{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,8]],"date-time":"2024-08-08T13:49:25Z","timestamp":1723124965729},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"3-4","license":[{"start":{"date-parts":[[2015,1,17]],"date-time":"2015-01-17T00:00:00Z","timestamp":1421452800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Ann Math Artif Intell"],"published-print":{"date-parts":[[2015,4]]},"DOI":"10.1007\/s10472-014-9445-3","type":"journal-article","created":{"date-parts":[[2015,1,16]],"date-time":"2015-01-16T05:46:39Z","timestamp":1421387199000},"page":"311-334","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Lattice-based and topological representations of binary relations with an application to music"],"prefix":"10.1007","volume":"73","author":[{"given":"Anton","family":"Freund","sequence":"first","affiliation":[]},{"given":"Moreno","family":"Andreatta","sequence":"additional","affiliation":[]},{"given":"Jean-Louis","family":"Giavitto","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,1,17]]},"reference":[{"key":"9445_CR1","doi-asserted-by":"crossref","unstructured":"Wille, R.: Restructuring lattice theory: An approach based on the hierarchy of concepts. In: Rival, I. (ed.) Ordered sets: proceedings of the NATO Advanced Study Institute held at Banff, Canada, August 28 to September 12, 1981. D. Reidel Pub. Co. (1982)","DOI":"10.1007\/978-94-009-7798-3_15"},{"key":"9445_CR2","unstructured":"Barbut, M., Monjardet, B.: Ordre et Classification: Alg\u00e8bre et Combinatoire. Hachette (1970)"},{"issue":"1","key":"9445_CR3","doi-asserted-by":"crossref","first-page":"84","DOI":"10.2307\/1969768","volume":"56","author":"CH Dowker","year":"1952","unstructured":"Dowker, C.H.: Homology groups of relations. Ann. Math 2nd Series 56(1), 84\u201395 (1952)","journal-title":"Ann. Math 2nd Series"},{"issue":"2","key":"9445_CR4","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/S0020-7373(72)80029-4","volume":"4","author":"RH Atkin","year":"1972","unstructured":"Atkin, R.H.: From cohomology in physics to q\u2013connectivity in social science. Int. J. Man Mach. Stud. 4(2), 139\u2013167 (1972)","journal-title":"Int. J. Man Mach. Stud."},{"key":"9445_CR5","volume-title":"Connectivity, Complexity, and Catastrophe in Large-Scale Systems","author":"JL Casti","year":"1979","unstructured":"Casti, J.L.: Connectivity, Complexity, and Catastrophe in Large-Scale Systems. Wiley, New York (1979)"},{"issue":"4","key":"9445_CR6","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1016\/S0020-7373(80)80021-6","volume":"12","author":"LC Freeman","year":"1980","unstructured":"Freeman, L.C.: Q-analysis and the structure of friendship networks. Int. J. Man Mach. Stud. 12(4), 367\u2013378 (1980)","journal-title":"Int. J. Man Mach. Stud."},{"key":"9445_CR7","unstructured":"Johnson, J.: Transport Planning and Control, Chapter The dynamics of Large Complex Road Systems. Oxford University Press, pp. 165\u2013186 (1991)"},{"issue":"3","key":"9445_CR8","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1016\/S0377-2217(97)00308-1","volume":"103","author":"L Duckstein","year":"1997","unstructured":"Duckstein, L., Nobe, S.A.: q-analysis for modeling and decision making. Eur. J. Oper. Res. 103(3), 411\u2013425 (1997)","journal-title":"Eur. J. Oper. Res."},{"issue":"2","key":"9445_CR9","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1006\/aama.2000.0710","volume":"26","author":"H Barcelo","year":"2001","unstructured":"Barcelo, H., Kramer, X., Laubenbacher, R., Weaver, C.: Foundations of a connectivity theory for simplicial complexes. Adv. Appl. Math. 26(2), 97\u2013128 (2001)","journal-title":"Adv. Appl. Math."},{"issue":"10","key":"9445_CR10","doi-asserted-by":"crossref","first-page":"1771","DOI":"10.1016\/j.ins.2011.01.016","volume":"181","author":"VG Kaburlasos","year":"2011","unstructured":"Kaburlasos, V.G.: Special issue on information engineering applications based on lattices. Inf. Sci. 181(10), 1771\u20131773 (2011)","journal-title":"Inf. Sci."},{"issue":"2","key":"9445_CR11","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1080\/17459737.2011.614448","volume":"5","author":"MJ Catanzaro","year":"2011","unstructured":"Catanzaro, M.J.: Generalized Tonnetze. J. Math. Music 5(2), 117\u2013139 (2011)","journal-title":"J. Math. Music"},{"key":"9445_CR12","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-59830-2","volume-title":"Formal Concept Analysis. Mathematical Foundations","author":"B Ganter","year":"1999","unstructured":"Ganter, B., Wille, R.: Formal Concept Analysis. Mathematical Foundations. Springer\u2013Verlag, Berlin and Heidelberg (1999)"},{"key":"9445_CR13","doi-asserted-by":"crossref","unstructured":"Atkin, R.H.: Q-analysis. A hard language for the soft sciences. Futures, 492\u2013499 (1978)","DOI":"10.1016\/0016-3287(78)90049-6"},{"key":"9445_CR14","volume-title":"Algebraic Topology","author":"A Hatcher","year":"2002","unstructured":"Hatcher, A.: Algebraic Topology. Cambridge University Press, Cambridge (2002)"},{"key":"9445_CR15","volume-title":"Elements of Algebraic Topology","author":"JR Munkres","year":"1984","unstructured":"Munkres, J.R.: Elements of Algebraic Topology. The Benjamin\/Cummings Publication Company, Menlo Park (1984)"},{"key":"9445_CR16","doi-asserted-by":"crossref","unstructured":"Bigo, L., Giavitto, J.-L., Spicher, A.: Building topological spaces for musical objects. In: Mathematics and Computation in Music, volume 6726 of LNCS. Springer, Paris (2011)","DOI":"10.1007\/978-3-642-21590-2_2"},{"key":"9445_CR17","doi-asserted-by":"crossref","unstructured":"Rehding, A.: Hugo Riemann and the Birth of Modern Musical Thought. Number 11 in New Perspectives in Music History and Criticism. Cambridge University Press (2003)","DOI":"10.1017\/CBO9780511481369"},{"key":"9445_CR18","doi-asserted-by":"crossref","unstructured":"Lewin, D.: Generalized musical intervals and transformations. Yale University Press (2007 reedition by Oxford University Press) (1987)","DOI":"10.1093\/acprof:oso\/9780195317138.001.0001"},{"key":"9445_CR19","first-page":"151","volume":"80","author":"GD Halsey","year":"1978","unstructured":"Halsey, G.D., Hewitt, E.: Eine gruppentheoretische Methode in der Musiktheorie. Jahresbericht der Deutschen Mathematiker-Vereinigung 80, 151\u2013207 (1978)","journal-title":"Jahresbericht der Deutschen Mathematiker-Vereinigung"},{"key":"9445_CR20","volume-title":"Enumeration of chord sequences. In: Sound and Music Computing","author":"N Collins","year":"2012","unstructured":"Collins, N.: Enumeration of chord sequences. In: Sound and Music Computing. Aalborg University Copenhangen, Denmark (2012). SMC"},{"key":"9445_CR21","doi-asserted-by":"crossref","unstructured":"Reiner, D.L.: Enumeration in music theory. Am. Math. Mon., 51\u201354 (1985)","DOI":"10.2307\/2322196"},{"key":"9445_CR22","unstructured":"Fripertinger, H., Voitsberg, G.: Enumeration in musical theory. Institut f\u00fcr Elektronische Musik (IEM) (1992)"},{"issue":"1","key":"9445_CR23","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/S0012-365X(98)00285-4","volume":"199","author":"H Fripertinger","year":"1999","unstructured":"Fripertinger, H.: Enumeration of mosaics. Discret. Math. 199(1), 49\u201360 (1999)","journal-title":"Discret. Math."},{"key":"9445_CR24","unstructured":"Fripertinger, H.: Enumeration and construction in music theory. In: Proceedings of the Diderot Forum on Mathematics and Music (Vienna), pp. 170\u2013203 (1999)"},{"key":"9445_CR25","doi-asserted-by":"crossref","unstructured":"Mazzola, G., Muzzulini, D., Hofmann, G.R.: Geometrie der T\u00f6ne: Elemente der Mathematischen Musiktheorie. Birkh\u00e4user (1990)","DOI":"10.1007\/978-3-0348-7427-4"},{"key":"9445_CR26","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-0348-8141-8","volume-title":"The topos of music","author":"G Mazzola","year":"2002","unstructured":"Mazzola, G., et al.: The topos of music. Birkh\u00e4user, Basel (2002)"},{"issue":"5783","key":"9445_CR27","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1126\/science.1126287","volume":"313","author":"D Tymoczko","year":"2006","unstructured":"Tymoczko, D.: The geometry of musical chords. Science 313(5783), 72\u201374 (2006)","journal-title":"Science"},{"key":"9445_CR28","unstructured":"Mazzola, G.: Gruppen und Kategorien in der Musik: Entwurf einer mathematischen Musiktheorie, volume 10 of Reasearch and Exposition in Mathematics. Heldermann (1985)"},{"key":"9445_CR29","doi-asserted-by":"crossref","unstructured":"Bigo, L., Andreatta, M., Giavitto, J.-L., Michel, O., Spicher, A.: Computation and visualization of musical structures in chord-based simplicial complexes. In: Yust, J., Wild, J., Burgoyne, J.A. (eds.) Mathematics and Computation in Music, volume 7937 of Lecture Notes in Computer Science, pp 38\u201351. Springer, Berlin Heidelberg (2013)","DOI":"10.1007\/978-3-642-39357-0_3"},{"key":"9445_CR30","unstructured":"Nestke, A.: Paradigmatic motivic analysis. In: Perspectives in Mathematical and Computational Music Theory, Osnabr\u00fcck Series on Music and Computation, pp. 343\u2013365 (2004)"},{"key":"9445_CR31","doi-asserted-by":"crossref","unstructured":"Wille, R.: Musik und Mathematik: Salzburger Musikgespr\u00e4ch 1984 unter Vorsitz von Herbert von Karajan, chapter Musiktheorie und Mathematik, pp. 4\u201331. Springer (1985)","DOI":"10.1007\/978-3-642-95474-0_2"},{"key":"9445_CR32","first-page":"366","volume":"1","author":"T Noll","year":"2004","unstructured":"Noll, T., Brand, M.: Morphology of chords. Perspect. Math. Comput. Music Theory 1, 366 (2004)","journal-title":"Perspect. Math. Comput. Music Theory"},{"key":"9445_CR33","doi-asserted-by":"crossref","unstructured":"Schlemmer, T., Andreatta, M.: Using formal concept analysis to represent chroma systems. In: Mathematics and Computation in Music, pp. 189\u2013200. Springer (2013)","DOI":"10.1007\/978-3-642-39357-0_15"},{"key":"9445_CR34","unstructured":"Forte, A.: The Structure of Atonal Music. Yale University Press (1973)"},{"key":"9445_CR35","doi-asserted-by":"crossref","unstructured":"Lewin, D.: Forte\u2019s interval vector, my interval function, and Regener\u2019s common-note function. J. Music Theory, 194\u2013237 (1977)","DOI":"10.2307\/843489"},{"key":"9445_CR36","doi-asserted-by":"crossref","unstructured":"Bresson, J., Agon, C., Assayag, G.: Openmusic: Visual programming environment for music composition, analysis and research. In: Proceedings of the 19th ACM International Conference on Multimedia, pp. 743\u2013746. ACM (2011)","DOI":"10.1145\/2072298.2072434"},{"key":"9445_CR37","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1016\/S0012-365X(96)00255-5","volume":"167","author":"RC Read","year":"1997","unstructured":"Read, R.C.: Combinatorial problems in the theory of music. Discret. Math. 167, 543\u2013551 (1997)","journal-title":"Discret. Math."},{"key":"9445_CR38","doi-asserted-by":"crossref","unstructured":"Brou\u00e9, M.: Les tonalit\u00e9s musicales vues par un math\u00e9maticien. Le temps des savoirs (Revue de l\u2019Institut Universitaire de France), pp. 37\u201378. Odile Jacob (2001)","DOI":"10.3917\/oj.rouss.2002.01.0041"},{"issue":"2","key":"9445_CR39","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1007\/s10472-010-9198-6","volume":"59","author":"T Schlemmer","year":"2010","unstructured":"Schlemmer, T., Schmidt, S.E.: A formal concept analysis of harmonic forms and interval structures. Ann. Math. Artif. Intell. 59(2), 241\u2013256 (2010)","journal-title":"Ann. Math. Artif. Intell."},{"key":"9445_CR40","doi-asserted-by":"crossref","unstructured":"Borchmann, D., Ganter, B.: Concept lattice orbifolds \u2014 first steps. In: Ferr\u00e9, S., Rudolph, S. (eds.) Formal Concept Analysis: 7th International Conference, ICFCA 2009 Darmstadt, Germany, May 21\u201324, 2009 Proceedings. Springer Verlag, Berlin and Heidelberg (2009)","DOI":"10.1007\/978-3-642-01815-2_2"},{"key":"9445_CR41","unstructured":"Fripertinger, H.: Remarks on rhythmical canons. In: Fripertinger, H., Reich, L. (eds.) Proceedings of the Colloquium on Mathematical Music Theory, volume 347 of Grazer Math. Ber. pp. 73\u201390. Graz, Austria (2004)"}],"container-title":["Annals of Mathematics and Artificial Intelligence"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10472-014-9445-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10472-014-9445-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10472-014-9445-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,26]],"date-time":"2022-04-26T22:23:00Z","timestamp":1651011780000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10472-014-9445-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1,17]]},"references-count":41,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2015,4]]}},"alternative-id":["9445"],"URL":"https:\/\/doi.org\/10.1007\/s10472-014-9445-3","relation":{},"ISSN":["1012-2443","1573-7470"],"issn-type":[{"value":"1012-2443","type":"print"},{"value":"1573-7470","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,1,17]]}}}