## Abstract

Musical performance and composition imply hypergestural transformation from symbolic to physical reality and vice versa. But most scores require movements at infinite physical speed that can only be performed approximately by trained musicians. To formally solve this divide between symbolic notation and physical realization, we introduce complex time (C-time) in music. In this way, infinite physical speed is “absorbed” by a finite imaginary speed. Gestures thus comprise thought (in imaginary time) and physical realization (in real time) as a world-sheet motion in space-time, corresponding to ideas from physical string theory. Transformation from imaginary to real time gives us a measure of artistic effort to pass from potentiality of thought to physical realization of artwork. Introducing C-time we define a musical kinematics, calculate Euler-Lagrange equations, and, for the case of the elementary gesture of a pianist’s finger, solve corresponding Poisson equations that describe world-sheets which connect symbolic and physical reality.

Original language | English (US) |
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Title of host publication | Mathematics and Computation in Music - 5th International Conference, MCM 2015, Proceedings |

Editors | Tom Collins, David Meredith, Anja Volk |

Publisher | Springer Verlag |

Pages | 137-148 |

Number of pages | 12 |

ISBN (Print) | 9783319206028 |

DOIs | |

State | Published - 2015 |

Event | 5th International Conference on Mathematics and Computation in Music, MCM 2015 - London, United Kingdom Duration: Jun 22 2015 → Jun 25 2015 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 9110 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 5th International Conference on Mathematics and Computation in Music, MCM 2015 |
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Country/Territory | United Kingdom |

City | London |

Period | 6/22/15 → 6/25/15 |

### Bibliographical note

Publisher Copyright:© Springer International Publishing Switzerland 2015.

## Keywords

- Complex time
- Euler-lagrange equation
- Hypergestures
- Performance theory
- String theory
- World-sheets of space-time