{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:53:41Z","timestamp":1760237621607,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,8,14]],"date-time":"2022-08-14T00:00:00Z","timestamp":1660435200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Temari balls are traditional Japanese toys and artworks. The variety of their geometries and tessellations can be investigated formally and computationally with the means of combinatorics. As a further step, we also propose a musical application of the core idea of Temari balls. In fact, inspired by the classical idea of music of spheres and by the CubeHarmonic, a musical application of the Rubik\u2019s cube, we present the concept of a new musical instrument, the SphereHarmonic. The mathematical (and musical) description of Temari balls lies in the wide background of interactions between art and combinatorics. Concerning the methods, we present the tools of permutations and tessellations we adopted here, and the core idea for the SphereHarmonic. As the results, we first describe a classification of structures according to the theory of groups. Then, we summarize the main passages implemented in our code, to make the SphereHarmonic play on a laptop. Our study explores an aspect of the deep connections between the mutually inspiring scientific and artistic thinking.<\/jats:p>","DOI":"10.3390\/a15080286","type":"journal-article","created":{"date-parts":[[2022,8,14]],"date-time":"2022-08-14T21:09:06Z","timestamp":1660511346000},"page":"286","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Temari Balls, Spheres, SphereHarmonic: From Japanese Folkcraft to Music"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3606-3436","authenticated-orcid":false,"given":"Maria","family":"Mannone","sequence":"first","affiliation":[{"name":"Department of Engineering, University of Palermo, 90128 Palermo, Italy"},{"name":"European Centre for Living Technology (ECLT), Dipartimento di Scienze Ambientali, Informatica e Statistica (DAIS), Ca\u2019 Foscari University of Venice, 30172 Venice, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1756-0162","authenticated-orcid":false,"given":"Takashi","family":"Yoshino","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Toyo University, Kawagoe 3508585, Japan"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1031","DOI":"10.1119\/1.11968","article-title":"Dante and the 3-Sphere","volume":"47","author":"Peterson","year":"1979","journal-title":"Am. 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