gregorio
Headphoneus Supremus
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Now you have called the perception of two pitches "imaginary". I would like to clarify. To me imaginary means I'm hallucinating. I think we need to acknowledge that our perception of two pitches is correlated to the real-world sound. You have also used the word "abstract" which I think is more accurate-- an abstraction refers to a concept that lumps together a lot of detail/variation into a single concept.
We are getting into semantics here. The perception of the two pitches is abstractly correlated to two of the frequencies but we don't hear two pitches, we hear two piano notes. From the maybe 30 or more (I'm plucking a figure off the top of my head, there maybe considerably more) different frequencies created by the vibrating strings in the piano, our brain has selected two to perceive as the pitch of our notes and then has used the remaining frequencies to create the timbre of the notes.
If we listen to a sine wave at 440Hz we hear a pure pitch which we could call an A, if we play that same sine wave but surrounded by other sine waves of the correct amplitudes and frequencies we could now perceive that same sine wave as part of the timbre of one of the lower surrounding sine waves, say the one at 220Hz. In other words, that identical 440Hz sine wave could be used as part of the brain's construction of a completely unrelated piano note. The reality is, nothing about that original 440Hz sine wave has changed, what has changed is our perception of it, an aural illusion if you will. Now, do we say the note is abstract, because some constituent part of it is abstractly related to parts of the resultant frequency spectrum or do we say it is imaginary because the entire construct which we call a "note" doesn't exist in reality, only in an illusory perception?
Don't forget, I've simplified here, the reality is that the brain has not constructed these piano notes directly from the sound waves created by the strings inside the piano but from their reflections from the piano lid and the acoustic environment. A piano in an anechoic chamber without a lid sounds very strange indeed and many would not recognise it.
Another thing I think we should acknowledge--
We hear two pitches, right?
A member of a western audience or a western trained musician would, but others may not. A highly trained mastering engineer would probably be able to focus into some of the more prominent individual harmonics and also be able to identify other constituents of the sound such as reflections, etc.
Well the sound may be very complex, but think about what's happening in the physical world-- we struck two keys on the piano, and two sets of strings (each set being nearly identically tuned) are vibrating.
So our perception is correlated with the real world in that sense.We hear two things, and two keys were struck.
So when our brains "make sense" of that complex wash of sound, they come up with a perception that has elements which exactly matches the real world.
That is because we have manipulated the real world to fit our perception. The piano isn't an item which existed and then one day someone decided to use it as a musical instrument, it was designed from scratch as a musical instrument. The fact is, when we hit a piano key a number of strings will vibrate, both those actually hit by the hammers and those producing sympathetic vibrations. Having separate keys for all the strings which vibrate would make a piano virtually impossible to play, so the piano's mechanism has been designed for one key = one note.
G