Proportions of a song

Take it out of context and it still has its shape

(as it plays in your head) like a square is a square whether it's a ten foot square of concrete or a square on a checkerboard. A sphere can be a marble or the earth.

A sphere is not "a sphere in comparison to a square."

A square does not need a contrasting circle to be a square.

Dimensions are needed for physical objects. But in your head, dimensions are only relevant if you're comparing an object to something else. But what is certain is proportion. Proportion is what identifies a sphere or a square, or... a melody.

So it is I can have a song in my head, a song which somebody else composed and which I know well. I savor a rather accurate representation of the song, only to find, when I open my vocal chords with the intention to hum along, that the song in my head is in no key. It's free as an untethered bird in my head. I can chase it all around the circle of fifths, and it's not attached anywhere! Even the voices in the song retain their respective qualities, without being attached to a particular key, which would be impossible in the physical world. If I try to hum along out loud, I may find the song is, in dimensional terms, very low, or very high. But as long as I don't try and match the song with my voice, there is no low or high in untethered head-music, except within the song.

Thus I love roman-numerals in music theory rather than specific keys. I'm thinking people with perfect pitch would not be able to relate to the above, because as I understand it, the notes in their head correlate to real life pitches.