Audio Enhancement of Physical Models of Musical Instruments Using Optimal Correction Factors: The Recorder Case

Abstract

A simulation of a musical instrument is considered to be a successful one when there is a good resemblance between the model’s synthesized sound and the real instrument’s sound. In this work, we propose the integration of physical modeling (PM) methods with an optimization process to regulate a generated digital signal. Its goal is to find a new set of values of the PM’s parameters’ that would lead to a synthesized signal matching as much as possible to reference signals corresponding to the physical musical instrument. The reference signals can be: (a) described by their acoustic characteristics (e.g., fundamental frequencies, inharmonicity, etc.) and/or (b) the signals themselves (e.g., impedances, recordings, etc.). We put this method into practice for a commercial recorder, simulated using the digital waveguides’ PM technique. The reference signals, in our case, are the recorded signals of the physical instrument. The degree of similarity between the synthesized (PM) and the recorded signal (musical instrument) is calculated by the signals’ linear cross-correlation. Our results show that the adoption of the optimization process resulted in more realistic synthesized signals by (a) enhancing the degree of similarity between the synthesized and the recorded signal (the average absolute Pearson Correlation Coefficient increased from 0.13 to 0.67), (b) resolving mistuning issues (the average absolute deviation of the synthesized from the recorded signals’ pitches reduced from 40 cents to the non-noticeable level of 2 cents) and (c) similar sound color characteristics and matched overtones (the average absolute deviation of the synthesized from the recorded signals’ first five partials reduced from 41 cents to 2 cents).

Keywords

• correlation
• musical instruments
• optimization
• physical modeling
• recorder
• tuning