https://hackerpaper.kaipfister.de/p/1203.5101/Collected HN comments and submissions linking this paper.enMon, 02 Nov 2026 11:16:22 GMThttps://news.ycombinator.com/item?id=46887460urn:hackerpapers:mention:1203.5101:46887460Wed, 04 Feb 2026 16:01:29 GMT<p>There is actually an interesting mathematical method for piano tuning that takes harmonics into account [1]. The core idea is to minimize the integral over the logarithm of the sum of all spectra. This basically favors spectra that are smeared out less. Instead of the logarithm, one could also use another sublinear function, such as the square root, but I guess it just makes for a better story to call it „piano entropy tuner“. The paper also shows a nice plot about the „stretched tuning“ that you mentioned. [1] https://arxiv.org/abs/1203.5101</p><p><a href="https://hackerpaper.kaipfister.de/p/1203.5101/">Paper and discussion history</a>. A mention is not an endorsement.</p>physics.class-ph