Mathematics has been used to describe, analyse and create music for millennia. The use of specific mathematical apparatus is manifest in the organization of basic musical notions into forms or objects that inhabit a sonorous landscape. The collecting of musical units into a set constitutes a starting point for analysing a musical object under different mathematical structures, and although there is no unified approach, musical analysis and composition use geometry and discrete mathematics to describe different musical relations (particularly group theory) (...) in the process of modelling the basic elements of music, such as scales, intervals, chords or rhythms. (shrink)

The article presents philosophical views on music in the context of the transformations of the worldview from Antiquity to the Modern Time. In this research author also mentions the contemporary issues, and uses her own philosophical concept of the music, which can be described as following: the value of music as a substance and the way of the valuable interaction of a person with the world affirm the essence of musical being, in which the invariable principle of Harmony, the principle (...) of Chaos-Form movement, is preserved. Music expresses the fluid essence of the world and changes of being in space and time. Philosophy of music as a field of philosophical knowledge considers music from ontological-epistemological and phenomenological-axiological prospectives, as something more than just a form of art. It explores the deep, ultimate foundations of the existence of music as such and the philosophical and aesthetic foundations of musical art. Since ancient times music has been a representation of the world in the human conscience and served as the harmonic equivalent of cosmological philosophy, mathematics, astronomy, and astrophysics. The scientific view on music was enriched in the Modern Time by the expanded view on the cosmo-sound space reflected in musical art, which at the same time transforms the mathematical ideas of geometricity, squareness etc. The tendency to create integral world music in the musical practice of the XX-XXI centuries explains the attempt of mankind to present music by modern methods of composing musical art as an expression of fear towards the secret Harmony of universal existence, and, on the other hand - as a form of search for salvation and mental balance, intuitively reflecting what is happening in natural science, which more and more points to the abyss of unknowable universe, and the unstable place of man in the world. (shrink)

Simply by formulating a question about the nature of ancient Greek poetry or music, any modern English speaker is already risking anachronism. In recent years especially, scholars have reminded one another that the words ‘music’ and ‘poetry’ denote concepts with no easy counterpart in Greek. μουσική in its broadest sense evokes not only innumerable kinds of structured movement and sound but also the political, psychological and cosmic order of which song, verse and dance are supposed to be perceptible manifestations. Likewise, (...) ποίησις and the ποιητικὴ τέχνη can encompass all kinds of ‘making’, from the assembly of a table to the construction of a rhetorical argument. Of course, there were specifically artistic usages of these terms—according to Plato, ‘musical and metrical production’ was the default meaning of ποίησις in everyday speech. But even in discussions which restrict themselves to the sphere of human art, we find nothing like the neat compartmentalization of harmonized rhythmic melody on the one hand, and stylized verbal composition on the other, which is often casually implied or expressly formulated in modern comparisons of ‘music’ with ‘poetry’. For many ancient theorists the City Dionysia, a dithyrambic festival and a recitation of Homer all featured different versions of one and the same form of composition, a μουσική or ποιητική to which λόγοι, γράμματα and συλλαβαί were just as essential as ἁρμονία, φθόγγοι, ῥυθμός and χρόνοι. (shrink)

There is no question, of course, that music is a temporal art. Stravinsky, noting that it is inconceivable apart from the elements of sound and time, classifies it quite simply as "a certain organization in time, a chrononomy."1 His definition stands as part of a long and honored tradition that encompasses such diverse figures as Racine, Lessing, and Schopenhauer. Schopenhauer, putting the case in its strongest terms, remarks that music is "perceived solely in and through time, to the complete exclusion (...) of space," thus making explicit the opposition between time and space and ruling out the latter as a possible area for legitimate musical experience. Yet anyone familiar with the philosophical and theoretical literature dealing with music must be struck by the persistence with which spatial terminology and categories appear. Indeed, it would seem to be impossible to talk about music at all without invoking spatial notions of one kind or another. Thus in discussing even the most elementary aspects of pitch organization—and among the musical elements, only pitch, we should remember, is uniquely musical—one finds it necessary to rely upon such spatially oriented oppositions as "up and down," "high and low," "small and large" , and so on. Space, then, pace Schopenhauer, apparently forms an inseparable part of the musical experience. · 1. Igor Stravinsky, Poetics of Music in the Form of Six Lessons, trans, Arthur Knodel and Ingolf Dahl , p. 28. Robert P. Morgan is active as both a music composer and theorist. A professor of music at the University of Chicago, he is currently composing a concerto for flute, oboe, and string orchestra to be performed at Swarthmore College. His previous contribution to Critical Inquiry, "On the Analysis of Recent Music," appeared in the Autumn 1977 issue. Anthony Gilbert responds to the current essay in "Musical Space: A Composer's View". (shrink)

This article intends, firstly, to enrich the study of the role that the concept of tone plays in Kantian idea of reason, by extending it to the analysis of music as art of sounds, which the Critique of Judgment fulfills. Secondly, it aims to determine the grounds that could explain why the mathematics, due to the specificity of the philosophical method and the physical reception of music, respectively, are itself incapable to express the procedures of reason and of the art (...) of sounds. Finally, it points out a similarity between reason and music concerning their common rejection of succumbing to the Schwärmerei, although the distance which divides them as two contrary ways to exercise and promote the life and its feeling.O artigo tenciona, primeiramente, enriquecer o estudo da função que o conceito de tom desempenha na ideia kantiana de razão, ao estendê-lo à análise da música como arte dos sons que a Crítica do Juízo contém. Em segundo lugar, propõe-se determinar os motivos pelos quais a matemática se revela incapaz, devido à especificidade do método filosófico e à corporalidade da recepção musical, respectivamente, de expressar o modo de proceder da razão e da arte dos sons. Finalmente, aponta-se para uma semelhança entre música e razão, no que diz respeito à rejeição que compartilham da queda na Schwärmerei, apesar da distância que se estabelece entre ambas enquanto duas maneiras contrárias de exercitar e fomentar a vida e o sentimento dela. (shrink)

This thesis is directed towards a philosophy of music by attention to conceptions and perceptions of space. I focus on melody and harmony, and do not emphasise rhythm, which, as far as I can tell, concerns time rather than space. I seek a metaphysical account of Western Classical music in the diatonic tradition. More specifically, my interest is in wordless, untitled music, often called 'absolute' music. My aim is to elucidate a spatial approach to the world combined with a curiosity (...) about the nature of the Pythagorean intervals. Thus one question I seek to answer is: What do the Pythagorean intervals import to music? In their original formulation by Pythagoras, and further, by Plato, their import seemed mystical and analogous to a 'harmony of the spheres.' In this spatial approach, the Pythagorean intervals are indicative of infinite depth. The faculty of hearing alone does not ordinarily spatially locate sources. Hearing is ordinarily combined with sight in order to spatially locate a sound. Yet we talk about music as if it were spatially located, that is, as if it were a visible object with a surface and themes or 'objects'. I explore the faculty of vision and consider in what ways the processes of vision might be similar to and distinct from audition. My source for this approach is David Marr's book 'Vision' and his theory of the 2 1/2-dimensional sketch. In a medium in which there is no spatial location, it is important to situate the listener. Newton solved the problem of location by demonstrating the effects of gravity. P. F. Strawson claims that an analogy of distance is required in hearing to situate the listener, that is, a sense of nearer to and further from a source or object that permits a perception of distance. I claim that in music, the key signature and the scalar relations of musical themes provide this analogy of distance. The works of Plato, Aristotle, Descartes, Leibniz, and Newton are studied for their accounts of motion, bodies, and space. From these metaphysicians can be gleaned elements of music that include form, motion, timbre, dynamics, and attraction. By incorporating motion, I aim to show that although we may not know the true nature of space, we can learn from hearing music that space is perceptible in other than three dimensions. (shrink)

continent. 2.2 (2012): 66–75 ~*~ We’re Doomed. Pessimism is the night-side of thought, a melodrama of the futility of the brain, a poetry written in the graveyard of philosophy. Pessimism is a lyrical failure of philosophical thinking, each attempt at clear and coherent thought, sullen and submerged in the hidden joy of its own futility. The closest pessimism comes to philosophical argument is the droll and laconic “We’ll never make it,” or simply: “We’re doomed.” Every effort doomed to failure, every (...) project doomed to incompletion, every life doomed to be unlived, every thought doomed to be unthought. Pessimism is the lowest form of philosophy, frequently disparaged and dismissed, merely the symptom of a bad attitude. No one ever needs pessimism, in the way that one needs optimism to inspire one to great heights and to pick oneself up, in the way one needs constructive criticism, advice and feedback, inspirational books or a pat on the back. No one needs pessimism, though I like to imagine the idea of a pessimist activism. No one needs pessimism, and yet everyone—without exception—has, at some point in their lives, had to confront pessimism, if not as a philosophy then as a grievance—against one’s self or others, against one’s surroundings or one’s life, against the state of things or the world in general. There is little redemption for pessimism, and no consolation prize. Ultimately, pessimism is weary of everything and of itself. Pessimism is the philosophical form of disenchantment—disenchantment as chanting, a chant, a mantra, a solitary, monophonic voice rendered insignificant by the intimate immensity surrounding it. In pessimism, the first axiom is a long, low, funereal sigh. ~*~ We’re Still Doomed. No one has time for pessimism. After all, there are only so many hours in a day. Whatever our temperament, happy or sad, engaged or disengaged, we know pessimism when we hear it. The pessimist is usually understood as the complainer, forever pointing out what is wrong with the world without ever once offering a solution. But more often than not pessimists are the quietest of philosophers, submerging their own sighs within the lethargy of discontent. What little sound it makes is of interest to no one—“I’ve heard it all before,” “tell me something I don’t know,” sound and fury, signifying nothing. In raising problems without solutions, in posing questions without answers, in retreating to the hermetic, cavernous abode of complaint, pessimism is guilty of that most inexcusable of Occidental crimes—the crime of not pretending it’s for real. Pessimism fails to live up to the most basic tenet of philosophy—the “as if.” Think as if it will be helpful, act as if it will make a difference, speak as if there is something to say, live as if you are not, in fact, being lived by some murmuring non-entity both shadowy and muddied. Had it more self-assurance and better social skills, pessimism would turn its disenchantment into a religion, possibly calling itself The Great Refusal. But there is a negation in pessimism that refuses even such a Refusal, an awareness that, from the start, it has already failed, and that the culmination of all that is, is that all is for naught. Pessimism tries very hard to present itself in the low, sustained tones of a Requiem Mass, or the tectonic rumbling of Tibetan chant. But it frequently lets loose dissonant notes at once plaintive and pathetic. Often, its voice cracks, its weighty words abruptly reduced to mere shards of guttural sound. ~*~ Maybe It’s Not So Bad, After All. If we know pessimism when we hear it, this is because we’ve heard it all before—and we didn’t need to hear it in the first place. Life is hard enough. What you need is a change of attitude, a new outlook, a shift in perspective... a cup of coffee. If we have no ears for pessimism, this is because it is always reducible to something as reliably mutable as a voice. If pessimism is so frequently disparaged, it is because it brings everyone down, determined as it is to view each day as a bad day, if only by virtue of the fact that it is not yet a bad day. For pessimism the world is brimming with negative possibility, the collision of a bad mood with an impassive world. In fact, pessimism is the result of a confusion between the world and a statement about the world, a confusion that also prevents it from fully entering the hallowed halls of philosophy. If pessimism is so often dismissed, this is because it is often impossible to separate a “bad mood” from a philosophical proposition (and do not all philosophies stem from a bad mood?) The very term “pessimism” suggests a school of thought, a movement, even a community. But pessimism always has a membership of one—maybe two. Ideally, of course, it would have a membership of none, with only a scribbled, illegible note left behind by someone long forgotten. But this seems unrealistic, though one can always hope. ~*~ Anatomy of Pessimism. Though it may locate itself at the margins of philosophy, pessimism is as much subject to philosophical analysis as any other form of thought. Pessimism’s lyricism of failure gives it the structure of music. What time is to the music of sorrow, reason is to a philosophy of the worst. Pessimism’s two major keys are moral and metaphysical pessimism, its subjective and objective poles, an attitude towards the world and a claim about the world. For moral pessimism, it is better not to have been born at all; for metaphysical pessimism, this is the worst of all possible worlds. For moral pessimism the problem is the solipsism of human beings, the world made in our own image, a world-for-us. For metaphysical pessimism, the problem is the solipsism of the world, objected and projected as a world-in-itself. Both moral and metaphysical pessimism are compromised philosophically; moral pessimism by its failure to locate the human within a larger context, and metaphysical pessimism by its failure to recognize the complicity in the very claim of realism. This is how pessimism makes its music of the worst, a generalized misanthropy without the anthropos . Pessimism crystallizes around this futility—it is its amor fati , rendered as musical form. ~*~ Melancholy of Anatomy. There is a logic of pessimism that is fundamental to its suspicion of philosophical system. Pessimism involves a statement about a condition . In pessimism each statement boils down to an affirmation or a negation, just as any condition boils down to the best or the worst. With Schopenhauer, that arch-pessimist, the thinker for whom the philosopher and the curmudgeon perfectly overlap, we see a no-saying to the worst, a no-saying that secretly covets a yes-saying (through asceticism, mysticism, quietism), even if this hidden yes-saying is a horizon at the limits of comprehension. With Nietzsche comes the pronouncement of a Dionysian pessimism, a pessimism of strength or joy, a yes-saying to the worst, a yes-saying to this world as it is. And with Cioran yet another variation, futile yet lyrical, a no-saying to the worst, and a further no-saying to the possibility of any other world, in here or out there. With Cioran one approaches, but never reaches, an absolute no-saying, a studied abandonment of pessimism itself. The logic of pessimism moves through three refusals: a no-saying to the worst (refusal of the world-for-us, or Schopenhauer’s tears); a yes-saying to the worst (refusal of the world-in-itself, or Nietzsche’s laughter); and a no-saying to the for-us and the in-itself (a double refusal, or Cioran’s sleep). Crying, laughing, sleeping—what other responses are adequate to a life that is so indifferent? ~*~ Cosmic Pessimism. Both moral and metaphysical pessimism point to another kind, a pessimism that is neither subjective nor objective, neither for-us nor in-itself, and instead a pessimism of the world-without-us. We could call this a cosmic pessimism ... but this sounds too majestic, too full of wonder, too much the bitter aftertaste of the Great Beyond. Words falter. And so do ideas. And so we have a cosmic pessimism, a pessimism that is first and last a pessimism about cosmos , about the necessity and possibility of order. The contours of cosmic pessimism are a drastic scaling-up or scaling-down of the human point of view, the unhuman orientation of deep space and deep time, and all of this shadowed by an impasse, a primordial insignificance, the impossibility of ever adequately accounting for one’s relationship to thought—all that remains of pessimism is the desiderata of affects—agonistic, impassive, defiant, reclusive, filled with sorrow and flailing at that architectonic chess match called philosophy, a flailing that pessimism tries to raise to the level of an art form (though what usually results is slapstick). ~*~ Song of Futility. An ethics of futility pervades pessimism. Futility, however, is different from fatality, and different again from simple failure (though failure is never simple). Failure is a breakage within the heart of relations, a fissure between cause and effect, a fissure hastily covered over by trying and trying again. With failure, there is always plenty of blame to go around; it’s not my fault, it’s a technical difficulty, it’s a miscommunication. For the pessimist, failure is a question of “when,” not “if”—failure as a metaphysical principle. Everything withers and passes into an obscurity blacker than night, everything from the melodramatic decline of a person’s life to the banal flickering moments that constitute each day. Everything that is done undone, everything said or known destined for a kind of stellar oblivion. When scaled up in this way, failure becomes fatality. Fatality is the hermeticism of cause and effect. In fatality, everything you do, whatever you do, always leads to a certain end, and ultimately to the end—though that end, or the means to that end, remain shrouded in obscurity. Nothing you do makes a difference because everything you do makes a difference. Hence the effects of your actions are hidden from you, even as you deceive yourself into thinking that, at last, this time you will outwit the order of things. By having a goal, planning ahead, and thinking things through carefully, we attempt, in a daily Prometheanism, to turn fatality to our advantage, to gain a glimpse of an order that seems buried deeper and deeper in the fabric of the universe. But even fatality has its comforts. The chain of cause and effect may be hidden from us, but that’s just because disorder is the order we don’t yet see; it’s just complex, distributed, and requires advanced mathematics. Fatality still clings to the sufficiency of everything that exists... When fatality relinquishes even this idea, it becomes futility. Futility arises out of the grim suspicion that, behind the shroud of causality we drape over the world, there is only the indifference of what exists or doesn’t exist; whatever you do ultimately leads to no end, an irrevocable chasm between thought and world. Futility transforms the act of thinking into a zero-sum game. ~*~ Song of the Worst. At the center of pessimism lies the term pessimus , “the worst,” a term as relative as it is absolute. The worst is about as bad as it gets, “the worst” as “the best” in disguise, shrouded by the passage of time or the twists and turns of fortune. For the pessimist, “the worst” is the propensity for suffering that gradually occludes each living moment, until it eclipses it entirely, overlapping perfectly in death... which, for the pessimist, is no longer “the worst.” Pessimism is marked by an unwillingness to move beyond “the worst,” something only partially attributable to a lack in motivation. In pessimism “the worst” is the ground that gives way beneath every existent—things could be worse, and , things could be better. “The worst” invariably implies a value judgment, one made based on scant evidence and little experience; in this way, pessimism’s greatest nemesis is its moral orientation. Pessimism’s propositions have all the gravitas of a bad joke. Perhaps this is why the true optimists are the most severe pessimists—they are optimists that have run out of options. They are almost ecstatically inundated by the worst. Such an optimism is the only possible outcome of a prolonged period of suffering, physical or metaphysical, intellectual or spiritual. But does this not also describe all the trials and tribulations of each day—in short, of “life?” It seems that sooner or later we are all doomed to become optimists of this sort (the most depressing of thoughts...) ~*~ Song of Doom. Rather than serving as a cause for despair, gloom and doom are the forms of consolation for any pessimist philosophy. Neither quite affects nor quite concepts, gloom and doom transform pessimism into a mortification of philosophy. Doom is not just the sense that all things will turn out badly, but that all things inevitably come to an end, irrespective of whether or not they really do come to an end. What emerges from doom is a sense of the unhuman as an attractor, a horizon towards which the human is fatally drawn. Doom is humanity given over to unhumanity in an act of crystalline self-abnegation. Gloom is not simply the anxiety that precedes doom. Gloom is literally atmospheric, climate as much as impression, and if people are also gloomy, this is simply the by-product of an anodyne atmosphere that only incidentally involves human beings. Gloom is more climatological than psychological, the stuff of dim, hazy, overcast skies, of ruins and overgrown tombs, of a misty, lethargic fog that moves with the same languorousness as our own crouched and sullen listening to a disinterested world. In a sense, gloom is the counterpoint to doom—what futility is to the former, fatality is to the latter. Doom is marked by temporality—all things precariously drawn to their end—whereas gloom is the austerity of stillness, all things sad, static, and suspended, a meandering smoke hovering over cold lichen stones and damp fir trees. If doom is the terror of temporality and death, then gloom is the horror of a hovering stasis that is life. At times I like to imagine that this realization alone is the thread that connects the charnel ground Aghori and the graveyard poets. ~*~ Song of Spite. There is an intolerance in pessimism that knows no bounds. In pessimism spite begins by fixing on a particular object of spite—someone one hardly knows, or someone one knows too well; a spite for this person or a spite for all of humanity; a spectacular or a banal spite; a spite for a noisy neighbor, a yapping dog, a battalion of strollers, the meandering idiot walking in front of you on their smart phone, large loud celebrations, traumatic injustices anywhere in the world regurgitated as media blitz, spite for the self-absorbed and overly performative people talking way too loud at the table next to you, technical difficulties and troubleshooting, the reduction of everything to branding, spite of the refusal to admit one’s own errors, of self-help books, of people who know absolutely everything and make sure to tell you, of all people, all living beings, all things, the world, the spiteful planet, the inanity of existence... Spite is the motor of pessimism because it is so egalitarian, so expansive, it runs amok, stumbling across intuitions that can only half-heartedly be called philosophical. Spite lacks the confidence and the clarity of hatred, but it also lacks the almost cordial judgment of dislike. For the pessimist, the smallest detail can be an indication of a metaphysical futility so vast and funereal that it eclipses pessimism itself—a spite that pessimism carefully places beyond the horizon of intelligibility, like the experience of dusk, or like the phrase, “it is raining jewels and daggers.” ~*~ Song of Sleep. A paraphrase of Schopenhauer: what death is for the organism, sleep is for the individual. Pessimists sleep not because they are depressed, but because for them sleep is a form of ascetic practice. Sleep is the askesis of pessimism. If, while sleeping, we have a bad dream, we abruptly wake up, and suddenly the horrors of the night vanish. There is no reason to think that the same does not happen with the bad dream we call “life.” ~*~ Song of Sorrow. Nietzsche, commenting on pessimism, once castigated Schopenhauer for taking things too lightly. He writes: ...Schopenhauer, though a pessimist, really —played the flute. Every day, after dinner: one should read his biography on that. And incidentally: a pessimist, one who denies God and the world but comes to a stop before morality—who affirms morality and plays the flute... what? Is that really—a pessimist? We know that Schopenhauer did possess a collection of instruments, and we also know that Nietzsche himself composed music. There is no reason to think that either of them would ever banish music from the Republic of philosophy. But Nietzsche’s jibes at Schopenhauer are as much about music as they are about pessimism. For the pessimist who says no to everything and yet finds comfort in music, the no-saying of pessimism can only be a weak way of saying yes—the weightiest statement undercut by the flightiest of replies. The least that Schopenhauer could’ve done is to play the bass. I’m not a big fan of the flute, or, for that matter, wind instruments generally. But what Nietzsche forgets is the role that the flute has historically played in Greek tragedy. In tragedy, the flute ( aulos ) is not an instrument of levity and joy, but of solitude and sorrow. The Greek aulos not only expresses the grief of tragic loss, but it does so in a way that renders weeping and singing inseparable from each other. The classicist Nicole Loraux calls this the mourning voice . Set apart from the more official civic rituals of funerary mourning, the mourning voice of Greek tragedy constantly threatens to dissolve song into wailing, music into moaning, and the voice into a primordial, disarticulate anti-music. The mourning voice delineates all the forms of suffering—tears, weeping, sobbing, wailing, moaning, and the convulsions of thought reduced to an elemental unintelligibility. In the collapsed space between the voice that speaks and the voice that sings, pessimism discovers its mourning voice. Pessimism: the failure of sound and sense, the disarticulation of phone and logos . Have we rescued Schopenhauer from Nietzsche? Probably not. Perhaps Schopenhauer played the flute to remind himself of the real function of the mourning voice—sorrow, sighs, and moaning rendered indistinguishable from music, the crumbling of the human into the unhuman. Failure par excellence of pessimism. ~*~ Song of Nothing. In Buddhist thought, the First Noble Truth of existence is encapsulated in the Pali term dukkha , conventionally translated as “suffering,” “sorrow,” or “misery.” The Buddhist teachings are clear, however, that this is an objective claim, and not simply one point of view among others. Existence is suffering and sorrow—and yet this is not, the teachings tell us, a pessimistic attitude. It is likely that Schopenhauer, reading the Buddhist texts available to him, recognized some filiation with the concept of dukkha . But dukkha is a multi-faceted term. There is, certainly, dukkha in the usual sense of the suffering, strife, and loss associated with living a life. But this is, in turn, dependent on the finitude and temporality of dukkha , existence as determined by impermanence and imperfection. And this ultimately points to the way in which both suffering and finitude are grounded by the paradoxical groundlessness of dukkha as a metaphysical principle—the insubstantiality and the emptiness of all that is. Beyond what is worse to me, beyond a world ordered for the worst, there is the emptiness of dukkha as an impersonal suffering... the tears of the cosmos. In this context, it is easy to see how Schopenhauer’s pessimism attempts to compress all the aspects of dukkha into a nothingness at the core of existence, a Willlessness coursing through the Will. Though one thing for certain is that with Schopenhauer we do not find the “ever-smiling” countenance of Buddhism—or do we? The texts of the Pali Canon also contain lists of the different types of happiness—including the happiness of renunciation and the strange happiness of detachment. But Buddhism considers even the different types of happiness as part of dukkha , in this final sense of nothingness or emptiness. Perhaps Schopenhauer understood Buddhism better than he is usually given credit for. Thus the experiment of Schopenhauer’s philosophy—the point at which a Western pessimus and an Eastern dukkha overlap or exchange glances. Empty sorrow, a lyricism of indifference. The result is a strange, and ultimately untenable, nocturnal form of Buddhism. ~*~ Cioran once called music a “physics of tears.” If this is true, then perhaps metaphysics is its commentary. Or its apology. ~*~ Pessimism would be more mystical were it not for its defeatism. Mysticism is much too proactive for the pessimist, and pessimism too impassive even for the mystic. At the same time, there is something enviable about mysticism—despite its sufferings. There is a sense in which pessimists are really failed mystics. ~*~ You, the Night, and the Music. In a suggestive passage, Schopenhauer once noted that, “music is the melody to which the world is the text." Given Schopenhauer’s view on life—that life is suffering, that human life is absurd, that the nothingness before my birth is equal to the nothingness after my death—given all this, one wonders what kind of music Schopenhauer had in mind when he described music as the melody to which the world is text—was it opera, a Requiem Mass, a madrigal, or perhaps a drinking song? Or something like Eine kleine Nachtmusik , a little night music for the twilight of thought, a sullen nocturne for the night-side of logic, an era of sad wings sung by a solitary banshee. Perhaps the music Schopenhauer had in mind is music eliminated to non-music. A whisper would suffice. Perhaps a sigh of fatigue or resignation, perhaps a moan of despair or sorrow. Perhaps a sound just articulate enough that it could be heard to dissipate. ~*~ Teach me to laugh through tears. ~*~ Pessimism always falls short of being philosophical. My back aches, my knees hurt, I couldn’t sleep last night, I’m stressed-out, and I think I’m finally coming down with something. Pessimism abjures all pretenses towards system—towards the purity of analysis and the dignity of critique. We didn’t really think we could figure it out, did we? It was just passing time, taking a piss, something to do, a bold gesture put forth in all its fragility, according to rules that we have agreed to forget that we made up in the first place. Every thought marked by a shadowy incomprehension that precedes it, and a futility that undermines it. That pessimism speaks, in whatever voice, is the singing testimony to this futility and this incomprehension—take a chance and step outside, lose some sleep and say you tried... ~*~ Is there a music of pessimism? And would such a music be audible? ~*~ The impact of music on a person compels them to put their experience into words. When this fails, the result is a faltering of thought and language that is itself a kind of music. Cioran writes: “Music is everything. God himself is nothing more than an acoustic hallucination.” ~*~ If a thinker like Schopenhauer has any redeeming qualities, it is that he identified the great lie of Western culture—the preference for existence over non-existence. As he notes: “If we knocked on the graves and asked the dead whether they would like to rise again, they would shake their heads.” In Western cultures it is commonly accepted that one celebrates birth and mourns death. But there must be a mistake here. Wouldn’t it make more sense to mourn birth and celebrate death? Strange though, because the mourning of birth would, presumably, last the entirety of that person’s life, so that mourning and living would the be same thing. ~*~ To the musical idea of the harmony of the universe corresponds the philosophical principle of sufficient reason. Like the music of mourning, pessimism gives voice to the inevitable breakdown of word and song. In this way, music is the overtone of thought. ~*~ The Patron Saints of Pessimism. The patron saints of pessimism watch over suffering. Laconic and sullen, the patron saints of pessimism never seem to do a good job at protecting, interceding, or advocating for those who suffer. Perhaps they need us more than we need them. Lest we forget, there do exist patron saints of philosophy, but their stories are not happy ones. There is, for instance, the fourth century Saint Catherine of Alexandria, or Catherine of the Wheel, named after the torture device used on her. A precocious fourteen year old scholar, Catherine was subject to continual persecution. After all forms of torture failed—including the “breaking wheel”—the emperor finally settled for her decapitation, a violent yet appropriate reminder of the protector of philosophers. There are also patron saints of music and musicians, but theirs too are sad stories. In the second century, Saint Cecilia was also subject to persecution and torture. As she knelt to receive the blade that would separate her head from her body, she ardently sang a song to God. It took three attempts before she was fully decapitated, all the while she continued, perhaps miraculously, to sing. Does pessimism not deserve its own patron saints, even if they are unworthy of martyrdom? But in our search, even the most ardent nay-sayers frequently lapse into brief moments of enthusiasm—Pascal’s love of solitude, Leopardi’s love of poetry, Schopenhauer’s love of music, Nietzsche’s love of Schopenhauer, and so on. Should one then focus on individual works of pessimism? We could include Kierkegaard’s trilogy of horror— Sickness Unto Death , The Concept of Dread , and Fear and Trembling —but all these are undermined by their fabricated and unreliable authors. Besides, how can one separate the pessimist from the optimist in works like Unamuno’s The Tragic Sense of Life , Shestov’s Postetas Clavium , or Edgar Saltus’ under-read The Philosophy of Disenchantment ? Even in cases where the entire corpus of an author is pessimistic, the project always seems incomplete—witness Cioran’s trajectory, from his first book, On the Heights of Despair , to the last unpublished notebooks of acrid and taut aphorisms. And this is to say nothing of literary pessimism, from Goethe’s sorrowful Werther, to Dostoevsky’s underground man, to Pessoa’s disquiet scribbler; Baudelaire’s spleen and ennui, the mystical Satanism of Huysmans and Strindberg, the hauntologies of Mário de Sá-Carniero, Izumi Kyoka, H.P. Lovecraft, grumpy old Beckett... even the great pessimist comedians. All that remains are singular, perhaps anomalous statements of pessimism, a litany of quotes and citations crammed into fortune cookies. Patron saints are traditionally named after a locale, either a place of birth or of a mystical experience. Perhaps the better approach is to focus on the places where pessimists were forced to live out their pessimism—Schopenhauer facing an empty Berlin lecture hall, Nietzsche mute and convalescent at the home of his sister, Wittgenstein the relinquished professor and solitary gardener, Cioran grappling with Alzheimer’s in his tiny writing alcove in the Latin Quarter. ~*~ There’s a ghost that grows inside of me, damaged in the making, and there’s a hunt sprung from necessity, elliptical and drowned. Where the moving quiet of our insomnia offers up each thought, there’s a luminous field of grey inertia, and obsidian dreams burnt all the way down. ~*~ If pessimism has any pedagogical value, it is that the failure of pessimism as a philosophy is inextricably tied to the failure of pessimism as voice. I read the following, from Shestov’s The Apotheosis of Groundlessness : When a person is young he writes because it seems to him he has discovered a new almighty truth which he must make haste to impart to forlorn humankind. Later, becoming more modest, he begins to doubt his truths: and then he tries to convince himself. A few more years go by, and he knows he was mistaken all round, so there is no need to convince himself. Nevertheless he continues to write, because he is not fit for any other work, and to be accounted a superfluous person is so horrible. (shrink)

Iannis Xenakis (1922–2001), composer, architect, engineer and media artist, designed together with Le Corbusier the Philips-pavilion for the 1958 Brussels World Fair. This pavilion is an early example of (“hybrid”) combined media and architectural space as it contained a Poème Électronique, an electronic synthesis of visual projections (conceived by Le Corbusier ) and acoustic events (composed by Varèse). The pavilion's architecture with its hyperbolic-paraboloid shells had a dynamic expression. Xenakis continued this research into complex material architectural forms. He also worked (...) on the complex ephemeral architectures of light and sound events. What is specific to Xenakis is the way he used forms in different fields and transferred them from one field to another, from engineering to music, from music to architecture and visual events. This experience of working simultaneously and applying the same (mental) structures in different fields opened him the way (partly supported by the universal computer instrument) for the practice of transferring mathematical-scientific structures into artistic production. In this context Xenakis pleads for the development of a “General Morphology”, a research concerned with the understanding of form and its generation. Xenakis's ‘material’ architectural work is to be seen in continuity with his architectures of music and light. (shrink)

continent. 1.4 (2011): 286—310. This mad play of writing —Stéphane Mallarmé Somewhere in between mathematics and theory, light and dark, physicality and projection, oscillates the poetry of Alessandro De Francesco. The texts hold no periods or commas, not even a capital letter for reference. Each piece stands as an individual construction, and yet the poetry flows in and out of the frame. Images resurface from one poem to the next, haunting the reader with reincarnations of an object lost in the (...) grass or a representation of a pear in a Dutch still life, embedded in cycles of cinematic close ups and multiple dimensions. As a whole, De Francesco’s oeuvre suggests, to use the title of one of his works, a redefinition —linguistic, epistemological, personal. The poem The End (un’agenda) (The End (an agenda)) opens with a quote by literary theorist Maurice Blanchot, which may be translated as follows: Speaking is not seeing. Speaking frees thought from this optical imperative that in the Western tradition, for thousands of years, has subjugated out approach to things, and induced us to think under the guaranty of light or under the threat of its absence.[1] In writing, De Francesco seeks to redefine our approach to things. His poems, like Blanchot’s writings, speak to both illuminate and to obscure. The reader hangs in an absence of reality within language that necessitates an attempt at interpretation, yet renders such a search ultimately futile. De Francesco draws the anonymous images that appear in this poem from the city of Paris, his current home. The fragmented narrative depicts an inner doubt of realness, calling for a confirmation of a physical existence beyond verbalization and cogitation. Cyclical references to film throw into question the reliability of the reality he creates. The light, sometimes red and safe, other times absent and murky, cannot necessarily be trusted as a guaranteed means of illumination. Blanchot’s distinction between language and visualization, and the relationship of each to reality, though linked specifically to The End (un’agenda) , can be a lens through which to read any of the three works that follow. assente obliqua (absent oblique) is composed of descriptions of six still life paintings, ranging from Dutch masterpieces of the seventeenth century to 1960s minimalism. The actual images of the paintings are absent, and the text is the sole source and object of a virtual reality created around the artwork. “Absent oblique” refers to the light source placed outside of the frame, which both informs and distracts viewing of the scene. Although mere description can be unreliable and unsatisfying in its necessary limitation, the representational act of description is shown as more than just a human want. It is a need, a means by which to grapple with an unsure reality. As the illustrations progress, they descend into abstraction and chaos. The precariously placed plate triggers the movement: the bottle bursts and the objects collapse into the movement of a tracking film camera. corpo estraneo in moto ascensionale (foreign body in ascending motion) is prose poetry in action. Its objective tone of description is skewed by the subjectivity of the narrative as horrific images are relayed in fragmented but matter-of-fact manner. A “foreign body” is both a mass of cancerous cells, and a corporeal description, and the poem takes the reader on a journey back and forth between the two, destination unclear. Beyond a questioning of the real, corpo estraneo in moto ascensionale is an examination of the possible. De Francesco’s poetry becomes a camera obscura through which to observe the constant flux of light and dark that blurs our reality. His work is colored by the idea of apo koinou , a Greek term meaning “from the common” that involves a construction of two clauses with a shared word or phrase. Through such melting of meaning, De Francesco creates a fluid ambiguity that is nonetheless grounded in bodily concepts. In assente obliqua , the reader is confronted with a description of a still life that rapidly transforms into a more chilling scene: the membrane of the mushroom in the basket emerges behind the white cloth a body could hide itself that asks for help In the realm of pure description, there is a mushroom that peeks out from behind a white cloth in a basket. Behind the white cloth, too, there could be a body, hiding, asking for help. Such an elision elicits disorienting mistrust in temporality, but also expands the planar possibilities of syntactical meaning. A white cloth is not merely a construct in still life painting, but veil that both shields and reveals potential mysteries. It is a proposed alternative to a traditional Western binary of subjectivity and objectivity. The apo koinou construction is rare in modern English, having slipped out of use after its resurgence in Old English poetry. De Francesco reintroduces this blur of object and subject relations into a modern light. He draws inspiration from a device used by Gruppo 63 founder and avant-garde poet Antonio Porta tended toward repetition of phrases in third person perspective. In Italian, it is perfectly grammatically correct to omit the subject, including only a verb conjugation. Gender, even humanity unknown, the subject dissolves into the action, thus giving to the poetry the power to change the reader’s perception of who or what is actually acting. To further push the relative boundaries of experience, De Francesco expands his written poetry into what he calls “reading environments.” In these sound experiments, De Francesco’s voice reading his poetry is manipulated by real time digital voice processing. The written is transformed to the spoken, and then injected with currents of electric sound. “At each activation of word in the darkness,” (from The End (un’agenda) ) language is permutated into a nonphysical yet all-encompassing being. In these projects, realized all over Europe, De Francesco continues his examination of the word’s potency beyond the page and into an “n-dimensional space,” where the lines between nature and affect are intertwined. To publish excerpts of De Francesco’s oeuvre is to show screen shots of full-length film, to read pull quotes from a philosophy treatise. In these poems, there are questions, not to be answered, but to be questioned again. The words will oscillate in and out of the square construction found in his poems, out of the borders of the page, out of the rectangle of the laptop screen. NOTES (1) Blanchot, Maurice. The Infinite Conversation . Trans. Susan Hanson. Minneapolis: University of Minnesota Press, 1993. 27. EDITORS' NOTE The .pdf above contains about twenty pages of translation and the original Italian poetry. Below we provide only a brief account. The End (an agenda) Parler, ce n’est pas voir. Parler libère la pensée de cette exigence optique qui, dans la tradition occidentale, soumet depuis des millénaires notre approche des choses et nous invite à penser sous la garantie de la lumière ou sous la menace de l’absence de lumière. —Maurice Blanchot in this n-dimensional space i could spy on myself from the cracks while going back and forth from the summer to the wardrobe from the night to the parking lot but something filters in through the half-closed shutters becomes an event enunciation we stay without explanation like parallel curves on the back of a solid growing older she enters the garden always repeats certain phrases the elevator to be redone the neighbor’s music the steps the pavement furls like the leaves of a fern when touched she is framed from behind while she moves rocking she covers distances slowly a bag overflows from the wardrobe something stirs inside but then the suitcase comes open not even by my hand it’s the objects that are starting to filter out the little red haired monster watches idling the appointments written on one of your agendas two years old still seem urgent each letter holds itself upright on the page with flourishes and arabesques each angle has its own geography i’m trying to describe the path the fingers trace on the carpet the zipper takes the opposite route we are suspended on the stairs above the water in the center is the summer seen from above the darkness of the city passes from one headlight to the next the surfaces of our arms cohere and are shiny underneath the blinking of a sign each pore is an open expanse the body dreams the hair gives form to the possible some daring swimmers were throwing themselves into the seine they swam upstream up to the first quay look there could exist behind the screen a room where even when the lamp is out and the curtains drawn even when the suitcase wasn’t closed everything seemed red everything calm construction of a four-dimensional tetrahedron by R. Courant – H. Robbins, What is Mathematics? Oxford University Press, 1941  . (shrink)

In spite of differences the thought of Bernays, Dooyeweerd and Gödel evinces a remarkable convergence. This is particularly the case in respect of the acknowledgement of the difference between the discrete and the continuous, the foundational position of number and the fact that the idea of continuity is derived from space (geometry – Bernays). What is furthermore similar is the recognition of what is primitive (and indefinable) as well as the account of the coherence of what is unique, such as (...) when Gödel observes something quasi-spatial character of sets. It is shown that Dooyeweerd’s theory of modal aspects provides a philosophical framework that exceeds his own restrictive understanding of infinity )to the potential infinite) and at the same time makes it possible to account for key insights found in the thought of Bernays and Gödel. When Laugwitz says that discreteness rules within the sphere of the numerical, he says nothing more than what Dooyeweerd had in mind with his idea that discrete quantity, as the meaning-nucleus of the arithmetical aspect, qualifies every element within the structure of the quantitative aspect. And when Bernays says that analysis expresses the idea of the continuum in arithmetical language his mode of speech is equivalent to saying that mathematical analysis could seen as being founded upon the spatial anticipation within the modal structure of the arithmetical aspect. The view of the actual infinite (the at once infinite) in terms of an “as if” approach (Bernays), that is, as appreciated as a regulative hypothesis through which every successively infinite multiplicity of numbers could be envisaged as being giving all at once, as an infinite totality, provides a sound understanding of the at once infinite and makes it plain why every form of arithmeticism fails. Such attempts have to call upon Cantor’s proof on the non-denumerability of the real numbers – and this proof pre-supposes the use of the at once infinite which, in turn, pre-supposes the (irreducibile) spatial order of simultaneity and the patial whole-parts relation. (shrink)

continent. 2.1 (2012): 6–21. The French philosopher and novelist Tristan Garcia was born in Toulouse in 1981. This makes him rather young to have written such an imaginative work of systematic philosophy as Forme et objet , 1 the latest entry in the MétaphysiqueS series at Presses universitaires de France. But this reference to Garcia’s youthfulness is not a form of condescension: by publishing a complete system of philosophy in the grand style, he has already done what none of (...) us in the older generation of speculative realists has done so far. His book is sophisticated, erudite, rigorous, imaginatively rich, and abundant in worldly wisdom– despite the author’s conclusion that wisdom does not exist. The quality and scope of Forme et objet took few observers by surprise, since Garcia has been treated as an emerging philosopher to watch across half a decade of Parisian oral tradition. But Garcia was not just the subject of rumor, being already well known to the French public as a writer of fiction. His debut novel, La meilleure part des hommes , 2 was awarded the 2008 Prix de Flore 3 and has already appeared in English as Hate: A Romance . 4 His follow-up novel, Mémoires de la jungle , 5 made clever use of a chimpanzee narrator. Nor was Garcia only published as a novelist before last November: his philosophical study L’Image 6 had already appeared when the author was just twenty-six, a year before he was crowned by the muses at the historic Café de Flore. And then in 2011, just months before the appearance of Forme et objet , Garcia published a widely distributed work entitled Nous, animaux et humains , 7 with its focus on Jeremy Bentham’s ideas about animals. Given this prolific and versatile track record, an optimistic scenario might envisage the young Garcia as one of those combined literary/philosophical talents who appear intermittently in France across the centuries: Jean-Paul Sartre is merely the most famous recent case. While more time is needed to see how Garcia will channel his impressive mental energies, Forme et objet displays such breadth of insight that its author has a good chance to emerge as one of the leading philosophers of his generation. If we accept Aristotle’s dictum that the peak mental age is fifty-one, then to read Garcia’s massive book is to gain some idea of what European philosophy might look like in the futuristic-sounding 2030’s. The present article is confined to Forme et objet . At 486 pages, the work is obviously daunting in size. Indeed, it is even longer than it sounds, given that many of its early sections are printed in a smaller typeface to designate them as supplemental commentary to the main flow of the argument. But while the length of the book reportedly led to delays in French publication, and will probably slow the inevitable appearance of an English translation, the length of the book should not deter interested readers– much of it results from Garcia’s teacherly writing style. Whereas Quentin Meillassoux’s prose displays an arctic economy of means, Garcia’s style is reminiscent of the repeated lessons of oral classroom proceedings. Rarely is the reader given fewer than three or four chances to master an idea before the author moves on to the next. In practice, the style feels welcoming rather than long-winded. Otherwise, the structure of Forme et objet is surprisingly simple. There is a useful Introduction of less than twenty pages. Then comes Book I: Formally , running to approximately 135 pages. Here Garcia outlines the most basic features of a thing “no matter what it is,” or n’importe quoi , an everyday phrase that Garcia shapes into a technical term. This part of the book feels at times like a more amiable version of Hegel’s Science of Logic , a parallel emphasized further by the threefold articulation of its theme: 1. Thing; 2. Thing and World; 3. Being and Understanding. This is followed by the much longer Book II: Objectively , totaling more than 300 pages. It contains sixteen essay-like meditations on specific kinds of objects—including time, animals, humans, history, gender, and death. Here each chapter rolls smoothly into the next, making this second part of the book feel more like a different work of Hegel: The Phenomenology of Spirit . But these are merely analogies. Garcia is no Hegelian, even if the book contains a few dialectical flourishes that seem to reflect his early enthusiasm for the Frankfurt School. Forme et objet ends with a six-page Coda, followed by the usual page of acknowledgments. In what follows, I will briefly summarize each of these four parts of the book before ending with some more general remarks. Before doing so, it will be useful to situate Garcia biographically (as much as I am able) and philosophically. Though Toulouse is his native city, his formative years were spent largely in Algeria, where his family has deep roots. During our sole private conversation, Garcia mentioned that his parents are professors of literature. 8 As a student of philosopher Garcia flourished so early that many of his current ideas date to his teenaged years: “There are sentences in Forme et objet that I wrote when I was seventeen,” he said in response to a question on that cold night on the Canal St.-Martin. I recalled that remark when reading his brilliant account, late in the book, of the central role of adolescence in contemporary culture. While many prodigies blow through their formal academic training without serious obstruction, Garcia’s student memories are rich in tales of isolation and struggle, though equally rich in gratitude for a half-dozen or so exceptional teachers who provided the intellectual space he needed: Meillassoux and Alain Badiou are simply two of the most prominent figures on that list. Though there are many points of agreement between Garcia’s philosophical position and my own, he not only reached his position years before reading my work, 9 he arrived along a rather different path: not through phenomenology, but via the Frankfurt School, which may be one of the reasons for his profound fascination with aesthetics. Garcia’s cultural background is as broad as one could wish: he is no less informed about punk rock and European football leagues than about the spiritualist roots of Bergson’s philosophy. Curious about everything and contemptuous towards nothing, Garcia can be expected to write insightfully on dozens of topics in the years to come. Given that his philosophy is so personally tantalizing in its agreements and disagreements with my own, and given the great internal richness of Forme et objet itself, the present review is no better than a first effort at coming to terms with the challenges posed by this minstrel from the rising generation. This is especially intriguing for older Generation X’ers like me, since confrontation with the younger generation is one of the many themes treated insightfully in Garcia’s book. 1. Introduction Garcia begins in defense of a so-called “flat ontology,” in which all things are equally things. While Roy Bhaskar 10 used this term pejoratively to refer to anti-realist philosophies that flatten everything onto an epistemic plane of human access, Manuel DeLanda 11 (an admirer of Bhaskar) reversed it into the positive principle that all realities are equally realities. Similar notions can be found in the “absistence” of Alexius Meinong, 12 the “irreduction” of Bruno Latour, 13 and my own critique 14 of the undermining/overmining pair. Also noteworthy is Levi Bryant’s use of the term “flat ontology” throughout The Democracy of Objects 15 and his earlier essay “The Ontic Principle.” 16 But for Garcia, flatness is only one face of the cosmos, and one that he ultimately declares to be rather impoverished. Even so, he always remains an advocate of a flat ontology. Insofar as everything is equally something, no matter what it is ( n’importe qui ), everything is equally a thing, equally solitary in its relation with world. This is why his book abounds in those long lists of random, ontologically equivalent entities that Ian Bogost has playfully termed “Latour Litanies.” 17 The first litany in Garcia’s book runs as follows: “We live in this world of things, where a cutting of acacia, a gene, a computer-generated image, a transplantable hand, a musical sample, a trademarked name, or a sexual service are comparable things.” (7) Yet Garcia is frankly dualistic; his flat ontology only lasts until page 159 and the end of Book I (entitled “Formally”), which deals entirely with things that are equally things. Thereafter Garcia turns his attention from things to objects, which are not flat in the least, but engage in hierarchical relations with one another. In agreement with both DeLanda and the speculative realists, Garcia proclaims that his book “proposes to put to the test a thought about things rather than a thought about our thought about things .” (8) Just as ducklings are “imprinted” (9) after hatching and treat the first creature they see as their mother, philosophers are imprinted by the idea with which they begin. Hence, philosophies that begin with human access will never truly find their way back to things. This makes Garcia rather suspicious of twentieth century philosophy, since “the twentieth century—to which in some way this work proposes to bid adieu—has been a period of theorizing modes of access to things rather than things...” (9) Among other possible benefits of the philosophy of things that Garcia proposes, it is fully able to account for thought as a special variant of things, while the reverse is not possible.(10) In Book I of Forme et objet , Garcia’s “things” are so flat, so de-determined, that he is forced to renounce some of the most basic features ascribed to things by most realists. As he tells us in his foreboding third footnote: “We will maintain that the solitude [of things] is less than unity, less than identity, and that it does not imply acceptance (any more than refusal) of the principle of non-contradiction.” (11) In a contemporary world cluttered with too many things, Garcia’s flat and formal plane provides us with some breathing room: “The formal plan of thought enables or re-enables us to cut short all accumulation—whether of knowing, experience, or action—by a simplicity, an impoverished surface...” (13) As Garcia says elsewhere in responding to a Deleuzian critic of the book, his starting point in flat ontology is designed to obstruct the claims of both analytic philosophy and Hegelianism: “Hence, this work seeks to protect each thing—real, imaginary, inconsistent, contradictory—both against Ockham’s Razor and against the Aufhebung or dialectical process.” 18 Yet contrary to the equalizing spirit of many flat ontologies, “we will add to our formal ontology of the equal, an objective ontology of the unequal.” (13) But initially, Garcia joins all flat ontologists in holding that everything is irreducible: “this irreducibility, which we will term the ‘chance’ of each thing... also marks the refusal of a positive thought that reduces things exclusively to natural things, or social things, or historical things, etc.” (15) This irreducible “chance” of a thing emerges as an important technical term in the book, always paired with its inverted brother, the “price to pay” ( prix à payer ). On pages 17-19, we find the only diagrams in the book. What they illustrate is that Garcia wishes to avoid two equally dangerous extremes. The first is the philosophy of substance, featuring the thing-in-itself as a mighty river fed by attributes as if by subordinate tributary streams. This model can be found in many of the classic thinkers of West and East alike. In it, “there is obviously a hierarchization between that which is dragged towards something other than itself, and this other which serves it as an ontological support while supporting its proper being.” (16) For Garcia, the second extreme worth avoiding is the philosophy of events: “One thus conceives trajectories of being, identified as events, facts, powers, intensities, or intentionality. These vectors of being come first, bearing and supporting being, displacing it, but without ever finding a stopping point, a buffer, an objective consistency.” (17) The first model gives us a thing too wrapped up in itself, too compact . This word “compact” (the French and the English are the same) is another technical term for Garcia. But if the “compact” model of things leads us to something more than things, the philosophy of events gives us less than things, by dissolving them into a play of vectors. Garcia’s alternative lies midway between these two extremes: Being enters the thing, being comes out of it. And a thing is nothing other than the difference between the enters and the being that comes out. Thus, the circuit of being is never halted. In the thing, there is never the thing-in-itself. And the thing is never in-itself, but outside of itself. Nonetheless, being is not eventally “pollinated” by vectors: it possesses an objecting halting-point... (19) This single idea is the key to Garcia’s book: the thing is neither a self-contained durable lump nor some sort of evental flux. Instead, the thing is the difference between its various components and its relations with its environment. Or stated differently: “the price to pay for this disposition is a circulation of being that systematically distinguishes two senses of things: that which is in the thing , and that in which the thing is , or that which encompasses it and that which it encompasses,” (19) translating comprendre here as “encompass.” 19 In a beautiful description of a piece of black slate, Garcia sums up the various minerals, qualities, and shapes that compose [ comprend ] it, and calls them “that which is in the thing,” (20) noting that this tells us nothing about “that in which [the slate] is”—namely, all the various situations in which the black slate can be found. Instead, the slate is the difference between these two: the most characteristic principle of Garcia’s philosophy. 2. Formally Book One of Forme et objet , “Formally,” is concerned with the formal equality of all things in a flat world. “Two questions mark the boundaries of reflection: of what is everything composed [ composé ], and: what do all things compose?” (27) Looking downward, we wish to know what everything is made of; looking upward, we want to know the ultimate result of the combination of all things. Here we must turn our attention to the thing n’importe quoi— no matter what it is. (30) Anything with finite qualities is obviously too specific to be relevant to global ontological questions. To an equal degree, something possessing all qualities (think of Whitehead’s God) 20 would not be n’importe quoi either, since it would still be too definite, even if incredibly vast. The same holds for contradictions, since these all differ from each other. The square circle, the non-white black white, and the non-city city are all too distinct to count as the thing no matter what it is. The n’importe quoi must be devoid of all specific qualities, including contradictory ones. In one of the more intriguing points in his book, so reminiscent of Meinong, Garcia proclaims that “the ‘no matter what it is’ is neither a reality nor an abstract construction, nor both of these at once; the ‘no matter what it is’ is simply the plane of equality of that which is real, that which is possible, that which is inexistent, that which is past, that which is impossible, that which is true, that which is false, that which is bad.”(39-40) Since everything has two faces, it would be a grievous mistake to focus on just one of them at the expense of the other, as physicalism or materialism do when reducing the world to minuscule physical underpinnings. For scientistic materialism, “it is either atoms, particles, or fields of force... which are the things.” (47-48) Moreover, “these more-than-things are accompanied by less-than-things: for example, ideas or facts of consciousness are determined by the state of matter and are not autonomous things, but manifestations reduced to secondary effects of material processes...” (48) On this point, Garcia’s position is in complete accord with my own critique of undermining and overmining. 21 Where we disagree is that Garcia is more deeply suspicious of the notion of substance, which I view as salvageable with a few needed changes, while Garcia sees this operation as hopeless: “A substance, in the history of philosophy, is the more-than-thing par excellence.” (51) Another agreement between our positions is visible when Garcia claims (correctly, in my opinion) “that it is vain to distinguish between things which are material and those which are not.” (52) Yet we also find an even more important disagreement, since for Garcia withdrawal cannot be the quality of a thing. Instead, the absence of a thing is simultaneous with it, embodied in all that is not it– the absence of the sculpture of a woman is to be found in the mold that appears at the same time as it, and thus withdrawal must be viewed as an “event” rather than as something pertaining to an object. For Garcia, nothing withdraws beyond access. Since we must distinguish between “that which is something” and “that which something is,” and since the former is identified with “no matter what it is is” and the latter with “ not no matter what it is,” we can say that “everything is thus a milieu, a fragile link between ‘no matter what it is’ and ‘ not no matter what it is.’” (62) And here we find Garcia’s critique of the thing-in-itself: “A thing is never defined en bloc . We can affirm that a thing is this or that, but that does not suffice. It is still necessary to state precisely that which is this thing .” (62) Stated differently, “something is not in itself : for that which is in the thing is not the thing, and that in which the thing is is not the thing.” (62) And here Garcia and I, facing the same evidence, draw opposite conclusions. For me, the fact that nothing can be identified with either its components or its concrete location means that the thing must be something in-itself distinct from both of these. Yet for Garcia, to be in-itself would mean to be identified with just one of these two extreme terms, and hence the thing can only be the difference between them. Garcia is equally suspicious of the classical tendency to view “unity” as a property of the thing, since in his eyes unity is too relational a property to belong to things. (65) While specific things are situated determinately with respect to other things, we are still speaking here about the thing no matter what it is, and this can be viewed only in terms of solitude, which all things share: a human being, a hand, or a chair or all equally things insofar as they are on their own , not insofar as they are one . (64) A thing is alone, and relates only to the one thing that is not another thing: world. In a striking parallel to my own argument for a partial revival of occasionalism, Garcia tells us that “the things communicate only by their solitude: it is because everything is equally on its own in the world that things can be together, enmeshed in one another.” (67) Alone in their solitude, things all relate to world, which serves as a mediator allowing them to become mixed up in one another. As we have seen, one reason that nothing can be in itself is because everything is in something else. For Garcia, “to be in something and to be something are equivalent.” (69) Stated more broadly, “being is thus the difference between the two aspects of each thing: that which is it, and that which it is.” (70) And even more vividly: “a thing is almost like a sack: there is that which one puts in the sack and that which remains outside the sack.” (70) But not quite like a sack, “since a thing is not a thin skin or film. Instead, a thing is comparable to a sack that is immaterial and without thickness: it is nothing other than the difference between that which is this thing and that which thing is, between content and container.” (71) Nothing can be in-itself because everything is two selves at once. For example, we cannot say that our self is defined by our consciousness: “Everything has a self because nothing is in itself. The self is not the quality of that which is related to itself (which is conscious, for example) or which thinks itself related to itself. Nonetheless, for an entity called ‘conscious’ to be related to itself, it is necessary that this very relation should be another thing than the self to which it is related.” (71) Consciousness cannot be the self, precisely because it is other than that of which it is conscious. Nothing is able to grasp itself. The self is “the function by which being and composition [ compréhension ] are mutually excluded...” (72) The self is “the point of shadow of everything that projects some light...” (72) The in-itself faces two opposite dangers: “For something to be in-itself is to be a self. Something which is a self flies out through one of its two sides... Stated differently, being in-itself is simply the possibility of a double failure.” (73) The in-itself can be termed compact : “There remains to us a means of thinking that which does not fully enter into the world, though without exiting from it. This means is what we call the compact.” (76) In a sense, the compact is the opposite of the world. For in the case of the world, everything enters it and it enters nothing; as for the compact, it enters the world (since it is something, after all) while nothing enters it. (77) The compact marks the presence of the impossible in the world. (78) It is not impossible, but possible only on the condition that it fails. (78) The time has come to speak of where a thing is located. “The sole condition of a thing is that of being in another thing than itself, and thus in another thing than something.” (78) A condition is “that which determines something, that which forms something, that in which something is.” (78) As for humans, “the condition of someone is his situation; my social condition is that which socially determines me, my place and my function...” (79) More generally, “to be conditioned is to find oneself reduced to that in which one is.” (79) Everything is conditioned, but nothing is reducible to this condition. To determine the condition of something is to determine in what it is. A thing is located in that which contradicts it, just as a statue exists in its mold, which is precisely that which it is not. Since the thing is finite and definite, its condition or form must be infinite and indefinite. That in which all things are is the world, which Garcia also terms “the whole.” (81) “To try to be in-itself is to attempt to remain outside the world. And indeed, to try to be in-itself is only a path of entry into the world.” (83) For Garcia, “the world is not the pre-existent container of the things it contains, a priori , nor the construction by the mind of a fictional ensemble of all things, a posteriori .” (85) Instead, the world is simultaneous with all things; the two always go together. The world cannot be a determinate world, such as the physical universe or mathematical space, since these are already too specific and limited. “Every determinate world, which is in fact a universe , is a ‘big thing’ [ grosse chose ]: it is a set, however vast, of composite things which itself embodies a thing.” (85) Every determinate world is really just a “big thing.” Stated differently, “it is nothing other than a balanced milieu between the things that compose it and the thing that it composes.” (85) We generally picture the world as a physical univer. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:IntroductionLori A. Custodero and Anna NeumannIn this symposium, three scholars present the genesis, meaning, and artfulness of creative work and its realization as aesthetic experience within three educational fields. Lori A. Custodero, working out of music education, provides a perspective emanating from an aesthetic of childhood wonder and playfulness; David T. Hansen, writing out of philosophy of education, discusses how being fully present in the teaching moment leads to (...) meaningful experience; and Anna Neumann, who writes out of the field of higher education studies, represents scholars as engaged in intellectual pursuits, often framed aesthetically, and as struggling to hold on to precious time for creation. Aware of the inherent tensions in learning environments from child care centers to graduate schools, we address ways in which our research has revealed people's sustained pursuit of imagined possibilities, oftentimes amidst perceived impediments.Creative work involves imagining possibilities whereby individuals, alone and together, pose personally relevant questions and pursue fluent pathways of inquiry within the shared meanings of cultural context. At its finest, such work is artful, simultaneously responding to and emanating from immediate circumstance and past experience. It is malleable and vulnerable and compelling, fusing familiar images and surprising perceptions into new "equilibria... stable, even though moving" whereby "changes interlock and sustain one another."1 As scholars and teachers committed to learning, we strive to create and discern meaning between established understandings and emerging ideas and images. As we dance between reception and action, between insight and "onsight,"2 fully attentive to the perceived potentials in our work, we move toward synchrony, experiencing the aesthetic. The realizations that arise from experiences such as these — new or newly reconfigured words, sounds, images, movement, and ideas — express new balances of sense and feeling and, sometimes, beauty. Whether in the shared, artfully expressive vocalizations between the newborn infant and mother or in the scientist's finessing patience with elegant mathematical imagery, creative work invites a drawing together of what we know and what we struggle to know. Over time, the interplay of this work and its realization, [End Page 33] what Dewey refers to as "movement and culmination,"3 creates a momentum that serves to define lives as aesthetic.We have created this symposium as a space for considering the meanings of the aesthetic in lives — from its earliest instantiations in the experiences of infants and young children, to its developed expression in the professional (in this case, intellectual) efforts of adults pursuing scholarly careers, to its representation in teaching as intergenerational fusions of knowledge, learning, and lives. We see the aesthetic as both native and learned; as individually held and formed and felt, and as collectively created and voiced, the product of lives in intersection; as marking bounded moments in time (those instants of compelling "present-ness") and as spreading through years, well beyond bounded present-ness, perhaps as memory. Yet while striving to define the aesthetic in lives, we also strive to understand lives, individually and interactively, as lodgings for the aesthetic, as locations that give shape, form, and voice to beauty and insight, to creativity and learning. As we explore the lives in which the aesthetic finds its home, and within which it forms, we wonder about the extent to which the aesthetic may, in its turn, illuminate the strivings of those lives, including human desires to create, know, learn, understand, sense. We are then collectively concerned with the meanings of the aesthetic in lives and about the lives themselves as "moving spaces" within which the aesthetic can grow.We pursue this theme, centered on the power of the aesthetic to illuminate human lives, out of a realization that current understandings of what it means to be human — and especially what it means to learn and create — have been framed within the rubrics of the social sciences, certainly in productive ways. And yet we suggest that the artful, though powerful in its abilities to voice emotion and beauty, has not been employed as intensively as it might in efforts to understand what it means to create and learn as virtues of human existence, as perhaps the ultimate of human strivings. We hope that these symposium papers will help invigorate such... (shrink)

Music is the carrier through which human beings express their emotions. It can clean up their hearts and seek emotional resonance. The combination of music and artificial intelligence, when music meets artificial intelligence, the mathematical logic part of data and algorithm replaces the image thinking, resulting in automatic music production. The basic principle of music creation is to use artificial intelligence technology to conduct in-depth training on a large number of songs, and then build a database. Then, within a certain (...) period of time, extract a segment from several songs, and then decompose it to form a new melody. The automatic music production is the collision of music and technology. With the flying of code and notes, it creates a different kind of beauty. Music culture is a new field of music application. With its refreshing audio-visual effect, it has made people have a new understanding of music and has become a hot topic in current mass cultural activities. The sound quality characteristics of music culture programs determine the characteristics of simple, fast and efficient design. However, the current audio and video design still stays in the traditional audio and video form design, with low design efficiency, long cycle, high cost and high requirements for designers. In view of the fact that the traditional audio and video design mode in China's music and cultural programs cannot meet the needs of performance programs at present, this paper proposes a design scheme of audio and visual effects of music and cultural programs with intelligent devices as the core, and develops a complete set of audio and visual effects aided design system on this basis. (shrink)

Sounds are heard, sometimes even felt, but in most cases they remain unseen. This ephemeral and invisible nature of sound was already considered a problem when the science of acoustics took form in the seventeenth century. The fact that sound could not be seen was described as a significant hindrance to its understanding. But it was precisely during this time that a wide variety of sounds attracted broad scientific attention across Europe. Scholars, natural philosophers, and mathematicians investigated and experimented (...) with sound and musical instruments and developed theories of hearing. This article looks at the role of images, diagrams, and visualization techniques in late seventeenth-century acoustics, bringing together the history of sound and the history of scientific images. Focusing on water and light as the dominant analogies for sound, the article demonstrates that visualization was an important tool for thinking about sound and allowed for the circulation of theories and experiments. At the same time, the epistemic status of these images remained contested, as there was no single model that could explain the different ways sound behaves as it moves through space and that could be visualized. (shrink)

The ties between music and philosophy are strong and venerable, as they date back to the very beginnings of the latter. According to the ancient tale, Pythagoras, when passing by a smithy one day, noticed that the hammers make sounds of different pitch and, more importantly, that some of the pitch combinations feel pleasant on the ear while the others sound rather harsh. Intrigued by this phenomenon, the ancient sage began to further investigate it with the so called monochord (being (...) just a plank with a string attached to it which could be shortened at any chosen position to alter the pitch). Thus he discovered that the successions of two sounds that sound pleasant (or, to use a more technical term, consonant) could be achieved if the string is being shortened by 1:2, 2:3 or 3:4. Pythagoras could not be more satisfied with this finding, as it proved his claim that the universe is, on its hidden and true level, based upon an intelligible mathematical structure, and, moreover, that a key to understanding this structure is the Holy Tetractys, a figure representing the first four natural numbers in the form of a regular triangle. (shrink)

Although never an easy feat, tracing the connections between sounds, spaces and objects becomes easier the higher up the social scale one goes in the Early Modern period. The survival of documentary and material evidence helps to identify musical repertories that were known to have been performed in specific spaces on particular instruments. Given the lack of comparative sources at lower social levels, is it possible to establish relationships between these three elements in non-courtly contexts? This chapter considers non-courtly ‘music-rooms’, (...) addressing how practical material and conceptual motivations forged links between music and domestic space in this period. It goes on to examine broader, perhaps unexpected, connections between musical sound and the material culture of the Early Modern domestic interior. (shrink)

This article discusses listening that is appropriate to sound art and the associated changes in the paradigms, or thought patterns, that occur so often when we move from visual to aural perception. The distinction between historically accepted and rejected sounds is used to show how putting sounds in cages has fashioned a form of listening and of life. Twentieth-century experimental music and, especially, the music and the reflections of John Cage have opened these cages of sound and at the (...) same time weakened the visual paradigm for intellectual knowledge. This article examines sound art as a place where artistic practices coincide with certain theoretical issues centered on sound. The centrality of sound is approached first, and music and sound art are discussed in relation to space. Second, the attention to sound in the reception of prominent examples of sound art focuses on site-specific relationships with the city and with listening. The article concludes by affirming the need for an aesthetic reflection that takes into consideration the implications of these profound transformations. However, that is another cage yet to be opened. (shrink)

In the realm of language a special case of mimetic illusion is the calembour, where the sound of a phrase signifies something else than what is written. At the end of the XVI century the artistic expression of this phenomenon gave birth to the paintings of Arcimboldo, who separated the contour of an object form the linear organization of the surface, in order to feature another object, through a kind of “polyphonic” dissociation between meaning and form. Strangely enough, (...) nothing has been written, in modern musicology, about the musical analogue of this phenomenon, but one can prove that it was not confined to paintings. The art of dissociating signs and meanings, was very well known by musicians not only through poetics, but also through musical mathematics, and above all by the study of the ancient Greek theory of metabolai, about the qualitative change of an harmonic form through the ambiguity created with others forms. (shrink)

Experimental encounters in music and beyond opens a necessary dialogue on experimental practices in the arts and negotiates their place in contemporary society. Going beyond the music-historical usage of the term "experimental", this book reimagines experimentation as an open working definition encompassing multiple forms of artistic attitudes and processes. The texts, images, and sounds offer multiple traces, faces, and spaces, revealing what experimentalism in music and the wider arts entails today. With perspectives from a range of disciplines - from choreography (...) through composition to philosophy and beyond - the different experiences and artistic projects documented and discussed explore the complexity of experimentation in a way that is all the richer for being never-ending."--Page 4 of cover. (shrink)

The public sphere, in which religion is lived and in which religious singing functions, is briefly discussed and related to manipulated truths and ‘fake news’ regarding the use of spiritual songs and hymns as religious and cultural offerings, with reference especially to texts displaying a disregard for responsible hermeneutical principles. A plea is made not only for a practical theology that engages critically with the fundamentals of the current culture and the use of religious symbols in public, but also for (...) a sounding theology that reflects on communication through singing and other forms of art in the public space of worship as well as in the more ‘visible’ public sphere whilst creating beauty in the process of reflection. Through this means, spaces of resonance could be opened where people become participants drawn in into a performance of practical theology, reflecting together on the religion they live and finding new ways of voicing their faith in the public sphere, unveiling aspects of authenticity and truth. Contribution: From an interdisciplinary perspective fitting the scope of the journal, it is shown how hymns, texts and music draw people into a performance of a practical theology reflecting on lived religion, while finding new ways of performing the sacred in the public sphere – in the process thus opening up aspects of truth in a world of fake news. (shrink)

Music-Dance explores the identity of choreomusical work, its complex authorship and its modes of reception as well as the cognitive processes involved in the reception of dance performance. Scholars of dance and music analyse the ways in which a musical score changes its prescriptive status when it becomes part of a choreographic project, the encounter between sound and motion on stage, and the intersection of listening and seeing. As well as being of interest to musicologists and choreologists considering issues such (...) as notation, multimedia and the analysis of performance, this volume will appeal to scholars interested in applied research in the fields of cognition and neuroscience. The line-up of authors comprises representative figures of today's choreomusicology, dance historians, scholars of twentieth-century composition and specialists in cognitive science and performance studies. Among the topics covered are multimedia and the analysis of performance; the notational practice of choreographers and the parallel attempts of composers to find a graphic representation for musical gestures; and the experience of dance as a paradigm for a multimodal perception, which is investigated in terms of how the association of sound and movement triggers emotions and specific forms of cognition. (shrink)

Screenwriters and film directors have long been fascinated by the challenges of representing the listening experience on screen. While music has played a central role in film narrative since the conception of moving pictures, the representation of music listening has remained a special occurrence.In Situated Listening: The Sound of Absorption in Classical Cinema, author Giorgio Biancorosso argues for a redefinition of the music listener as represented in film. Rather than construct the listener as a reverential concertgoer, music analyst, or gallery (...) dweller, this book instead shows how films offer a new way of thinking about listening as distributed experience, an activity made public and shareable across vast cultural spaces rather than an insular motion. It shows how cinema functions as not only a reservoir of established modes of listening, but also an agent in the development of new listening practices. As Biancorosso argues, many films have perpetuated a long-existing paradox of music as a means of silencing. Consider an aggressive score overlaying battle scenes or a romantic scene conveying unspoken intimacy. In the place of conversational exchange exists a veil of sound in the form of music, and Situated Listening explains why this function influences both the course of interpretation and empathy experienced by film spectators. By focusing on cinematic, physical, and emotional scenery surrounding a character, viewers can recognize aspects of their own lives, developing a deeper empathy for each fictional character through real and shared listening practices. (shrink)

Professor Michael Edgeworth McIntyre is an eminent scientist who has also had a part-time career as a musician. From a lifetime's thinking, he offers this extraordinary synthesis exposing the deepest connections between science, music, and mathematics, while avoiding equations and technical jargon. He begins with perception psychology and the dichotomization instinct and then takes us through biological evolution, human language, and acausality illusions all the way to the climate crisis and the weaponization of the social media, and beyond that into (...) the deepest parts of theoretical physics - demonstrating our unconscious mathematical abilities. He also has an important message of hope for the future. Contrary to popular belief, biological evolution has given us not only the nastiest, but also the most compassionate and cooperative parts of human nature. This insight comes from recognizing that biological evolution is more than a simple competition between selfish genes. Rather, he suggests, in some ways it is more like turbulent fluid flow, a complex process spanning a vast range of timescales. Professor McIntyre is a Fellow of the Royal Society of London (FRS) and has worked on problems as diverse as the Sun's magnetic interior, the Antarctic ozone hole, jet streams in the atmosphere, and the psychophysics of violin sound. He has long been interested in how different branches of science can better communicate with each other and with the public, harnessing aspects of neuroscience and psychology that point toward the deep 'lucidity principles' that underlie skilful communication. (shrink)

The subject of the study. The article analyzes a number of aspects of Brahms' intermezzo Op. 119 No. 3 in order to detect non-classical tendencies manifested in the structure of the musical fabric and the principles of shaping in this work. Research methodology. In the course of the study, the method of holistic analysis was used, which includes consideration of the features of harmony, textural originality, thematic processes and form-forming patterns in the Brahms intermezzo Op. 119 No. 3. Elements (...) of comparative analysis were also applied. The scientific novelty of the work consists in the fact that as a result of the research it was possible to identify a number of non-classical qualities of Brahms' music, namely: the homogeneity of the sound fabric, a weak degree of differentiation of relief and background in texture, the absence of common forms of sound and passive fragments in musical form. The conceptual kinship of Brahms' principles of working with musical material with the technique of interpenetration of object and space, which became widespread in painting at the beginning of the XX century, was also discovered. Conclusions, the results obtained allow us to conclude that Brahms' intermezzo Op. 119 No. 3 implements a number of non-classical principles of working with musical material that anticipate the discoveries of composers of the Novovensky school. The results of the research can be used in the process of further study of Brahms' creativity and various theoretical aspects of music at the turn of the XIX–XX centuries, as well as in performing and pedagogical practice. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy of Music Education Review 12.2 (2004) 181-186 [Access article in PDF] Response to June Boyce-Tillman, "Towards an Ecology of Music Education" Claudia Gluschankof Levinsky College of Education, Israel I begin with two confessions. First, music was not my favorite class at school. I cannot even recall what we did there. It did not at all connect with the powerful, meaningful place that music had in my private life, (...) where I loved to sing with my family, and play and sing in ensembles in classes at a private music school. The private piano lessons were fine, but I found no joy in practicing on my own. Music was for me-and still is-a communal experience, associated with personal choice. School did not, and probably could not, provide that.Second, during a recent marketing meeting at the college where I teach and work, I finally said aloud, "I am not sure that I can market a product in which I don't believe." Being a teacher in overcrowded, resource-poor schools where parents are less involved yet more interfering and being expected to conform to standards and to act more as a producer of school ceremonies and festivals and less as a music educator is not a profession I would recommend entering. Boyce-Tillman's paper offers a model for music education in which the corrective emotional experience, in my own case, becomes a remedial object lesson in the setting of the music classroom and a reason to recommend music school teaching as a rewarding profession.Boyce-Tillman calls us to conceive of music "as intimately related to human society and the environment rather than as a discrete and separated category of knowing." Her position is in tune with Christopher Small's coined term "musicking": The act of musicking establishes in the place where it is happening a set of relationships, and it is in those relationships that the meaning of the act lies. They are to be found not only between those organized sounds which are [End Page 181] conventionally thought of as being the stuff of musical meaning but also between the people who are taking part, in whatever capacity, in the performance; and they model, or stand as metaphor for, ideal relationships as the participants in the performance imagine them to be: relationships between person and person, between individual and society, between humanity and the natural world and perhaps the supernatural world.1The five interlocking areas proposed in Boyce-Tillman's model are present in Small's musicking: the relationships among the sounds parallel the area called Materials; the relationships between people and sounds may parallel the area called Expression, which refers to the personal meaning given to the organized sounds. "In the area of Construction, effectiveness often depends on the right management of repetition and contrast within a particular idiom." Such a particular idiom is part of the style ideal of a particular culture. It is defined in terms of form and content, and expresses some inner quality of the society that produced it. The style ideal can be characterized by different factors (for example, historical period, geographic location, school, manner of performance, individual composer, and so on) and can be examined in terms of musical components (form, texture, harmony, melody).2According to Boyce-Tillman, the area of Values "is related to the context of the music-making experience. All musical experiences are culturally related." Because values are shared by groups, I found this present in the relationships be-tween a subculture and the larger society, in its broader meaning. The fifth area is Spirituality, defined by Boyce-Tillman as "the ability to transport the audience to a different time/space dimension." That different time/space dimension may be understood as the supernatural world, referred to by Small.Small sees the greatest challenge to music educators today to be that of providing "that kind of social context for informal as well as formal musical interaction that leads to real development and to the musicalizing of the society as a whole,"3... (shrink)

Who produces sound and music? And in what spaces, localities and contexts? As the production of sound and music in the 21st Century converges with multimedia, these questions are critically addressed in this new edited collection by Samantha Bennett and Eliot Bates. Critical Approaches to the Production of Music and Sound features 16 brand new articles by leading thinkers from the fields of music, audio engineering, anthropology and media. Innovative and timely, this collection represents scholars from around the world, revisiting (...) established themes such as record production and the construction of genre with new perspectives, as well as exploring issues in cultural and virtual production. (shrink)

This article proposes approaching the phenomenon of sound as a fabric of relationships. Critiquing the notion of a sound object as it has become defined thanks to the fixity enabled by sound recording, it focuses on the characteristics of sound that converge towards a relational approach and suggests that there is an inextricable link between the vibrating object, the milieu in which the vibration spreads and the subject who listens. It is probably for this reason that current research — whether (...) in music, sound art or other disciplines that centre on sound, from sound studies to environmental ecology — implicitly seeks to move beyond the concept of sound alone in favour of compounds that combine sound with other elements. While the notions of sound ‘spaces’ and sound ‘environments’ appear as the default options here, three other compounds in particular highlight, in their own way, the relational approach: ‘soundscapes’, ‘sound milieus’, and sound ‘ambiances’ and ‘atmospheres’. (shrink)

From Ancient Greek times, music has been seen as a mathematical art, and the relationship between mathematics and music has fascinated generations. This collection of wide ranging, comprehensive and fully-illustrated papers, authored by leading scholars, presents the link between these two subjects in a lucid manner that is suitable for students of both subjects, as well as the general reader with an interest in music. Physical, theoretical, physiological, acoustic, compositional, and analytical relationships between mathematics and music are unfolded and explored (...) with focus on tuning and temperament, the mathematics of sound, bell-ringing and modern compositional techniques. (shrink)

Summary The resonator and the tuning fork were major instruments in acoustics in the latter half of the nineteenth-century. In particular, the third Baron Rayleigh made extensive use of these instruments throughout his long career as an experimentalist. These instruments underwent a number of alterations during their use as central experimental tools in acoustics. Functional and structural alterations were introduced in the adaptation of these instruments to several major acousticians’ experimental settings. Rayleigh not only adopted the two instruments as objects (...) of mathematical and experimental investigation but also employed them ingeniously for various purposes. His continuing creation of a variety of uses and forms of these instruments contributed to focusing acoustics on pure tones and musical sounds until the early twentieth century. (shrink)

Language experience clearly affects the perception of speech, but little is known about whether these differences in perception extend to non-speech sounds. In this study, we investigated rhythmic perception of non-linguistic sounds in speakers of French and German using a grouping task, in which complexity was manipulated. In this task, participants grouped sequences of auditory chimeras formed from musical instruments. These chimeras mimic the complexity of speech without being speech. We found that, while showing the same overall grouping preferences, the (...) German speakers showed stronger biases than the French speakers in grouping complex sequences. Sound variability reduced all participants’ biases, resulting in the French group showing no grouping preference for the most variable sequences, though this reduction was attenuated by musical experience. In sum, this study demonstrates that linguistic experience, musical experience, and complexity affect rhythmic grouping of non-linguistic sounds and suggests that experience with acoustic cues in a meaningful context is necessary for developing a robust grouping preference that survives acoustic variability. (shrink)

This paper gives a formalization of general topology in second-order arithmetic using countably based MF spaces. This formalization is used to study the reverse mathematics of general topology. For each poset P we let MF denote the set of maximal filters on P endowed with the topology generated by {Np | p ∈ P}, where Np = {F ∈ MF | p ∈ F}. We define a countably based MF space to be a space of the form MF for (...) some countable poset P. The class of countably based MF spaces includes all complete separable metric spaces as well as many nonmetrizable spaces. The following reverse mathematics results are obtained. The proposition that every nonempty Gδ subset of a countably based MF space is homeomorphic to a countably based MF space is equivalent to [Formula: see text] over ACA0. The proposition that every uncountable closed subset of a countably based MF space contains a perfect set is equivalent over [Formula: see text] to the proposition that [Formula: see text] is countable for all A ⊆ ℕ. The proposition that every regular countably based MF space is homeomorphic to a complete separable metric space is equivalent to [Formula: see text] over [Formula: see text]. (shrink)

One is a science, the other an art; one useful, the other seemingly decorative, but mathematics and music share common origins in cult and mystery and have been linked throughout history. Emblems of Mind is Edward Rothstein’s classic exploration of their profound similarities, a journey into their “inner life.” Along the way, Rothstein explains how mathematics makes sense of space, how music tells a story, how theories are constructed, how melody is shaped. He invokes the poetry of Wordsworth, the anthropology (...) of Le;vi-Strauss, the imagery of Plato, and the philosophy of Kant. Math and music, Rothstein shows, apply comparable methods as they create their abstractions, display similar concerns with ratio and proportion, and depend on metaphors and analogies to create their meanings. Ultimately, Rothstein argues, they reveal the ways in which we come to understand the world. They are images of the mind at work and play; indeed, they are emblems of Mind itself. Jacques Barzun called this book “splendid.” Martin Gardner said it was “beautifully written, marvelous and entertaining.” It will provoke all serious readers to think in new ways about the grand patterns in art and life. “Lovely, wistful. . . . Rothstein is a wonderful guide to the architecture of musical space, its tensions and relations, its resonances and proportions. . . . His account of what is going on in the music is unfailingly felicitous.”— New Yorker “Provocative and exciting. . . . Rothstein writes this book as a foreign correspondent, sending dispatches from a remote and mysterious locale as a guide for the intellectually adventurous. The remarkable fact about his work is not that it is profound, as much of the writing is, but that it is so accessible.”— Christian Science Monitor. (shrink)

A quasi-order Q induces two natural quasi-orders on $${\mathcal{P}(Q)}$$, but if Q is a well-quasi-order, then these quasi-orders need not necessarily be well-quasi-orders. Nevertheless, Goubault-Larrecq (Proceedings of the 22nd Annual IEEE Symposium 4 on Logic in Computer Science (LICS’07), pp. 453–462, 2007) showed that moving from a well-quasi-order Q to the quasi-orders on $${\mathcal{P}(Q)}$$ preserves well-quasi-orderedness in a topological sense. Specifically, Goubault-Larrecq proved that the upper topologies of the induced quasi-orders on $${\mathcal{P}(Q)}$$ are Noetherian, which means that they contain no (...) infinite strictly descending sequences of closed sets. We analyze various theorems of the form “if Q is a well-quasi-order then a certain topology on (a subset of) $${\mathcal{P}(Q)}$$ is Noetherian” in the style of reverse mathematics, proving that these theorems are equivalent to ACA 0 over RCA 0. To state these theorems in RCA 0 we introduce a new framework for dealing with second-countable topological spaces. (shrink)