Mon Sep 18, 2023 3:09 pm
I would like to comment on the article by the author Martin Ehlbeck. To introduce myself: I am a professor of physics and am familiar with the physics of coupled oscillators. When we model the properties of two or more coupled pipes, we do so by describing them as coupled nonlinear oscillators.
The author presents a quantitative argument for the difference between the electronically sampled sound of a pipe organ and its original sound. He does this by counting all possible pairs of sounding pipes with close frequencies. He develops this argument from the well-known phenomenon that the frequencies of two nearby pipes, slightly out of tune with each other, attract each other. In the language of physics, we would rather call this phenomenon synchronization. It is a well-known phenomenon that can be observed in many physical systems.
The author more or less correctly names the underlying basic phenomenon, that is the coupling of two pipes in close neighborhood and with close but slightly different frequencies - he calls synchronization a merging process. However, he seems not to be aware that, first, the coupling process is a threshold process, i.e., it works only above a minimum amplitude and coupling strength. Secondly, he neglects that the coupling strength decreases rapidly with the distance between the pipes. Thus, synchronization occurs only between pipes of close frequency and sufficiently close spatial distance from each other. Therefore, his argument to count the number of errors in the digital sound image is nonsensical.
The whole subject is well covered in the profound references cited by the author. I wish the author had digested their content better.