Pianos actually often even employ a form of stretch tuning ( https://en.wikipedia.org/wiki/Stretched_tuning https://en.wikipedia.org/wiki/Stretched_tuning ) - w

Pianos actually often even employ a form of stretch tuning ( https://en.wikipedia.org/wiki/Stretched_tuning https://en.wikipedia.org/wiki/Stretched_tuning ) - which gets even more complex, as the OP only refers to sinus tones, which don't have any melodic overtones. Things get even more fun with this. Otherwise, you're right. Historic tunings often tried to optimize for a certain base scale (often times C major), while leaving behind a really bad sounding tuning at the other side of the circle of fifths ( https://en.wikipedia.org/wiki/Wolf_interval https://en.wikipedia.org/wiki/Wolf_interval ). Modern pianos are usually equal tempered, which is the strategy of leaving every scale equally bad off - but on the other hand being able to play in all keys without sounding too bad (The famous "well-tempered piano" is referring to this historic change in tuning strategies with small pieces written in all different kinds of keys, all of which would have sounded weird before). The more I learned about tuning, the more complex, beautiful and sad this topic became for me: http://blogs.scientificamerican.com/roots-of-unity/the-saddest-thing-i-know-about-the-integers/ http://blogs.scientificamerican.com/roots-of-unity/the-sadde... It's fascinating and even a little philosophical that we can get so close to perfection with the 12 step tuning - but never, ever completely attain it. By the way - That's part of the reason why choirs and orchestras often sound so good: As most other non-fixed-string instruments are able to do a slight adjustment in pitch, they can actually play perfect intervals in any chord, dynamically adjusting to any scale.