In our master's thesis, we explored various factors that lead to a deviation of the natural frequencies of the string in string instruments from the well-known values that are derived for an ideal string. We concluded that there are quite a few reasons for these deviations (inharmonicity) and that many models have already been developed. Most of those models challenge one of the assumptions that hold for an ideal string model. We also added a new model that takes into account the effect of the bow force on the natural frequencies of a string. From the theoretical part, we can conclude that a model for the total inharmonicity is by no means a simple one. The main reason for this is that it depends on many different sources of inharmonicity and many different variables. The number of experiments required to validate such a model would therefore be very extensive. For that reason, we concluded to only make a qualitative representation of the model. The actual frequencies of a real string were measured on a double bass. The sound signals we recorded were converted from the time to the frequency domain by means of a Fast Fourier Transform algorithm. When conducting the experiments, we focused on the A-string, which we excited by bowing and with pizzicato. We concluded that the level of inharmonicity is measurable and that it can also be heard. According to our experiments, the inharmonicity of a new string is lower than the inharmonicity of an old string.
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