Print version ISSN 1806-1117
Rev. Bras. Ensino Fís. vol.34 no.2 São Paulo Apr./June 2012
Music and entropy
One of the easiest jobs an editor of a physics journal can have is trying to convince his audience of the beauty of science in general and physics in particular. We do not need to be reminded of that, but sometimes we come across works that bring back to mind the reason why we chose this profession one day and why we believe it was the right choice: H. Hinrichsen's article on entropy and music is such a work.
The basic idea of the article is that the stretching of tunes employed by professional piano tuners is not random. If pianos were tuned with mathematical precision, i.e. if we tuned them to the precise frequency of each note, it would sound out of tune. This is because the strings of a piano are not ideal oscillators: due to their intrinsic stiffness, when being hit by a hammer, higher modes are excited and we do not get the pure sounds we want, but there are some corrections which are stiffness-dependent. Professional tuners have known that and try to compensate by matching higher harmonics, a process known as stretching. When these higher harmonics lock in, we perceive the sound as being pleasant (this is known as equal-temperament. There are other ways of tuning musical instruments, each age having its preferences). The question is why this is so. Prof. Hinrichsen suggests it has to do with entropy.
The history behind this article is interesting: one day before travelling to Brazil to work on a joint Brazilian-German cooperation project, H. Hinrichsen gave a talk before an audience composed mostly of high-school teachers. The theme chosen was entropy and, while devising a way of presenting this rather abstruse concept, he came upon the idea after watching a professional tuner working on the family piano recently bought. It was not his purpose to write about his findings, but after giving this same talk in Porto Alegre, the response was so overwhelmingly positive that we were able to convince him to put his ideas on paper. After submitting the article, he posted the preliminary version in the ArXiv . To everyone's great surprise, it caused a stir [2-4]. Most comments center upon the possible demise of professional tuners, even though the author's original idea had nothing to do with that: his motivation was understanding why pianos are tuned the way they are. Being the son of professional musicians, Prof. Hinrichsen exhibits a mastery at handling not only the physics behind musical instruments but also connecting Shannon's Entropy with a seemingly unrelated problem: the tuning of an upright piano.
As editor, it is a rewarding experience to publish articles like this one. We would like to thank H. Hinrichsen for sharing it with us and showing, once more, that simple ideas may lead to exciting and new vistas on applications of Physics.
Silvio R. Dahmen