Pythagorean Tuning: Pentatonic and Heptatonic Scale
References
- [1] Grzegorz Bancerek. On the structure of Mizar types. In Herman Geuvers and Fairouz Kamareddine, editors, Electronic Notes in Theoretical Computer Science, volume 85, pages 69–85. Elsevier, 2003.10.1016/S1571-0661(04)80758-8
- [2] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41–46, 1990.
- [3] Grzegorz Bancerek, Czesław Bylinski, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8_17.10.1007/978-3-319-20615-8_17
- [4] Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pąk. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6.10.1007/s10817-017-9440-6604425130069070
- [5] François Baskevitch. Les représentations de la propagation du son, d’Aristote à l’Encyclopédie. PhD thesis, Université de Nantes, France, 2008.
- [6] Adam Grabowski, Artur Korniłowicz, and Christoph Schwarzweller. On algebraic hierarchies in mathematical repository of Mizar. In M. Ganzha, L. Maciaszek, and M. Paprzycki, editors, Proceedings of the 2016 Federated Conference on Computer Science and Information Systems (FedCSIS), volume 8 of Annals of Computer Science and Information Systems, pages 363–371, 2016. doi:10.15439/2016F520.10.15439/2016F520
- [7] Bernard Parzysz and Yves Hellegouarch. Musique et mathématique: (suivi de) Gammes naturelles. Number 53. Association des Professeurs de Mathématiques de l’Enseignement Public (APMEP), Paris, 1984.
Language: English
Page range: 239 - 269
Accepted on: Sep 29, 2018
Published on: Mar 2, 2019
Published by: University of Białystok
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Keywords:
Related subjects:
© 2019 Roland Coghetto, published by University of Białystok
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.