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- Candace Brower (2008). Paradoxes of Pitch Space. Music Analysis 27 (1):51-106.Parallels between the mathematics of tiling, which describes geometries of visual space, and neo-Riemannian theory, which describes geometries of musical space, make it possible to show that certain paradoxes featured in the visual artworks of M. C. Escher also appear in the pitch space modelled by the neo-Riemannian Tonnetz . This article makes these paradoxes visually apparent by constructing an embodied model of triadic pitch space in accordance with principles drawn from the mathematics of tiling, on the one hand, and from cognitive science, on the other – specifically, the notion that our experience of pitch relationships is governed in part by the metaphorical projection of patterns abstracted from embodied experience known as image schemas. These paradoxes are illustrated with reference to passages drawn from four compositions to whose expressive character such paradoxes contribute: the fifteenth-century motet 'Absalon fili mi'; the finale of Haydn's String Quartet in G major, Op. 76 No. 1; Brahms's Intermezzo in B minor, Op. 119 No. 1; and Wagner's Parsifal.Reading list | Discuss | Edit | Categorize |My bibliography
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This enjoyable book presents a potpourri of paradoxes with the purpose of showing how they connect to serious philosophical issues. The main paradoxes are Zeno's, the sorites, Newcomb's problem, the paradoxes of confirmation, the surprise examination, and the paradoxes of self-reference. A final chapter defends the assumption that contradictions are unacceptable and an appendix throws in sixteen minor paradoxes. Along the way, R. M. Sainsbury peppers the reader with helpful queries and provocative asides.
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| | Scholar | More options ... This book explores the mismatch between perception and physical reality, and describes the many factors that influence the perception of space including the ...
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| | Scholar | At my library | More options ... My concern in this paper is with the aspect of the phenomenal character of visual experience that pertains to its spatial dimension. I shall refer to this aspect as visual space. Kant famously claimed that the representation of space is the a priori form of the faculty of sensibility. This claim is sometimes interpreted as the view that visual space is a pictorial canvas contributed by the mind on which sensations such as color experiences are organized. This reading, whether it is correct or not, consists of at least two independent claims. First, visual space is contributed by the mind. Second, visual space is a pictorial canvas. Both of theses claims, of course, demand further explication. However.
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| | Scholar | More options ... Extending on an earlier paper [Found. Phys. Ltt., 16(4) 343–355, (2003)], it is argued that instants of time and the instantaneous (including instantaneous relative position) do not actually exist. This conclusion, one which is also argued to represent the correct solution to Zeno’s motion paradoxes, has several implications for modern physics and for our philosophical view of time, including that time and space cannot be quantized; that contrary to common interpretation, motion and change are compatible with the “block” universe and relativity; and that time, space, and space-time too, cannot exist. Instead, motion and change become the major players.
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| | Scholar | More options ... We identify a class of paradoxes that are neither set-theoretical or semantical, but that seem to depend on intensionality. In particular, these paradoxes arise out of plausible properties of propositional attitudes and their objects. We try to explain why logicians have neglected these paradoxes, and to show that, like the Russell Paradox and the direct discourse Liar Paradox, these intensional paradoxes are recalcitrant and challenge logical analysis. Indeed, when we take these paradoxes seriously, we may need to rethink the commonly accepted methods for dealing with the logical paradoxes.
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| | Scholar | More options ... There exist well-known conundrums, such as measure theoretic paradoxes and problems of contact, which, within the context of classical physics, can be used to argue against the existence of points in space and space-time. I examine whether quantum mechanics provides additional reasons for supposing that there are no points in space and space-time.
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| | Other links: dx.doi.org | Scholar | At my library | More options ... There exist well‐known conundrums, such as measure‐theoretic paradoxes and problems of contact, which, within the context of classical physics, can be used to argue against the existence of points in space and space‐time. I examine whether quantum mechanics provides additional reasons for supposing that there are no points in space and space‐time.
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| | Scholar | More options ... Some sounds have pitch, some do not. A tuba’s notes are lower pitched than a flute’s, but the fuzz from an untuned radio has no discernible pitch. Pitch is an attribute in virtue of which sounds that possess it can be ordered from “low” to “high”. Given how audition works, physics has taught us that frequency determines what pitch a sound auditorily appears to have.
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| | Scholar | More options ... Reading list
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| | Other links: jstor.org | Scholar | At my library | More options ... Discussion of Candace Brower, Paradoxes of pitch space
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