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The Musical-Mathematical Mind pp 131–141Cite as

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

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Abstract

This investigation is a departure point for understanding what Pythagoreanism can mean today, how can harmony be conceived at several time scales and what might a hierarchical model of form together with an algebra of perception entail for music composition. The study of qualitative aspects of music through mathematics is made by taking James Tenney’s theory of musical form together with Alain Badiou’s ‘objective phenomenology’ in order to imagine new ways of composing music.

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Notes

  1. 1.

    For an account of these problems and their history see [2].

  2. 2.

    For more details on this entanglement and its compositional uses see [5]. The seminal research on the two facets of harmony initially took shape in the fascinating book [6].

  3. 3.

    An octave or a fifth, for instance, lie close to a given pitch in harmonic space, while in 12 tone equal temperament, a semitone, which is harmonically relatively far, would be the nearest interval.

  4. 4.

    In the wake of Tenney, two of his colleagues have proceeded to study each of these aspects in turn through morphological [12] and structural metrics [13].

  5. 5.

    Some suggestions in this direction are pursued in [14].

  6. 6.

    For more on this interesting topic of abstraction and material, see [15].

  7. 7.

    It is beyond the scope of this article to provide a comprehensive account of Badiou’s theory. For more information see [10, 11, 16].

  8. 8.

    To further our investigations we might turn away from Badiou towards more mathematically oriented literature. Also, Badiou’s theory of change and the Event is not directly relevant to our purposes (although it is not incompatible either).

  9. 9.

    I’m interested in establishing collaborations both with musimathicians as well as with mathemusicians in order to find out what can be made of these ideas.

  10. 10.

    “As the thought experiment is fully immersed within the material system, it permits the abstracting force to assume material behaviors and new generative schema otherwise unavailable to an isolated account of thought trapped in naive intuitions of itself.”[15], p. 24.

References

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Author information

Authors and Affiliations

  1. Conservatorio de las Rosas, Santiago Tapia 334, 58000, Morelia, CP, Mexico

    Juan Sebastián Lach Lau

Authors
  1. Juan Sebastián Lach Lau
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Correspondence to Juan Sebastián Lach Lau .

Editor information

Editors and Affiliations

  1. CENIDIM-INBA, Centro Nacional de las Artes (CENART), Coyoacán, Distrito Federal, Mexico

    Gabriel Pareyon

  2. División de Electrónica y Computación (CUCEI), Universidad de Guadalajara, Guadalajara, Jalisco, Mexico

    Silvia Pina-Romero

  3. Universidad de Cañada, Teotitlan de Flores Magón, Oaxaca, Mexico

    Octavio A. Agustín-Aquino

  4. Departamento de Matemáticas, UNAM Facultad de Ciencias, Coyoacán, Distrito Federal, Mexico

    Emilio Lluis-Puebla

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Lach Lau, J.S. (2017). Proportion, Perception, Speculation: Relationship Between Numbers and Music in the Construction of a Contemporary Pythagoreanism. In: Pareyon, G., Pina-Romero, S., Agustín-Aquino, O., Lluis-Puebla, E. (eds) The Musical-Mathematical Mind. Computational Music Science. Springer, Cham. https://doi.org/10.1007/978-3-319-47337-6_14

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  • DOI: https://doi.org/10.1007/978-3-319-47337-6_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-47336-9

  • Online ISBN: 978-3-319-47337-6

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