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)

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)

This article analyzes the treatment of music in Buddhist monastic life through the rules on music in Buddhist canon law within the six extant traditions, which are preserved in Chinese, Tibetan, Pāli, and fragmentary Sanskrit manuscripts. These texts distinguish and differentiate instrumental and vocal music, presenting song, dance, and instrumental music as a triad and further subdividing vocal music into reciting, chanting, and singing. The performance and consumption of singing is strictly prohibited. Regulations on chanting (...) and recitation are mutually exclusive and context dependent. Chanting is required on two occasions: when one praises the Buddha’s virtues and when one performs the Tridaṇḍaka ritual. Chanting is prohibited on three other occasions: when one recites the Prātimokṣasūtra and other ordinary Buddhist texts, and when one preaches Dharma. These regulations demonstrate that text and context are decisive in determining what forms of vocal music are appropriate in Buddhist practice. The use of embellished chanting is reserved for performing rituals whose primary goal is to please divine recipients but must be prohibited when clear articulation is expected for educating the audience. Given that making or consuming vocal music is not a criminal offense, yet is strictly regulated, I argue that the establishment of Buddhist canon law was compelled by a pressing demand to demarcate and maintain a social boundary between the Buddhist monastic order and the lay community of adherents. (shrink)

Fergus Kelly: Thinking in Threes: The Triad in Early Irish Literature Brian Pullan: Charity and Usury: Jewish and Christian Lending in Renaissance and Early Modern Italy Noel Malcolm: The Crescent and the City of the Sun: Islam and the Renaissance Utopia of Tommaso Campanella H. R. Woudhuysen: The Foundations of Shakespeare's Text J. G. A. Pocock: The Re-Description of Enlightenment Andrew Hadfield: Michael Drayton and the Burden of History Eric Foner: Abraham Lincoln: The Great Emancipator? Gillian Beer: Revenants and Migrants: (...) Hardy, Butler, Woolf and Sebald Stephen Banfield: Scholarship and the Musical: Reclaiming Jerome Kern Brian Simpson: The Rule of Law in International Affairs Christopher Bayly: 'The Nation Within': British India at War 1939-47 John Vickers: Economics for Consumer Policy Gillian Feeley-Harnik: The Geography of Descent Susan Gathercole: Working Memory and Learning During the School Years Lothar Ledderose: Carving Stone Sutras before the World Ends: The Inscription of 1118 CE at Cloud Dwelling Monastery near Beijing. (shrink)

Few will, I think, doubt that the Trio from the Minuetto movement of Mozart's G Minor Symphony seems simple, direct, and lucid—even guileless. Its melodies are based upon common figures such as triads and conjunct diatonic motion. No hemiola pattern, often encountered in triple meter, disturbs metric regularity. With the exception of a subtle ambiguity..., rhythmic structure is in no way anomalous. There are no irregular or surprising chord progressions; indeed, secondary dominants and chromatic alterations occur very frequently. The (...) instrumentation is quite conventional, and no unusual registers are employed. In this essay, Leonard B. Meyer, Benjamin Franklin Professor of music and humanities at the University of Pennsylvania, further explores and details the significance of theories advanced in his book, Explaining Music: Essays and Explorations. His previous contribution to Critical Inquiry, "Concerning the Sciences, the Arts - AND the Humanities," appeared in our first issue. (shrink)

We explore Peirce’s pragmatic conception of sign action, as a distributed and emergent view of cognition and exemplify with the emergence of classical ballet. In our approach, semiosis is a temporally distributed process in which a regular tendency towards certain future outcomes emerges out of a history of sign actions. Semiosis self-organizes in time, in a process that continuously entails the production of more signs. Emergence is a ubiquitous condition in this process: the translation of signs into signs cannot be (...) inferred from the properties of the components of a semiotic triad alone, but has to take into account a complex interaction between a micro-semiotic and macro-semiotic level of description. This interaction can be understood as an interplay of potentialities and tendencies, or upward constitutive determinative relations and downward selective determinative relations. According to this view, emergence is a central defining condition of processes of meaning. Ballet is a sign in action. The emergence of classical ballet is a self-regulatory process, in which a system of different kinds of cognitive artifacts (musical, bodily/motor, spatial/architectonic) and agents obtained a stable semiotic relation throughout many phases of development between the 16th and the 19th Century. One case is the development of the verticality of dance in classical ballet as a semiotic relation connecting proscenium arch stages, dancing bodies, and audiences. This development is micro-semiotically determined by the spatial constraints of the proscenium arch stage, and macro-semiotically determined by a historical construction of the dancing body as a sign within a network of semiotic chains, such as the intersemiotic regulation of body of the dancer by principles coming from painting. This is not only the emergence of actual meaning, but also the emergence of an open-ended field of potential and general meanings, an autonomous tendency of development. To say that ballet, as sign action, emerges, is to say that cognitive artifacts such as dancer’s bodies, stages and audience’s point of view, musical compositions, costumes, all sorts of supporting institutions, etc, constitute a niche for sign action, interacting according to tendencies of development that didn’t exist before. (shrink)

Ioulia Podoroga | : Dans cet article, je pose le problème des rapports entre philosophie et littérature à partir du cas de Boris Pasternak, dont la vie et l’oeuvre permettent d’envisager une nouvelle articulation entre les deux disciplines, en mobilisant un schème paradoxalement hégélien. Schème hégélien, car fait de trois mouvements, de sa pratique musicale vers la philosophie pour aboutir à une relève dans la poésie. Mais schème anti-hégélien, parce que la triade hégélienne est inversée : la philosophie est le (...) moyen-terme, mais qui reste central, dans l’acheminement vers l’accomplissement du système par la poésie. | : In this article I raise the problem of the relationship between philosophy and literature basing it on the case-study of Boris Pasternak’s writings, whose life and work enable us to envisage a new linkage between the two disciplines by mobilizing a paradoxically Hegelian scheme. Hegelian scheme because of its three movements : from his musical practice towards poetry via philosophy. But anti-Hegelian scheme, because the Hegelian triad is reversed : philosophy is the medium-term but still central in the movement towards the completion of the system by poetry. (shrink)

Que la fin de l'art et celle de la philosophie s'entrelacent, la civilisation récente semble en donner l'image. Et pourtant, à creuser le 20e siècle dans sa singularité passionnante autant qu'effrayante, on apprend à reconfigurer les questions de l'oeuvre artistique et de la vérité discursive sous l'égide du problème clef qu'est le langage. Les présocratiques et la musique depuis Nietzsche ; la triade des nouveaux-venus au 18e siècle : esthétique, criticisme transcendantal et philosophie du langage ; les sciences humaines modernes (...) face à l'art et le mythe ; enfin, les rapports entre l'espace poético-musical et l'architecture autour de l'oeuvre d'art dite totale, étrangement ressuscitée parmi nous : le projet de réunir ces thèmes permet d'accéder aux racines d'une Europe plus importante que celle des technocrates. (shrink)

In his second book on art, Weiss groups the nine basic arts into three triads in accordance with whether their characteristic products are created spaces--architecture, sculpture, painting; created time--musicry, story, poetry; or created movement --music, the theatre, the dance. The approach of any art to its undertaking and the nature of its achievement is distinctive; none duplicates the task, nor borrows the logic, of the others. Weiss also discusses some "compound arts," including photography and the movies. Through the (...) vigor of his language, and the sensitivity of his appraisals, he provokes fresh insight into both the specific arts and the entire artistic enterprise.--S. M. W. (shrink)