Energy conserving schemes for the simulation of musical instrument contact dynamics

Collisions are an innate part of the function of many musical instruments. Due to the nonlinear nature of contact forces, special care has to be taken in the construction of numerical schemes for simulation and sound synthesis. Finite difference schemes and other time-stepping algorithms used for musical instrument modelling purposes are normally arrived at by discretising a Newtonian description of the system. However because impact forces are non-analytic functions of the phase space variables, algorithm stability can rarely be established this way. This paper presents a systematic approach to deriving energy conserving schemes for frictionless impact modelling. The proposed numerical formulations follow from discretising Hamilton's equations of motion, generally leading to an implicit system of nonlinear equations that can be solved with Newton's method. The approach is first outlined for point mass collisions and then extended to distributed settings, such as vibrating strings and beams colliding with rigid obstacles. Stability and other relevant properties of the proposed approach are discussed and further demonstrated with simulation examples. The methodology is exemplified through a case study on tanpura string vibration, with the results confirming the main findings of previous studies on the role of the bridge in sound generation with this type of string instrument

Re-Sonification of Objects, Events, and Environments

abstract: Digital sound synthesis allows the creation of a great variety of sounds. Focusing on interesting or ecologically valid sounds for music, simulation, aesthetics, or other purposes limits the otherwise vast digital audio palette. Tools for creating such sounds vary from arbitrary methods of altering recordings to precise simulations of vibrating objects. In this work, methods of sound synthesis by re-sonification are considered. Re-sonification, herein, refers to the general process of analyzing, possibly transforming, and resynthesizing or reusing recorded sounds in meaningful ways, to convey information. Applied to soundscapes, re-sonification is presented as a means of conveying activity within an environment. Applied to the sounds of objects, this work examines modeling the perception of objects as well as their physical properties and the ability to simulate interactive events with such objects. To create soundscapes to re-sonify geographic environments, a method of automated soundscape design is presented. Using recorded sounds that are classified based on acoustic, social, semantic, and geographic information, this method produces stochastically generated soundscapes to re-sonify selected geographic areas. Drawing on prior knowledge, local sounds and those deemed similar comprise a locale's soundscape. In the context of re-sonifying events, this work examines processes for modeling and estimating the excitations of sounding objects. These include plucking, striking, rubbing, and any interaction that imparts energy into a system, affecting the resultant sound. A method of estimating a linear system's input, constrained to a signal-subspace, is presented and applied toward improving the estimation of percussive excitations for re-sonification. To work toward robust recording-based modeling and re-sonification of objects, new implementations of banded waveguide (BWG) models are proposed for object modeling and sound synthesis. Previous implementations of BWGs use arbitrary model parameters and may produce a range of simulations that do not match digital waveguide or modal models of the same design. Subject to linear excitations, some models proposed here behave identically to other equivalently designed physical models. Under nonlinear interactions, such as bowing, many of the proposed implementations exhibit improvements in the attack characteristics of synthesized sounds.Dissertation/ThesisPh.D. Electrical Engineering 201

A digital waveguide-based approach for Clavinet modeling and synthesis

The Clavinet is an electromechanical musical instrument produced in the mid-twentieth century. As is the case for other vintage instruments, it is subject to aging and requires great effort to be maintained or restored. This paper reports analyses conducted on a Hohner Clavinet D6 and proposes a computational model to faithfully reproduce the Clavinet sound in real time, from tone generation to the emulation of the electronic components. The string excitation signal model is physically inspired and represents a cheap solution in terms of both computational resources and especially memory requirements (compared, e.g., to sample playback systems). Pickups and amplifier models have been implemented which enhance the natural character of the sound with respect to previous work. A model has been implemented on a real-time software platform, Pure Data, capable of a 10-voice polyphony with low latency on an embedded device. Finally, subjective listening tests conducted using the current model are compared to previous tests showing slightly improved results

Spatially distributed computational modeling of a nonlinear vibrating string

Värähtelevän kielen epälineaarinen käyttäytyminen saa monissa kielisoittimissa aikaan soittimelle luonteenomaisen ja helposti tunnistettavan äänen. Laadukkaan kielisoitinsynteesin vuoksi onkin tärkeää, että nykyaikaiset äänisynteesimenetelmät ottavat huomioon myös kielten epälineaarisuudet. Tässä diplomityössä esitellään kaksi uutta synteesimenetelmää, jotka fysikaalisen mallinnuksen avulla simuloivat epälineaarisia näpättyjä kieliä paikkajakautuneesti, keskittyen jännitysmodulaation tuottamiin epälineaarisuuksiin. Toinen menetelmistä käyttää hajautettuja murtoviivesuotimia digitaalisen aaltojohtomallin viivesilmukan pituuden ajonaikaisessa virittämisessä, kun taas toinen hyödyntää murtoviivesuotimia äärelliseen erotukseen pohjautuvan mallin aikaresoluution muuttamisessa ajon aikana. Jännitysmodulaation suuruus arvioidaan kummankin mallin tapauksessa jokaisella aika-askeleella kielen pidentymästä. Molempien mallien simulaatiotulokset esitellään ja niitä verrataan toisiinsa sekä myös mitattuihin arvoihin. Epälineaarisen aaltojohtomallin avulla on toteutettu reaaliaikainen kantelemalli.Nonlinearities in string instruments are responsible for several interesting acoustical features, resulting in characteristic and easily recognizable tones. For this reason, modern synthesis models have to be capable of modeling this nonlinear behavior, when high quality results are desired. This thesis presents two novel physical modeling algorithms for simulating the tension modulation nonlinearity in plucked strings in a spatially distributed manner. The first method uses fractional delay filters within a digital waveguide structure, allowing the length of the string to be modulated during run time. The second method uses a nonlinear finite difference approach, where the string state is approximated between sampling instants also using fractional delay filters, thus allowing run-time modulation of the temporal sampling location. The magnitude of the tension modulation is evaluated from the elongation of the string at every time step in both cases. Simulation results of the two models are presented and compared. Real-time sound synthesis of the kantele, a traditional Finnish plucked-string instrument with strong effect of tension modulation, has been implemented using the nonlinear digital waveguide algorithm

Model-based digital pianos: from physics to sound synthesis

International audiencePiano is arguably one of the most important instruments in Western music due to its complexity and versatility. The size, weight, and price of grand pianos, and the relatively simple control surface (keyboard) have lead to the development of digital counterparts aiming to mimic the sound of the acoustic piano as closely as possible. While most commercial digital pianos are based on sample playback, it is also possible to reproduce the sound of the piano by modeling the physics of the instrument. The process of physical modeling starts with first understanding the physical principles, then creating accurate numerical models, and finally finding numerically optimized signal processing models that allow sound synthesis in real time by neglecting inaudible phenomena, and adding some perceptually important features by signal processing tricks. Accurate numerical models can be used by physicists and engineers to understand the functioning of the instrument, or to help piano makers in instrument development. On the other hand, efficient real-time models are aimed at composers and musicians performing at home or at stage. This paper will overview physics-based piano synthesis starting from the computationally heavy, physically accurate approaches and then discusses the ones that are aimed at best possible sound quality in real-time synthesis