complicitinitiate
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My piano teacher usually hummed the first few bars of a piece to identify it when the title was not sufficient. When I try to emulate this with a new piece it's much slower to go "note -> D -> D-sound". If it's a piece I've heard before, at some point my head fills in the rest without reading further, and then I only have to verify the score matches the sound in my head. This seems to agree with your hypothesis.
Top-down notation reminds me of vertical scrolling rhythm games like DDR and also Synthesia (though I have no experience with Synthesia specifically). My difficulties in learning to read piano sheet music... (read more)
A - I also use scale degrees for this. I'm not fast enough to sight-read and transpose at the same, but I sometimes switch to intervals when transposing a single melody line. Most of my experience transposing and playing comes from trying to play songs on Bb trumpet written for concert pitch. I had some note-to-note mappings memorized from frequent use, but not anymore.
B - Definitely plausible to me. Something along the lines of "when all you have is a hammer" and certain modes of thinking being more useful than others for certain skills. I don't have any particular examples, but I think in math there are quite a few abstractions / extensions of lower level concepts that are a lot more 'natural' if you think about them in a certain way.
C - Can't think of any.
D - Agree with Anomylous on this one.