When you play G and B open and tune them to eliminate beating, you're in pretty bad shape because you're making a "just" (integer ratio) major 3rd which is quit

When you play G and B open and tune them to eliminate beating, you're in pretty bad shape because you're making a "just" (integer ratio) major 3rd which is quite far from an equal temperament major 3rd. When you play B and E open and tune them to eliminate beating, you're in okay shape because you're making a "just" (integer ratio) perfect 4th which is not terribly far from an equal temperament perfect 4th. See my earlier comment [0] with all the numbers if you want to quantity "pretty bad" vs "okay". In that comment, my initial references to footnotes 3 and 4 should actually be 2 and 3, but it's too late to correct it. [0] https://news.ycombinator.com/item?id=31145233 https://news.ycombinator.com/item?id=31145233