: Why can any song can be played starting from any note? I'm a complete beginner and trying to understand the basics of music theory these days. I guess I have a good ear and can play most songs by ear on guitar and piano and

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Playing a single pitch has no emotional impact. The way we understand pitch information is not dependent on frequency. A C and an F# sound the same in isolation. However, the CHANGE between two pitches ("interval") translates into something we all attach some feeling/emotion to, and each different interval translates to a different feeling. If you play the same piece of music starting from any given note, all of the interval information is completely unchanged and so we recognize it as the "same".

(Intervals can manifest "horizontally" as the difference between two adjacent pitches in a melody line or "vertically" as the difference between pitches that sound simultaneously within a chord.)

It's kind of like how we only feel changes in speed, but not how fast we're going at any given moment...

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This is because most people have a sense of relative pitch, so as you say, as long as the intervals (tone distances) are kept the same, the piece of music is recognisable.

Think about how we recognise things visually for a moment. You'd recognise a computer mouse, or a car, or an apartment block whether it was to your left or right, or above you or below you, or whether the thing was close to you or far away. That's because you don't recognise it as a fixed image, but a 'pattern' that can always be recognised from the relationships that the parts of that thing have with each other.

So because (as you say) C,D,Eb and E,F#,G represent the same pattern of intervals - a tone step, then a half tone step - most people hear it as recognisably the same tune.

Moving a piece up and down in pitch like this is called transposing.