{"title":"On Kepler's geometric approach to consonances","authors":"Urs Frauenfelder","doi":"arxiv-2409.04119","DOIUrl":null,"url":null,"abstract":"Kepler's thinking is highly original and the inspiration for discovering his\nfamous third law is based on his rather curious geometric approach in his\nHarmonices mundi for explaining consonances. In this article we try to use a\nmodern mathematical approach based on Kepler's ideas how to characterize the\nseven consonances with the help of the numbers of edges of polygons\nconstructible by ruler and compass.","PeriodicalId":501155,"journal":{"name":"arXiv - MATH - Symplectic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Symplectic Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.04119","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Kepler's thinking is highly original and the inspiration for discovering his
famous third law is based on his rather curious geometric approach in his
Harmonices mundi for explaining consonances. In this article we try to use a
modern mathematical approach based on Kepler's ideas how to characterize the
seven consonances with the help of the numbers of edges of polygons
constructible by ruler and compass.
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