that both foreground technical processes, often prioritizing those processes over concerns of content. The burgeoning field of natural aesthetics enables us to comprehend how one can appreciate the beauty and sublimity of staggeringly complex aesthetic objects and impressions.
I Introduction
Continued scholarly interest in serial music—evinced quite strongly in recent publications by Arnold Whittall, M. J. Grant, and Joseph Straus—indicates that much remains for us to learn about this approach to composition.1 But despite the fact that serialism is a mainstay of collegiate music instruction in both theory and history courses, and also that Schoenberg’s first completely twelve-tone work (Suite für Klavier, Op. 25) will soon reach the centennial mark, many people still struggle to appreciate serial music—or, at the very least, struggle to relate to what it is that preoccupies serial composers. This article offers three metaphorical spaces that provide models for appreciating the praxis and general aesthetics of serial composition. These metaphors enable us to understand serialism as a manifestation of creative and reflective impulses that is connected in many ways to other areas of the humanities. For this reason, the article does not engage analytically with specific pieces from serial repertoire (although certain works are mentioned along the way). Rather, it provides curious instructors and students with inroads to understanding and appreciating serialism within a greater continuum of human endeavor. In doing so, it addresses not only those students who are skeptical of or disinterested in serial music, but also scholars who only seem to be able to appreciate serialism from a distance without finding a human connection to it. The article also suggests some pedagogical applications that encourage students to synthesize these ideas in analyses of serial works, in comparison with other kinds of musical works, and even across other disciplines.
Before our metaphors are more precisely explained, we must unpack the term “serialism” itself. Authors tend to avoid short definitions in this area. A comparison of some relatively recent texts is illustrative. Whittall (2008) prefers a prolonged discussion that initially differentiates serialism from tonal music, but then provides a detailed discussion encompassing both theoretical facets and historical perspectives.2 While he leaves no doubt in the reader’s mind of what the subject at hand really is, no concise definition emerges. Straus’s scope is limited to composers working in North America. He comes close to a working definition when he makes the distinction between the terms “twelve-tone” music (concerning pre-composed parsings of the chromatic aggregate) and “serial” music (concerning pre-composed orderings of the aggregate), claiming further that “t is perfectly possible to write twelve-tone music that is not serial, and serial music that is not twelve-tone.”3 This distinction is fine for Straus’s purposes, but we will not be so specific. As Grant is primarily concerned with the Darmstadt school (but also with European post-war composers and critics in general), her references to serialism point only to the practices of European composers associated with it. Rather than assert her own definition, she prefers to put various ideas of Eimert, Pousseur, Boulez, Stockhausen, and others in dialogue throughout her fascinating book. Robert P. Morgan defines serialism as “[m]usic constructed according to permutations of a group of elements placed in a certain order or series. These elements may include pitches, durations, or virtually any other musical values.”4 While this gives us a point of departure, readers may find that it falls short of the mark in light of scholars (discussed below) who recognize a false divide between serial and aleatoric music.5
For present purposes, I define serialism as the practice of creating music that is a reflection of pre-compositional ideas-as-ordered-processes to a significant extent. Pre-composition involves imposing rules or limitations upon a musical space before the content of a specific musical work exists there—a space into which a musical work can evolve. In serial music, pre-composition is the act of determining compositional parameters before engaging in the actual act of composition, and these parameters must concern the ordering of elements to some degree. Thus, the twelve-tone music of the Second Viennese School is serial, but so are the post-war compositions of Pierre Boulez, Karlheinz Stockhausen, and Milton Babbitt. However, other works with pre-compositional restraints on ordering that are neither strictly twelve-tone nor integrally serial (such as those by Nono or Xenakis) are also included.
The next term to unpack is “metaphor.” The study of metaphors has been an increasingly popular topic among scholars in the humanities since the 1960s. In the field of education, researchers have addressed the roles and value of metaphors as aids to learning.6 Metaphors in this article, however, are intended as aids to appreciation, and this is an important difference. Petrie and Oshlag make much the same distinction, differentiating instructive (learning) and comparative (appreciation) metaphors.7
[R]adically new knowledge results from a change in modes of representation of knowledge, whereas a comparative metaphor occurs within the existing representations which serve to render the comparison sensible. The comparative level of metaphor might allow for extensions of already existing knowledge, but it would not provide a new form of understanding.
Similarly, Michael Spitzer differentiates a “cognitive metaphor,” or “metaphor as model” from a “poetic metaphor,” or “metaphor as trope.”8 Poetic, or “trope” metaphors are not based on rigid or irreducible schemata. They cannot directly assist in depicting musical objects, or in depicting relationships between specific musical objects. They are equally unlikely to help readers probe the depths of a score. As aids to appreciation, however, the “poetic” or “comparative” metaphors discussed below can help readers relate to serialism. The metaphors in this article are intended to refer to an aspect of music that is already understood (for as difficult as serialism may be to define precisely, it is safe to assume that the concept of what makes serial works different from other musical works is fairly easy to grasp). These metaphors do not address specific musical objects or processes. Rather, they engage with a general compositional approach. They invite creative ways of imagining serialism, and in doing so they situate the compositional practice more soundly within the arena of human creativity and experience.
As the title of this article indicates, the discussion below explores metaphors of language, art, and nature. To be sure, most readers are aware that these metaphorical spaces are already well-worn in discussions of music in general. Literature abounds in all three of these areas, and while it is well beyond the scope of this study to engage with all of this scholarship, this article does address some recent and important resources. Section II, “Music and Language,” considers relationships between serialism and auxiliary (i.e., artificially-constructed) languages. Section III, “Music and Visual Art,” discusses the tendency of both composers and visual artists to foreground technique, and goes so far as to address issues of autonomy. The final metaphorical space, “Music and Nature” (Section IV) considers recent literature on natural aesthetics and suggests that the path to enjoying serial music may not be as cerebral and artificial as one might think. Section V provides a brief conclusion that discusses how these comparative metaphors can create opportunities for learning.
II Music and Language
Literature on relationships between language and music are unquestionably abundant. Adorno discusses this relationship but eventually dismisses it, essentially arguing that languages consist of lexemes that convey specific meanings, while music does not.9 More recent historical accounts occur in Mark Evan Bonds’s Wordless Rhetoric, which champions the rhetorical attributes of eighteenth-century music, Michael Spitzer’s Metaphor and Musical Thought, which addresses the linguistic metaphor as it occurs in the Baroque era, and in Lawrence Zbikowski’s Conceptualizing Music, which mainly considers theorists from the eighteenth and nineteenth centuries.10 Curious readers will find more interdisciplinary perspectives by John Sloboda (psychology/cognition), David Lidov (philosophy/semiotics), and even more recently, M. J. Grant (history/aesthetics).11 The latter part of the twentieth century witnessed the development of musical semiotics, led by the pioneering work of Jean-Jacques Nattiez—which introduced a new field of inquiry that applies Saussurean principles of linguistic semiology to music.12
In short, the relationship between music and language is a multifaceted one that has fascinated thinkers for a long time. But what is it about music that makes us search for its connections to language? What is it that language can tell us about music? Surely, there are many ways to answer these questions, but somewhere near the heart of this relationship is the fact that language and music are both domains in which listeners ascribe or infer meaning in response to organized sounds. And while Adorno is correct in claiming that we cannot usually assign lexical meaning to musical sounds, we can find meaningful relationships among them. It follows that music-as-language metaphors can help us understand relationships between organization and meaning in sound.
So what does serialism have to do with language? Natural languages evolve over time, meeting the changing needs of speakers and cultures. In the Western world, tonal music has evolved in a comparable way, meeting the changing needs of its participants. On the other hand, serial music involves new systems of sound organization. These systems are created relatively quickly by a single person, rather than by a group of participants over time. The linguistic analog is glossopoeia, the practice of inventing artificial, or “auxiliary” languages. The new grammars, morphologies, etc. behind auxiliary languages are analogous to pre-compositional designs behind serial works in that both are based on artificially constructed systems of meaning. Rather than dismiss serialism as overly cerebral or contrived—as many seem inclined to do—we can recognize an impulse behind the development of serialism that is analogous to mankind’s need to construct and refine the means by which it communicates.
There are over nine hundred known artificial languages, the earliest of which (created, incidentally, by Hildegard von Bingen) arose in the twelfth century.13 This impulse to create new languages often arises from dissatisfaction with prevailing means of communication. Linguist Arika Okrent observes, “[t]he primary motivation for inventing new language has been to improve upon natural language, to eliminate its design flaws, or rather the flaws it has developed for lack of conscious design.”14 Similarly, Arden Smith notes linguists’ desire to “recapture the supposed perfection of the language of Adam,” where “words more accurately corresponded to the things they signified.”15 A natural language can develop flaws in any number of ways, including irregularities, polysemy, a lack (or unwieldy profusion) of cases, pronouns, or tenses, etc. It also retains flaws by not evolving a way that readily adopts to communicative needs. In linguistics, this has given rise to the subfield of pragmatics (the study of non-verbal communication).
One who creates an auxiliary language seeks to eliminate this messiness by creating a more streamlined system of communication. In order to rectify such flaws, many endeavor to create a more concise language—one that conveys as much information as possible with minimal redundancies and ambiguities. This often results in the creation of innovative aspects of grammar that non-speakers find alien.16 Consider, for example, John Quijada’s auxiliary language Ithkuil, which has markers for “evidential basis,” “cognitive intent,” and “objective vs. subjective descriptions,” among many others.17 Despite the abundance of information Ithkuil can convey, the language is remarkably concise.18 Joshua Foer’s article on Quijada and his language gives the following description of Marcel Duchamp’s “Nude Descending a Staircase,” with translation.19
Aukkras êqutta ogvëuļa tnou’elkwa pal-lši augwaikštülnàmbu
An imaginary representation of a nude woman in the midst of descending a staircase in a step-by-step series of tightly integrated ambulatory bodily movements which combine into a three-dimensional wake behind her, forming a timeless, emergent whole to be considered intellectually, emotionally, and aesthetically.
Similarly, serial composers recognized “flaws” in tonal music. Consider, by example, the following excerpt from Schoenberg’s “Composition with Twelve Tones.”20
In the last hundred years, the concept of harmony has changed tremendously through the development of chromaticism…. [T]he concept of tonality had to develop first into the concept of extended tonality. Very soon it became doubtful whether [tonic] still remained the centre to which every harmony and harmonic succession should be referred. Furthermore, it became doubtful whether a tonic appearing at the beginning, at the end, or at any other point really had a constructive meaning. Richard Wagner’s harmony had promoted a change in the logic and constructive power of harmony. One of its consequences was the so-called impressionistic use of harmonies, especially practiced by Debussy. . . In this way, tonality was already dethroned in practice, if not in theory.
Here, the man who is widely regarded as the first serial composer, acknowledges the messiness, or flaws of tonality at the turn of the twentieth century. What he preferred instead—and what he advocated—was concision and brevity, as expressed in the following quotations.
My music must be brief. Concise! In two notes: not built but expressed.21
The difficulty for the public to understand my music is the conciseness and the shortness.22
But the foremost characteristic of these pieces in statu nascendi were their extreme expressiveness and their extraordinary brevity.23
Great art must proceed to precision and brevity.24
The similarity between the linguistic impulse to create newer and more concise means of communication and the musical impulse to depart from tonal practice for the same ends is a compelling one. Pierre Boulez seems to concur in his notorious “Schoenberg is Dead” essay, where he claims “Schoenberg’s discoveries were essentially morphological,” that they evolved from the aftermath of “Wagnerian vocabulary,” and culminated in a “suspension of the tonal language” (268–269).25 His reliance on linguistic metaphors here is too strong to ignore, but it is perhaps even more telling that Boulez continues to employ them when he denounces Schoenberg, claiming that “he organized the language elements thus obtained by a pre-existing rhetoric, not a serial one.”26
Boulez’s criticism that Schoenberg’s reliance on tonal forms and rhythms was vestigial (and therefore anathema to modernist or post-modernist principles) points to another relationship between serial composers and language inventors. The popularity of auxiliary languages increased rapidly in the late nineteenth century with the introduction of Volapük and Esperanto in the 1880s, which used aspects of known, natural languages.27 Like the inventors of these languages, early twelve-tone composers retained certain familiar elements to attract participants (such are the vestigial elements of Schoenberg, to which Boulez objected so vehemently). While Esperanto is currently considered the most widely spoken auxiliary language, it is also a forerunner to the majority of auxiliary languages known today.28 In this way, the surge of interest in auxiliary languages is roughly contemporaneous with what Schoenberg recognized as the onset of tonality’s dissolution and the resultant search for an alternative system of musical composition.
The metaphorical space that encompasses practices of serial composition and language construction does, however, break down at a certain point. The creators of both Volapük and Esperanto (and other language creators since) intended their languages to serve as international lingua franca—used for casual parlance, to be sure, but more importantly, these languages were intended to facilitate scientific and political discourse in a medium that favored no nation’s native tongue. One could argue that composers of the Second Viennese School shared this intention, but the serialists of subsequent generations certainly did not. This is particularly relevant to the composers of the Darmstadt School, who were commendably international, with notable members hailing from France, Belgium, and Italy, in addition to Germany.29 The problem is that later serial composers had no shared system. They did not seem to expect their “auxiliary” compositional languages to be co-opted by any of their colleagues. Moreover, it is not even enough to claim that Pousseur’s serialism differs from that of Maderna, Boulez, or Stockhausen; serial approaches differ considerably across a single composer’s oeuvre. What serial composers and creators of auxiliary languages shared was on the level of the creative impulse, and that is the level at which the metaphor of serialism-as-auxiliary language is applicable.
The examples above do, however, support the argument that there is a remarkable relationship between the motivations of serial composers and language inventors. In both fields, they arose from a concern with the flaws in communicative systems that developed naturally. And, they both addressed those concerns by developing new systems of communication—systems that were both generally preoccupied with clarity and concision. In fairness, serialism and auxiliary languages also invite a common criticism, which is that their quests for elegance both resulted in impractical systems.30 It is not a coincidence that writers have used four-dimensional cubes to account for organization within Boulez’s Structures 1a, and that Quijada’s Ithkuil has 69 consonants, 17 vowels, 81 noun cases, 22 verb categories, and 1800 suffixes.31 Nonetheless, these two fascinating fields of human endeavor do have common ground, and from this we find a strong argument that the creative impulse behind serialism is related to a long-standing human need for clarity and concision.
III Music and Visual Art
Writers have found many connections between the fields of music and the visual arts over the centuries, and recent scholarship indicates a continuing interest. Spitzer gives a compelling, if abstract, account of harmony and/as painting in the seventeenth century, citing illustrations and writings by Kircher, Burmeister, Bernard, and others. Jeannie Guerrero and Karen Bottge have been quite specific in describing metaphorical mappings.32 Guerrero invites readers to compare Luigi Nono’s choral works to the paintings of Tintoretto (1518–94) with respect to depth, space, and density. Bottge investigates personal correspondences between Victor Hammer (painter) and Heinrich Schenker that discuss how perspective in renaissance painting relates to structural layers in tonal music. Walter Frisch dedicates a chapter of his study of music and German modernism to relationships with art, using Theodor Adorno’s concept of convergence [Konvergenz] to touch upon the work of Max Klinger, Johannes Brahms, Wassily Kandinsky, and Arnold Schoenberg.33 Grant comes closest to our present concerns by addressing serial music directly. In contextualizing European cultural history between world wars, she discusses conceptual overlap between serialists (defined broadly) and the artists Piet Mondrian and Paul Klee.34 She also investigates relationships between and serial art (which emerged in the 1960s) and serial music, seeming to reveal more of what the latter has in common with minimalist music than with the Darmstadt school.35 She notes, however, that both prioritize synchronic perception over diachronic perception at a deeper level, share an apparent disregard for ordering at a macro-structural level, as well as a general disregard for the evolutionary history of their disciplines.
While there are already numerous mappings between art and music, this article discusses a connection involving technique.36 I submit that the metaphorical space encompassing music and visual art can also involve aspects of technique and production. Generally speaking, both serial music and abstract art foreground technical means to considerable extents. First, we may consider increasing emphasis on technique in modern and post-modern music. Consider works by Iannis Xenakis (e.g., Polytope de Montréal,Tetras, Kottos, Windungen) require string players to grind the bow into the string or the bridge, or Varèse’s indications for percussive use of a flute’s keys in Density 21.5. In a manner of speaking, these instrumental techniques that add texture and dimension to sound are, examples of impasto in musical performance—where evidence of the technique required for production is an integral part of the musical object. Similarly, we can regard how serial music provides examples of impasto in musical composition by foregrounding pre-compositional techniques. Concert music of the twentieth century eclipses music from the tonal era with respect to the role compositional technique plays in creating meaning. David Lidov makes a trenchant observation about this.
The naturalism of the signifier in European concert music from the Renaissance through the nineteenth century determines that we should attend to techniques only by exception.37 On the side of composition, fugue is an exception. On the side of performance, bravura. The one represents invention and learning, the other, magic. For the rest, poeisis must give rise to a “natural” result so that poeisis will be invisible to aesthesis. This ideal does not hold for the twentieth century, a time when how things were made took on more significance in composition. . . With the Neoclassicism of the 1920s, the how of composition, no longer mythologized as inspiration or humbled as unconscious craft became part of the public aesthetic object, as a sign of artistic intention.38
Although Lidov does not clarify what he means by “Neoclassicism,” a fair amount of the chapter that follows this excerpt engages with the work of Schoenberg. Five decades earlier, Adorno’s comments on modernist music (again, not serialism specifically) take note of a similar trend.
The objective development of the musical material and of musical methods—one could say the level of development of the technical productive forces of music—has unquestionably outrun the subjective forces of production, i.e., the form of the response of the composers themselves.39
Today, the discrepancy between the subjective state of composition and the technical development that is identified by catchwords like integral composition and electronics has grown infinite. Compositional subject and compositional objectivity face each other across an abyss. This often leads to an opposite result compared to the previous generation.40
Adorno’s statements are admittedly cautionary, advising readers of the pitfalls of certain modernist tendencies. However, they are still relevant here. These observations (along with Lidov’s) resonate with statements from art critics and historians—particularly with those that discuss painting. Grant’s discussion of the “rise of abstraction” in art after the second World War observes how “debates on abstract art. . . revolved not around that ‘what’ of art, but the ‘how.’ ”41 Similarly, cultural historian Eugene Lunn notes how “modern artists, writers, and composers, often draw attention to the media or materials with which they are working, the very process of creation in their own craft.”42 At a level more accessible to the general reading public, Michael Wood, Bruce Cole, and Adelheid Gealt discuss the advent of abstraction in Western art during the second half of the nineteenth century within the impressionistic style. Their description of Claude Monet makes special mention of technical developments and the underlying material itself.
His increasingly personal experiments with layering strokes of paint, with the relationships between colors and his amorphous forms, evolved, as Turner’s works had done, into images where paint alone became the subject.43
When an art’s media start to replace its content and become the object of portrayal, a paradigm shift begins to take place. In the visual arts, this trend becomes increasingly obvious from 1870 onward, where the palette knife replaces the paintbrush in many works.44 The rise of the palette knife reflects an artistic intention to leave evidence of the application of color in all of the varied textures that result. Beyond the effects of palette knife, we witness the foregrounding of technique in other areas, such as the action paintings of Willem de Kooning and Jackson Pollock.”45 See, for example, Pollock’s Convergence or Full Fathom Five, as well as de Kooning’s Painting 1948, which all vividly convey the gestures used to produce them. Even in de Kooning’s somewhat later works (such as his “Woman” paintings), where recognizable figurative composition returns, the energy of his brushstrokes already begin to obscure the subject in a manner that is obviously intentional. In these, the communication of a technical process of creation is clearly part of their appeal.
Outside of painting, we can see a growing interest in “how” over “what” on the surfaces of Alberto Giacometti's sculptures, where rough indentations from fingers—remnants of the forces and processes that gave the sculptures dimension and shape—are left for viewers to engage, allowing them to construe their own realism or project their own agency. It is evident in the bolder (and earlier) departures of bricolage and assemblage—movements concerned more with how materials were put together than with what the materials themselves might convey, or with what any intended meaning might even arise from the juxtaposition of disparate elements.
Some have argued that pre-compositional serial structure is not necessarily constitutive of an ultimate musical object and that an aesthetic experience of a serial work, though dependent on that structure, should not necessarily be understood as a direct response to an immediate perception of serial relationships.46 From this it would follow that serial technique may not be as foregrounded as I claim here, and that something else—a “net effect” of all pre-compositional parameters, along with innumerable contextual factors involving setting, performer, listener, etc.—is the emergent musical object in a serial work. Then again, one could make the same argument for the appreciation of visual arts where techniques of production figure prominently. A drip painting of Pollock conveys a dizzying network of movements and energies that evokes an approach to expression rather than a traceable collection of individual movements. We often appreciate the ‘net effect’ of such a work when we can step back and find the appropriate viewing distance. When appreciating works of bricolage or assemblage, we depend on our stepping back and apprehending the tension across whole works rather than the properties of each separate material. We may take a similar approach in listening to serial works. The dizzying networks of relationships (and non-relationships) created by pre-compositional planning can have net effects that we judge and appreciate once a proper listening distance is found—a distance that mediates diachronic (in time) and synchronic (holistic, outside of time) hearing. Whether we appreciate a technique itself or the result of that technique, the fact remains that more than one field of modernist or postmodernist creativity features creative processes that leave indelible traces on their products.
The topic of action paintings also raises the question of whether subjecting artistic expression to such unusually impactful techniques actually reflects an obsession with control or a relinquishment of it. Art critic and historian Hal Foster addresses this very issue in a passage on Jackson Pollock.
Although we can marvel today at Pollock’s amazing technical know-how, the fact is that in his drip paintings he relinquished part of his authorship. By avoiding any direct contact with the canvas splayed on the floor, by letting gravity and the viscosity of the paint play a major role in the outcome of his works, and by abandoning the paintbrush, Pollock lost the anatomical connection that had traditionally linked the artist’s hand, brush, and canvas. He wavered on the issue of control, ….his attempt at automatism was deemed by his peers to be too much of a breakdown of authorial mastery.”47
This too, resonates with commentary on serialism, starting with the composers themselves. Many found that the pre-compositional stage allowed one to take the ego out of composition and enabled the creation of an aesthetically delimited space into which a musical work may evolve. Pierre Boulez claims that he “wanted to use the potential of a given material to find out how far automatism in musical relationships would go.”48 Paul Griffiths notes how “Stockhausen in Kreuzspiel took pleasure in making forms that were themselves automatic, and that sprang from how the material was constituted and deployed.”49 Such commentary often leads to observations along the lines that serial and aleatoric music have at least as much in common as they do in difference.50 Joseph Auner discusses the serialist Boulez and John Cage (pioneer of aleatoric music) as kindred spirits, noting that “nstead of relying on personal taste, expression and emotion, they and many of their contemporaries were attracted to abstract systems that minimized the role of the composer’s individuality and subjectivity.”51 Grant notes the “inherent [i.e., ostensible] paradox that serialism did a U-turn by employing aleatoric methods from the mid-1950s.”52
So, are serial composers overly demanding egotists obsessed with controlling every aspect of performance, or is it more accurate to compare them to hands-off, absentee gods in a Newtonian ‘clockwork universe?’ In composition as in painting, adherence to technique can allow a relinquishment of control while still subjecting materials to strict, immutable laws. We learn from both music and the visual arts that relationships between artists (including composers) and their media are continuously in flux. As these relationships change, the degrees to which artists expend their creative energy in either technical considerations or subjective concerns change, too.
But what aspects of serial music remain for us to appreciate after renewed consideration of motivations (as in auxiliary languages) or technical foregrounding (as in visual art)? The bulk of the answer to this question lies in the overwhelming details in the serial works themselves, as we perceive them. One could argue that the overall effect from all of the details in a Pollock painting is just as overwhelming as that produced from all of the simultaneous processes of an integrated serial work like Boulez’s Le Marteau sans Maitre. Both kinds of works invite the question of whether such overwhelming detail is a good thing or not, and this brings us to our third metaphor, “Music as Nature.”
IV Music and Natural Aesthetics
Metaphors involving music and nature are no less common than the other metaphor types discussed above. Not only do Spitzer’s accounts of “melody-as-life” metaphors summarize a good deal of organicist thought in the nineteenth century, but much earlier theories of Musica universalis (i.e., music of the heavenly spheres) point to mankind’s need to find connections between music and an even broader conception of nature. Composers, too, have drawn from the natural world.53 However, specific discussions of relationships between the natural world and serial music are harder to find.54 Thankfully, Edward T. Cone provides one in the final chapter of his influential Musical Form and Musical Performance.55 There, he first distinguishes “synoptic” understanding, which appreciates artworks as unified wholes, from “immediate apprehension,” a localized mode of appreciation that takes in smaller details as well as short-range connections among those details. Cone argues that in appreciating the natural world, we can approach synoptic appreciation, but we usually cannot get there. Far more often, we can only begin to approach a view of total form in nature. Our perspective is limited spatially by what we are able to apprehend with our senses, and also temporally due to the persistence of natural processes. He asserts that natural objects present “artistic surfaces” primarily capable of localized understanding, as they “defeat attempts at synoptic comprehension and respond to the immediate mode of perception only.”56
Cone’s observations become relevant to serial music soon after he notes how representational works of art are “imaginative re-creations of the natural aesthetic continuum.” He refers first to a novel, which functions as a specific re-creation within a continuum that is “the entire world of thought and action.” He also cites examples from painting, where the frame delimits the range of things viewed, but alludes to a broader world.57 (In fact, Cone refers specifically to action paintings, noting that those canvases “suggest that the kind of thing we see within the frame is also going on beyond its boundaries.”58 ) Curiously, he then observes that “music, by contrast . . . is unique among the arts in lacking in principle any embedding continuum.” Soon thereafter, however, he claims that “totally determined serial music gives the effect of being a segment of an indefinitely extensible twelve-tone continuum,” and that the apparently arbitrary quality of such works’ beginnings and endings, as well as the “fortuitous nature of their inner connections” relegate their aesthetic accessibility—as in the appreciation of nature—to the immediacy of artistic surfaces.59 Cone’s discussion thereby reveals an especially exclusive correspondence between serial music and the natural world.
I submit that if we take Cone’s conclusion at face value and allow ourselves to find a way to appreciate serial music that is somehow analogous to how we appreciate nature, we will find some compelling connections. If nature and music are both phenomenal (i.e., perceptible through the senses), then nature-as-music metaphors can help us understand perception. Quite often, the natural world offers us vistas and other sensations of overwhelming complexity and breathtaking beauty. The way we appreciate beauty of such extent is entirely in alignment with Cone’s “immediate apprehension.” Humans cannot comprehend the innumerable natural processes that have given form to the image of a forest crowded with bare trees against a bright and clear winter sky (a vista of seemingly infinite complexity), let alone those that have shaped, colored, and textured a vast landscape like the Grand Canyon. However, what we often do appreciate—often along with an immediately recognizable beauty—is the knowledge that unknown and untraceable processes have taken place, but without them, so much of the beautiful or sublime in natural phenomena would not exist.
Writers on aesthetics of nature frequently broach the topic of how we might interpret nature on its own terms rather than through lenses of artistic appreciation. Can we appreciate the call of a bird without understanding it as a musical gesture, or enjoy beautiful views without comparing their composition to the masterworks of great painters?60 Malcolm Budd’s stance on this is representative, and worth quoting in full.
Given that the natural world has not been designed to be an object of aesthetic interest, then if the natural world is to be appreciated as what it is, it must be recognized as having been formed by, and to be the continuing locus of physical, chemical, geological, ecological, meteorological, and evolutionary processes, all of which take place in complete indifference to the aesthetic beholder. It might appear to follow from this that any instance of the aesthetic appreciation of nature as nature that is not superficial must be informed by an understanding of the natural processes that have brought about and that are at work in the object of appreciation, and that the fuller understanding the deeper the appreciation. But this conclusion will follow only if aesthetic appreciation of nature must be superficial unless knowledge of an item’s origin and the forces responsible for its appearance inform a person’s observation of the item, and only if aesthetic appreciation is deeper the more it is penetrated by and the product of such knowledge. And that condition is questionable.61
Budd makes two important points here, which I will address in reverse order. He closes the passage by challenging the notion that an understanding of the underlying processes that shape a natural object—though they may be foregrounded and perceptible at a surface level—is necessary for appreciation. This applies to serialism, too. Compositional techniques may play a more significant role than ever before in the determination of a musical work’s form, but a listener’s understanding of those techniques may still not be a necessary condition for the appreciation of that work. Budd’s first point is that we should not apply artistic criteria to the appreciation of nature. It arises from a concern that what we commonly understand as artistically satisfying limits our understanding of what is appreciable in the natural world and impoverishes our working preconceptions of beauty and sublimity. One of the most important charges of natural aesthetics is to caution people against viewing nature in artistic terms, and much of the scholarship in Budd’s field involves determining appropriate criteria for appreciating nature. However, when we consider how serialism and the natural world both present us with overwhelming complexity in the form of myriad details that are often only individually understandable or locally relatable, we can actually invite listeners to do the reverse—that is, to experience something artistic on nature’s terms. In this way, the larger and arguably more influential domain sets the standards.
V Conclusion
The foregoing applies three metaphorical spaces to different aspects of serial music. Each of these discussions opens by citing a fair amount of literature concerning non-serial music. Music-as-language, music-as-art, and music-as-nature have been popular metaphors for centuries, and the fact that these spaces apply so well to serialism suggests that ordered, pre-composed music is not as contrived or misguided as one might think at first blush.
Lakoff and Johnson’s commendable research in the field of metaphor theory has enabled us to teach in a way that encourages students to approach the unknown through the known.62 Their claim, that “our ordinary conceptual system, in terms of which we both think and act, is fundamentally metaphorical in nature,” supports the argument that metaphorical constructs are perfectly normal inroads to learning.63 By introducing and explaining concepts in metaphorical terms, teachers can structure how students process those concepts and even retain them.
However, the metaphors above are only aids to appreciation. As the introduction states, they do not lead directly to new understanding. But in opening minds to new ways of thinking about concepts that are already familiar, these metaphors can create the inroads that eventually do lead to new understanding. One such inroad involves the difference between description and analysis. Prominent music theory pedagogues have noted how instruction in music theory courses often mistakes the latter—an account of surface details and event successions—for the former—a deeper understanding of meaning that arises from considering the whole. Michael Rogers states that “[t]he most basic problem in defining analysis is to distinguish it from description.”64 This is especially relevant to serial music. Schoenberg often questioned or decried outright those twelve-tone ‘analyses’ that only consist of determining the identities of row forms in a piece. His letter to Rudolf Kolish states that such impoverished attempts at analysis “only lead to what I’ve been dead against: seeing how it is done, whereas I have always helped people to see: what it is!”65
By allowing students to understand the thinking behind serial music, these metaphors help us avoid being mired in row counting or the like, and they can provide the openings that invite actual analytical insight. By understanding the similar creative impulses underlying serialism and invented languages, we understand that both endeavors arise from a need to communicate more clearly. This understanding enables us to ask questions such as these.
“What aesthetic principle(s) does the serial organization of this piece convey?”
“How are these principles conveyed in non-serial music?” “What is different/similar?”
“How does the serial composition manage to express these principles in more than one musical parameter simultaneously? Do the effects of these parameters reinforce each other, or work against each other?”
In light of contemporaneous (or nearly contemporaneous) developments in visual arts, we understand that serialism is not singular in its foregrounding of technique or its relinquishment of authorial control. Many forms of art have found expressivity within such constraints. Knowing that such works of visual art invite different modes of perception—modes that appreciate technique in addition to content—the questions that arise would be comparative.
“Now that we know the serial processes in this work, how does that knowledge change the way we listen in terms of what we listen for, what we listen to, or what we expect?”
“Consider the adjustment of visual criteria required to appreciate Vincent Van Gogh’s Starry Night (in comparison to a work of realist art), which involves retaining our appreciation for color relationships, but simplify our expectations for perspective, object boundaries and overall realism. How might we similarly adjust our aural criteria to appreciate the third movement of Ruth Crawford’s Diaphonic Suite?”
Finally, by understanding how the overwhelming detail of concurrent processes can elicit profound awe and an appreciation of the sublime, we recognize the connection between serial works in light of the natural world.
“How do the overwhelming criss-crossing processes in Stockhausen’s Kreuzspiel resonate with the overwhelming geological processes evident in this panorama?”
“Some geological layers within this canyon remain discrete, while some penetrate or overlap. Where do similar relationships obtain among musical parameters?”
These comparative metaphors show us how serialism relates to three vast fields of human activity. Teaching the appreciation of serial music from interdisciplinary perspectives is a positive development. While it might have seemed that the topic of serial music would never work its way into a general education course in the humanities, it just might find a way in now. If this happens, we may even consider the metaphors above to be of the learning variety—but within the context of a broader field of study—and musicians and non-musicians will acquire broader perspectives about their world.
Notes
1See Whittall. Serialism; Straus, Twelve-Tone Music in America; and Grant. Serial Music, Serial Aesthetics.
2Whitall, Serialism, 1–16.
3Straus, Twelve Tone Music in America, xviii.
4Morgan, “Serialism,” in Don Michael Randel, ed. The Harvard Dictionary of Music, 772.
5While definitions of aleatoric music (sometimes called “indeterminate” or music) do not vary as much as those for serialism, I offer the following definition for this article’s purposes: aleatoric music is music whose structure involves some amount of chance, or randomness. Consider John Cage’s I Ching, whose organization was determined by coin tosses, or Terry Riley’s In C, where an unspecified number of instrumentalists play through a series of short melodies, repeating each an number of times that is not pre-determined.
6Petrie and Oshlag, “Metaphor and Learning” and Sticht “Educational Uses of Metaphor,” in Andrew Ortony, ed. Metaphor and Thought.
7Petrie and Oshlag, “Metaphor and Learning,” 585. Emphasis in the original.
8Spitzer, Metaphor and Musical Thought, 54. Spitzer’s conception of poetic metaphor is admittedly indebted to Hester, The Meaning of Poetic Metaphor.
9Adorno, “Music, Language, and Composition.”
10Spitzer, Metaphor and Musical Thought; Bonds, Wordless Rhetoric, and Zbikowski, Conceptualizing Music.
11See John Sloboda, The Musical Mind, 11–66 and Exploring the Musical Mind, 175–190; Lidov, Is Language a Music?; Grant, Serial Music, Serial Aesthetics, 131–164; and Lerdahl, “Cognitive Constraints.”
12Nattiez, Music and Discourse.
13The name of the language is Lingua Ignota. See Higley, Hildegard of Bingen’s Unknown Language.
14Okrent, In the Land of Invented Languages, 11. Only within the last century has the motivation to provide a universal international language for business, science, and politics arisen. See Jespersen, “Interlinguistics.”
15Smith “Confounding Babel,” 19.
16Another much earlier example than the excerpt from Ithkuil that follows is a translation from Wilkins’s Philosophical Language (published 1668) in Okrent, Land of Invented Languages, 58–75.
17See http://www.ithkuil.net/00_intro.html (accessed 13 May, 2015).
18The majority of translations from auxiliary languages into English in Okrent, Land of Invented Languages result in a notable increase in length. See also Weiner and Marshal, “Tolkein’s Invented Languages,” 78, who observe the concentrated grammar of J. R. R. Tolkien’s Quenya.
19See Foer, “Utopian for Beginners.”
20Schoenberg, “Composition with Twelve Tones,” 216.
21A letter to Ferrucio Busoni dated August, 1909; see Auner, A Schoenberg Reader, 70.
22This quotation was extracted from a NBC radio talk on November 19, 1933. See http://www.schoenberg.at/index.php/en/alfred-lundell-interview-with-arnold-schoenberg Accessed 15 May, 2015.
23Schoenberg, “Composition with Twelve Tones,” 217.
24Schoenberg, “Brahms the Progressive,” 414.
25Boulez, Pierre. Stocktakings from an Apprenticeship, 268–275.
26Ibid., 274.
27Other auxiliary languages do the same. See Smith, “Confounding Babel,” 39–44, and Okrent, In the Land of Invented Languages, 88–92.
28Arden Smith notes that “[e]stimates of current Esperanto speakers hover around a million.” See “Confounding Babel,” 38.
29On a smaller scale, Henri Pousseur expresses this sentiment in terms of changing relationships between composers, performers, works, and the listening public in the classical era, Webern’s era, and post-1945. See Henri Pousseur, “Music, Form and Practice”; Grant summarizes the argument in Serial Music, Serial Aesthetics: 208–209.
30Fred Lerdahl, “Cognitive Constraints,” 256–257.
31Four-dimensional cubes are discussed in Paul Lombardi and Michael Wester, “A Tesseract in Boulez’s ‘Structures 1a,’ ” Music Theory Spectrum 30/2 (2008): 339–59.
32Jeannie Ma. Guerrero, “Non-Conventional Planar Designs”; Karen M. Bottge, “Lessons in Pure Visibility.”
33Walter Frisch. German Modernism, Music and the Arts.
34Grant, Serial Music, Serial Aesthetics, 34–38, 251–52.
35Ibid., 171–77.
36As this article could not accommodate a complete review of literature on music and visual art, the review above provides a regrettably small sample. For a number of non-musical perspectives, see The Routledge Companion to Music and Visual Culture.
37By “naturalism of the Signifier,” Lidov refers to Umberto Eco’s concept of natural signs. Unlike artificial signs, natural signs do not have a man-made source. In this case, Lidov adopts the concept to refer to natural epistemologies underlying tonal music (i.e., both tonality’s rootedness in nature through the overtone series, as well as to the aforementioned “naturalness” of the tonal language with respect to the way it has evolved).
38Lidov, Is Language a Music? 183.
39Adorno, “Difficulties,” 648.
40Ibid., 649–50.
41Grant, Serial Music, Serial Aesthetics, 20–21. Here, she cites Jost Hermand, Kultur im Wiederaufbau.
42Eugene Lunn, “Modernism in Comparative Perspective,” 32.
43Michael Wood, Bruce Cole, and Adelheid Gealt, 1989. Art of the Western World, 246.
44Painters at least as early as Rembrandt (1606–1669) have used the palette knife to apply paint directly to canvases, but certainly not over an entire canvas, as many modern painters do. The practice became increasingly popular toward the end of the nineteenth century. Paul Cezanne (1839–1906) is generally recognized as the first artist to do this at an early career stage.
45The term “action painting” was coined by Harold Rosenberg, “The American Action Painters.”
46Chapter 1 of Elizabeth Marvin’s dissertation “A Generalized Theory of Musical Contour” provides an overview of sources addressing this, including Milton Babbitt, Words About Music; Edward T. Cone, “Beyond Analysis”; and David Lewin, “Behind the Beyond.” See also Grant, Serial Music, Serial Aesthetics, 217–228 which discusses both Fred Lerdahl, “Cognitive Constraints,” and Helmut Kirchmeyer, Strawinsky: Zeitgeschichte im Persönlichkeitbild.
47Hal Foster, Yve-Alain Bois, Benjamin H. D. Buchloh. Art Since 1900, 350.
48Pierre Boulez and Célestin Deliège, Conversations with Célestin Deliège.
49Paul Griffiths, Modern Music and After, 45.
50See also Robert P. Morgan, Twentieth-Century Music.
51Joseph Auner, Music in the Twentieth and Twenty-First Centuries, 191.
52Grant, Serial Music, Serial Aesthetics, 131.
53For a recent study, see Denise Von Glahn, Music and the Skillful listener: American Women Compose the Natural World (Bloomington: Indiana University Press, 2013); see also The Sounds of Place: Music and the Cultural Landscape (Boston: Northeastern University Press, 2003), which engages with mankind’s changing relationships with natural spaces.
54See, however, discussions of Xenakis’s works such as Polytope de Montréal in James Harley, Xenakis: His Life and Music. (New York: Taylor & Francis, 2004), 48–50.
55Edward T. Cone. Musical Form and Musical Performance, 88–98.
56Ibid., 93
57Ibid, 93–94.
58Ibid., 95.
59Ibid., 95–96.
60See, for example, Malcolm Budd, The Aesthetic Appreciation of Nature, 90–148; Allen Carlson, Aesthetics and the Environment, 102–125, 129–137; Emily Brady, Aesthetics of the Natural Environment, 52–85. See also Arnold Berleant, “The Aesthetics of Art and Nature,” 76–88; Yuriko Saito, “Appreciating Nature on its Own Terms,” 141–155; and Ronald Moore, “Appreciating Natural Beauty as Natural,” 214–231 in The Aesthetics of Natural Environments.
61Budd, The Aesthetic Appreciation of Nature, 121. Emphasis in the original.
62See George Lakoff and Mark Johnson, Metaphors We Live By, and Philosophy in the Flesh.
63bid., 3.
64See Michael R. Rogers, Teaching Approaches in Music Theory, 74; See also John D. White and William Lake, Guidelines for College Teaching of Music Theory, 128–129.
65Arnold Schoenberg, Letters, 164.
Bibliography
Adams, Michael. “Esperanto’s Zenith.” In From Elvish to Klingon: Exploring Invented Languages, edited by Michael Adams, 234–241. New York: Oxford University Press, 2011.
Adorno, Theodor. “Music, Language, and Composition.” In Essays on Music. Edited by Richard Leppert, 113–126. Translated by Susan H. Gillespie. Berkeley: University of California Press, [1956]. 2002.
______. “Difficulties.” In Essays on Music. Edited by Richard Leppert, 644–679. Translated by Susan H. Gillespie. Berkeley: University of California Press, [1966]. 2002.
Auner, Joseph. A Schoenberg Reader: Documents of a Life. New Haven: Yale University Press, 2001.
______. Music in the Twentieth and Twenty-First Centuries. New York: W. W. Norton & Co., 2013.
Babbitt, Milton. Words About Music. Edited by Stephen Dembski and Joseph N. Straus. Madison: University of Wisconsin Press, 1987.
Berleant, Arnold. “The Aesthetics of Art and Nature.” In The Aesthetics of Natural Environments, edited by Allen Carlson Arnold Berleant, 76–88. Peterborough, Ontario: Broadview Press Ltd, 2004.
Bonds, Mark Evan. Wordless Rhetoric: Musical Form and the Metaphor of the Oration. Cambridge: Harvard University Press, 1991.
Bottge, Karen M. “Lessons in ‘Pure Visibility’ (reine Sichtbarkeit): Victor Hammer’s Correspondence with Heinrich Schenker.” Music Theory Spectrum 37/1 (2015): 25–50.
Boulez, Pierre. Stocktakings from an Apprenticeship. Oxford: Oxford University Press. 1991.
Boulez, Pierre and Célestin Deliège 1977. Conversations with Célestin Deliège. London: Eulenburg Books, 1976.
Brady, Emily. Aesthetics of the Natural Environment. Edinburgh University Press, 2003.
Budd, Malcolm. The Aesthetic Appreciation of Nature: Essays on the Aesthetics of Nature. Oxford: Clarendon Press, 2006.
Carlson, Allen. Aesthetics and the Environment: The Appreciation of Nature, Art and Architecture. New York: Routledge, 2002.
Cone, Edward T. “Beyond Analysis.” Perspectives of New Music 6/1 (1967): 33–51.
______. Musical Form and Musical Performance. New York: W. W. Norton & Co., 1968.
Foer, Joshua. “Utopian for Beginners.” The New Yorker (December 24, 2012).
Foster, Hal, Yve-Alain Bois, Benjamin H. D. Buchloh. Art Since 1900: Modernism Antimodernism Postmodernism. New York: Thames & Hudson, 2004.
Frisch, Walter. German Modernism, Music and the Arts. Oakland, CA: University of California Press: 2007.
Grant, M. J. Serial Music, Serial Aesthetics: Compositional Theory in Post-War Europe. New York: Cambridge University Press, 2001.
Griffiths, Paul. Modern Music and After: Directions Since 1945, 3rd ed. New York: Oxford University Press, 2011.
Guerrero, Jeannie Ma. “Non-Conventional Planar Designs in the Works of Nono and Tintoretto.” Music Theory Spectrum 22/1 (2010): 26–43.
Harley, James. Xenakis: His Life and Music. New York: Taylor & Francis, 2004.
Hermand, Jost. Kultur im Wiederaufbau: die Bundesrepublik Deutschland 1945–1965. Munich: Nymphenburger, 1986.
Hester Marcus. The Meaning of Poetic Metaphor: An Analysis in Light of Wittgenstein’s Claim that Meaning is Use, The Hague: Mouton & Co., 1967.
Higley, Sarah. Hildegard of Bingen’s Unknown Language: An Edition, Translation, and Discussion. New York: MacMillan, 2007.
Jespersen, Otto. “Interlinguistics.” In International Communication: A Symposium on the Language Problem, 95–120. London: K. Paul, Trench, Trubner & Co. Ltd., 1931.
Kirchmeyer, Helmut. Strawinsky: Zeitgeschichte im Persönlichkeitbild. Grundlagen und Voraussetzungen zur modernen Konstrucktionstechnik. (Kölner Beiträge zur Musikforschung 10). Regensburg: Gustav Bosse, 1958.
Lakoff, George and Mark Johnson. Metaphors We Live By. Chicago: University of Chicago Press, 1980.
______. Philosophy in the Flesh: The Embodied Mind and Its Challenge to Western Thought. New York: Basic Books, 1999.
Lerdahl, Fred. “Cognitive Constraints on Compositional Systems.” In Generative Processes in Music: The Psychology of Performance, Improvisation, and Composition. Edited by John Sloboda, 231–259. Oxford: Clarendon Press, 1988.
Lewin, David. “Behind the Beyond.” Perspectives of New Music 7/2 (1969): 59–69.
Lidov, David. Is Language a Music? Writings on Musical Form and Signification. Bloomington: Indiana University Press, 2004.
Lombardi, Paul and Michael Wester, “A Tesseract in Boulez’s Structures 1a.” Music Theory Spectrum 30/2 (2008): 339–59.
Lunn, Eugene. “Modernism in Comparative Perspective.” In Art of the Twentieth Century. Edited by Jason Gaiger and Paul Wood. New Haven: Yale University Press, 2003.
Marvin, Elizabeth. “A Generalized Theory of Musical Contour: Its Application to Melodic and Rhythmic Analysis of Non-Tonal Music and Its Perceptual and Pedagogical Implications.” PhD diss, Eastman School of Music, 1989.
Moore, Ronald. “Appreciating Natural Beauty as Natural.” In The Aesthetics of Natural Environments, edited by Allen Carlson Arnold Berleant, 214–231. Peterborough, Ontario: Broadview Press Ltd, 2004.
Morgan, Robert P. Twentieth-Century Music. New York: W. W. Norton & Co., 1991.
Nattiez, Jean-Jacques. Music and Discourse: Toward a Semiology of Music. Translated by Carolyn Abbate. New York: Princeton University Press, 1990.
Okrent, Arika. In the Land of Invented Languages: Adventures in Linguistic Creativity, Madness, and Genius. New York: Random House, 2010.
Petrie, Hugh G., and Rebecca S. Oshlag, “Metaphor and Learning.” In Metaphor and Thought. Edited by Andrew Ortony, 579–609. New York: Cambridge University Press, 1993.
Pousseur, Henri. “Music, Form and Practice (an attempt to reconcile some contradictions).” Die Reihe 6 [1960]. Translated by Margaret Shenfield, 77–93. Bryn Mawr, PA: Theodore Presser Co., 1964.
Randel, Don Michael, editor. The Harvard Dictionary of Music. 4th ed. Cambridge: Harvard University Press, 2003.
Rogers, Michael R. Teaching Approaches in Music Theory: An Overview of Pedagogical Philosophies. 2nd ed. Carbondale: Southern Illinois University Press, 2004.
Rosenberg, Harold. “The American Action Painters.” Art News 51/8 (1952).
Saito, Yuriko. “Appreciating Nature on its Own Terms.” In The Aesthetics of Natural Environments. Edited by Allen Carlson and Arnold Berleant, 141–155. Peterborough, Ontario: Broadview Press Ltd., 2004.
Schoenberg, Arnold. Letters. Edited by E. Stein. Translated by Eithne Wilkens and Ernst Kaiser. New York: St. Martin’s Press, 1965.
______. “Composition with Twelve Tones.” In Style and Idea: Selected Writings, 60th Anniversary Edition. Edited by Leonard Stein, 214–245. Translated by Leo Black. Berkeley: University of California Press, [1941] 1975.
______. “Brahms the Progressive.” In Style and Idea: Selected Writings, 60th Anniversary Edition. Edited by Leonard Stein, 398–442. Translated by Leo Black. Berkeley: University of California Press, [1947] 1975.
Shephard, Tim and Anne Leonard, eds. The Routledge Companion to Music and Visual Culture. New York: Taylor & Francis, 2014.
Sloboda, John. The Musical Mind: The Cognitive Psychology of Music. New York: Oxford University Press, 1986.
______. Exploring the Musical Mind: Cognition, Emotion, Ability, Function. New York: Oxford University Press, 2005.
Smith, Arden R. “Confounding Babel: International Auxiliary Languages.” In From Elvish to Klingon: Exploring Invented Languages. Edited by Michael Adams, 17–48. New York: Oxford University Press, 2011.
Spitzer, Michael. Metaphor and Musical Thought. University of Chicago Press, 2004.
Sticht, Thomas G. “Educational Uses of Metaphor.” In. Metaphor and Thought. Edited by Andrew Ortony, 621–632. New York: Cambridge University Press, 1993.
Straus, Joseph N. Twelve-Tone Music in America. New York: Cambridge University Press, 2009.
Von Glahn, Denise. The Sounds of Place: Music and the Cultural Landscape. Boston: Northeastern University Press, 2003.
______. Music and the Skillful Listener: American Women Compose the Natural World. Bloomington: Indiana University Press, 2013.
Weiner, E. S. C. and Jeremy Marshall. “Tolkien’s Invented Languages.” In From Elvish to Klingon: Exploring Invented Languages. Edited by Michael Adams, 75–110. New York: Oxford University Press, 2011.
White, John D. and William Lake. Guidelines for College Teaching of Music Theory, 2nd ed. Lanham, MD: Scarecrow Press, 2002.
Whittall, Arnold. Serialism. New York: Cambridge University Press, 2008.
Wood, Michael, Bruce Cole, and Adelheid Gealt. Art of the Western World: From Ancient Greece to Post-Modernism. New York: Summit Books, 1989.
Zbikowski, Lawrence. Conceptualizing Music: Cognitive Structure, Theory, and Analysis. New York: Oxford University Press, 2002.
Internet Resources
(accessed 13 May, 2015)
Ithkuil: A Philosophical Design for a Hypothetical Language.
Foer, Joshua “Utopian for Beginners” The New Yorker 88/41, 2012: 86–97. h
Schoenberg, Arnold, and Alfred Lundell. Transcription of a radio interview broadcast 19 November, 1933, available at the website for the Arnold Schoenberg Center.