Chords are not pure sets of tones or notes. They are mainly characterized by their matrices. A chord matrix is the pattern of all the lengths of intervals given without further context. Chords are well-structured invariants. They show their inner logical form. This opens up the possibility to develop a molecular logic of chords. Chords are our primitive, but, nevertheless, already interrelated expressions. The logical space of internal harmony is our well-known chromatic scale represented by an (...) infinite line of integers. Internal harmony is nothing more than the pure interrelatedness of two or more chords. We consider three cases: chords inferentially related to subchords, pairs of chords in the space of major–minor tonality and arbitrary chords as arguments of unary chord operators in relation to their outputs. One interesting result is that chord negation transforms any pure major chord into its pure minor chord and vice versa. Another one is the fact that the negation of chords with symmetric matrices does not change anything. A molecular logic of chords is mainly characterized by combining general rules for chord operators with the inner logical form of their arguments. (shrink)

RESUMEN Nos adentramos en esos procesos de subjetivación en los que el músico de jazz experimenta en sí otras formas de corporalidad, que se dirimen entre sujeción a esquemas y ruptura de los corsés por una teatralidad en escena. Aparentemente, en la improvisación prima lo subversivo y la reificación del músico como autor libre; sin embargo, observamos empíricamente una corporalidad plural que trasciende el espacio de la escena y que facilita que todos los actores intervengan en el proceso de creación. (...) Hallamos una red de solidaridad que desplaza continuamente los puntos fijos por donde transita la música; así, cuando a un músico le falta el aire, su compañero le da el relevo. Si lo fundamental en la praxis de la música son las continuas alternativas que ofrece, concluimos con una reflexión ética sobre la naturaleza transitoria de la música y su temporalidad kairológica, en la que el músico, sintiendo la brevedad del instante de la nota que muere cuando nace, se reencuentra con lo insignificante de la que está hecha su condición humana. ABSTRACT We enter these processes of subjectivation in which the jazz musician experiences in himself other forms of corporeality, which are settled between subjection to schemes and breakup of the corsets by a theatricality on stage. Apparently, in improvisation what is subversive and the reification of the musician as a free author take priority; nevertheless, we empirically observe a plural corporeality that goes beyond the space of the scene and that facilitates that all the actors take part in the process of creation. We found a solidarity network that continuously displaces the fixed points where music circulates; thus, when a musician is short of breath, his partner takes over. If what is fundamental in the praxis of music is the continuous alternatives it offers, we conclude with an ethical reflection on the transitory nature of music and its kairological temporality, in which the musician, feeling the briefness of the instant of the note that dies when it is born, joins the insignificance of his human condition. (shrink)

With mathematical reconstructions and philosophical arguments I show that Toomer's 1973 paper never contained any conclusive evidence for his claims that Hipparchus had a 3438'-based chord table, and that the Indians used that table to compute their sine tables. Recalculating Toomer's reconstructions with a 3600' radius -- i.e. the radius of the chord table in Ptolemy's Almagest, expressed in 'minutes' instead of 'degrees' -- generates Hipparchan-like ratios similar to those produced by a 3438' radius. It is therefore possible that the (...) radius of Hipparchus's chord table was 3600', and that the Indians independently constructed their 3438'-based sine table. (shrink)

Two old problems in probability theory involving the concept of randomness are considered. Data obtained with one of them--Bertrand's chord problem--demonstrate the equivocality of this term in the absence of a definition or explication of assumptions underlying its use. They also support two propositions about probabilistic thinking: (1) upon obtaining an answer to a question of probability, people tend to see it as the answer, overlooking tacit assumptions on which it may be based, and tend not to consider the possibility (...) of other assumptions from which different answers would follow; (2) perceptual balance--moderate uniformity of density of distribution--is a determinant of the degree to which a two-dimensional pattern is perceived as random. (shrink)

Most studies of motifs of biological regulatory networks focus on the analysis of asymptotical behaviours, but transient properties are rarely addressed. In the line of our previous study devoted to isolated circuits 19:172–178, 2003), we consider chorded circuits, that are motifs made of an elementary positive or negative circuit with a chord, possibly a self-loop. We provide detailed descriptions of the boolean dynamics of chorded circuits versus isolated circuits, under the synchronous and asynchronous updating schemes within the logical formalism. To (...) this end, we address the description of the trajectories in the dynamics of isolated circuits with coding techniques and adapt them for chorded circuits. The use of the logical modeling gives access to mathematical tools allowing complete analytical analysis of basic yet important motifs. In particular, we show that whatever the chosen updating rule, the dynamics depends on a small number of parameters. (shrink)

A critical issue in perception is the manner in which top‐down expectancies guide lower level perceptual processes. In speech, a common paradigm is to construct continua ranging between two phonetic endpoints and to determine how higher level lexical context influences the perceived boundary. We applied this approach to music, presenting participants with major/minor triad continua after brief musical contexts. Two experiments yielded results that differed from classic results in speech perception. In speech, context generally expands the category of the expected (...) stimuli. We found the opposite in music: The major/minor boundary shifted toward the expected category, contracting it. Together, these experiments support the hypothesis that musical expectancy can feed back to affect lower‐level perceptual processes. However, it may do so in a way that differs fundamentally from what has been seen in other domains. (shrink)

And he unflinchingly confronts the Wagner whose paranoia, egocentricity, and anti-Semitism are as repugnant as his achievements are glorious."--Jacket.

In this paper I will introduce the reader to Carl Stumpf’s philosophy through a discussion of a problem about simultaneous perception of several objects. This problem is at the heart of several of his works and therefore well suited for my purpose.

As an artist I admittedly scrutinize all of the theories related to the arts closely. I do this for a number of reasons. The obvious one is that I have a deeply felt personal relationship with the subject matter. Less obvious is my experience in general. My early research was motivated by a desire to discover the historical circumstances that led to the difficulty in fitting visual art into the discussions I encountered. Generally, it seemed that the dominant framework trivialized (...) what I considered the most important aspects of the creative process. Over time I concluded that developing an interdisciplinary approach offered the best option for expanding views, although it is not an easy task. Establishing areas of commonality across a range of disciplines must somehow accommodate the ways in which each has developed a research agenda that seems to serve its core needs. In consciousness studies, for example, we have a field that relies heavily on scientific research and humanistic methodologies when building the philosophical models scholars use to structure theories. This methodology is not only removed from the nuts and bolts of art, it is also easily manipulated in discourse on art due to the ease with which we can fit aspects of art into the philosophical framework. Clearly this approach fits nicely with philosophically defined concepts such as meaning, emotion, and other elusive modes. In addition, using the well-honed categories aids in bracketing themes such as metaphor, interpretation, subjectivity, language and history. Nonetheless, in reading through the studies, I repeatedly conclude that the voices of practitioners need to be included to a greater degree. (shrink)

Events between which we have no epistemic reason to discriminate have equal epistemic probabilities. Bertrand’s chord paradox, however, appears to show this to be false, and thereby poses a general threat to probabilities for continuum sized state spaces. Articulating the nature of such spaces involves some deep mathematics and that is perhaps why the recent literature on Bertrand’s Paradox has been almost entirely from mathematicians and physicists, who have often deployed elegant mathematics of considerable sophistication. At the same time, the (...) philosophy of probability has been left out. In particular, left out entirely are the philosophical ground of the principle of indifference, the nature of the principle itself, the stringent constraint this places on the mathematical representation of the principle needed for its application to continuum sized event spaces, and what these entail for rigour in developing the paradox itself. This book puts the philosophy and its entailments back in and in so doing casts a new light on the paradox, giving original analyses of the paradox, its possible solutions, the source of the paradox, the philosophical errors we make in attempting to solve it and what the paradox proves for the philosophy of probability. The book finishes with the author’s proposed solution—a solution in the spirit of Bertrand’s, indeed—in which an epistemic principle more general than the principle of indifference offers a principled restriction of the domain of the principle of indifference. (shrink)

How might artificial neural networks (ANNs) inform cognitive science? Often cognitive scientists use ANNs but do not examine their internal structures. In this paper, we use ANNs to explore how cognition might represent musical properties. We train ANNs to classify musical chords, and we interpret network structure to determine what representations ANNs discover and use. We find connection weights between input units and hidden units can be described using Fourier phase spaces, a representation studied in musical set theory. We (...) find the total signal coming through these weighted connection weights is a measure of the similarity between two Fourier structures: the structure of the hidden unit's weights and the structure of the stimulus. This is surprising because neither of these Fourier structures is computed by the hidden unit. We then show how output units use such similarity measures to classify chords. However, we also find different types of units—units that use different activation functions—use this similarity measure very differently. This result, combined with other findings, indicates that while our networks are related to the Fourier analysis of musical sets, they do not perform Fourier analyses of the kind usually described in musical set theory. Our results show Fourier representations of music are not limited to musical set theory. Our results also suggest how cognitive psychologists might explore Fourier representations in musical cognition. Critically, such theoretical and empirical implications require researchers to understand how network structure converts stimuli into responses. (shrink)

Bertrand's random-chord paradox purports to illustrate the inconsistency of the principle of indifference when applied to problems in which the number of possible cases is infinite. This paper shows that Bertrand's original problem is vaguely posed, but demonstrates that clearly stated variations lead to different, but theoretically and empirically self-consistent solutions. The resolution of the paradox lies in appreciating how different geometric entities, represented by uniformly distributed random variables, give rise to respectively different nonuniform distributions of random chords, and (...) hence to different probabilities. The principle of indifference appears consistently applicable to infinite sets provided that problems can be formulated unambiguously. (shrink)

Weight systems on chord diagrams play a central role in knot theory and Chern-Simons theory; and more recently in stringy quantum gravity. We highlight that the noncommutative algebra of horizontal chord diagrams is canonically a star-algebra, and ask which weight systems are positive with respect to this structure; hence we ask: Which weight systems are quantum states, if horizontal chord diagrams are quantum observables? We observe that the fundamental gl(n)-weight systems on horizontal chord diagrams with N strands may be identified (...) with the Cayley distance kernel at inverse temperature beta=ln(n) on the symmetric group on N elements. In contrast to related kernels like the Mallows kernel, the positivity of the Cayley distance kernel had remained open. We characterize its phases of indefinite, semi-definite and definite positivity, in dependence of the inverse temperature beta; and we prove that the Cayley distance kernel is positive (semi-)definite at beta=ln(n) for all n=1,2,3,... In particular, this proves that all fundamental gl(n)-weight systems are quantum states, and hence so are all their convex combinations. We close with briefly recalling how, under our "Hypothesis H", this result impacts on the identification of bound states of multiple M5-branes. (shrink)

Auditory perception is traditionally conceived as the perception of sounds — a friend’s voice, a clap of thunder, a minor chord. However, daily life also seems to present us with experiences characterized by the absence of sound — a moment of silence, a gap between thunderclaps, the hush after a musical performance. In these cases, do we positively hear silence? Or do we just fail to hear, and merely judge or infer that it is silent? This longstanding question remains controversial (...) in both the philosophy and science of perception, with prominent theories holding that sounds are the only objects of auditory experience and thus that our encounter with silence is cognitive, not perceptual. However, this debate has largely remained theoretical, without a key empirical test. Here, we introduce a novel empirical approach, presenting experimental evidence that silence can be genuinely perceived (not just cognitively inferred). We ask whether silences can ‘substitute’ for sounds in event-based auditory illusions — empirical signatures of auditory event representation in which auditory events distort perceived duration. Seven experiments introduce three new ‘silence illusions’ — the one-silence-is-more illusion, silence-based warping, and the oddball-silence illusion — each adapted from a prominent perceptual illusion previously thought to arise only from sounds. Subjects were immersed in ambient noise interrupted by silences structurally identical to the sounds in the original illusions. In all cases, silences elicited temporal distortions perfectly analogous to the illusions produced by sounds. Our results suggest that silence is truly heard, not merely inferred, introducing a general approach for studying absence perception. (shrink)

The most reliable source for a reconstruction of Galileo's progress toward a science of motion is the series of undated fragmentary notes on that subject preserved in Codex A of the Galilean manuscripts at Florence. A gathering of such fragments was published by Favaro in the National Edition of Galileo's works, following the Discorsi. The more sophisticated fragments are clearly associated with the composition of that work, and show a definite and consistent understanding of acceleration. Eliminating those, it will be (...) found that the earlier notes fall into recognizable groups. First, there are some that refer to “moment of gravity”, or to the impetus of a body along a line of descent, and are associated with the discussion of inclined planes in De motu. Second, some refer to descent along arcs and chords of circles, associated with Galileo's letter of 29 November 1602 to Guido Ubaldo. These first two groups of notes do not explicitly refer to accelerated motion, and should not be assumed to do so implicity, where such an assumption can be avoided. (shrink)

What Nietzsche Really Said gives us a lucid overview -- both informative and entertaining -- of perhaps the most widely read and least understood philosopher in history. Friedrich Nietzsche's aggressive independence, flamboyance, sarcasm, and celebration of strength have struck responsive chords in contemporary culture. More people than ever are reading and discussing his writings. But Nietzsche's ideas are often overshadowed by the myths and rumors that surround his sex life, his politics, and his sanity. In this lively and comprehensive (...) analysis, Nietzsche scholars Robert C. Solomon and Kathleen M. Higgins get to the heart of Nietzsche's philosophy, from his ideas on "the will to power" to his attack on religion and morality and his infamous Übermensch (superman). What Nietzsche Really Said offers both guidelines and insights for reading and understanding this controversial thinker. Written with sophistication and wit, this book provides an excellent summary of the life and work of one of history's most provocative philosophers. (shrink)

Three experiments investigated the modularity of harmonic expectations that are based on cultural schemata despite the availability of more predictive veridical information. Participants were presented with prime–target chord pairs and made an intonation judgment about each target. Schematic expectation was manipulated by the combination of prime and target, with some transitions being schematically more probable than others. Veridical information in the form of prime–target previews, local transition probabilities, or valid versus invalid previews was also provided. Processing was facilitated when a (...) schematically probable target chord followed the prime. Furthermore, this effect was independent of all manipulations of veridical expectation. A solution to L. B. Meyer's (1967b) query "On Rehearing Music" is suggested, in which schematic knowledge contributes to harmonic expectation in a modular manner regardless of whether any veridical knowledge exists. (shrink)

Brown, Neil The New Atheism has been a remarkable marketing phenomenon of the first decade of this century. The various authors obviously struck a modern chord in the developed world, where a steadily increasing number of people describe themselves as belonging to no religion. They would seem also to be a radically secular response in the West to the rise of militant Islam, especially since the World Trade Center attack in 2001.

Castalia Communications' posters have been putting answers up on the walls for generations of musicians. The original Guitar poster is still the most complete guide to the guitar ever made. It contains a wealth of information for all guitar players, no matter what styles they play or their levels of musical accomplishment. Poster includes: Movable Chord & Scale Forms * Chord & Scale Table * Table of Keys * Notes of the Neck * Basic Chords * Open Tunings * (...) Circle of Fifths * Great Staff * and more! (shrink)

‘I see well enough what poor Kant would be at’ said James Mill on first looking into the Kritik der reinen Vernunft . No one would wish to say that the reception of Kant in England has remained at this level: abundance of sound scholarship, innumerable Kant seminars and the swell of interest in transcendental argument which has developed since the Second World War all exist to prove the contrary. But in spite of all that, Mill's response still touches a (...) chord in English breasts. We are prone to think Kant a conjurer. If we are to accept, or even to work seriously with, any version of Kantianism it must be a demythologized, logically aseptic version. Strawson's Kant, for instance, is a Kant freed from the ‘strained analogy’ between the study of the conditions of sense, or intelligibility, and the study of the human cognitive system. And in moral philosophy too, the English Kantianism chiefly represented by the work of Professor R. M. Hare has scrupulously avoided those parts of Kant's ethics which have a suspiciously speculative flavour: the notion of an unqualified good, for example, or that of treating moral agents as Ends-in-Themselves; and more generally the whole notion, which permeates Kant's moral philosophy, that morality can only ultimately be understood in terms of a set of ideal relationships that entirely transcend all considerations of common-sense mutual accommodation or rational self-interest: transcend all such considerations so radically, in fact, as to point mutely towards the possibility of a life after death. (shrink)

On 12 March 2020, the Norwegian government instigated measures to limit the spread of COVID-19, the most drastic policies of any Norwegian government in peacetime. A particularly Norwegian metaphor used when introducing those measures concerned the “dugnad” tradition, a cultural practice of voluntary work carried out as a community. This article traces the trajectory of dugnad metaphors related to COVID-19 in Norwegian public discourse, to shed light on the aptness of their use. Aptness is measured in terms of “resonance,” the (...) public reception to the metaphor. It follows a threefold categorization: imposition, endorsement, or resistance, all of which are divided into inductively developed subcategories. The data consists of all relevant concordances of the lexeme DUGNAD appearing from March 2020-June 2021 in one of the three largest Norwegian national online newspapers. Findings indicate that the imposition of the dugnad struck a chord with the Norwegian people; supportive statements far outweighed those of opposition and continued throughout the investigated period, even though national government officials mostly stopped using the dugnad metaphor after May 2020. Resistance was nevertheless also present from the outset, reaching a renewed peak around March 2021. Aptness thus varies over time, a finding with implications for future pandemic communication. (shrink)

Social protection programs have been an important part of development process and planning in India since its Independence. However, after sixty-five years, around one-fourth of its population lives in poverty. Despite a plethora of social protection programs, vulnerable groups among the poor have not been well targeted. However, the recent paradigm shift towards rights-based legislations may have hit the right chord with its self-targeting mechanism. The Right to Work, or the Mahatma Gandhi National Rural Employment Guarantee Act (MGNREGA) provided employment (...) to almost 55 million households and spending nearly 8 billion US dollars in April 2010–March 2011. Participation of women and socially backward groups has been exceptionally high. This paper analyzes the policy provisions, implementation and monitoring mechanism of MGNEGA to argue that policy designs with legal enforceable mechanisms and collaborative governance systems can lead to empowerment of the marginalized sections. (shrink)

When Georg von der Gabelentz’s book Die Sprachwissenschaft was published, the historical-comparative paradigm was the dominant perspective in empirical linguistic enquiry, and the then current theory of language was fijirmly rooted in language psychology. While itself based in this tradition, Gabelentz’s Sprachwissenschaft nevertheless strikes another chord, which sets it apart from contemporary sources. This chapter argues that the book is particularly noteworthy for its wide-ranging bottom-up approach to linguistic phenomena and its propensity to conceive of language both as object and (...) instrument of enquiry in a sense akin to the ‘reflexive’ stance that later would become a hallmark of Edmund Husserl’s phenomenology. The ‘phenomenological mindset’ can in particular be retraced in the way a diffferent philosophy of the language sciences and theory of meaning take shape in Die Sprachwissenschaft. (shrink)

The ‘real’ issue concerns the status of qualia, that is, the subjective sensory states into which we are thrown when looking at a yellow leaf, hearing a musical chord, sniffing a camembert, or running our fingers over a piece of sandpaper. Is it possible to provide a satisfactory account of such states using only the resources of a materialist functionalism? Or is it the case -- as it has seemed to many, and as it seems to David Chalmers -- that (...) once we have said all there is to say about the physical basis of, and the functional role of, such states, there remains an uneliminable residue: the brute qualitative matter of ‘what it is like’ to sniff the camembert? Since it is extraordinarily hard to tackle this question head-on, we seek the leverage afforded by the notion of the philosopher's zombie, the point being that if we have a coherent intuition to the effect that there is indeed such a residue, then we ought to be able to conceive of the zombie. Just subtract the residue while leaving all the physical/functional stuff in place. Conversely, if it transpires that the notion of the philosopher's zombie breaks down under stress, this would seem to indicate that the intuition of the ineliminable residue is itself problematic. The ‘remedy’ for a belief in zombies is the sort of Dennettian exercise in imagination proposed in this paper. One must be forced to recognize the huge gulf between the simple informational economies of the thermostat, and even the PC, and the amazingly subtle and layered informational economy of a normal human being. Taking the PC, or the severely degraded registrations of actual blindsight victims, as the model, one may fool oneself into thinking one has imagined something when one has not really confronted its detailed implications. This piece will have accomplished its aim if it encourages a few readers to take the latter possibility more seriously than hitherto. (shrink)

We address how listeners perceive temporal regularity in music performances, which are rich in temporal irregularities. A computational model is described in which a small system of internal self‐sustained oscillations, operating at different periods with specific phase and period relations, entrains to the rhythms of music performances. Based on temporal expectancies embodied by the oscillations, the model predicts the categorization of temporally changing event intervals into discrete metrical categories, as well as the perceptual salience of deviations from these categories. The (...) model's predictions are tested in two experiments using piano performances of the same music with different phrase structure interpretations (Experiment 1) or different melodic interpretations (Experiment 2). The model successfully tracked temporal regularity amidst the temporal fluctuations found in the performances. The model's sensitivity to performed deviations from its temporal expectations compared favorably with the performers' structural (phrasal and melodic) intentions. Furthermore, the model tracked normal performances (with increased temporal variability) better than performances in which temporal fluctuations associated with individual voices were removed (with decreased variability). The small, systematic temporal irregularities characteristic of human performances (chord asynchronies) improved tracking, but randomly generated temporal irregularities did not. These findings suggest that perception of temporal regularity in complex musical sequences is based on temporal expectancies that adapt in response to temporally fluctuating input. (shrink)

The notion of recognition is an ethically potent resource for understanding human relational needs; and its negative counterpart, misrecognition, an equally potent resource for critique. Axel Honneth’s rich account focuses our attention on recognition’s role in securing basic self-confidence, moral self-respect, and self-esteem. With these loci of recognition in place, we are enabled to raise the intriguing question whether each of these may be extended to apply specifically to the epistemic dimension of our agency and selfhood. Might we talk intelligibly—while (...) staying in tune with Honneth’s concepts and their Hegelian key—of a generic idea of epistemic recognition? Such an idea might itself be seen to apply at the same three levels to indicate: first, basic epistemic self-confidence; second, our status as epistemically responsible; and third, a certain epistemic self-esteem that reflects the epistemic esteem we receive from others. The papers in this volume surely sound a chord in the affirmative, and together they steer us towards a multifaceted conception of how epistemic injustice is related to epistemic misrecognition, and indeed how we might construe a positive relation of epistemic recognition. (shrink)

How do listeners learn about the statistical regularities underlying musical harmony? In traditional Western music, certain chords predict the occurrence of other chords: Given a particular chord, not all chords are equally likely to follow. In Experiments 1 and 2, we investigated whether adults make use of statistical information when learning new musical structures. Listeners were exposed to a novel musical system containing phrases generated using an artificial grammar. This new system contained statistical structure quite different from (...) Western tonal music. Our results suggest that learners take advantage of the statistical patterning of chords to acquire new musical structures, similar to learning processes previously observed for language learning. (shrink)

According to Fleck, a fact is not something objectively given but rather a social event. Scientific facts are no exception, as can be seen through the annals of medicine. Fleck argues that if the physical sciences initially appear to be immune to such social conditioning, this misconception can be corrected by recognizing the similarities between the natural sciences and medicine both historically and epistemologically. Fleck's ideas are not new, having been presented by him in 1935, but it is only recently (...) that they have begun to strike a responsive chord. Kuhn was aware of Fleck's work when he began to promulgate his own ideas in the 1960s. But there are important differences as well as similarities which can only be appreciated once Fleck's own work has had a proper hearing. To this end the University of Chicago Press has published a translation-edition of the full monograph in 1979. In ‘On the question of the foundations of medical knowledge’, Fleck's own precis to this major work, he correctly foretold the dawning of the sociology of cognition. CiteULike Connotea Del.icio.us What's this? (shrink)

Through a series of provocative conversations, Frederick Luis Aldama and Herbert Lindenberger, who have written widely on literature, film, music, and art, locate a place for the discomforting and the often painfully unpleasant within aesthetics. The conversational format allows them to travel informally across many centuries and many art forms. They have much to tell one another about the arts since the advent of modernism soon after 1900—the nontonal music, for example, of the Second Vienna School, the chance-directed music and (...) dance of John Cage and Merce Cunningham, the in-your-faceness of such diverse visual artists as Francis Bacon, Pablo Picasso, Willem de Kooning, Egon Schiele, Otto Dix, and Damien Hirst. They demonstrate as well a long tradition of discomforting art stretching back many centuries, for example, in the Last Judgments of innumerable Renaissance painters, in Goya’s so-called “black” paintings, in Wagner’s Tristan chord, and in the subtexts of Shakespearean works such as King Lear and Othello. This book is addressed at once to scholars of literature, art history, musicology, and cinema. Although its conversational format eschews the standard conventions of scholarly argument, it provides original insights both into particular art forms and into individual works within these forms. Among other matters, it demonstrates how recent work in neuroscience may provide insights in the ways that consumers process difficult and discomforting works of art. The book also contributes to current aesthetic theory by charting the dialogue that goes on—especially in aesthetically challenging works—between creator, artifact, and consumer. (shrink)

Intended to introduce readers to the use of artificial neural networks in the study of music, this volume contains numerous case studies and research findings that address problems related to identifying scales, keys, classifying musical chords, and learning jazz chord progressions. A detailed analysis of networks is provided for each case study which together demonstrate that focusing on the internal structure of trained networks could yield important contributions to the field of music cognition.

Bertrand’s paradox ) can be considered as a cautionary memento, to practitioners and students of probability calculus alike, of the possible ambiguous meaning of the term ‘at random’ when the sample space of events is continuous. It deals with the existence of different possible answers to the following question: what is the probability that a chord, drawn at random in a circle of radius R, is longer than the side of an inscribed equilateral triangle? Physics can help to remove the (...) ambiguity by identifying an actual experiment, whose outcome is obviously unique and prescribes the physical variables to which the term ‘random’ can be correctly applied. In this paper, after briefly describing Bertrand’s paradox, we associate it with an experiment, which is basically a variation of the famous Buffon’s needle experiment for estimating the value of π. Its outcome is compared with the analytic predictions of probability calculus, that is with the probability distribution of variables whose uniform distribution can be considered a sound implementation of complete randomness. (shrink)

Use of the imagination is a key aspect of successful psychotherapeutic treatments. Psychotherapy helps clients get in touch with, awaken, and learn to trust their creative inner life, while therapists use their imaginations to mentalise the suffering other and to trace the unconscious stirrings evoked by the intimacy of the consulting room. Working from this premise, in _The Therapeutic Imagination_ _Jeremy Holmes_ argues unashamedly that literate therapists make better therapists. Drawing on psychoanalytic and literary traditions both classical and contemporary, Part (...) I shows how poetry and novels help foster therapists’ understanding of their own imagination-in-action, anatomised into five phases: attachment, reverie, logos, action and reflection. Part II uses the contrast between secure and insecure narrative styles in attachment theory and relates these to literary storytelling and the transformational aspects of therapy. Part III uses literary accounts to illuminate the psychiatric conditions of narcissism, anxiety, splitting and bereavement. Based on Forster’s motto, ‘Only Connect’, Part IV argues, with the help of poetic examples, that a psychiatry shorn of psychodynamic creativity is impoverished and fails to serve its patients. Clearly and elegantly written, and drawing on the author’s deep knowledge of psychoanalysis and attachment theory and a lifetime of clinical experience, _Holmes _convincingly links the literary and psychoanalytic canon. _The Therapeutic Imagination _is a compelling and insightful work that will strike chords for therapists, counsellors, psychoanalysts, psychiatrists and psychologists. (shrink)