What is conspicuously absent from discussions on this topic are:
variations in the design and setup of the instrument: stringing scale, strike point, voicing - hardness and shape of the felts, duplexing, resonance - to name but a few.
the role of the human ear and brain in the perception of sound: The brain continues to "hear" a note for up to 4 seconds, a phenomenon known as echoic memory, though the initial, more immediate sensation of sound lasts for about 0.1 seconds. This longer-term sensory memory allows the brain to process sounds like music and speech.
Initial sensation: For about 0.1 seconds (or 1/10th of a second), the brain maintains the sensory experience of the sound, which is why we can perceive echoes.
Echoic memory: The brain can hold onto sounds in "echoic memory" for much longer, with durations often lasting up to 4 seconds, though this can vary between individuals.
Processing: This echoic memory is crucial for understanding language, as it provides a buffer for the brain to process auditory information and distinguish between different sounds.
Factors influencing duration: Age, hearing impairment, and other brain conditions can affect how long echoic memory lasts
Briefly ...
if you were to set up a machine which can be calibrated to execute a precise velocity of key press, then apply the exact same key press to a Steinway D and a Yamaha CFX you would get two completely different sets of relative volumes of overtones.
the pianistic artist not only plays "the piano" -- they "play" the human ear -- using their own ear as a guide. Like a consummate chef who blends just the right amount of seasonings to create the exact overtones of flavor their palate demands, so the pianists use their ears and musical palate to blend the series of overtones to create the desired sensation on the listener's ears -- constantly mixing and adjusting the relative volumes and the degree of space or overlap of tones and overtones. There is a near-infinite number of combinations available to the artist with only two notes. If sounded together, the balance of the combined set of overtones is affected by which of the two -- if either -- is struck louder, and, depending on the notes, where and to what extent there is overlap of exact overtones or slightly disparate overtones, and how the ear and mind process them. If played in sequence, not only does the relative force of each note apply, but the distance between the first and second note. The mind has only heard the first note and is still processing it when the second note is joined -- causing the mind to now have to add the additional set of overtones to the ones it's already processing. Was the connection staccato? Legato? The second set of overtones will be processed differently in each case.
And not forgetting to include the acoustics of the room. Steinway's "sing" because playing the strings louder or softer produces a different timbre -- a different mix of overtones -- similar to the change in timbre that occurs naturally with the human voice and wind instruments as they move through their registers. Yamaha's do NOT "sing" because playing the strings louder or softer does NOT produce a different timbre. In comparing Yamaha's to Steinway's, Yamaha's have a much flatter spectrum of overtones over the range of volume and pitch -- which is exactly why they are preferred for some applications.
Yes -- you can measure and weigh and discuss physical and acoustic phenomena all you want. Failure to include the EXACT differences in the physical characteristics of each instrument -- and, again, the acoustics -- is the first shortcoming -- too much barking up the wrong tree. Failure to include the role of the human ear and mind in the process of hearing as it informs the performer and the listener is the second. It is not a single physical science -- it's the phenomena of human ear and mind that needs to be included in the assessment.
Rather than continue the debate over whether the pianist can affect the "tone" after the hammer is thrown to the string, what might be more beneficial would be to have the same composition(s):
- played by the same pianist in the same room on three to five different instruments.
- played by three to five different pianists on the same instrument in the same room
The conclusion will likely be that, while the build and setup of each instrument is a factor and provides the pianists the tools and parameters of what is available to them, the ultimate outcome is the manner in which the pianists utilize the tools and parameters available to them.
I wholeheartedly concur with pianoloverus ...