Take a binary array of length N, where N is in the hundreds to thousands range. Choose 2% of the bits to set to 1. Now you have a "sparse array".
Now, you want to use this sparse array to represent a note in a song. So you need every note to consistently map to a distinct* sparse array.
However, you also want to be able distinguish a note as being in one song or another. The representation should tell you not only that this is note A but note A in song X.
How might you do that? Well some portion of the ON bits could be held consistent for every A note and some could be used to represent specific contexts.
Stable and variable bits of you will.
Now if you look at two representations of the note A from two songs you'll see they're different. How different are they? Well you could just count the bits they have in common or not, or you can treat them as vectors. (Lines in high dimensional space) Then you can calculate the angle between those two lines. As that angle increases its easier to distinguish the two lines. They won't ever get to full "right angles" between them because of the shared stable bits, but they can be more or less orthogonal.
That's what's happening here. The brain is encoding notes in a way that it can both recognize A, but also recall it in different contexts.
*But not perfectly consistent, we use sparse representations because the brain is noisy and it's more energy efficient. Pretty close is good enough in the brain and you can encode a lot of values in 1000 choose 20 options.
It would make an interesting essay or monograph to descrbibe the various similes and metaphors that people have variously used to describe the working of the human mind. Descartes, I believe, thought the brain worked via a series of hydraulics, and the Victorians thought that it worked by some variant of electricity, both of these being "new" and possibly exciting technologies for their times. Notwithstanding the scientific versimillitude of these previous theories, it seems only fitting that computers occupy that role today.
Now, you want to use this sparse array to represent a note in a song. So you need every note to consistently map to a distinct* sparse array.
However, you also want to be able distinguish a note as being in one song or another. The representation should tell you not only that this is note A but note A in song X.
How might you do that? Well some portion of the ON bits could be held consistent for every A note and some could be used to represent specific contexts.
Stable and variable bits of you will.
Now if you look at two representations of the note A from two songs you'll see they're different. How different are they? Well you could just count the bits they have in common or not, or you can treat them as vectors. (Lines in high dimensional space) Then you can calculate the angle between those two lines. As that angle increases its easier to distinguish the two lines. They won't ever get to full "right angles" between them because of the shared stable bits, but they can be more or less orthogonal.
That's what's happening here. The brain is encoding notes in a way that it can both recognize A, but also recall it in different contexts.
*But not perfectly consistent, we use sparse representations because the brain is noisy and it's more energy efficient. Pretty close is good enough in the brain and you can encode a lot of values in 1000 choose 20 options.