Out of curiosity, I tried a variation of the experiment you suggested. Just below Middle C on the piano are A3, A#3, and B3. Tones are 220, 233, and 247 Hz. Near the top of the piano are A7, A#7, and B7. Tones are 3,520, 3,730, and 3,951 Hz (first link). I spread six tiny browser windows...