(Note: this is a work in progress...keeping it public to motivate me to finish it!)
When I first started studying classical music, there was a period in time when I got pretty obscessed with phasing, largely influenced from the early musics of Steve Reich. Over the course of several years I analyzed and practiced the process of musical phasing to the point where it could be explained and executed fairly succinctly. I felt this process of simplification was necessary in order for the technique to be used within an improvisatory context, since trying to perform Violin Phase or Piano Phase in whole proved to be quite a challenge. Phasing on simplified 1-3 note patterns made learning the technique much easier and much more pleasurable to learn, and I've used it as the model in which I teach this technique to other people.
For a while (maybe even now?) I was known as the "phasing guy" since I would pretty much try to "phase" with most people I improvised with. The nice thing about the technique was that since it was an auditory phenomenon rather than a type of stylistic practice, I was able to teach and perform the exercise to people outside of the classical music realm. I've also used the technique pretty extensively even in my own piano solo performances as well -- phasing between the right and left hands work pretty well, for the most part.
It may at first be helpful to listen to the two pieces to get an idea what the effect sounds like:
In both works, 12-beat patterns are used as its original material, which is then "phased" through the act of speeding up one pattern while the other pattern holds still. Phasing requires at least two voices, which requires either two instrumentalists or a polyphonic instrument of some sort that would allow for a right/left split between the two hands. (Which usually means a keyboard of some sort -- octave splits provide a pretty good approximation of phasing between unison patterns.)
The basic idea behind phasing is that there are two (or more) performers playing the same thing, which is then phased by having one of the performers "pull ahead" of the group by slightly increasing their tempo. The resultant effect is that, depending on the type of patterns you use, you get new harmonic and rhythmic combinations out of the process despite originating with identical types of material.
So, phasing with 1, 2, and 3 notes:
On an audible level, phasing on 1 note may sound fairly tedious and unremarkable, but it's useful in that it highlights what's exactly happening between the two patterns. One person (or one hand) plays one note over and over at a steady tempo, then the second person joins in. As one person begins to "pull ahead" of the other, then the notes start to go out of sync with eachother. There may be moments where the feeling is that the two patterns are in syncopation with one another, and this is normal. What the phasing process does, on its most basic level, is create a microscopic sycopation between the two patterns, which then resolves back into playing together back in tempo. An example:
[recording example -- will get on this]
Granted it's not the most exciting thing in the world to listen to, but this exercise tends to be immensely helpful for musicians -- it demystifies the technique to an understandable level, while at the same time giving the ear something to latch onto as the process unfolds.
Phasing with two notes is just like phasing with one note, only that there's two notes instead of one...well, OK, that's stating the obvious. The thing to listen for in this exercise is the new pattern combination that emerges out of the phasing process. As with the 1-note example, the first person chooses a 2-note pattern which is then replicated by the second, which is then "phased" by the process of one person speeding up slightly.
The difference here is that because there are two notes, the new pattern combination that emerges from the process will produce new harmonic combinations that becomes immediately audible to the ear. Probably better to listen to the recording than a long-winded explaination:
[recording example -- will get on this]
So, it starts on the 1)unison pattern which then moves to the 2)second pattern that comes out of the phasing process, then back to 1)unison. Still sounds very clinical and mechanical, but as with a lot of fundamentals, that's just how it goes.
Patterns with three notes and above start to become more interesting to listen to, since the process begins to form into a progression. For 3-note patterns, there will be the 1)unison, 2)second pattern, 3)third pattern, then back to the 1)unison again.
[example 3 -- coming soon!]
Phasing can be a somewhat of a bewildering experience, since it tends to go against most of our intuitions about how rhythm and repetition works. I've heard people equate it to auditory hallucinations, since it "produces" notes and rhythms that previously didn't exist. The trick is not to let the disorientation get to you and just allow for the patterns to naturally phase in and out. At times you may end up skipping a pattern or 2 or lose track of where you might be, but that is OK -- the main goal is to acquire the feeling of what it feels like to depart and lock back into different types of pattern combinations.
Once you get the hang of the technique it sort of becomes like riding a bike -- you never really forget how it "feels" to phase from that point on. After three notes and onward there is no significant difference in how the technique is applied, other than the fact that the patterns are longer and have more generative pattern combinations. So if you can master phasing between 1-3 notes, you've pretty much got it under your belt.
Using Phasing in a Musical Context
Of course, after getting through all of the technical stuff there's a time when you just have to make music! An older recording of the A-Tribute Ensemble's "Phasing Out":