Romariozen wrote:What you are trying to prove is that stretching is changing the harmonic series of one string. That's not true. Refer to wiki and to pianoteq. "In stretched tuning, two notes an octave apart, whose fundamental frequencies theoretically have an exact 2:1 ratio, are tuned slightly farther apart (a stretched octave)."
In Equal tempered scale minor second is twelfth root of two, when you raise it to the 12th power, you have a perfect doubled frequency an octave above. When you stretch your strings, the upper notes will be higher, which in turn means that relatively to the equal-tempered scale a chord played throughout the keyboard will have its notes closer to the natural overtones.
You were fooled someday.
I am not trying to "prove" anything. I am saying how things are for acoustic pianos, because that is what I know well for experience and study. I know absolutely nothing about PTQ besides being a casual user.
In any case, I must have explained myself wrong, because you understood the exact reverse of what it is. Stretching is not changing the harmonic series of one string. It's the exact opposite: the harmonic series of one string is NOT ideal, so the upper partials are NOT integer multiples of the fundamental. Close, but not exactly integers. That is what makes octave stretching a necessity (and an automatic thing) in an acoustic piano tuning.
Where do I find a list of all posts I upvoted? :(