{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T14:57:53Z","timestamp":1777474673183,"version":"3.51.4"},"reference-count":7,"publisher":"Walter de Gruyter GmbH","issue":"4","license":[{"start":{"date-parts":[[2018,12,1]],"date-time":"2018-12-01T00:00:00Z","timestamp":1543622400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/3.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018,12,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>In this article, using the Mizar system [3], [4], we define a structure [1], [6] in order to build a Pythagorean pentatonic scale and a Pythagorean heptatonic scale1 [5], [7].<\/jats:p>","DOI":"10.2478\/forma-2018-0022","type":"journal-article","created":{"date-parts":[[2019,5,9]],"date-time":"2019-05-09T03:10:02Z","timestamp":1557371402000},"page":"239-269","source":"Crossref","is-referenced-by-count":0,"title":["Pythagorean Tuning: Pentatonic and Heptatonic Scale"],"prefix":"10.2478","volume":"26","author":[{"given":"Roland","family":"Coghetto","sequence":"first","affiliation":[{"name":"Rue de la Brasserie 5, 7100 La Louvi\u00e8re , Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2019,3,2]]},"reference":[{"key":"2026042801413277535_j_forma-2018-0022_ref_001_w2aab3b7ab1b6b1ab1b1b1Aa","doi-asserted-by":"crossref","unstructured":"[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\u201385. Elsevier, 2003.10.1016\/S1571-0661(04)80758-8","DOI":"10.1016\/S1571-0661(04)80758-8"},{"key":"2026042801413277535_j_forma-2018-0022_ref_002_w2aab3b7ab1b6b1ab1b1b2Aa","unstructured":"[2] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41\u201346, 1990."},{"key":"2026042801413277535_j_forma-2018-0022_ref_003_w2aab3b7ab1b6b1ab1b1b3Aa","doi-asserted-by":"crossref","unstructured":"[3] Grzegorz Bancerek, Czes\u0142aw Bylinski, Adam Grabowski, Artur Korni\u0142owicz, Roman Matuszewski, Adam Naumowicz, Karol P\u0105k, 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\u2013279. 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","DOI":"10.1007\/978-3-319-20615-8_17"},{"key":"2026042801413277535_j_forma-2018-0022_ref_004_w2aab3b7ab1b6b1ab1b1b4Aa","doi-asserted-by":"crossref","unstructured":"[4] Grzegorz Bancerek, Czes\u0142aw Byli\u0144ski, Adam Grabowski, Artur Korni\u0142owicz, Roman Matuszewski, Adam Naumowicz, and Karol P\u0105k. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9\u201332, 2018. doi:10.1007\/s10817-017-9440-6.10.1007\/s10817-017-9440-6604425130069070","DOI":"10.1007\/s10817-017-9440-6"},{"key":"2026042801413277535_j_forma-2018-0022_ref_005_w2aab3b7ab1b6b1ab1b1b5Aa","unstructured":"[5] Fran\u00e7ois Baskevitch. Les repr\u00e9sentations de la propagation du son, d\u2019Aristote \u00e0 l\u2019Encyclop\u00e9die. PhD thesis, Universit\u00e9 de Nantes, France, 2008."},{"key":"2026042801413277535_j_forma-2018-0022_ref_006_w2aab3b7ab1b6b1ab1b1b6Aa","doi-asserted-by":"crossref","unstructured":"[6] Adam Grabowski, Artur Korni\u0142owicz, 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\u2013371, 2016. doi:10.15439\/2016F520.10.15439\/2016F520","DOI":"10.15439\/2016F520"},{"key":"2026042801413277535_j_forma-2018-0022_ref_007_w2aab3b7ab1b6b1ab1b1b7Aa","unstructured":"[7] Bernard Parzysz and Yves Hellegouarch. Musique et math\u00e9matique: (suivi de) Gammes naturelles. Number 53. Association des Professeurs de Math\u00e9matiques de l\u2019Enseignement Public (APMEP), Paris, 1984."}],"container-title":["Formalized Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/content.sciendo.com\/view\/journals\/forma\/26\/4\/article-p239.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/reference-global.com\/pdf\/10.2478\/forma-2018-0022","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T13:49:53Z","timestamp":1777384193000},"score":1,"resource":{"primary":{"URL":"https:\/\/reference-global.com\/article\/10.2478\/forma-2018-0022"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,1]]},"references-count":7,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2019,3,2]]},"published-print":{"date-parts":[[2018,12,1]]}},"alternative-id":["10.2478\/forma-2018-0022"],"URL":"https:\/\/doi.org\/10.2478\/forma-2018-0022","relation":{},"ISSN":["1898-9934","1426-2630"],"issn-type":[{"value":"1898-9934","type":"electronic"},{"value":"1426-2630","type":"print"}],"subject":[],"published":{"date-parts":[[2018,12,1]]}}}