Knots, Music and DNA.

@article{Mannone2018KnotsMA,
  title={Knots, Music and DNA.},
  author={Maria Mannone},
  journal={arXiv: General Mathematics},
  year={2018}
}
Musical gestures connect the symbolic layer of the score to the physical layer of sound. I focus here on the mathematical theory of musical gestures, and I propose its generalization to include braids and knots. In this way, it is possible to extend the formalism to cover more case studies, especially regarding conducting gestures. Moreover, recent developments involving comparisons and similarities between gestures of orchestral musicians can be contextualized in the frame of braided monoidal… 
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References

SHOWING 1-10 OF 72 REFERENCES
Introduction to gestural similarity in music. An application of category theory to the orchestra
Mathematics, and more generally computational sciences, intervene in several aspects of music. Mathematics describes the acoustics of the sounds giving formal tools to physics, and the matter of
Diagrams, gestures and formulae in music
TLDR
A comprising framework for mathematical music theory, which ramifies into an algebraic and a topological branch, achieved by the idea of the gestoid, an ‘algebraic’ category associated with the fundamental groupoid of a gesture.
Gestural Analysis and Classification of a Conductor’s Movements
TLDR
The gestures of the conductor referring to some concept of homotopy theory are studied, which anticipate and continuously prepare the gestures of each musician in the orchestra in a hierarchical structure that corresponds to the structure of the score.
Elements of a Future Vocal Gesture Theory
TLDR
The chapter ends with the proposal of a new neumatic notation for voice didactics and composition that can complete the information given by the musical score.
Narrating the origin of the universe through music: A case study
Our project is about the synthesis of a musical piece, based on the timeline of the Universe. We can understand music through visual and gestural analogies. In a similar way, popular descriptions of
Hypergestures in Complex Time: Creative Performance Between Symbolic and Physical Reality
TLDR
Introducing complex time in music introduces complex time (\(\mathbb {C}\)-time, which defines a musical kinematics, calculates Euler-Lagrange equations, and solves corresponding Poisson equations that describe world-sheets which connect symbolic and physical reality.
Gesture in performance with traditional musical instruments and electronics: Use of embodied music cognition and multimodal motion capture to design gestural mapping strategies
TLDR
Mapping strategies from a case study of electric guitar performance will be illustrated describing what motivated the choice of a multimodal motion capture system and how different solutions have been adopted considering both gestural meaning formation and technical constraints.
Molecular knots in biology and chemistry.
TLDR
The current knowledge on the various molecular knots found in naturally occurring biological systems (DNA, RNA and proteins), and those created by synthetic chemists are discussed, including recent developments in experimental and computational studies which are beginning to shed light into the complex interplay between these topologically intricate molecules.
Characterization of the degree of Musical non-Markovianity
Recently, as an aid for musical analysis, in computational musicology mathematical and informatics tools have been developed to quantitatively characterize some aspects of musical compositions. To a
Global functorial hypergestures over general skeleta for musical performance
TLDR
This article extends Lagrangian formalism to hypergestures that are defined functorially over general topological categories as addresses, are global, and are also defined for general skeleta.
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