Yes, tuning is magic. She is not black. One example. You will have a perfectly tuned piano and decide to change 1-2 strings in the bass. The reason is not important. You loosen and take out the strings, put in new ones, and the rest of the piano is out of tune. Not a lot, but it will set things off. You probably won't perceive it, you don't have that much of a trained ear. But Pianoscope will already show you. And you were just strumming a 2-string bass. But each of them acts on the piano 60 kg.
If you have a whole piano -1Hz and you tune it one Hz higher, the pull of all strings will increase by 1 ton.