DOCSLIB.ORG

Extensions of the Karplus-Strong Plucked-String Algorithm

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Extensions of the Karplus-Strong Plucked-String Algorithm ([WHQVLRQVRIWKH.DUSOXV6WURQJ3OXFNHG6WULQJ$OJRULWKP $XWKRU V 'DYLG$-DIIHDQG-XOLXV26PLWK 5HYLHZHGZRUN V 6RXUFH&RPSXWHU0XVLF-RXUQDO9RO1R 6XPPHU SS 3XEOLVKHGE\The MIT Press 6WDEOH85/http://www.jstor.org/stable/3680063 . $FFHVVHG Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. The MIT Press is collaborating with JSTOR to digitize, preserve and extend access to Computer Music Journal. http://www.jstor.org This content downloaded on Wed, 9 Jan 2013 14:25:21 PM All use subject to JSTOR Terms and Conditions DavidA. Jaffe and Julius 0. Smith Extensions of the Center for Computer Research in Music and Acoustics (CCRMA) StanfordUniversity Karplus-Strong California 94305 Stanford, Plucked-String Algorithm Introduction The String-SimulationAlgorithm In 1960, an efficient computational model for vi- The Karplus-Strongplucked-string algorithm is pre- brating strings, based on physical resonating, was sented in this issue of Computer Music Journal. proposed by McIntyre and Woodhouse (1960). This From our point of view, the algorithm consists of model plays a crucial role in their recent work on a high-order digital filter, which represents the bowed strings (McIntyre,Schumacher, and Wood- string; and a short noise burst, which represents house 1981; 1983), and methods for calibratingthe the "pluck." The digital filter is given by the dif- model to recorded data have been developed (Smith ference equation 1983). Yn-N + YN+ in Alex devised an = Xn + Yn-N yn-(N+1) Independently, 1978, Strong Yn Yn= 2 (1) efficient special case of the McIntyre-Woodhouse string model that produces remarkablyrich and re- where x. is the input signal amplitude at sample n, alistic timbres despite its simplicity (Karplusand y, is the output amplitude at sample n, and N is Strong 1983). Since then, Strong and Kevin Karplus the (approximate)desired pitch period of the note in have explored several variations and refinements of samples. The noise burst is defined by the with an on algorithm, emphasis small-system Au, n = 1 We have found that the 0, 1, 2,...,N- implementations. Karplus- xn = 0, n N, Strong algorithm can be used with equally impres- sive results on fast, high-power equipment. The where A is the desired amplitude, and un, [-1,1] is availability of multiplies, for example, allows sev- the output of a random-numbergenerator. The out- eral modifications and extensions that increase its put yn is taken beginning at time n = N in our usefulness and flexibility. These extensions are de- implementation. scribed in this paper. The developments were moti- vated by musical needs that arose during the composition of May All YourChildren Be Acrobats Analysis of the String Simulator (1981) for computer-generatedtape, eight guitars, and voice and Silicon Valley Breakdown (1982) for Before proceeding to practical extensions of the al- four-channel, computer-generatedtape, both writ- gorithm, we will describe the theory on which ten by David Jaffe.Our theoretical approachand many of them are based. Various concepts from the extensions based on it have also been applied to digital filter theory are employed. For a tutorial in- the McIntyre-Woodhousealgorithm (Smith 1983). troduction to digital filter theory, see the works by Smith (1982b) and Steiglitz (1974). The input-output relation of Eq. (1) may be ex- David A. Jaffeis also affiliated with the Music Departmentat StanfordUniversity, and Julius O. Smith is also affiliatedwith the Electrical EngineeringDepartment there. 1. In some situations, the sound more closely resembles a string Computer Music Journal,Vol. 7, No. 2, struck with a hammer or mallet than one plucked with a pick, Summer 1983, 0148-9267/83/020056-14 $04.00/0, but we will always use the term pluck when referringto the ? 1983 Massachusetts Institute of Technology. excitation. 56 Computer Music Journal This content downloaded on Wed, 9 Jan 2013 14:25:21 PM All use subject to JSTOR Terms and Conditions Fig.1. Blockdiagram for the basic stringsimulator. pressed differently by means of delay-operatornota- tion. We define the unit-sample delay operatord by the relation dkx A-Xn-k, where x, is an arbitrarysignal, and k is an integer. (The symbol A means "is defined as.")Thus, multi- plying a signal by dk delays the signal in time by k samples. In these terms, Eq. (1) becomes dNy + dN+lyn yn = tor is the following set of difference equations: L+d Vn = Yn-N =x+n 2 V= n + Vn- Solving for yn yields 2 = Xn1 yn xn + Wn Yn XI+d' (2) 1- dN The frequency response of a digital filter is de- 2 fined as the transfer function evaluated at z = e's = + where is the sam- We can convert linear delay-operatorequations cos(oT,) j sin(o Ts), T, in seconds is the inverse of the sam- immediately to z-transform equations by replacing pling period (Ts rate o = is radian is each time signal with its z-transform, and replacing pling fj, 27rf frequency, f in and = \-7. The re- d with z-'. It is customary to denote a time signal frequency Hz, j frequency of the simulator is then in lowercase letters (e.g., x) and the corresponding sponse string z-transform in uppercase letters (e.g., X(z)). The 1 H(e,Ts) = transferfunction of a (linear, time-invariant) digital He') 1 - Ha eiw sHb(es)' filter is the z-transform of the output signal divided where by the z-transform of the input. The transferfunc- tion of the string simulator is then found to be 1 + e- 'T = e-' T H|(e 2Ts) e 2cos(coT,/2) Y(z)Y _ 1 H(Z) A =X H X(z)x 1 l+z - = e-fTscos(rfTs) 2 Hb(es s) = e-iN = e- if.NT 1 In this it is to consider 1 - Ha(z)Hb(z)' paper necessary the am- plitude response and phase delay of the feedback fil- where ters separately.The amplitude response is defined as the magnitude of the frequency response, and 1 + z- it gives the gain of the filter as a function of fre- Ha(z) Q 2 quency. The phase delay is defined as minus the Hb(z) z-N complex angle of the frequency response divided by radian frequency, and it gives the time delay This form of the description is shown in Fig. 1. The (in seconds) experienced by a sinusoid at each feedback loop consists of a length N delay line frequency. Hb(z) in series with a two-point average Ha(z). Cor- The amplitude response of each component filter responding to this breakdown of the string simula- is given by Jaffeand Smith 57 This content downloaded on Wed, 9 Jan 2013 14:25:21 PM All use subject to JSTOR Terms and Conditions ___ Ga(f)A IHa(eiTs)I= cos(oT,/2)l = Icos(T7fT)l NTs + Ts/2 sec. Experience shows this to corre- spond well with perceived pitch. Gb(f) A IHbleews)I 1. Thus the delay line Hb is lossless, and the two- point average Ha exhibits a gain that decreases with Decayof "Harmonics" frequency according to the first quadrantof a co- sine. We will assume hereafter that all frequencies Since the signal is only quasi-periodic,it does not are restricted to the Nyquist limit, that is, Ifl consist of discrete sinusoids. Essentially, we have fs/2. In this range, we have (cos(i7fTj)= cos(1rfTs). many narrow "bands"of energy decaying to zero at It is convenient to define phase delay in units different rates. When these energy bands are cen- consisting of samples rather than seconds. The tered at frequencies that are an integer multiple of a phase delays of Ha and Hb in samples are given by lowest frequency, they will be referredto as har- monics. When the frequency components are not Pa(f)"- - / H(e'2) =1 necessarily uniformly the term will ~oT, 2' spaced, partial be used to emphasize the possibility of inharmo- nicity. Consider, then, a partial at frequency f Hz Pb(f) A - / Hb(e'S) = N. PfT, circulating in the loop. On each pass through the loop, it suffers an attenuation to the (Lz denotes the complex angle of z). The two-point equal loop- amplitude response, = that averagehas a phase delay equal to half a sample, Ga(f)Gb(f) cos(IrfTs); is, and the delay line has a phase delay equal to its one period's attenuation = cos(rfTs). length. Since the round-trip time in the N + Since the total loop consists of Haand Hbin se- loop equals 1/2 samples, the number of the ries, the loop gain and effective loop length are trips through loop after n samples (nTssec) is equal to n/(N + 1/2) = loop gain = G(f) Gb(f) = cos(rfT,), tfS/(N + 1/2). Thus the attenuation factor at time and t = nT, is given by tf5 loop length = Pa(f) + Pb(f) = N + 1/2 (samples) af(t) A [cos(7rfTs)]N + 2. (3) for each sinusoidal Hz. frequency f For example, an initial partial amplitude A at time In a we synthesizing single plucked-string note, 0 becomes amplitude Aaf(t) at time t seconds, feed in N of white noise at A samples amplitude where f is the frequency of the partial.
Load more

Recommended publications
  • The Science of String Instruments
    The Science of String Instruments Thomas D. Rossing Editor The Science of String Instruments Editor Thomas D. Rossing Stanford University Center for Computer Research in Music and Acoustics (CCRMA) Stanford, CA 94302-8180, USA [email protected] ISBN 978-1-4419-7109-8 e-ISBN 978-1-4419-7110-4 DOI 10.1007/978-1-4419-7110-4 Springer New York Dordrecht Heidelberg London # Springer Science+Business Media, LLC 2010 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer ScienceþBusiness Media (www.springer.com) Contents 1 Introduction............................................................... 1 Thomas D. Rossing 2 Plucked Strings ........................................................... 11 Thomas D. Rossing 3 Guitars and Lutes ........................................................ 19 Thomas D. Rossing and Graham Caldersmith 4 Portuguese Guitar ........................................................ 47 Octavio Inacio 5 Banjo ...................................................................... 59 James Rae 6 Mandolin Family Instruments........................................... 77 David J. Cohen and Thomas D. Rossing 7 Psalteries and Zithers .................................................... 99 Andres Peekna and Thomas D.
    [Show full text]
  • Tonal Quality of the Clavichord : the Effect of Sympathetic Strings Christophe D’Alessandro, Brian Katz
    Tonal quality of the clavichord : the effect of sympathetic strings Christophe d’Alessandro, Brian Katz To cite this version: Christophe d’Alessandro, Brian Katz. Tonal quality of the clavichord : the effect of sympathetic strings. Intl Symp on Musical Acoustics (ISMA), 2004, Nara, Unknown Region. pp.21–24. hal- 01789802 HAL Id: hal-01789802 https://hal.archives-ouvertes.fr/hal-01789802 Submitted on 21 Dec 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Proceedings of the International Symposium on Musical Acoustics, March 31st to April 3rd 2004 (ISMA2004), Nara, Japan 1-P1-7 Tonal quality of the clavichord: the effect of sympathetic strings Christophe d'Alessandro & Brian F.G. Katz LIMSI-CNRS, BP133 F-91403 Orsay, France [email protected], [email protected] Abstract part of the strings the “played strings”. Only few works have included efforts specifically devoted to the In the clavichord, unlike the piano, the slanting strings acoustics of the clavichord [2][3][4]. Experiments with between the bridge and the hitch pins are not damped physical modeling synthesis of the clavichord are with felt. The effect of these “sympathetic strings” on described in [5].
    [Show full text]
  • Modelling of Sympathetic String Vibrations Jean-Loic Le Carrou, François Gautier, Nicolas Dauchez, Joël Gilbert
    Modelling of Sympathetic String Vibrations Jean-Loic Le Carrou, François Gautier, Nicolas Dauchez, Joël Gilbert To cite this version: Jean-Loic Le Carrou, François Gautier, Nicolas Dauchez, Joël Gilbert. Modelling of Sympathetic String Vibrations. Acta Acustica united with Acustica, Hirzel Verlag, 2005, 91, pp.277 - 288. hal- 00474982 HAL Id: hal-00474982 https://hal.archives-ouvertes.fr/hal-00474982 Submitted on 21 Apr 2010 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Modelling of Sympathetic String Vibrations Jean-Lo¨ıc Le Carrou,∗ Francois Gautier, Nicolas Dauchez, and Jo¨el Gilbert Laboratoire d’Acoustique de l’Universit´edu Maine, UMR CNRS 6613, 72085 Le Mans Cedex 9, France (Dated: October 5, 2004) Abstract String instruments are usually composed of several strings connected to a vibrating body allowing efficient sound radiation. For some special string tunings, sympathetic vibrations can occur: if one string is excited, some others are also excited via the body. In order to investigate this phenomenon, an analytical model of a simplified generic string in- strument has been developed. The body of the instrument is represented by a beam clamped at both ends, to which several strings are attached.
    [Show full text]
  • Listening to String Sound: a Pedagogical Approach To
    LISTENING TO STRING SOUND: A PEDAGOGICAL APPROACH TO EXPLORING THE COMPLEXITIES OF VIOLA TONE PRODUCTION by MARIA KINDT (Under the Direction of Maggie Snyder) ABSTRACT String tone acoustics is a topic that has been largely overlooked in pedagogical settings. This document aims to illuminate the benefits of a general knowledge of practical acoustic science to inform teaching and performance practice. With an emphasis on viola tone production, the document introduces aspects of current physical science and psychoacoustics, combined with established pedagogy to help students and teachers gain a richer and more comprehensive view into aspects of tone production. The document serves as a guide to demonstrate areas where knowledge of the practical science can improve on playing technique and listening skills. The document is divided into three main sections and is framed in a way that is useful for beginning, intermediate, and advanced string students. The first section introduces basic principles of sound, further delving into complex string tone and the mechanism of the violin and viola. The second section focuses on psychoacoustics and how it relates to the interpretation of string sound. The third section covers some of the pedagogical applications of the practical science in performance practice. A sampling of spectral analysis throughout the document demonstrates visually some of the relevant topics. Exercises for informing intonation practices utilizing combination tones are also included. INDEX WORDS: string tone acoustics, psychoacoustics,
    [Show full text]
  • Sympathetic Vibration in a Piano
    Sympathetic vibration in a piano Jin Jack TAN(1), Armin KOHLRAUSCH(2), Maarten HORNIKX(3) (1)Department of Built Environment, Eindhoven University of Technology, Netherlands, [email protected] (2)Human Technology Interaction, Eindhoven University of Technology, Netherlands, [email protected] (3)Department of Built Environment, Eindhoven University of Technology, Netherlands, [email protected] Abstract Sympathetic vibration is a common phenomenon in musical instruments. In the piano, strings that are not struck directly by the hammer can vibrate sympathetically due to physical coupling. This effect will, for instance, occur when the una corda pedal is used in a grand piano. When depressed, the hammer shifts rightwards so that the leftmost string will be missed, striking only 1 out of 2 (or 2 out of 3) strings in a note at a same time. In order to understand the acoustical and perceptual differences in the notes played without and with una corda pedal depressed, the recordings of a piano for these two playing conditions are studied for all 88 keys. Differences arising in the frequency domains are found and presented alongside with discrepancies in three psychoacoustical descriptors, namely log-attack-time, temporal centroid and normalised spectral centroid. Future work in the form of listening test is planned. Keywords: piano, sympathetic vibration, una corda pedal, psychoacoustics 1 INTRODUCTION Sympathetic vibration is a physical phenomenon where a vibrating body that is initially at rest responds to another vibration in vicinity. In string-based musical instruments, sympathetic vibration is a common occurrence as strings vibrate sympathetically due to the excitation of other strings [1, 2].
    [Show full text]
  • Sympathetic String Modes in the Concert Harp Jean-Loic Le Carrou, François Gautier, Roland Badeau
    Sympathetic string modes in the concert harp Jean-Loic Le Carrou, François Gautier, Roland Badeau To cite this version: Jean-Loic Le Carrou, François Gautier, Roland Badeau. Sympathetic string modes in the concert harp. Acta Acustica united with Acustica, Hirzel Verlag, 2009, 95 (4), pp.744–752. hal-00945199 HAL Id: hal-00945199 https://hal.inria.fr/hal-00945199 Submitted on 25 Mar 2014 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Sympathetic modes in the concert harp Jean-Lo¨ıc Le Carrou and Fran¸cois Gautier∗ LAUM, CNRS, Universit´edu Maine, Av. O. Messiaen, 72085 LE MANS, France Roland Badeau T´el´ecom Paris (ENST) / CNRS LTCI, 46 rue Barrault, 75634 Paris Cedex 13, France (Dated: December 12, 2007) 1 Le Carrou et al.: Sympathetic modes in the concert harp Abstract The concert harp is composed of a soundboard, a cavity with sound holes and 47 strings. When one string is plucked, other strings are excited and induce a characteristic ‘halo of sound’. This phenomenon, called sympathetic vibrations is due to a coupling between strings via the instrument’s body. These sympathetic modes generate the presence of multiple spectral components in each partial of the tone.
    [Show full text]
  • Download Manual
    Table of Contents 1. Welcome to Noire ....................................................................................................... 1 1.1. About NOIRE ................................................................................................... 1 1.2. NOIRE’s Special Sound .................................................................................... 1 1.3. The Particles Engine ......................................................................................... 2 1.4. Two KONTAKT Instruments ............................................................................... 2 1.4.1. NOIRE Pure ........................................................................................... 2 1.4.2. NOIRE Felt ............................................................................................ 3 2. User Interface ............................................................................................................. 4 2.1. Piano Edit Page ................................................................................................ 5 2.1.1. Anatomy Area ........................................................................................ 6 2.1.2. Noises Area ........................................................................................... 7 2.1.3. Tone Area .............................................................................................. 8 2.1.4. Settings Area ......................................................................................... 9 2.2. FX Edit Page .................................................................................................
    [Show full text]
  • The Bowed String and Its Playability: Theory, Simulation and Analysis
    The bowed string and its playability: Theory, simulation and analysis Hossein Mansour Department of Music Research McGill University Montr´eal, Qu´ebec, Canada June 2016 A dissertation submitted to McGill University in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Music Technology c 2016 Hossein Mansour i Abstract This thesis describes the development of a highly refined physics-based model of a bowed string and its subsequent use to investigate several aspects of a bowed string, particularly its playability. Different components of a previously reported model are replaced by more accurate solutions, and several new features are added to make the model more realistic. Plucked-string simulations are described first, followed by enhancements to include the bow and the bowing process. Several properties of the simulated plucked response are compared to their designed values and to their experimental counterparts, which confirms the accuracy of the model and its parameters. An initial application of the model is focused on the minimum bow force above which the Helmholtz motion is sustainable. The Helmholtz motion is associated with the “speaking” sound of a bowed string, as opposed to its “whistling” or “crunching” sounds. An earlier theoretical relation for the minimum bow force is re-derived starting from a more robust assumption of an ideal stick-slip at the bowing point rather than a perfect sawtooth-shaped excitation force at the bridge. Simulations are used to evaluate and validate the improved accuracy of the new formulation. The revised relation makes some fundamentally different predictions that are confirmed by the simulations.
    [Show full text]
  • Bowed Strings and Sympathy, from Violins to Indian Sarangis Matthias Demoucron, Stéphanie Weisser
    Bowed strings and sympathy, from violins to indian sarangis Matthias Demoucron, Stéphanie Weisser To cite this version: Matthias Demoucron, Stéphanie Weisser. Bowed strings and sympathy, from violins to indian sarangis. Acoustics 2012, Apr 2012, Nantes, France. hal-00810608 HAL Id: hal-00810608 https://hal.archives-ouvertes.fr/hal-00810608 Submitted on 23 Apr 2012 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Proceedings of the Acoustics 2012 Nantes Conference 23-27 April 2012, Nantes, France Bowed strings and sympathy, from violins to indian sarangis M. Demoucrona and S. Weisserb aIPEM, Blandijnberg 2, 9000 Gent, Belgium bMus´ee des Instruments de Musique, Montagne de la Cour 2, 1000 Bruxelles, Belgium [email protected] 3593 23-27 April 2012, Nantes, France Proceedings of the Acoustics 2012 Nantes Conference The sarangi is an indian bowed string instrument that is characterized by a large set of sympathetic strings (some- times up to over 30), called taraf, going below the three main strings. The tuning of the taraf varies among players, but generally one part is tuned chromatically and diatonically, while the other part is tuned according to the rag of the musical piece, resulting in a rich and highly reverberant sound when the main strings are bowed.
    [Show full text]
  • Nord Piano 3 English User Manual V1x-Edition-D.Pdf
    NORD ELECTRO 5 USER MAnuAL OS V1.X | 1 User Manual English Nord Piano 3 OS Version: 1.x Edition: D Part No. 50446 Copyright Clavia DMI AB Edition: D 2 | NORD ELECTRO 5 USER MAnuAL OS V1.X The lightning flash with the arrowhead symbol within CAUTION - ATTENTION an equilateral triangle is intended to alert the user to the RISK OF ELECTRIC SHOCK presence of uninsulated voltage within the products en- DO NOT OPEN closure that may be of sufficient magnitude to constitute RISQUE DE SHOCK ELECTRIQUE a risk of electric shock to persons. NE PAS OUVRIR Le symbole éclair avec le point de flèche à l´intérieur d´un triangle équilatéral est utilisé pour alerter l´utilisateur de la presence à l´intérieur du coffret de ”voltage dangereux” non isolé d´ampleur CAUTION: TO REDUCE THE RISK OF ELECTRIC SHOCK suffisante pour constituer un risque d`éléctrocution. DO NOT REMOVE COVER (OR BACK). NO USER SERVICEABLE PARTS INSIDE. REFER SERVICING TO QUALIFIED PERSONNEL. The exclamation mark within an equilateral triangle is intended to alert the user to the presence of important operating and maintenance (servicing) instructions in the ATTENTION:POUR EVITER LES RISQUES DE CHOC ELECTRIQUE, NE literature accompanying the product. PAS ENLEVER LE COUVERCLE. AUCUN ENTRETIEN DE PIECES INTERIEURES PAR L´USAGER. Le point d´exclamation à l´intérieur d´un triangle équilatéral est CONFIER L´ENTRETIEN AU PERSONNEL QUALIFE. employé pour alerter l´utilisateur de la présence d´instructions AVIS: POUR EVITER LES RISQUES D´INCIDENTE OU D´ELECTROCUTION, importantes pour le fonctionnement et l´entretien (service) dans le N´EXPOSEZ PAS CET ARTICLE A LA PLUIE OU L´HUMIDITET.
    [Show full text]
  • Nord Grand English User Manual V1.5X-Edition-C.Pdf
    USER MANUAL Nord Grand English OS version: 1.5x Edition: C Part number: 50476 Copyright Clavia DMI AB Edition: C The lightning flash with the arrowhead symbol within CAUTION - ATTENTION an equilateral triangle is intended to alert the user to the RISK OF ELECTRIC SHOCK presence of uninsulated voltage within the products en- DO NOT OPEN closure that may be of sufficient magnitude to constitute RISQUE DE SHOCK ELECTRIQUE a risk of electric shock to persons. NE PAS OUVRIR Le symbole éclair avec le point de flèche à l´intérieur d´un triangle équilatéral est utilisé pour alerter l´utilisateur de la presence à l´intérieur du coffret de ”voltage dangereux” non isolé d´ampleur CAUTION: TO REDUCE THE RISK OF ELECTRIC SHOCK suffisante pour constituer un risque d`éléctrocution. DO NOT REMOVE COVER (OR BACK). NO USER SERVICEABLE PARTS INSIDE. REFER SERVICING TO QUALIFIED PERSONNEL. The exclamation mark within an equilateral triangle is intended to alert the user to the presence of important operating and maintenance (servicing) instructions in the ATTENTION:POUR EVITER LES RISQUES DE CHOC ELECTRIQUE, NE literature accompanying the product. PAS ENLEVER LE COUVERCLE. AUCUN ENTRETIEN DE PIECES INTERIEURES PAR L´USAGER. Le point d´exclamation à l´intérieur d´un triangle équilatéral est CONFIER L´ENTRETIEN AU PERSONNEL QUALIFE. employé pour alerter l´utilisateur de la présence d´instructions AVIS: POUR EVITER LES RISQUES D´INCIDENTE OU D´ELECTROCUTION, importantes pour le fonctionnement et l´entretien (service) dans le N´EXPOSEZ PAS CET ARTICLE A LA PLUIE OU L´HUMIDITET. livret d´instructions accompagnant l´appareil.
    [Show full text]
  • Physical Modeling of the Piano
    EURASIP Journal on Applied Signal Processing 2004:7, 926–933 c 2004 Hindawi Publishing Corporation Physical Modeling of the Piano N. Giordano Department of Physics, Purdue University, 525 Northwestern Avenue, West Lafayette, IN 47907-2036, USA Email: [email protected] M. Jiang Department of Physics, Purdue University, 525 Northwestern Avenue, West Lafayette, IN 47907-2036, USA Department of Computer Science, Montana State University, Bozeman, MT 59715, USA Email: [email protected] Received 21 June 2003; Revised 27 October 2003 A project aimed at constructing a physical model of the piano is described. Our goal is to calculate the sound produced by the instrument entirely from Newton’s laws. The structure of the model is described along with experiments that augment and test the model calculations. The state of the model and what can be learned from it are discussed. Keywords and phrases: physical modeling, piano. 1. INTRODUCTION the instrument. However, as far as we can tell, certain fea- tures of the model, such as hammer-string impulse func- This paper describes a long term project by our group aimed tions and the transfer function that ultimately relates the at physical modeling of the piano. The theme of this volume, sound pressure to the soundboard motion (and other sim- model based sound synthesis of musical instruments, is quite ilar transfer functions), are taken from experiments on real broad, so it is useful to begin by discussing precisely what instruments. This approach is a powerful way to produce re- we mean by the term “physical modeling.” The goal of our alistic musical tones efficiently, in real time and in a man- project is to use Newton’s laws to describe all aspects of the ner that can be played by a human performer.
    [Show full text]