Metaphor as a Structural Principle of Modern Musical Notation

This essay proposes that the picture of a broken circle encountered by Watt during the second part of his tale marks a crucial collision point between Beckett's literary and mathematical interests and triggers a process of fractal scaling self-similarity. Building on recent interest concerning the role of the mathematics and mathematical forms found in Beckett's work, I argue that the broken circle depicted in the picture from Watt is a geometric form which (re)appears within at least three interlocking scales throughout Beckett's novel-length prose: (i) its moment of arrival in the picture from Watt, (ii) a macroscopic reinscription in the names of the protagonists populating the five novels spanning Watt through to The Unnamable and (iii) buried within the narratological depths of How It Is. As a structural principle, the interminable irregularity of fractals offered Beckett a viable solution for what he considered the defining task of the modern artist: ‘to find a form to accommodate the mess’. Moreover, the specific shape selected for his fractal is shown to contain within its geometry one of Beckett's most universal and pressing concerns: the inevitable insufficiency of language. Therefore, although this essay restricts itself to examining Beckett's novel-length prose, the idea of a broken circle fractal promises to provide a valuable heuristic through which to reassess the author's other generic avenues. Fractals thus offer a means through which one can bind together the length and breadth of Beckett's oeuvre without ever reducing dynamic chaos to stable order.

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ZUR SUBMIKROSKOPISCHEN STRUKTUR DER RATTENSCHILDDRÜSE ELEKTRONENMIKROSKOPISCHE UNTERSUCHUNGEN AN DER BASIS DES SCHILDDRÜSENFOLLIKELS

Acta Endocrinologica ◽

10.1530/acta.0.xxxv0334 ◽

1960 ◽

Vol XXXV (III) ◽

pp. 334-350 ◽

Cited By ~ 10

Author(s):

U. Waller

Keyword(s):

Endothelial Cells ◽

Basement Membranes ◽

The Other ◽

Small Vesicle ◽

Thyroid Follicle ◽

Basal Secretion ◽

Structural Principle ◽

Thyroid Epithelial Cell ◽

Endocrine Organs ◽

Subendothelial Space

ABSTRACT This is a description of ultramicroscopic structures at the base of the thyroid follicle. The structural principle of the subendothelial or interfollicular space, namely basement membranes closely following both the endothelial cells of the capillaries and the epithelial cells of the thyroid, corresponds to that described by other authors in the other endocrine organs. Especially shown are small vesicle like decreases of intensity in the subendothelial space, causing bulges in both the subepithelial basement membrane and the membrane covering the endothelial cell pores thereby forming pseudopores. This membrane is in several parts a double one. The possible role played by the above mentioned structures in the basal secretion of the thyroid epithelial cell is discussed.

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The Beth Gazo in Musical Notation

10.31826/9781463217808 ◽

2012 ◽

Keyword(s):

Musical Notation

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NEWEST TECTONICS OF THE VISTULA SPIT AREA

Proceedings of International Conference "Managinag risks to coastal regions and communities in a changinag world" (EMECS'11 - SeaCoasts XXVI) ◽

10.21610/conferencearticle_58b43162bdb89 ◽

2017 ◽

Author(s):

Nikolay Dunaev ◽

Nadezhda Politova ◽

Nadezhda Politova

Keyword(s):

Baltic Sea ◽

Coastal Zones ◽

Structural Principle ◽

Modern Landscape ◽

Tectonic Pattern

The interests of forecasting of the area’s development simulate to take more attention to the study of its newest tectonics. The most informative tectonic pattern for the studies of coastal zones is neotectonic one, based on the structural principle, which shows the newly formed and inherited dislocations, reflected in the modern landscape and exodynamics of the earth's surface. The question of the manifestations of newest tectonics by way on the example of the Vistula Spit (Baltic Sea) is discussed.

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Musical Notation as the Externalization of Imagined, Complex Sound

The Oxford Handbook of Sound and Imagination, Volume 2 ◽

10.1093/oxfordhb/9780190460242.013.41 ◽

2019 ◽

pp. 190-218

Author(s):

Henrik Sinding-Larsen

Keyword(s):

Complex System ◽

Computer Programming ◽

Roman Catholic ◽

Complex Sound ◽

Musical Notation ◽

History Of ◽

Visual Description ◽

The Way

Henrik Sinding-Larsen analyzes how new tools for the visual description of sound revolutionized the way music was conceived, performed, and disseminated. Early on, the ancient Greeks had described pitches and intervals in mathematically precise ways. However, their complex system had few consequences until it was combined with the practical minds of Roman Catholic choirmasters around 1000 ce. Now, melodies became depicted as note-heads on lines with precise pitch meanings and with note names based on octaves. This graphical and conceptual externalization of patterns in sound paved the way for a polyphonic complexity unimaginable in a purely oral/aural tradition. However, this higher complexity also entailed strictly standardized/homogenized scales and less room for improvisation in much of notation-based music. Through the concept of externalization, lessons from the history of musical notation are generalized to other tools of description, and Sinding-Larsen ends with a reflection on what future practices might become imaginable and unimaginable as a result of computer programming.

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Non-Contact Online Detection of Concentricity Error

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.733.611 ◽

2015 ◽

Vol 733 ◽

pp. 611-614

Author(s):

Hong Zheng

Keyword(s):

Measurement System ◽

Three Dimensional ◽

Error Evaluation ◽

Dimensional Model ◽

Online Detection ◽

Three Dimensional Model ◽

Geometric Tolerance ◽

Structural Principle ◽

Circularity Error ◽

Cylindricity Error

This paper researches on the non-contact online detection of concentricity error, which mainly focus on the structural principle of the measurement system and the concentricity error evaluation methods. The paper using the method of projection, converting the three-dimensional model to a two-dimensional model and evaluating coaxially error. And it is validated by the simulation of MATLAB. In theory, the proposed measurement system can measure geometric tolerance, including coaxially error, cylindricity error, circularity error, etc.

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