{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,27]],"date-time":"2025-06-27T14:44:48Z","timestamp":1751035488706,"version":"3.40.3"},"publisher-location":"Cham","reference-count":11,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783031070143"},{"type":"electronic","value":"9783031070150"}],"license":[{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022]]},"DOI":"10.1007\/978-3-031-07015-0_12","type":"book-chapter","created":{"date-parts":[[2022,6,3]],"date-time":"2022-06-03T04:12:53Z","timestamp":1654229573000},"page":"140-152","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Transformations for Pairwise Well-Formed Modes"],"prefix":"10.1007","author":[{"given":"Thomas","family":"Noll","sequence":"first","affiliation":[]},{"given":"David","family":"Clampitt","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,6,4]]},"reference":[{"key":"12_CR1","unstructured":"Bulgakova, D.V., Buzhinsky, N., Goncharov, Y.O.: On balanced and abelian properties of circular words over a ternary alphabet. ArXiv:2012:15818 (2021). WORDS 2021"},{"key":"12_CR2","unstructured":"Clampitt, D.: Pairwise well-formed scales: structural and transformational properties. Ph.D. diss, SUNY at Buffalo (1997)"},{"key":"12_CR3","series-title":"Communications in Computer and Information Science","doi-asserted-by":"publisher","first-page":"464","DOI":"10.1007\/978-3-642-04579-0_46","volume-title":"Mathematics and Computation in Music","author":"D Clampitt","year":"2009","unstructured":"Clampitt, D.: Mathematical and musical properties of pairwise well-formed scales. In: Klouche, T., Noll, T. (eds.) MCM 2007. CCIS, vol. 37, pp. 464\u2013468. Springer, Heidelberg (2009). https:\/\/doi.org\/10.1007\/978-3-642-04579-0_46"},{"key":"12_CR4","doi-asserted-by":"crossref","unstructured":"Clampitt, D., Noll, T.: Modes, the height-width duality, and Handschin\u2019s tone character. Music Theory Online 17(1) (2011). http:\/\/www.mtosmt.org\/issues\/mto.11.17.1\/mto.11.17.1.clampitt_and_noll.html","DOI":"10.30535\/mto.17.1.2"},{"key":"12_CR5","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1016\/S0304-3975(96)00310-6","volume":"183","author":"A De Luca","year":"1997","unstructured":"De Luca, A.: Sturmian words: structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183, 45\u201383 (1997)","journal-title":"Theor. Comput. Sci."},{"key":"12_CR6","doi-asserted-by":"publisher","first-page":"354","DOI":"10.1016\/0097-3165(73)90084-8","volume":"15","author":"RL Graham","year":"1973","unstructured":"Graham, R.L.: Covering the positive integers by disjoint sets of the form $$\\{[n\\alpha + \\beta ]: n=1, 2, \\ldots \\}$$. J. Combin. Theory (A) 15, 354\u2013358 (1973)","journal-title":"J. Combin. Theory (A)"},{"key":"12_CR7","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107326019","volume-title":"Algebraic Combinatorics on Words","author":"M Lothaire","year":"2002","unstructured":"Lothaire, M.: Algebraic Combinatorics on Words. Cambridge University Press, Cambridge (2002)"},{"issue":"3","key":"12_CR8","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1080\/17459737.2018.1545056","volume":"12","author":"T Noll","year":"2018","unstructured":"Noll, T., Clampitt, D.: Kaleidoscope substitutions and pairwise well-formed modes: Major-Minor duality transformationally revisited. J. Math. Music 12(3), 171\u2013211 (2018)","journal-title":"J. Math. Music"},{"key":"12_CR9","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1007\/978-3-030-21392-3_10","volume-title":"Mathematics and Computation in Music","author":"T Noll","year":"2019","unstructured":"Noll, T., Clampitt, D.: Exploring the syntonic side of major-minor tonality. In: Montiel, M., Gomez-Martin, F., Agust\u00edn-Aquino, O.A. (eds.) MCM 2019. LNCS (LNAI), vol. 11502, pp. 125\u2013136. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-21392-3_10"},{"key":"12_CR10","doi-asserted-by":"crossref","unstructured":"Noll, T., Clampitt, D.: Supersymmetries for pairwise well-formed words (2022). (in preparation)","DOI":"10.1007\/978-3-031-07015-0_12"},{"key":"12_CR11","doi-asserted-by":"publisher","first-page":"402","DOI":"10.1016\/j.tcs.2010.10.007","volume":"412","author":"G Paquin","year":"2011","unstructured":"Paquin, G., Reutenauer, C.: On the superimposition of Christoffel words. Theor. Comput. Sci. 412, 402\u2013418 (2011)","journal-title":"Theor. Comput. Sci."}],"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\/978-3-031-07015-0_12","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,12]],"date-time":"2024-03-12T16:12:04Z","timestamp":1710259924000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-07015-0_12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022]]},"ISBN":["9783031070143","9783031070150"],"references-count":11,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-07015-0_12","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2022]]},"assertion":[{"value":"4 June 2022","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":"Atlanta, GA","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":"2022","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"21 June 2022","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"24 June 2022","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"8","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"mcm22022","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/mcm2022.org","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}