{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T20:31:04Z","timestamp":1769200264831,"version":"3.49.0"},"publisher-location":"Berlin, Heidelberg","reference-count":21,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783642393563","type":"print"},{"value":"9783642393570","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013]]},"DOI":"10.1007\/978-3-642-39357-0_1","type":"book-chapter","created":{"date-parts":[[2013,6,5]],"date-time":"2013-06-05T09:35:19Z","timestamp":1370424919000},"page":"1-18","source":"Crossref","is-referenced-by-count":24,"title":["The Torii of Phases"],"prefix":"10.1007","author":[{"given":"Emmanuel","family":"Amiot","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"1_CR1","unstructured":"Quinn, I.: A Unified Theory of Chord Quality in Equal Temperaments. Ph.D. dissertation, Eastman School of Music (2004)"},{"key":"1_CR2","doi-asserted-by":"crossref","unstructured":"Quinn, I.: General Equal Tempered Harmony. Journal of Music Theory 44(2)-45(1) (2006-2007)","DOI":"10.1353\/pnm.2007.0016"},{"issue":"3","key":"1_CR3","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1080\/17459730701654990","volume":"1","author":"E. Amiot","year":"2007","unstructured":"Amiot, E.: David Lewin and Maximally Even Sets. Journal of Mathematics and Music\u00a01(3), 157\u2013172 (2007)","journal-title":"Journal of Mathematics and Music"},{"key":"1_CR4","series-title":"CCIS","doi-asserted-by":"publisher","first-page":"258","DOI":"10.1007\/978-3-642-02394-1_24","volume-title":"Mathematics and Computation in Music","author":"D. Tymoczko","year":"2009","unstructured":"Tymoczko, D.: Three Conceptions of Musical Distance. In: Chew, E., Childs, A., Chuan, C.-H. (eds.) MCM 2009. CCIS, vol.\u00a038, pp. 258\u2013272. Springer, Heidelberg (2009)"},{"issue":"2","key":"1_CR5","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1215\/00222909-2009-004","volume":"51","author":"C. Callender","year":"2007","unstructured":"Callender, C.: Continuous Harmonic Spaces. Journal of Music Theory\u00a051(2), 277\u2013332 (2007)","journal-title":"Journal of Music Theory"},{"key":"1_CR6","doi-asserted-by":"crossref","unstructured":"Hoffman, J.: On Pitch-Class Set Cartography Relations between Voice-Leading Spaces and Fourier Spaces. Journal of Music Theory\u00a052(2) (2008)","DOI":"10.1215\/00222909-2009-016"},{"key":"1_CR7","volume-title":"Cognitive Foundations of Musical Pitch","author":"C. Krumhansl","year":"1990","unstructured":"Krumhansl, C.: Cognitive Foundations of Musical Pitch. Oxford University Press, New York (1990)"},{"key":"1_CR8","doi-asserted-by":"crossref","unstructured":"Tymoczko, D.: Geometrical Methods in Recent Music Theory. Music Theory Online\u00a016(1) (2010), http:\/\/www.mtosmt.org\/issues\/mto.10.16.1\/mto.10.16.1.tymoczko.html","DOI":"10.30535\/mto.16.1.7"},{"key":"1_CR9","volume-title":"The Geometry of Music","author":"D. Tymoczko","year":"2011","unstructured":"Tymoczko, D.: The Geometry of Music. Oxford University Press, New York (2011)"},{"issue":"2","key":"1_CR10","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1215\/00222909-2009-017","volume":"52","author":"D. Tymoczko","year":"2008","unstructured":"Tymoczko, D.: Set-Class Similarity, Voice Leading, and the Fourier Transform. Journal of Music Theory\u00a052(2), 251\u2013272 (2008)","journal-title":"Journal of Music Theory"},{"issue":"1","key":"1_CR11","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1080\/17459730601137716","volume":"1","author":"G. Mazzola","year":"2007","unstructured":"Mazzola, G., Andreatta, M.: Diagrams, Gestures and Formulae in Music. Journal of Mathematics and Music\u00a01(1), 23\u201346 (2007)","journal-title":"Journal of Mathematics and Music"},{"key":"1_CR12","volume-title":"Generalized Musical Intervals and Transformations","author":"D. Lewin","year":"1987","unstructured":"Lewin, D.: Generalized Musical Intervals and Transformations. Yale University Press, New Haven (1987)"},{"key":"1_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"196","DOI":"10.1007\/978-3-642-21590-2_15","volume-title":"Mathematics and Computation in Music","author":"R.W. Peck","year":"2011","unstructured":"Peck, R.W.: N th Roots of Pitch-Class Inversion. In: Agon, C., Andreatta, M., Assayag, G., Amiot, E., Bresson, J., Mandereau, J. (eds.) MCM 2011. LNCS, vol.\u00a06726, pp. 196\u2013206. Springer, Heidelberg (2011)"},{"issue":"2","key":"1_CR14","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1080\/17459737.2011.608819","volume":"5","author":"J. Mandereau","year":"2011","unstructured":"Mandereau, J., Ghisi, D., Amiot, E., Andreatta, M., Agon, C.: Discrete Phase Retrieval in Musical Structures. Journal of Mathematics and Music\u00a05(2), 83\u201398 (2011)","journal-title":"Journal of Mathematics and Music"},{"issue":"2","key":"1_CR15","doi-asserted-by":"publisher","first-page":"241","DOI":"10.2307\/843877","volume":"42","author":"J. Douthett","year":"1998","unstructured":"Douthett, J., Steinbach, P.: Parsimonious Graphs: A Study in Parsimony, Contextual Transformations, and Modes of Limited Transposition. Journal of Music Theory\u00a042(2), 241\u2013263 (1998)","journal-title":"Journal of Music Theory"},{"key":"1_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1007\/978-3-642-21590-2_16","volume-title":"Mathematics and Computation in Music","author":"R. Plotkin","year":"2011","unstructured":"Plotkin, R.: Cardinality Transformations in Diatonic Space. In: Agon, C., Andreatta, M., Assayag, G., Amiot, E., Bresson, J., Mandereau, J. (eds.) MCM 2011. LNCS, vol.\u00a06726, pp. 207\u2013219. Springer, Heidelberg (2011)"},{"issue":"3","key":"1_CR17","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1080\/17459737.2011.640469","volume":"5","author":"E. Amiot","year":"2011","unstructured":"Amiot, E., Sethares, B.: An Algebra for Periodic Rhythms and Scales. Journal of Mathematics and Music\u00a05(3), 149\u2013169 (2011)","journal-title":"Journal of Mathematics and Music"},{"key":"1_CR18","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"326","DOI":"10.1007\/978-3-642-21590-2_25","volume-title":"Mathematics and Computation in Music","author":"G. Baroin","year":"2011","unstructured":"Baroin, G.: The Planet-4D Model: An Original Hypersymmetric Music Space Based on Graph Theory. In: Agon, C., Andreatta, M., Assayag, G., Amiot, E., Bresson, J., Mandereau, J. (eds.) MCM 2011. LNCS, vol.\u00a06726, pp. 326\u2013329. Springer, Heidelberg (2011)"},{"key":"1_CR19","unstructured":"Carl\u00e9, M., Hahn, S., Matern, M., Noll, T.: Presentation of Fourier Scratching at MCM 2009, New Haven (2009), http:\/\/www.supercollider2010.de\/images\/papers\/fourier-scratching.pdf"},{"key":"1_CR20","series-title":"LNAI","doi-asserted-by":"publisher","first-page":"180","DOI":"10.1007\/978-3-642-21590-2_14","volume-title":"Mathematics and Computation in Music","author":"A.J. Milne","year":"2011","unstructured":"Milne, A.J., Carl\u00e9, M., Sethares, W.A., Noll, T., Holland, S.: Scratching the Scale Labyrinth. In: Agon, C., Andreatta, M., Assayag, G., Amiot, E., Bresson, J., Mandereau, J. (eds.) MCM 2011. LNCS (LNAI), vol.\u00a06726, pp. 180\u2013195. Springer, Heidelberg (2011)"},{"key":"1_CR21","doi-asserted-by":"publisher","first-page":"346","DOI":"10.1126\/science.1153021","volume":"320","author":"C. Callender","year":"2008","unstructured":"Callender, C., Quinn, I., Tymoczko, D.: Generalized Voice Leading Spaces. Science\u00a0320, 346\u2013348 (2008)","journal-title":"Science"}],"container-title":["Lecture Notes in Computer Science","Mathematics and Computation in Music"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-39357-0_1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,2,24]],"date-time":"2022-02-24T02:19:26Z","timestamp":1645669166000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-39357-0_1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"ISBN":["9783642393563","9783642393570"],"references-count":21,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-39357-0_1","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013]]}}}