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N2D3P9

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Mathematics and Computation in Music (MCM 2022)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13267))

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Abstract

N2D3P9 is a mathematical function which was developed to help in designing the Sagittal microtonal music notation. Given a rational number \(\frac{n}{d}\) representing a pitch (relative to some tonic note), N2D3P9 estimates its rank in popularity among all rational pitches in musical use. A low value of N2D3P9 indicates that the ratio is used often, and so should have a simple accidental symbol, while a high value indicates that the ratio is used rarely and so can have a more complex symbol if necessary. It may also be useful in designing rational scales or tunings.

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References

  1. Secor, G.D., Keenan, D.C.: Sagittal: A Microtonal Notation System. Xenharmonikôn, vol. 18 (2006). https://sagittal.org/sagittal.pdf. Accessed Mar 2022

  2. The Huygens-Fokker Foundation’s scale archive. https://www.huygens-fokker.org/microtonality/scales.html. Accessed Mar 2022

  3. Sagittal forum thread “developing a notational comma popularity metric”. https://forum.sagittal.org/viewtopic.php?f=4&t=493. Accessed Mar 2022

  4. New and Improved Solver - Microsoft 365 Blog. https://www.microsoft.com/en-us/microsoft-365/blog/2009/09/21/new-and-improved-solver/. Accessed Mar 2022

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Author information

Authors and Affiliations

  1. Brisbane, Australia

    Dave Keenan

  2. San Francisco, USA

    Douglas Blumeyer

Authors
  1. Dave Keenan
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  2. Douglas Blumeyer
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Corresponding authors

Correspondence to Dave Keenan or Douglas Blumeyer .

Editor information

Editors and Affiliations

  1. Georgia State University, Atlanta, GA, USA

    Mariana Montiel

  2. Technological University of the Mixteca, Huajuapan de León, Mexico

    Octavio A. Agustín-Aquino

  3. Universidad Politécnica de Madrid, Madrid, Spain

    Francisco Gómez

  4. Life University, Marietta, GA, USA

    Jeremy Kastine

  5. National Autonomous University of Mexico, Mexico City, Distrito Federal, Mexico

    Emilio Lluis-Puebla

  6. Georgia State University, Atlanta, GA, USA

    Brent Milam

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© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

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Cite this paper

Keenan, D., Blumeyer, D. (2022). N2D3P9. In: Montiel, M., Agustín-Aquino, O.A., Gómez, F., Kastine, J., Lluis-Puebla, E., Milam, B. (eds) Mathematics and Computation in Music. MCM 2022. Lecture Notes in Computer Science(), vol 13267. Springer, Cham. https://doi.org/10.1007/978-3-031-07015-0_26

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  • DOI: https://doi.org/10.1007/978-3-031-07015-0_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-07014-3

  • Online ISBN: 978-3-031-07015-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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