{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,13]],"date-time":"2026-06-13T17:55:05Z","timestamp":1781373305421,"version":"3.54.1"},"publisher-location":"Cham","reference-count":12,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032278265","type":"print"},{"value":"9783032278272","type":"electronic"}],"license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026]]},"DOI":"10.1007\/978-3-032-27827-2_15","type":"book-chapter","created":{"date-parts":[[2026,6,13]],"date-time":"2026-06-13T17:02:26Z","timestamp":1781370146000},"page":"250-264","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On Perfectly Balanced Sets: A\u00a0Computational Investigation"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7132-8642","authenticated-orcid":false,"given":"Paul","family":"Lascabettes","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3767-0361","authenticated-orcid":false,"given":"Alexandre","family":"Popoff","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7311-4741","authenticated-orcid":false,"given":"Moreno","family":"Andreatta","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,6,14]]},"reference":[{"key":"15_CR1","first-page":"30","volume":"230","author":"E Amiot","year":"2010","unstructured":"Amiot, E.: Sommes nulles de racines de l\u2019unit\u00e9. Bulletin de l\u2019Union des Professeurs de Sp\u00e9ciales 230, 30\u201335 (2010)","journal-title":"Bulletin de l\u2019Union des Professeurs de Sp\u00e9ciales"},{"key":"15_CR2","doi-asserted-by":"crossref","unstructured":"Amiot, E.: Music Through Fourier Space. Discrete Fourier Transform in Music Theory. Springer, Cham, Switzerland (2016)","DOI":"10.1007\/978-3-319-45581-5"},{"key":"15_CR3","doi-asserted-by":"crossref","unstructured":"Amiot, E.: Decompositions of nil sums of roots of unity. An Adaptation of \u201cSommes nulles de racines de l\u2019unit\u00e9\u201d. J. Math. Music 11(2\u20133), 67\u201375 (2017)","DOI":"10.1080\/17459737.2018.1453951"},{"key":"15_CR4","doi-asserted-by":"publisher","first-page":"370","DOI":"10.1016\/S1385-7258(53)50046-0","volume":"15","author":"NG de Bruijn","year":"1953","unstructured":"de Bruijn, N.G.: On the factorization of cyclic groups. Indag. Math. 15, 370\u2013377 (1953)","journal-title":"Indag. Math."},{"issue":"2\u20133","key":"15_CR5","doi-asserted-by":"publisher","first-page":"134","DOI":"10.1080\/17459737.2018.1450458","volume":"11","author":"N Carey","year":"2017","unstructured":"Carey, N.: Perfect balance and circularly rich words. J. Math. Music 11(2\u20133), 134\u2013154 (2017)","journal-title":"J. Math. Music"},{"key":"15_CR6","doi-asserted-by":"crossref","unstructured":"Jedrzejewski, F., Johnson, T.: The structure of Z-related sets. In: International Conference on Mathematics and Computation in Music, pp. 128\u2013137. Springer (2013)","DOI":"10.1007\/978-3-642-39357-0_10"},{"issue":"1","key":"15_CR7","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1006\/jabr.1999.8089","volume":"224","author":"TY Lam","year":"2000","unstructured":"Lam, T.Y., Leung, K.H.: On vanishing sums of roots of unity. J. Algebra 224(1), 91\u2013109 (2000)","journal-title":"J. Algebra"},{"issue":"2","key":"15_CR8","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1112\/S0025579300005210","volume":"12","author":"HB Mann","year":"1965","unstructured":"Mann, H.B.: On linear relations between roots of unity. Mathematika 12(2), 107\u2013117 (1965)","journal-title":"Mathematika"},{"issue":"2\u20133","key":"15_CR9","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1080\/17459737.2017.1395915","volume":"11","author":"AJ Milne","year":"2017","unstructured":"Milne, A.J., Bulger, D., Herff, S.A.: Exploring the space of perfectly balanced rhythms and scales. J. Math. Music 11(2\u20133), 101\u2013133 (2017)","journal-title":"J. Math. Music"},{"key":"15_CR10","doi-asserted-by":"crossref","unstructured":"Milne, A.J., Bulger, D., Herff, S.A., Sethares, W.A.: Perfect balance: a novel principle for the construction of musical scales and meters. In: International Conference on Mathematics and Computation in Music, pp. 97\u2013108. Springer (2015)","DOI":"10.1007\/978-3-319-20603-5_9"},{"issue":"2\u20134","key":"15_CR11","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1007\/BF02021312","volume":"1","author":"L R\u00e9dei","year":"1950","unstructured":"R\u00e9dei, L.: Ein Beitrag zum Problem der Faktorisation von endlichen abelschen Gruppen. Acta Math. Hungar. 1(2\u20134), 197\u2013207 (1950)","journal-title":"Acta Math. Hungar."},{"issue":"2","key":"15_CR12","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1112\/S0025579300004344","volume":"11","author":"IJ Schoenberg","year":"1964","unstructured":"Schoenberg, I.J.: A note on the cyclotomic polynomial. Mathematika 11(2), 131\u2013136 (1964)","journal-title":"Mathematika"}],"container-title":["Lecture Notes in Computer Science","Mathematics and Computation in Music"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-27827-2_15","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,13]],"date-time":"2026-06-13T17:02:29Z","timestamp":1781370149000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-27827-2_15"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"ISBN":["9783032278265","9783032278272"],"references-count":12,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-27827-2_15","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026]]},"assertion":[{"value":"14 June 2026","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"MCM","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Mathematics and Computation in Music","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Annandale-on-Hudson, NY","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"USA","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2026","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"23 June 2026","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"26 June 2026","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"10","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"mcm22026","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/sites.google.com\/bard.edu\/mcm2026\/home","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}