{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T02:59:53Z","timestamp":1742957993221,"version":"3.40.3"},"publisher-location":"Cham","reference-count":28,"publisher":"Springer Nature Switzerland","isbn-type":[{"type":"print","value":"9783031606373"},{"type":"electronic","value":"9783031606380"}],"license":[{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"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":[[2024]]},"DOI":"10.1007\/978-3-031-60638-0_8","type":"book-chapter","created":{"date-parts":[[2024,5,22]],"date-time":"2024-05-22T17:01:43Z","timestamp":1716397303000},"page":"97-110","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Hidden Categories: A New Perspective on\u00a0Lewin\u2019s Generalized Interval Systems and\u00a0Klumpenhouwer Networks"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3767-0361","authenticated-orcid":false,"given":"Alexandre","family":"Popoff","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7311-4741","authenticated-orcid":false,"given":"Moreno","family":"Andreatta","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,5,23]]},"reference":[{"key":"8_CR1","unstructured":"B\u00e9nabou, J.: Les distributeurs. Universit\u00e9 Catholique de Louvain, Institut de Math\u00e9matique Pure et Appliqu\u00e9e, Technical report (1973)"},{"key":"8_CR2","doi-asserted-by":"crossref","unstructured":"Cohn, R.: Weitzmann\u2019s regions, my cycles, and Douthett\u2019s dancing cubes. Music Theory Spectr. 22(1), 89\u2013103 (2000). http:\/\/www.jstor.org\/stable\/745854","DOI":"10.1525\/mts.2000.22.1.02a00040"},{"key":"8_CR3","doi-asserted-by":"crossref","unstructured":"Cohn, R.: Audacious Euphony: Chromaticism and the Triad\u2019s Second Nature. Oxford University Press, Oxford (2012)","DOI":"10.1093\/acprof:oso\/9780199772698.001.0001"},{"key":"8_CR4","doi-asserted-by":"crossref","unstructured":"Douthett, J., Steinbach, P.: Parsimonious graphs: a study in parsimony, contextual transformations, and modes of limited transposition. J. Music Theory 42(2), 241\u2013263 (1998). http:\/\/www.jstor.org\/stable\/843877","DOI":"10.2307\/843877"},{"issue":"1","key":"8_CR5","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1080\/17459737.2013.785724","volume":"7","author":"TM Fiore","year":"2013","unstructured":"Fiore, T.M., Noll, T., Satyendra, R.: Morphisms of generalized interval systems and $$PR$$-groups. J. Math. Music 7(1), 3\u201327 (2013). https:\/\/doi.org\/10.1080\/17459737.2013.785724","journal-title":"J. Math. Music"},{"key":"8_CR6","doi-asserted-by":"crossref","unstructured":"Hook, J.: Uniform triadic transformations. J. Music Theory 46(1\/2), 57\u2013126 (2002). http:\/\/www.jstor.org\/stable\/4147678","DOI":"10.1215\/00222909-46-1-2-57"},{"key":"8_CR7","unstructured":"Klumpenhouwer, H.: A Generalized Model of Voice-Leading for Atonal Music. Ph.D. thesis, Harvard University (1991)"},{"key":"8_CR8","unstructured":"Klumpenhouwer, H.: The inner and outer automorphisms of pitch-class inversion and transposition: some implications for analysis with Klumpenhouwer networks. Int\u00e9gral 12, 81\u201393 (1998). http:\/\/www.jstor.org\/stable\/40213985"},{"issue":"1","key":"8_CR9","first-page":"150","volume":"42","author":"O Kolman","year":"2004","unstructured":"Kolman, O.: Transfer principles for generalized interval systems. Perspect. New Music 42(1), 150\u2013189 (2004)","journal-title":"Perspect. New Music"},{"key":"8_CR10","unstructured":"Lewin, D.: Generalized Music Intervals and Transformations. Yale University Press, New Haven (1987)"},{"issue":"1","key":"8_CR11","doi-asserted-by":"publisher","first-page":"83","DOI":"10.2307\/746147","volume":"12","author":"D Lewin","year":"1990","unstructured":"Lewin, D.: Klumpenhouwer networks and some isographies that involve them. Music Theory Spectr. 12(1), 83\u2013120 (1990)","journal-title":"Music Theory Spectr."},{"key":"8_CR12","doi-asserted-by":"crossref","unstructured":"Lewin, D.: Musical Form and Transformation. Oxford University Press, Oxford (2007)","DOI":"10.1093\/acprof:oso\/9780195317121.001.0001"},{"key":"8_CR13","unstructured":"Mazzola, G.: Gruppen und Kategorien in der Musik. Heldermann (1985)"},{"key":"8_CR14","doi-asserted-by":"crossref","unstructured":"Mazzola, G.: Geometrie der T\u00f6ne : Elemente der mathematischen Musiktheorie. Birkh\u00e4user (1990)","DOI":"10.1007\/978-3-0348-7427-4"},{"key":"8_CR15","doi-asserted-by":"publisher","unstructured":"Mazzola, G., et al.: The Topos of Music: Geometric Logic of Concepts, Theory, and Performance. Birkh\u00e4user Verlag, Basel (2002). https:\/\/doi.org\/10.1007\/978-3-0348-8141-8","DOI":"10.1007\/978-3-0348-8141-8"},{"key":"8_CR16","doi-asserted-by":"crossref","unstructured":"Mazzola, G., Andreatta, M.: From a categorical point of view: K-Nets as limit denotators. Perspect. New Music 44(2), 88\u2013113 (2006). http:\/\/www.jstor.org\/stable\/25164629","DOI":"10.1353\/pnm.2006.0005"},{"issue":"3","key":"8_CR17","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1080\/17459730701774269","volume":"1","author":"G Mazzola","year":"2007","unstructured":"Mazzola, G., Andreatta, M.: Diagrams, gestures and formulae in music. J. Math. Music 1(3), 199\u2013200 (2007). https:\/\/doi.org\/10.1080\/17459730701774269","journal-title":"J. Math. Music"},{"issue":"1","key":"8_CR18","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1080\/17459737.2013.769637","volume":"7","author":"LA Piovan","year":"2013","unstructured":"Piovan, L.A.: A Tonnetz model for pentachords. J. Math. Music 7(1), 29\u201353 (2013). https:\/\/doi.org\/10.1080\/17459737.2013.769637","journal-title":"J. Math. Music"},{"issue":"1","key":"8_CR19","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1080\/17459737.2020.1825845","volume":"16","author":"A Popoff","year":"2022","unstructured":"Popoff, A.: On the use of relational presheaves in transformational music theory. J. Math. Music 16(1), 51\u201379 (2022). https:\/\/doi.org\/10.1080\/17459737.2020.1825845","journal-title":"J. Math. Music"},{"key":"8_CR20","doi-asserted-by":"publisher","unstructured":"Popoff, A., Agon, C., Andreatta, M., Ehresmann, A.: From K-Nets to PK-Nets: a categorical approach. Perspect. New Music 54(2), 5\u201363 (2016). https:\/\/doi.org\/10.7757\/persnewmusi.54.2.0005","DOI":"10.7757\/persnewmusi.54.2.0005"},{"key":"8_CR21","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1007\/978-3-319-20603-5_31","volume-title":"Mathematics and Computation in Music","author":"A Popoff","year":"2015","unstructured":"Popoff, A., Andreatta, M., Ehresmann, A.: A categorical generalization of klumpenhouwer networks. In: Collins, T., Meredith, D., Volk, A. (eds.) MCM 2015. LNCS (LNAI), vol. 9110, pp. 303\u2013314. Springer, Cham (2015). https:\/\/doi.org\/10.1007\/978-3-319-20603-5_31"},{"issue":"1","key":"8_CR22","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1080\/17459737.2017.1406011","volume":"12","author":"A Popoff","year":"2018","unstructured":"Popoff, A., Andreatta, M., Ehresmann, A.: Relational poly-Klumpenhouwer networks for transformational and voice-leading analysis. J. Math. Music 12(1), 35\u201355 (2018). https:\/\/doi.org\/10.1080\/17459737.2017.1406011","journal-title":"J. Math. Music"},{"key":"8_CR23","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1007\/978-3-030-21392-3_3","volume-title":"Mathematics and Computation in Music","author":"A Popoff","year":"2019","unstructured":"Popoff, A., Andreatta, M., Ehresmann, A.: Groupoids and wreath products of musical transformations: a categorical approach from poly-klumpenhouwer networks. In: Montiel, M., Gomez-Martin, F., Agust\u00edn-Aquino, O.A. (eds.) MCM 2019. LNCS (LNAI), vol. 11502, pp. 33\u201345. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-21392-3_3"},{"key":"8_CR24","doi-asserted-by":"crossref","unstructured":"Rahn, J.: Cool tools: Polysemic and non-commutative nets, subchain decompositions and cross-projecting pre-orders, object-graphs, chain-hom-sets and chain-label-hom-sets, forgetful functors, free categories of a net, and ghosts. J. Math. Music 1(1), 7\u201322 (2007)","DOI":"10.1080\/17459730601137542"},{"key":"8_CR25","doi-asserted-by":"crossref","unstructured":"Reenan, S., Bass, R.: Types and applications of $$p_{3,0}$$ seventh-chord transformations in late nineteenth-century music. Music Theory Online 22(2) (2016)","DOI":"10.30535\/mto.22.2.3"},{"key":"8_CR26","doi-asserted-by":"crossref","unstructured":"Rockwell, J.: Birdcage flights: a perspective on inter-cardinality voice leading. Music Theory Online 15(5) (2009)","DOI":"10.30535\/mto.15.5.4"},{"key":"8_CR27","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1007\/978-3-642-32784-1_3","volume-title":"Coalgebraic Methods in Computer Science","author":"P Soboci\u0144ski","year":"2012","unstructured":"Soboci\u0144ski, P.: Relational presheaves as labelled transition systems. In: Pattinson, D., Schr\u00f6der, L. (eds.) CMCS 2012. LNCS, vol. 7399, pp. 40\u201350. Springer, Heidelberg (2012). https:\/\/doi.org\/10.1007\/978-3-642-32784-1_3"},{"issue":"1","key":"8_CR28","doi-asserted-by":"publisher","first-page":"258","DOI":"10.2307\/833330","volume":"26","author":"DT Vuza","year":"1988","unstructured":"Vuza, D.T.: Some mathematical aspects of David Lewin\u2019s book generalized musical intervals and transformations. Perspect. New Music 26(1), 258\u2013287 (1988)","journal-title":"Perspect. New Music"}],"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\/978-3-031-60638-0_8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,22]],"date-time":"2024-05-22T17:02:18Z","timestamp":1716397338000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-60638-0_8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024]]},"ISBN":["9783031606373","9783031606380"],"references-count":28,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-60638-0_8","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2024]]},"assertion":[{"value":"23 May 2024","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":"Coimbra","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Portugal","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2024","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"18 June 2024","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"21 June 2024","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"9","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"mcm22024","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/www.uc.pt\/ceis20\/mcm24\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}