{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T07:01:56Z","timestamp":1773212516220,"version":"3.50.1"},"reference-count":17,"publisher":"MIT Press - Journals","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computer Music Journal"],"published-print":{"date-parts":[[2015,9]]},"abstract":"<jats:p> Ordinary differential equations (ODEs) have been studied for centuries as a means to model complex dynamical processes from the real world. Nevertheless, their application to sound synthesis has not yet been fully exploited. In this article we present a systematic approach to sound synthesis based on first-order complex and real ODEs. Using simple time-dependent and nonlinear terms, we illustrate the mapping between ODE coefficients and physically meaningful control parameters such as pitch, pitch bend, decay rate, and attack time. We reveal the connection between nonlinear coupling terms and frequency modulation, and we discuss the implications of this scheme in connection with nonlinear synthesis. The ability to excite a first-order complex ODE with an external input signal is also examined; stochastic or impulsive signals that are physically or synthetically produced can be presented as input to the system, offering additional synthesis possibilities, such as those found in excitation\/filter synthesis and filter-based modal synthesis. <\/jats:p>","DOI":"10.1162\/comj_a_00314","type":"journal-article","created":{"date-parts":[[2015,9,11]],"date-time":"2015-09-11T03:19:08Z","timestamp":1441941548000},"page":"46-58","source":"Crossref","is-referenced-by-count":8,"title":["Sound Synthesis Based on Ordinary Differential Equations"],"prefix":"10.1162","volume":"39","author":[{"given":"Nikolaos","family":"Stefanakis","sequence":"first","affiliation":[{"name":"UP Transfer GmbH University of Potsdam Am Neuen Palais 10 14469 Potsdam, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Markus","family":"Abel","sequence":"additional","affiliation":[{"name":"Ambrosys GmbH Albert-Einstein-Str. 1\u20135 14467 Potsdam, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andr\u00e9","family":"Bergner","sequence":"additional","affiliation":[{"name":"Native Instruments GmbH Schlesische Stra\u00dfe 29\u201330 10997 Berlin, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"281","reference":[{"key":"p_1","first-page":"1586","author":"Ahnert K.","year":"2011","journal-title":"International Conference on Numerical Analysis and Applied Mathematics"},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1162\/comj.2006.30.2.32"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1121\/1.3651097"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.45.5524"},{"issue":"7","key":"p_7","first-page":"526","volume":"21","author":"Chowning J.","year":"1973","journal-title":"Journal of the Audio Engineering Society"},{"key":"p_10","first-page":"1","author":"Damiani F.","year":"2000","journal-title":"Proceedings of the International Conference on Devices, Circuits and Systems, pp. S92"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.49.4955"},{"key":"p_14","doi-asserted-by":"publisher","DOI":"10.1109\/89.279282"},{"key":"p_17","doi-asserted-by":"publisher","DOI":"10.1121\/1.1916516"},{"key":"p_18","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.45.712"},{"key":"p_19","doi-asserted-by":"publisher","DOI":"10.2307\/3679940"},{"key":"p_20","doi-asserted-by":"publisher","DOI":"10.1162\/014892601750302589"},{"key":"p_21","doi-asserted-by":"publisher","DOI":"10.1162\/014892699559869"},{"key":"p_22","doi-asserted-by":"publisher","DOI":"10.1162\/014892699559878"},{"key":"p_24","doi-asserted-by":"publisher","DOI":"10.2307\/3680960"},{"key":"p_25","first-page":"1178","author":"Stefanakis N.","year":"2014","journal-title":"Proceedings of the Joint International Computer Music Conference and Sound and Music Computing Conference"},{"key":"p_27","doi-asserted-by":"publisher","DOI":"10.1109\/89.841212"}],"container-title":["Computer Music Journal"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mitpressjournals.org\/doi\/pdf\/10.1162\/COMJ_a_00314","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,12]],"date-time":"2021-03-12T21:33:49Z","timestamp":1615584829000},"score":1,"resource":{"primary":{"URL":"https:\/\/direct.mit.edu\/comj\/article\/39\/3\/46-58\/94533"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,9]]},"references-count":17,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2015,9]]}},"alternative-id":["10.1162\/COMJ_a_00314"],"URL":"https:\/\/doi.org\/10.1162\/comj_a_00314","relation":{},"ISSN":["0148-9267","1531-5169"],"issn-type":[{"value":"0148-9267","type":"print"},{"value":"1531-5169","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,9]]}}}