Physical Models of Wind Instruments : A Generalized Excitation Coupled with a Modular Tube Simulation Platform

To develop real-time simulations of wind instruments, digital waveguides filters can be used as an efficient representation of the air column. Many aerophones are shaped as horns which can be approximated using conical sections. Therefore the derivation of conical waveguide filters is of special interest. When these filters are used in combination with a generalized reed excitation, several classes of wind instruments can be simulated. In this paper we present the methods for transforming a continuous description of conical tube segments to a discrete filter representation. The coupling of the reed model with the conical waveguide and a simplified model of the termination at the open end are described in the same way. It turns out that the complete lossless conical waveguide requires only one type of filter.Furthermore, we developed a digital reed excitation model, which is purely based on numerical integration methods, i.e., without the use of a look-up table.

Sound Synthesis for Contact-Driven Musical Instruments via Discretisation of Hamilton's Equations

Physical modelling of musical instruments involves studying nonlinear interactions between parts of the instrument. These can pose several difficulties concerning the accuracy and stability of numerical algorithms. In particular, when the underlying forces are non-analytic functions of the phase-space variables, a stability proof can only be obtained in limited cases. An approach has been recently presented by the authors, leading to unconditionally stable simulations for lumped collision models. In that study, discretisation of Hamilton’s equations instead of the usual Newton’s equation of motion yields a numerical scheme that can be proven to be energy conserving. In this paper, the above approach is extended to collisions of distributed objects. Namely, the interaction of an ideal string with a flat barrier is considered. The problem is formulated within the Hamiltonian framework and subsequently discretised. The resulting nonlinearmatrix equation can be shown to possess a unique solution, that enables the update of the algorithm. Energy conservation and thus numerical stability follows in a way similar to the lumped collision model. The existence of an analytic description of this interaction allows the validation of the model’s accuracy. The proposed methodology can be used in sound synthesis applications involving musical instruments where collisions occur either in a confined (e.g. hammer-string interaction, mallet impact) or in a distributed region (e.g. string-bridge or reed-mouthpiece interaction).

Validity of the Global Physical Activity Questionnaire (GPAQ) in assessing levels and change in moderate-vigorous physical activity and sedentary behaviour

Background

Feasible, cost-effective instruments are required for the surveillance of moderate-to-vigorous physical activity (MVPA) and sedentary behaviour (SB) and to assess the effects of interventions. However, the evidence base for the validity and reliability of the World Health Organisation-endorsed Global Physical Activity Questionnaire (GPAQ) is limited. We aimed to assess the validity of the GPAQ, compared to accelerometer data in measuring and assessing change in MVPA and SB.

Participants (n = 101) were selected randomly from an on-going research study, stratified by level of physical activity (low, moderate or highly active, based on the GPAQ) and sex. Participants wore an accelerometer (Actigraph GT3X) for seven days and completed a GPAQ on Day 7. This protocol was repeated for a random sub-sample at a second time point, 3–6 months later. Analysis involved Wilcoxon-signed rank tests for differences in measures, Bland-Altman analysis for the agreement between measures for median MVPA and SB mins/day, and Spearman’s rho coefficient for criterion validity and extent of change.

95 participants completed baseline measurements (44 females, 51 males; mean age 44 years, (SD 14); measurements of change were calculated for 41 (21 females, 20 males; mean age 46 years, (SD 14). There was moderate agreement between GPAQ and accelerometer for MVPA mins/day (r = 0.48) and poor agreement for SB (r = 0.19). The absolute mean difference (self-report minus accelerometer) for MVPA was −0.8 mins/day and 348.7 mins/day for SB; and negative bias was found to exist, with those people who were more physically active over-reporting their level of MVPA: those who were more sedentary were less likely to under-report their level of SB. Results for agreement in change over time showed moderate correlation (r = 0.52, p = 0.12) for MVPA and poor correlation for SB (r = −0.024, p = 0.916).

Levels of agreement with objective measurements indicate the GPAQ is a valid measure of MVPA and change in MVPA but is a less valid measure of current levels and change in SB. Thus, GPAQ appears to be an appropriate measure for assessing the effectiveness of interventions to promote MVPA.