Last summer, I wrote a few jazz tunes with the intention of building my portfolio from which to choose original pieces for my upcoming graduate recital (finally happening, this coming Sunday). "Junior Rounding Third" and "The Original Deluxe Aggravation" were two resulting pieces of this process. Neither of those made it into the final set list for the recital, but another from that summer did. I waited to post it because it went through a few revisions.
It's called "The Kármán Line." I began with the specific intention to use a harmonic concept I discovered a few years ago. I wrote about it in 2008: Beyond Conventional Extensions. I think of it as taking Lydian and Dorian sounds beyond the 13th extension, continuing the pattern of alternating major and minor thirds established up to that point. Over a maj7 chord: 1 3 5 7 9 #11 13 #15 17 #19 etc. Over a m7 chord: 1 b3 5 b7 9 11 13 15 17 19 etc. You end up introducing the b9, #5, #9 over Lydian harmony, and the 3, 7, #11 over Dorian harmony. The melody of this tune sits right on the edge of the traditional Lydian/Dorian sounds and those extended extensions.
One of my professors articulates the same sounds with the concept of "Double Lydian," in which you play the Lydian scale a perfect fourth below the root. (Triple, Quadruple, and Quintuple Lydian are also possible by moving the root down in successive perfect fourths.) He doesn't like the results over Dorian, as the major third is introduced too quickly and clashes with the minor third. I dig it though.
As for the title, I found it by Googling myself. The first result is usually the Wikipedia page for Joseph Albert Walker, American test pilot and astronaut. From reading about him, I learned about the Kármán line, which defines the boundary between the Earth's atmosphere and outer space at 100km above sea level. It is the point at which air becomes so thin that an aircraft must exceed orbital velocity (the speed required for a spacecraft to remain in orbit) in order to maintain lift. Pilot Joe Walker made two spaceplane flights past this threshold in 1963, the only such flights ever made until 2004. He died in 1966 during a formation flight for a publicity photo.
“The Kármán Line” is about what it might be like to drift beyond that line and back (sans roaring engines).