{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,21]],"date-time":"2025-09-21T17:20:28Z","timestamp":1758475228367,"version":"3.37.3"},"reference-count":42,"publisher":"Acoustical Society of America (ASA)","issue":"4","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2021,10,1]]},"abstract":"<jats:p>String excitation by the tangent in the clavichord is a unique mechanism. The tangent, keeping in contact with the string after the initial strike, continuously controls the string tension. Four main flexible subsystems are considered in the clavichord: the tangent\/key subsystem, the string subsystem, the bridge-soundboard subsystem, and the string damper subsystem. A modal description of the dynamics of these subsystems is proposed. Parameters of the subsystems are estimated on a copy of a historical instrument by Hubert (1784). The different subsystems and their couplings are modeled using a modal Udwadia\u2013Kalaba formulation. The string-tangent interaction is modeled via the intermittent contact dynamics, using the Kirchoff\u2013Carrier string model. Realistic string, soundboard, and tangent motions are obtained using a time-domain synthesis scheme that computes the dynamics of the uncoupled subsystems and the constraints resulting from coupling between them. Simulated motions of the model in response to a driving force on the key are analyzed. The results are consistent with experimental measurements and published data on the dynamics of the clavichord. The model is able to reproduce the main acoustic features of the instrument: force on the key for intonation control, key velocity for dynamic nuances control, and constant spectral slope for varying dynamic nuances.<\/jats:p>","DOI":"10.1121\/10.0006438","type":"journal-article","created":{"date-parts":[[2021,10,4]],"date-time":"2021-10-04T17:43:25Z","timestamp":1633369405000},"page":"2350-2363","update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":7,"title":["Toward a physical model of the clavichord"],"prefix":"10.1121","volume":"150","author":[{"given":"Jean-Th\u00e9o","family":"Jiolat","sequence":"first","affiliation":[{"name":"Institut Jean Le Rond d'Alembert, \u00c9quipe Lutheries-Acoustique-Musique, Sorbonne Universit\u00e9, CNRS 1 , F-75005 Paris, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2629-8752","authenticated-orcid":false,"given":"Christophe","family":"d'Alessandro","sequence":"additional","affiliation":[{"name":"Institut Jean Le Rond d'Alembert, \u00c9quipe Lutheries-Acoustique-Musique, Sorbonne Universit\u00e9, CNRS 1 , F-75005 Paris, France"}]},{"given":"Jean-Lo\u00efc","family":"Le Carrou","sequence":"additional","affiliation":[{"name":"Institut Jean Le Rond d'Alembert, \u00c9quipe Lutheries-Acoustique-Musique, Sorbonne Universit\u00e9, CNRS 1 , F-75005 Paris, France"}]},{"given":"Jos\u00e9","family":"Antunes","sequence":"additional","affiliation":[{"name":"Applied Dynamics Laboratory, Instituto Superior T\u00e9cnico, Centro de Ci\u00eancias e Tecnologias Nucleares 2 , Bobadela, Portugal"}]}],"member":"231","published-online":{"date-parts":[[2021,10,4]]},"reference":[{"key":"2023080508274643100_c1","first-page":"53","article-title":"Every player's first grammatica","author":"Brauchli","journal-title":"De Clavicordio"},{"volume-title":"The Clavichord","year":"1998","key":"2023080508274643100_c2"},{"volume-title":"Zur Klangwirkung von Klavichord, Cembalo und Fl\u00fcgel (On the Sound Effect of the Clavichord, Harpsichord and Grand Piano)","year":"1940","key":"2023080508274643100_c3"},{"key":"2023080508274643100_c4","doi-asserted-by":"publisher","first-page":"89","DOI":"10.2307\/841506","article-title":"A scientific approach to the clavichord","volume":"20","year":"1967","journal-title":"Galpin Soc. J."},{"journal-title":"De Clavicordio","article-title":"Keylever, tangent and string\u2013A preliminary analysis of clavichord touch and action","author":"Brauchli","key":"2023080508274643100_c5"},{"issue":"5","key":"2023080508274643100_c6","doi-asserted-by":"publisher","first-page":"1476","DOI":"10.1121\/1.385781","article-title":"Some notes on the clavichord","volume":"69","year":"1981","journal-title":"J. Acoust. Soc. Am."},{"first-page":"309","article-title":"String excitation: Piano, harpsichord and clavichord","year":"1993","key":"2023080508274643100_c7"},{"issue":"4","key":"2023080508274643100_c8","doi-asserted-by":"publisher","first-page":"2173","DOI":"10.1121\/1.3478783","article-title":"On the dynamics of the clavichord: From tangent motion to sound","volume":"128","year":"2010","journal-title":"J. Acoust. Soc. Am."},{"key":"2023080508274643100_c9","first-page":"201","article-title":"Tonal portrait of the clavichord","author":"Brauchli","journal-title":"De Calvicordio"},{"issue":"1","key":"2023080508274643100_c10","doi-asserted-by":"publisher","first-page":"87","DOI":"10.7202\/1062430ar","article-title":"Le paradoxe du clavicorde et la technique de bach au clavier\u201d (\u201cThe clavichord paradox and Bach's keyboard technique\u201d)","volume":"6","year":"2019","journal-title":"Rev. Music. OICRM"},{"issue":"1","key":"2023080508274643100_c11","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1162\/01489260360613353","article-title":"Commuted waveguide synthesis of the clavichord","volume":"27","year":"2003","journal-title":"Comput. Music J."},{"key":"2023080508274643100_c12","unstructured":"See https:\/\/modartt.com\/neupert for listening the physical model of a clavichord (Last viewed 9\/20\/21)."},{"key":"2023080508274643100_c13","unstructured":"J.\u2008Chabassier, \u201cMod\u00e9lisation et simulation num\u00e9rique d'un piano par mod\u00e8les physiques\u201d (\u201cModeling and numerical simulation of a piano\u201d), Ph.D. thesis, Ecole Polytechnique X, Palaiseau, France, 2012."},{"first-page":"1085","article-title":"Mod\u00e9lisation du piano et couplage cordes-chevalet\u201d (\u201cModeling of the piano and string-bridge coupling","year":"2014","key":"2023080508274643100_c14"},{"key":"2023080508274643100_c15","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1007\/s11831-016-9164-5","article-title":"Historical origin and recent development on normal directional impact models for rigid body contact simulation: A critical review","volume":"24","year":"2017","journal-title":"Arch. Comput. Methods Eng."},{"key":"2023080508274643100_c16","doi-asserted-by":"publisher","first-page":"262","DOI":"10.1016\/j.jsv.2014.11.017","article-title":"Energy conserving schemes for the simulation of musical instrument contact dynamics","volume":"339","year":"2015","journal-title":"J. Sound Vib."},{"issue":"1","key":"2023080508274643100_c17","doi-asserted-by":"publisher","first-page":"155","DOI":"10.3813\/AAA.918813","article-title":"Numerical modeling of collisions in musical instruments","volume":"101","year":"2015","journal-title":"Acta Acust. united Acust."},{"issue":"5","key":"2023080508274643100_c18","doi-asserted-by":"publisher","first-page":"3195","DOI":"10.1121\/1.5039740","article-title":"Nonsmooth contact dynamics for the numerical simulation of collisions in musical string instruments","volume":"143","year":"2018","journal-title":"J. Acoust. Soc. 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Speech Signal Process."},{"issue":"4","key":"2023080508274643100_c28","doi-asserted-by":"publisher","first-page":"744","DOI":"10.3813\/AAA.918202","article-title":"Sympathetic string modes in the concert harp","volume":"95","year":"2009","journal-title":"Acta Acust. united Acust."},{"issue":"5","key":"2023080508274643100_c29","doi-asserted-by":"publisher","first-page":"3045","DOI":"10.1121\/1.4871360","article-title":"Predicting the decay time of solid body electric guitar tones","volume":"135","year":"2014","journal-title":"J. Acoust. Soc. Am."},{"key":"2023080508274643100_c30","unstructured":"A.\u2008Pat\u00e9, \u201cLutherie de la guitare \u00e9lectrique solid body: Aspects m\u00e9caniques et perceptifs\u201d (\u201cLutherie of the solid body electric guitar: Mechanical and perceptual aspects\u201d), Ph.D. thesis, Paris VI, Paris, 2014."},{"issue":"1","key":"2023080508274643100_c31","doi-asserted-by":"publisher","first-page":"6232","DOI":"10.1016\/j.ifacol.2017.08.1026","article-title":"Transfer function estimation in system identification toolbox via vector fitting","volume":"50","year":"2017","journal-title":"IFAC-PapersOnLine"},{"issue":"5","key":"2023080508274643100_c32","first-page":"945","article-title":"Plucked guitar transients: Comparison of measurements and synthesis","volume":"90","year":"2004","journal-title":"Acta Acust. united Acust."},{"issue":"1","key":"2023080508274643100_c33","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1023\/A:1009724704839","article-title":"An improved formulation for constrained mechanical systems","volume":"2","year":"1998","journal-title":"Multibody Syst. Dyn."},{"volume-title":"Vorlesungen Uber Mechanik","year":"1883","key":"2023080508274643100_c34"},{"issue":"2","key":"2023080508274643100_c35","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1090\/qam\/12351","article-title":"On the non-linear vibration problem of the elastic string","volume":"3","year":"1945","journal-title":"Q. Appl. Math."},{"issue":"6","key":"2023080508274643100_c36","doi-asserted-by":"publisher","first-page":"1475","DOI":"10.1088\/0143-0807\/32\/6\/003","article-title":"The potential energy density in transverse string waves depends critically on longitudinal motion","volume":"32","year":"2011","journal-title":"Eur. J. Phys."},{"first-page":"520","volume-title":"M\u00e9canique de la Corde Vibrante","year":"1993","key":"2023080508274643100_c37"},{"issue":"4","key":"2023080508274643100_c38","doi-asserted-by":"publisher","first-page":"1058","DOI":"10.1115\/1.2919487","article-title":"Geometric elimination of constraint violations in numerical simulation of Lagrangian equations","volume":"116","year":"1994","journal-title":"J. Mech. Des."},{"issue":"4","key":"2023080508274643100_c39","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1007\/s11044-016-9530-y","article-title":"On the constraints violation in forward dynamics of multibody systems","volume":"39","year":"2017","journal-title":"Multibody Syst. Dyn."},{"key":"2023080508274643100_c40","unstructured":"See https:\/\/www.musimediane.com\/numero7\/ALESSANDRO\/ for viewed high speed video of the string motion in the vicinity of the tangent (Last viewed 9\/20\/21)."},{"issue":"4","key":"2023080508274643100_c41","doi-asserted-by":"publisher","first-page":"1917","DOI":"10.1121\/1.1458024","article-title":"Yin, a fundamental frequency estimator for speech and music","volume":"111","year":"2002","journal-title":"J. Acoust. Soc. 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