For the intervals they look at in the article, the perfect 4th and 5th, 31-EDO is worse -- about 5 cents of error, versus about 2. What 31-EDO has is a major t

For the intervals they look at in the article, the perfect 4th and 5th, 31-EDO is worse -- about 5 cents of error, versus about 2. What 31-EDO has is a major third that's almost dead-on, and a minor third that's a lot closer. https://en.wikipedia.org/wiki/31_equal_temperament#Interval_size https://en.wikipedia.org/wiki/31_equal_temperament#Interval_... 41-EDO though has a perfect 4th and 5th that are closer than 12-EDO, being off by about half a cent rather than about 2 cents. In fact, 41-EDO is better at every commonly-used interval than 12-EDO, plus it adds a lot of very good 7-limit intervals too (i.e. ratios with sevens in them like 7:4, which is way off in 12-EDO). By a weird set of mathematical coincidences, 41-EDO is actually quite playable on guitar with the right layout. The trick is to omit half the frets and tune the strings so that each string has the notes that the strings above and below it lack. Tuning by major 3rds, you get a whole lot of useful notes clustered where they're easy to play. There's a handful of us (in Portland mostly) trying to promote this idea: https://kiteguitar.com/ https://kiteguitar.com/