Radley Balko links to an article at Slate explaining the maddening trade-offs involved in tuning keyboard and fretted instruments. I was blissfully unaware of the concept of musical temperament and just assumed that musical notes were perfectly laid out in simple, integral frequency ratios. Thanks, Balko, for making me feel even stupider about music theory.
My introduction to playing music was on a trumpet in the sixth grade, which meant I had a very narrow perspective: one note at a time. I could hear when I didn't harmonize with another person's instrument, but that was either a matter of tuning, or a simple result of someone playing the wrong note. Not until high school did the band directors even attempt a cursory sketch of music theory: major, minor, and perfect intervals. Otherwise, it was just rote learning. Play what's on the page.*
Being a math geek, it always bothered me that the notes on a major scale were not symmetrical, making each letter two semitones apart--the reason there isn't a black key between every white key on a piano. Why not use a hexatonic, or whole tone scale, so an octave involved six notes instead of the seven notes in a diatonic scale? Put a black key between each white key and adjust accordingly. A C-major scale would no longer be void of accidentals, but wouldn't that force neophyte musicians to grasp just exactly how a major interval differs from a perfect interval? Alas, the symmetry of such a scale was swapped out for the concept of the tonic. Having done most of my playing on a one-note horn, and never having been taught improvisation, I still only have a fuzzy grasp of harmonics. The idea of connecting that to what's on sheet music and what's on a piano or guitar comes as naturally to me as playing Boggle in Spanish. I have a rookie-level ability to pronounce printed words (I have to look up how to pronounce words like "ciudad") and would be an abysmal failure at writing down words I know by ear ("quatro" vs. "cuatro").
Another mystery to me was the "Every Good Boy Does Fine" vs. "Good Boys Do Fine Always" discrepancy (treble clef versus bass clef). It didn't matter to me when I stuck to one instrument. But after a few lessons on the classical guitar (which was already rough going), I was asked to take lessons on the electric bass guitar to replace another student (Chris W.**) in the jazz band, because he was moving. If I recall correctly, his family had a change of plans so he quickly returned and I was spared the agony of compounding two unfamiliar tasks--playing a string instrument and reading bass clef. Unfortunately, it also meant I never resumed the classical guitar lessons.
* On my list of most embarrassing moments is the time I was hired at age 17 to be part of a trumpet trio playing Christmas music in front of a large congregation. At the last minute, we were told to transpose to another key to make it easier for the pianist. The other two more experienced players said "no problem" but I managed to inject a plethora of sour notes. "A little bit of humiliation goes a long way."
**My Best Man at my wedding, Carlos, played with Chris in a band, doing gigs for high school parties. They were often arguing over what songs to play. As a bassist, Chris was always wanting to play Rush songs, which are heavy on Geddy Lee's bass playing. Chris was most famous in the high school band for keeping a book of quotes of our band director's humorous impromptu aphorisms. After it became well-known, Mr. M. would add, "Put that in your little book, Mr. W!" afterwards.