My third semester in the SDSU graduate program in jazz studies is underway. I'm in a grad seminar on jazz theory, in which about ten students and a professor sit around talking about jazz for two and a half hours every Wednesday night. Our current reading material is Dave Liebman's A Chromatic Approach to Jazz Harmony and Melody. It's some heavy stuff.

Every few weeks, students of the seminar are required to submit a journal with thoughts and reactions to the reading, class discussions, and any relevant outside topics on jazz. Here's my first one.

Liebman Reading

"Outside" sounds like the chromatic variations displayed in Liebman's book tend to make more sense when the listener can follow, consciously or not, a context for the new ideas. The main context employed so far is that of superimposition. When the soloist's line follows a predictable path that the listener has experienced elsewhere, but is not necessarily the actual path implied by the song's harmony, then the listener is bound to hear the line as simultaneously foreign and familiar. I'm seeing wider applications for this concept as I consider it. New developments in any kind of art require some foreign element, something that appreciators of the art haven't experienced before. However, to be accepted and understood by audiences, the new art must also have a familiar element, some widely known context or evidence of history and influences. Imagining a listener's first encounter with Charlie Parker, for example, it's clear that an intimacy with blues and swing-era music will increase the listener's appreciation for the new sounds. Similarly, some new developments amount to a juxtaposition of familiar elements, as in the combination of jazz harmony with samba rhythmic textures to form bossa nova. In this case, the foreign element is simply a unique juxtaposition of familiar elements.

Clifford Brown vs. Sonny Rollins

After discussing the differences between Clifford Brown's and Sonny Rollins's solo on "Pent Up House," I realized something about their playing in general that I've felt before but never consciously identified. Clifford seems to have impeccable control over the language of bebop while Sonny's playing represents a more sophisticated application of that language. Clifford's playing focuses on the short-term, with satisfying tension and cadence embedded in his lines. He develops ideas into fascinating variations, but I couldn't trace anything back for more than one or two choruses in this particular solo. Sonny, on the other hand, draws his ideas from a broader time frame, quoting the original melody as well as the last few notes of Clifford's solo. While both players displayed cohesive development throughout their six-chorus solos, I felt like Sonny's was a more complete composition in that every note sounded like it was played with an awareness of its position within the entire recording, not just the preceding few bars.

Tristano's "Turkish Mambo"

We listened to a few Lennie Tristano recordings in class, among them "Turkish Mambo," a layered recording of three repeating patterns and an improvised lead part. The instructor mentioned that the time signature is ambiguous. I heard the piece begin with a steady hi-hat pulse and seven-beat repeating figure on the piano. After this sound had settled, a second riff began. It was difficult to discern in the context of the first, but I eventually heard it repeating every six beats. Since 7 and 6 share no common factors, the beginnings of these two riffs will coincide once every 42 beats (7 * 6 = 42). Then a third layer was introduced, a five-beat repeating riff. It will now take 210 beats (7 * 6 * 5 = 210) for the beginnings of all three riffs to coincide. That's 30 repeats of the seven-note riff, 35 repeats of the six-note riff, and 42 repeats of the five-note riff.

Double Lydian

I learned about the "Double Lydian" concept in a private lesson on 14 Sep 2010. I had previously stumbled upon this concept myself almost three years ago. I had been experimenting with substituting a iiim7 over a Imaj7. Omitting the root of a maj9 arpeggio, you get 3 5 7 9, or 1 b3 5 b7 built on the 3. Given the root's tendency to resolve down to the 7 over a maj7 chord, replacing it with the 9 yields a more stable sound. So I was trying to play over a Cmaj7, for example, as if it were an Em7. Instinctively, I often included the C# in this approach, applying a Dorian sound to the Em7. I made this "mistake" several times, and I actually started getting used to it. I gave the concept considerable thought, found other methods of arriving at the same result, and discovered that it could be taken much further.

My first approach was with Dorian and Lydian scales. I knew that one could use the m7 arpeggio built on the 3 of a maj7 chord or the maj7 arpeggio built on the b3 of a m7 chord to get an upper structure sound. I also knew that Lydian and Dorian are the most consonant scales over static maj7 and m7 harmony, respectively. So I started applying these scales to the elevated arpeggios of a maj7 chord: Dorian on the iiim7, Lydian on the Vmaj7, Dorian on the viim7, etc. This process replaced the root with a b2, then the 5 with a #5, then the 2 with a #2.

My second approach was based on harmony. Conventionally, a maj7 chord extended to its limit is spelled 1 3 5 7 9 #11 13, and that's where it stops. Prompted by the alternating maj7 and m7 arpeggios built on each other's third degree, I realized that this full arpeggio alternated major thirds with minor thirds all the way to the 13. Continuing the pattern would yield a #15 rather than a return to the root, the same replaced note I got from applying Dorian to the iiim7. Extending the pattern yields the same sequence of replacements. I gravitated toward this approach because it gave me a context for introducing the new notes. If I were emphasizing the fundamental chord tones in a given passage, playing the b9 over a maj7 chord wouldn't make any sense. If I were instead emphasizing the upper extensions, the 9, #11, and 13, then the b9 would have a framework for its peculiar sound. I experimented with this and found that it greatly aided my ears in understanding this foreign sound.

A third perspective on this concept, and the means by which it was explained to me in the recent private lesson, is by shifting the root of the Lydian scale to the 5 of a maj7 chord. Applying the Lydian instead of the major scale to a maj7 chord is already shifting its root from the 4 (the diatonic norm) to the 1. Taking this a step further results in a "Double Lydian," a Lydian scale built on the 5, which replaces the root of the chord with a b9. Extending the concept results in all the same replacements as above: "Triple Lydian," a Lydian scale built on the 2, replaces the 5 with a #5; "Quadruple Lydian," a Lydian scale built on the 6, replaces the 2 with a #2.