Modeling Musical Rhythm Mutations with Geometric Quantization

AbstractAugustine’s account in the Confessions Book IX of his ecstasy at Ostia remains unsurpassed in its poetic force, yet unusual, as a description of religious experience, in two particular respects. First of all, what he describes is not a “vision” of God, but an experience of listening. Second, it is not a solitary but a shared experience (e.g., with his mother, Monica). This essay considers the significance of these two elements by analyzing the relation between his description in Book IX and the understanding of rhythm that he develops in De musica. Drawing also on Book X (on memory) and Book XI (on time-consciousness) in the Confessions, I investigate a particular type of flowing memory – what I call, “perfect” memory – that characterizes the temporally ordered movements of musical rhythm, showing that it is in this type of memory that Augustine finds God.

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Deficits in musical rhythm perception in children with specific learning disabilities

Neurorehabilitation ◽

10.3233/nre-208013 ◽

2021 ◽

pp. 1-7

Author(s):

Vasudha Hande ◽

Shantala Hegde

Keyword(s):

Learning Disabilities ◽

Learning Disability ◽

Language Processing ◽

Phonological Processing ◽

Specific Learning Disability ◽

Specific Learning Disabilities ◽

Target Language ◽

Rhythm Perception ◽

Musical Rhythm ◽

Specific Learning

BACKGROUND: A specific learning disability comes with a cluster of deficits in the neurocognitive domain. Phonological processing deficits have been the core of different types of specific learning disabilities. In addition to difficulties in phonological processing and cognitive deficits, children with specific learning disability (SLD) are known to also found have deficits in more innate non-language-based skills like musical rhythm processing. OBJECTIVES: This paper reviews studies in the area of musical rhythm perception in children with SLD. An attempt was made to throw light on beneficial effects of music and rhythm-based intervention and their underlying mechanism. METHODS: A hypothesis-driven review of research in the domain of rhythm deficits and rhythm-based intervention in children with SLD was carried out. RESULTS: A summary of the reviewed literature highlights that music and language processing have shared neural underpinnings. Children with SLD in addition to difficulties in language processing and other neurocognitive deficits are known to have deficits in music and rhythm perception. This is explained in the background of deficits in auditory skills, perceptuo-motor skills and timing skills. Attempt has been made in the field to understand the effect of music training on the children’s auditory processing and language development. Music and rhythm-based intervention emerges as a powerful intervention method to target language processing and other neurocognitive functions. Future studies in this direction are highly underscored. CONCLUSIONS: Suggestions for future research on music-based interventions have been discussed.

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Cortical Plasticity Induced by Short-Term Multimodal Musical Rhythm Training

PLoS ONE ◽

10.1371/journal.pone.0021493 ◽

2011 ◽

Vol 6 (6) ◽

pp. e21493 ◽

Cited By ~ 60

Author(s):

Claudia Lappe ◽

Laurel J. Trainor ◽

Sibylle C. Herholz ◽

Christo Pantev

Keyword(s):

Cortical Plasticity ◽

Short Term ◽

Musical Rhythm

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Modeling complexity in musical rhythm

Complexity ◽

10.1002/cplx.20291 ◽

2009 ◽

pp. NA-NA ◽

Cited By ~ 1

Author(s):

Cheng-Yuan Liou ◽

Tai-Hei Wu ◽

Chia-Ying Lee

Keyword(s):

Musical Rhythm

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Generalized operator-valuedpq-symbols and geometric quantization

Functional Analysis and Its Applications ◽

10.1007/bf01080015 ◽

1995 ◽

Vol 29 (2) ◽

pp. 133-135 ◽

Cited By ~ 1

Author(s):

A. V. Karabegov

Keyword(s):

Geometric Quantization ◽

Generalized Operator

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Topological field theories on manifolds with Wu structures

Reviews in Mathematical Physics ◽

10.1142/s0129055x17500155 ◽

2017 ◽

Vol 29 (05) ◽

pp. 1750015 ◽

Cited By ~ 6

Author(s):

Samuel Monnier

Keyword(s):

Topological Field Theories ◽

Geometric Quantization ◽

Discrete Symmetry ◽

Local System ◽

Field Theories ◽

Simons Theory ◽

General Point ◽

Topological Field ◽

Generalized Cohomology ◽

Chern Simons

We construct invertible field theories generalizing abelian prequantum spin Chern–Simons theory to manifolds of dimension [Formula: see text] endowed with a Wu structure of degree [Formula: see text]. After analyzing the anomalies of a certain discrete symmetry, we gauge it, producing topological field theories whose path integral reduces to a finite sum, akin to Dijkgraaf–Witten theories. We take a general point of view where the Chern–Simons gauge group and its couplings are encoded in a local system of integral lattices. The Lagrangian of these theories has to be interpreted as a class in a generalized cohomology theory in order to obtain a gauge invariant action. We develop a computationally friendly cochain model for this generalized cohomology and use it in a detailed study of the properties of the Wu Chern–Simons action. In the 3-dimensional spin case, the latter provides a definition of the “fermionic correction” introduced recently in the literature on fermionic symmetry protected topological phases. In order to construct the state space of the gauged theories, we develop an analogue of geometric quantization for finite abelian groups endowed with a skew-symmetric pairing. The physical motivation for this work comes from the fact that in the [Formula: see text] case, the gauged 7-dimensional topological field theories constructed here are essentially the anomaly field theories of the 6-dimensional conformal field theories with [Formula: see text] supersymmetry, as will be discussed elsewhere.

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