%0 Journal Article %1 springerlink:10.1007/s10472-010-9198-6 %A Schlemmer, Tobias %A Schmidt, Stefan %D 2010 %I Springer Netherlands %J Annals of Mathematics and Artificial Intelligence %K FCA Begriffsverband Mathematik Verbände MaMu tspub myown Musik %N 2 %P 241-256 %R 10.1007/s10472-010-9198-6 %T A formal concept analysis of harmonic forms and interval structures %U http://dx.doi.org/10.1007/s10472-010-9198-6 %V 59 %X While small concept lattices are often represented by line diagrams to better understand their full structure, large diagrams may be too complex to do this. However, such a diagram may still be used to receive new ideas about the inherent structure of a concept lattice. This will be demonstrated for a certain family of formal contexts arising from mathematical musicology. In particular, we investigate how chord patterns can be characterised by their interval structure. For such contexts of pattern structures, it turns out that each corresponding concept lattice incorporates two competing building principles, one emanating from the top the other from the bottom of the lattice.

@article{springerlink:10.1007/s10472-010-9198-6, abstract = {While small concept lattices are often represented by line diagrams to better understand their full structure, large diagrams may be too complex to do this. However, such a diagram may still be used to receive new ideas about the inherent structure of a concept lattice. This will be demonstrated for a certain family of formal contexts arising from mathematical musicology. In particular, we investigate how chord patterns can be characterised by their interval structure. For such contexts of pattern structures, it turns out that each corresponding concept lattice incorporates two competing building principles, one emanating from the top the other from the bottom of the lattice.}, added-at = {2013-02-02T14:42:55.000+0100}, affiliation = {FR Mathematik, Institut f{\"u}r Algebra, Technische Universit{\"a}t Dresden, 01062 Dresden, Germany}, author = {Schlemmer, Tobias and Schmidt, Stefan}, bdsk-file-1 = {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}, bdsk-file-2 = {YnBsaXN0MDDUAQIDBAUGCQpYJHZlcnNpb25UJHRvcFkkYXJjaGl2ZXJYJG9iamVjdHMSAAGGoNEHCFRyb290gAFfEA9OU0tleWVkQXJjaGl2ZXKoCwwXGBkdJCVVJG51bGzTDQ4PEBEUViRjbGFzc1dOUy5rZXlzWk5TLm9iamVjdHOAB6ISE4ACgAOiFRaABIAGWWFsaWFzRGF0YVxyZWxhdGl2ZVBhdGjSDRobHFdOUy5kYXRhgAVPEQIgAAAAAAIgAAIAAAxNYWNpbnRvc2ggSEQAAAAAAAAAAAAAAAAAAADCWLRVSCsAAAHjApEfQSBmb3JtYWwgY29uY2VwdCBhbiMxRTMwRjI1LnBkZgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAeMPJcncYEgAAAAAAAAAAAABAAQAAAkgAAAAAAAAAAAAAAAAAAAACVNjaGxlbW1lcgAAEAAIAADCWJg1AAAAEQAIAADJ3EQoAAAAAQAUAeMCkQAgFS8AB/PnAAfz2gAAcEIAAgBWTWFjaW50b3NoIEhEOlVzZXJzOnNjaGxlbW1lOkRvY3VtZW50czpQYXBlcnM6U2NobGVtbWVyOkEgZm9ybWFsIGNvbmNlcHQgYW4jMUUzMEYyNS5wZGYADgBiADAAQQAgAGYAbwByAG0AYQBsACAAYwBvAG4AYwBlAHAAdAAgAGEAbgBhAGwAeQBzAGkAcwAgAG8AZgAgAGgAYQByAG0AbwBuAGkAYwAgAGYAbwByAG0AcwAwAC4AcABkAGYADwAaAAwATQBhAGMAaQBuAHQAbwBzAGgAIABIAEQAEgBaVXNlcnMvc2NobGVtbWUvRG9jdW1lbnRzL1BhcGVycy9TY2hsZW1tZXIvQSBmb3JtYWwgY29uY2VwdCBhbmFseXNpcyBvZiBoYXJtb25pYyBmb3JtczAucGRmABMAAS8AABUAAgAP//8AANIeHyAhWCRjbGFzc2VzWiRjbGFzc25hbWWjISIjXU5TTXV0YWJsZURhdGFWTlNEYXRhWE5TT2JqZWN0XxBBUGFwZXJzL1NjaGxlbW1lci9BIGZvcm1hbCBjb25jZXB0IGFuYWx5c2lzIG9mIGhhcm1vbmljIGZvcm1zMC5wZGbSHh8mJ6InI1xOU0RpY3Rpb25hcnkACAARABoAHwApADIANwA6AD8AQQBTAFwAYgBpAHAAeACDAIUAiACKAIwAjwCRAJMAnQCqAK8AtwC5At0C4gLrAvYC+gMIAw8DGANcA2EDZAAAAAAAAAIBAAAAAAAAACgAAAAAAAAAAAAAAAAAAANx}, bdsk-url-1 = {http://dx.doi.org/10.1007/s10472-010-9198-6}, biburl = {https://www.bibsonomy.org/bibtex/230f1967e66b755f5b9646dabfa19d87c/ks-plugin-devel}, date-added = {2011-04-26 10:25:59 +0200}, date-modified = {2011-04-26 10:27:40 +0200}, doi = {10.1007/s10472-010-9198-6}, groups = {public}, interhash = {26f979c709d467111e2edb6f4aa67301}, intrahash = {30f1967e66b755f5b9646dabfa19d87c}, issn = {1012-2443}, issue = {2}, journal = {Annals of Mathematics and Artificial Intelligence}, keyword = {Computer_Science}, keywords = {FCA Begriffsverband Mathematik Verbände MaMu tspub myown Musik}, note = {10.1007/s10472-010-9198-6}, number = 2, pages = {241-256}, publisher = {Springer Netherlands}, timestamp = {2013-02-02T14:42:55.000+0100}, title = {A formal concept analysis of harmonic forms and interval structures}, url = {http://dx.doi.org/10.1007/s10472-010-9198-6}, username = {keinstein}, verfuegbar = {Online;privat}, volume = 59, year = 2010 }