The Musical-Mathematical Mind

1. Front Matter

   Pages i-xxix

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2. Extended Counterpoint Symmetries and Continuous Counterpoint

   • Octavio A. Agustín-Aquino

   Pages 1-7

3. Gödel-Vector and Gödel-Address as Tools for Genealogical Determination of Genetically-Produced Musical Variants

   • Carlos de Lemos Almada

   Pages 9-16

4. A Survey of Applications of the Discrete Fourier Transform in Music Theory

   • Emmanuel Amiot

   Pages 17-28

5. Gestures on Locales and Localic Topoi

   • Juan Sebastián Arias

   Pages 29-39

6. On the Structural and the Abstract in My Compositional Work

   • Clarence Barlow

   Pages 41-51

7. A Proposal for a Music Writing for the Visually Impaired

   • Teresa Campos-Arcaraz

   Pages 53-60

8. Group Theory for Pitch Sequence Representation: From the Obvious to the Emergent Complexity

   • Emilio Erándu Ceja-Cárdenas

   Pages 61-69

9. Mazzola’s Escher Theorem

   • Yemile Chávez-Martínez, Emilio Lluis-Puebla

   Pages 71-78

10. The Mechanics of Tipping Points: A Case of Extreme Elasticity in Expressive Timing

    • Elaine Chew

    Pages 79-88

11. Lexicographic Orderings of Modes and Morphisms

    • David Clampitt

    Pages 89-97

12. Music of Quantum Circles

    • Micho Đurđevich

    Pages 99-110

13. Partitiogram, Mnet, Vnet and Tnet: Embedded Abstractions Inside Compositional Games

    • Pauxy Gentil-Nunes

    Pages 111-118

14. Algebraic Combinatorics on Modes

    • Franck Jedrzejewski

    Pages 119-130

15. Proportion, Perception, Speculation: Relationship Between Numbers and Music in the Construction of a Contemporary Pythagoreanism

    • Juan Sebastián Lach Lau

    Pages 131-141

16. Topos Echóchromas Hórou (The Place of the Tone of Space). On the Relationship Between Geometry, Sound and Auditory Cognition

    • Jaime Alonso Lobato-Cardoso

    Pages 143-151

17. Models and Algorithms for Music Generated by Physiological Processes

    • Jaime Alonso Lobato-Cardoso, Pablo Padilla-Longoria

    Pages 153-159

18. Music, Expectation, and Information Theory

    • D. Gareth Loy

    Pages 161-169

19. Gestural Dynamics in Modulation: (Towards) a Musical String Theory

    • Guerino Mazzola

    Pages 171-188

20. Manuel M. Ponce’s Piano Sonata No. 2 (1916): An Analysis Using Signature Transformations and Spelled Heptachords

    • Mariana Montiel

    Pages 189-197

This book presents a deep spectrum of musical, mathematical, physical, and philosophical perspectives that have emerged in this field at the intersection of music and mathematics. In particular the contributed chapters introduce advanced techniques and concepts from modern mathematics and physics, deriving from successes in domains such as Topos theory and physical string theory.

The authors include many of the leading researchers in this domain, and the book will be of value to researchers working in computational music, particularly in the areas of counterpoint, gesture, and Topos theory.

• Counterpoint
• Music Theory
• Gesture Theory
• Improvisation
• Algorithmic Music
• Automated Composition Systems
• Musical Morphologies
• Topos Theory

“It is impossible to summarize a work of such depth. Suffice it to say that abstract algebra, topology, number theory, geometry, and so on are all involved. If you are a serious devotee of musical-mathematical theory and have a very extensive background in both areas, the book will be a treasure.” (James Van Speybroeck, Computing Reviews, April, 2018)​

• CENIDIM-INBA, Centro Nacional de las Artes (CENART), Coyoacán, Mexico

  Gabriel Pareyon

• División de Electrónica y Computación (CUCEI), Universidad de Guadalajara, Guadalajara, Mexico

  Silvia Pina-Romero

• Universidad de Cañada, Teotitlan de Flores Magón, Mexico

  Octavio A. Agustín-Aquino

• Departamento de Matemáticas, UNAM Facultad de Ciencias, Coyoacán, Mexico

  Emilio Lluis-Puebla

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