Accesso libero

Pythagorean Tuning: Pentatonic and Heptatonic Scale

INFORMAZIONI SU QUESTO ARTICOLO

Cita

[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)80758-8Search in Google Scholar

[2] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41–46, 1990.Search in Google Scholar

[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_17Open DOISearch in Google Scholar

[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/s10817-017-9440-6604425130069070Open DOISearch in Google Scholar

[5] François Baskevitch. Les représentations de la propagation du son, d’Aristote à l’Encyclopédie. PhD thesis, Université de Nantes, France, 2008.Search in Google Scholar

[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:10.15439/2016F520.10.15439/2016F520Search in Google Scholar

[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.Search in Google Scholar

eISSN:
1898-9934
ISSN:
1426-2630
Lingua:
Inglese
Frequenza di pubblicazione:
4 volte all'anno
Argomenti della rivista:
Computer Sciences, other, Mathematics, General Mathematics