Firstly, you got the ratio thing backwards. A perfect fifth is 1:1.5. an equally tempered fifth is 1:1498... Secondly the explanation is good. A string under t

Firstly, you got the ratio thing backwards. A perfect fifth is 1:1.5. an equally tempered fifth is 1:1498... Secondly the explanation is good. A string under tension (such as in a grand piano) has all kinds of weird things going on with the harmonics (mostly, they all go sharp). When tuning pianos this is called stretching. You can read about it on Wikipedia: https://en.m.wikipedia.org/wiki/Piano_tuning https://en.m.wikipedia.org/wiki/Piano_tuning quite far down in that article. Edit: apparently I got the tension thing wrong. Lower tension and higher stiffness are what makes the lowest octave of the grand piano exhibit inharmonicity. To quote the wikipedia article on inharmonicity:"The less elastic the strings are (that is, the shorter, thicker, smaller tension or stiffer they are), the more inharmonicity they exhibit "