[ethanhein]

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.

[MikeBattaglia]

I can't comment regarding how you think is best to teach your students. This is now a popular blog post that has gone viral on HackerNews to a much wider audience of well-educated people, so you should expect people will clarify these things on here. I'm talking mostly about stuff like this:

> Five hundred years ago, however, it would have made a very big difference. Before the advent of temperament systems, D-sharp and E-flat were two different notes. They weren’t just written differently; they sounded different. You can compare the historical versions of these notes yourself in this track I made... My track is tuned in a system called five-limit just intonation

^ These are not the historical versions of those notes. 5-limit just intonation was not in widespread use in Western Europe 500 years ago. 500 years is not before the advent of temperament systems. And so on. Teach this to your students however you think is best, but people on here may be interested to know that.

[ethanhein]

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.