(So, aside from the fact that one doesn't have to hold the strings down all the way to the fretboard, but rather just enough that they touch the fret, which saves one from having Marianas-sized trenches in one's fingers, which I am the last person in the world to have figured out,) I learned that when I play the piano, I don't perceive a lot of variance in difficulty among any of the chords I might want to play. I hit the keys and the sound comes out. Probably this is partly because I've been playing the piano for fifteen years, but I think it has something to do with the nature of the instrument, too. On the piano, a B Major triad is isomorphic to an A Major triad, right? Same interval vector. You just shift your hand over a little bit without changing its position. "You do too change position." Well, okay, fine, you move your pinkie a little bit north, but the black keys aren't inherently special!1 They're small and black because that's what was convenient for Western tonal music 600 years ago! I'm sure everyone else knew this already, but it's just so interesting to me that we all think of the piano as this entirely compositional-system-agnostic thing, and it just isn't.
On the guitar, a chord change is a linear transformation. (Moving your hand forward or backward a fret, keeping it in the same position, would give you a different interval vector.) Some major triads take more effort than others. In fact, you can hear the tension and strain in my singing voice as I struggle to simultaneously play a B chord that doesn't suck. Luckily, this actually adds to the piece since tension is desirable on the dominant. You just aren't supposed to sound calm and unstrained while singing phrases like, "I love you/It's not just the Prozac talkin'." The chord shouldn't be easy to play, dammit! It all makes sense!
While traditional musical set theory focuses on the makeup of musical objects and describes operations that can be performed on them, transformational theory focuses on the intervals or types of musical motion that can be described between the musical events in real music. According to Lewin's description of this change in emphasis, "[The transformational] attitude does not ask for some observed measure of extension between reified 'points'; rather it asks: 'If I am at s and wish to get to t, what characteristic gesture should I perform in order to arrive there?'"
Hell yeah. When I listen to music, I don't so much hear things immediately identifiable as "melody", "harmony", "arrangement", "instrumentation". I hear changes. I hear spaces between things. We need to read this book.
- Right? They're just more integers, right? I think this was how I slid through the whole second half of Jazz Arranging.