ethanhein

Every once in a while I get a giant traffic bump on an old post, and it's because someone shared it here. It's always a nice surprise. Thanks for reading!

Meantone is a modification of three-limit just intonation to try to better approximate the thirds from five-limit just intonation. I know that it is historically inaccurate to say that meantone follows from five-limit, but in order to understand the point of meantone's existence, you have to know about five-limit as the standard that meantone is aiming for. I should probably rephrase my post to say that meantone follows logically from five-limit, not that it follows historically.

All humans (and some monkeys) can detect octaves, but that does not mean that all humans consider octaves to be equivalent. That's a culturally specific convention. It's a very widespread convention thanks to Europe's wide cultural reach, but it's very much not a universal one.

Split keys may have been common for a while, but I think we can agree that in the long term, they did not catch on.

I'm the guy who wrote the blog post, and I want to offer some clarity. Usually when people say "Pythagorean" tuning they are talking about three-limit just intonation, not five-limit. In three-limit, the major third is indeed tuned to 81/64, which sounds pretty terrible. That might explain why medieval people thought thirds were a dissonant interval. Five-limit just intonation tunes major thirds to 5/4.

I know that pure five-limit just wasn't ever a prevalent tuning system, but all the temperament systems are based on it, so it seems reasonable to present it as a kind of baseline, the "ground truth" from which the meantone and well temperaments are departing to a greater and lesser degree. As to the dates, I have read a bunch of histories of tuning, and the main conclusion they present is that there was no uniform (or even predominant) tuning standard until 12-TET, so simplification is necessary. I am definitely open to the idea that 1500 isn't close enough to the "real" widespread advent of temperament to use as an approximation and that I should instead be saying 1400 or whenever.

I wrote a blog post summarizing this research. The idea is that the swirls specify turns of the tuning pegs to modify meantone temperament. It's more or less pure speculation, but it does produce a very nice-sounding tuning, almost equal temperament but not uniform across the keys. https://www.ethanhein.com/wp/2020/what-does-the-well-tempere...

Hi, I'm the author of the blog post. I said that 5-limit is the basis for systems like meantone, which is true. Meantone systems take 5-limit as their starting point and then modify it. I deliberately skated over the specifics of how meantone works on purpose, because I have too much experience watching my students' eyes glaze over when I talk about this kind of thing. I'm trying to strike a balance between giving correct information and not turning people away.

Hi folks, I'm the author of the blog post linked above, and I got about ten times as many hits on the post as usual today, so thanks for reading!