Thoughts In Closing

A final thought as I close out the blog entries that I feel is relevant to the reading and to my thoughts as of late involves the shape of music through time. If we can imagine space as static in each moment in time, and time as an extra kind of space in which normal space resides, then perhaps there are shapes and patterns within spacetime itself that are analogous to what we can visualize in normal 3-dimensional space. The easiest is to imagine time as linear, and so if we could see all of time at once (which in itself carries all kinds of paradoxes), our lives would appear as long, undulating snakes (for those that have read Slaughterhouse Five by Kurt Vonnegut, think Tralfamadorians). What would a shape or regularity in a 4-dimensional world look like? My thought is that things that are static within time itself must create a pattern since the same is true for that which is static in 3-space. As an example, human habits and routines would trace out magnificent patterns through time since there would be an element of repetition in those patterns. Most people wake in the morning and head to the bathroom to shower, and so that would be a recurrence in this 4-dimensional world.

It seems to me that the human mind is geared toward symmetry, regularity, and patterns. Music is rich in such traits. When you listen to a song with a steady beat, that beat is somewhat constant in time. It is recursive and so it has a strong sense of regularity which we tend to latch on to. Recorded music, then, no matter how random it was at the time of recording, will also trace out a pattern since it will have the same structure each time it is played. So where does improv fit into all of this? Improvised music, when not recorded but played only once, seems to break the mold. It becomes a one-of-a-kind artifact in spacetime, an oddity if you will, to be treasured in the present and to never recur again in the same form. Perhaps this is why we are so interested in it and some people abhor it. On the one hand, we can appreciate the fact that it is not recursive and so is something new and fresh from the regularity that we enjoy. However, for those that prefer regularity too much, those that will play a score note for note as it is written without any deviation from the sheet music, we can see why improvisation can be terrifying since it is reaching out into new territory that will only be seen once and then never seen again. From my experience in this class, from playing and reading, I feel as though I can embrace the abnormality of improvisation in the music world for it offers plenty of new ground to be covered and explored.

Maximal Chaos and Complexity Measures

I was glad to see that my analogy between musical "spaces" and abstract mathematical spaces made it into the discussion in Chapter 4 which I just finished reading. Apparently I was one step ahead of the game.

An interesting notion in the reading that paralleled my current research in my Complex Analysis class involved the "complexity measure." In trying to quantify the amount of complexity in an improvised piece one may choose to analyze many different features or even the piece as a whole to see what elements change the song as a whole. In much the same way, I am currently working with a couple fellow students to identify what causes maximal chaos in a complex system.

Borgo makes the point that throughout the course of an improvised piece, if the performers choose to branch into unfamiliar playing styles or note sequences, the listeners may become uncomfortable or feel distant to the music being played. With increasing amounts of chaos in the music, this could spell trouble for the performer-audience relationship. Likewise, when creating music with The John Fox Company, one of the things we have explicitly tried to avoid while performing music is an extreme amount of chaos. The nature of the music is already unconventional as it is, with the conglomeration of odd sounds being layered on top of each other in a sea of electronic chaos. Too many strange sounds on top of each other may begin to sound like a drone or may become unintelligible, and the surprises we are able to create in the music become drowned out and thus the musical experience is less effective.

In the mathematical research in complex analysis, we take a similar approach to the problem of achieving maximal chaos. Without going into too much detail, we have essentially picked specific families of functions that are generalized and we can easily study the behavior of under iteration, and we play with different methods of iteration in order to produce the most "picture" which translates into maximal chaos. The more stuff going on in our graph, the more chaos is present. By restricting ourselves to such familiar functions, we are doing what many improvisers do in their music; that is, the improviser of music will choose phrases wisely or stick to a particular chord progression in order to maintain the element of surprise as well as the audience's attention. The element of familiarity avoids alienating the audience, in much the same way that well-understood functions give us a starting point in research and allow us to draw sensible conclusions rather than give us information that could be interpreted many ways if we are not familiar with the dynamics of the functions.

Uh oh.

Thus far in the class I have felt fairly comfortable with my performances in front of everyone else when improvising. Whether it was on trumpet or guitar I feel as though I've been able to explore different sounds and techniques comfortably and I never really felt threatened by the audience as everyone was equally understanding and in the same boat as I was. However, the tables were certainly turned during the performance the day before Symposium. I went into the performance just as though it were only my classmates before me in the audience so that some of the pressure was off. The activity with the class as a whole, both in the opening song and the end, I felt went very well and I played through that just as though I was not being judged by people who had not heard our work before. The part that became shaky and really tested my ability to improvise was when the John Fox Company had to perform.

We decided the week before to just go into it without any plan other than the theme of the song was "the crazy bus" which is a theme we had used in class before. Other than that, we were free to do what we wanted and we wished to rely on the moment itself rather than have more plans and structure. We were all definitely on board with the idea, and so we hooked our instruments up and got ready to play. After we had played, we noticed one of the cables for the guitar was loose, and so I was unable to contribute anything on the guitar to the song which made me really nervous at the time because I was only prepared to do guitar work since that's what I had done all along. Nate was familiar with the Kaoss pad and keyboard, and Ben had a good handle on the microphone and loop pedal. It was when I was unable to make any noise with the guitar that I knew the true test was there. This was perhaps the most nerve-wracking and yet educational experience in terms of improvisation. I had always relied on my equipment working and so never gave a thought as to what I would do should it fail. The true improvisation came out when I realized my safety plan was gone; I was in front of an audience of people eager to hear what we were about to do and I had no back up plans. I think we made a good recovery though, as Nate manned the Kaoss pad, Ben on the loop pedal and vocals, and I played around with the keyboard. I have no idea how to work a piano other than play the James Bond theme and Funky Town, so I felt like I had to finally step up to the plate and let loose on it. While the song didn't progress as I had expected based on our past performances for the class, I feel as though we truly improvised, more so than before given the circumstances of the situation, and I think that outcome is even better than going in with a plan and following it. That's when I truly felt the urgency, if I can call it that, of the improvisation in the moment. I'm glad it worked out that way.

Abstract Spaces and Their Superposition on Physical Reality

An interesting point was made in the reading that I thought was worth discussing here. Borgo mentions the habit that people have of using sensory verbs out of context; for example, "I see what you mean," or "can you shed some light on this subject for me." Such uses of the words or phrases are not coincidental to me. My understanding of consciousness and its ties with physical reality (whatever that means) is that though the two cannot be separated, it seems to me that there are things outside of a conscious mind (physical objects, for example) that are observed by the senses of a sentient being and there are symbols in the mind (not letters, or even real objects, but merely something that happens in the brain when a word is said, or an action is perceived) that are slowly built up and interconnected in such a way that rational thought is then possible by the "communication" between such symbols.

It is sensible then that we should describe ways of understanding things with verbs associated with the senses, since our senses are our source of input, our way of connecting with external stimuli. What we typically refer to is our actions within space and time. However, when we start using sensory terminology within music, we are not particularly using our senses in the same manner as with physical space. Rather, we are giving this "musical space" properties of its own. The sound we perceive begins to take on texture, volume has its highs and lows, and note duration is discrete or continuous.

Though this is not a physical space in terms of space and time, it is nonetheless visible in our minds and we should thus be unafraid to explore it in its entirety. Perhaps it is infinite, or perhaps there are boundaries, but surely we have a long way to go before we find them, for music is continuously evolving and taking on new sounds everyday. I think writing a piece of music can be likened to charting a map, and each detailed note implies a more specific route in our musical space. Improvisation, then, is a highly exploratory method of traversing this space. It's as though you're flown to this magical land, dropped off, and told to have fun. Of course, the route is not fixed, and every spot is accessible in one way or another by any given location.

While this space seems abstract, it is not unlike an abstract mathematical space such as a Hilbert space. We can operate on it in numerous ways and we can chart particular shapes or patterns by well-defined rules. We can even create abstract objects that accurately describe physical phenomena, all by using abstractions that originate in the mind. In a similar fashion, we can create musical objects and patterns in our musical space that correspond to triggered thoughts of physical reality or even emotions which elicit physical reactions in our bodies. In this sense the musical space and physical reality are interconnected by means of the mind, in the same way mathematical spaces are attached to physical realities.

This analogy is important, in my opinion, because much in the same way we can predict physical phenomena through mathematical reasoning, we should be able to chart new territory in a musical space that is capable of manipulating thoughts and emotions in new ways. I also think that perhaps the collective consciousness of a group of improvising performers is due to exploring the same local regions of musical space and perhaps even traveling together through the space, which establishes a connection between two or more different conscious minds.

I Am Certain That I Am Uncertain

Can we be certain there is uncertainty in music? We sure can. When you hear a song on the radio, typically it is of the teleological variety; that is, you can identify the hook of the song, and maybe even predict some of the tried-and-true chord changes. The moments where a feeling of suspense is building in the music only to be followed by a release is all too familiar to anyone that has experienced music. But what happens when you lose that sense of direction in the music, that orientation that is so easily achieved in teleological music?

Improvisation is a credible answer in this particular case, and it seems to fly in the face of the world we know of music. Prior to experiencing improvised music in depth, music to me has always seemed to fit into that teleological category, though I never identified it as such. It was just something I inherently knew. I knew that although a storm was brewing on the horizon of a musical composition, there would be a hint of sunshine just beyond, a place where I would be safe among the sound so to speak. After exposure to truly improvised music, all bets were off. No longer did I "know" that there was a safe haven; now I have to be prepared for anything, to become an active listener and participant in the music around me.

In a way I feel as though this uncertainty is not unlike that which came packaged up with new physical laws introduced by quantum mechanics (which, coincidentally, features its own "Uncertainty Principle"). The world prior to Einstein and Heisenberg was merely a world of Laplacian determinism, a place where if you knew one state of the universe at a particular time, you could in theory predict what would happen some arbitrary time later. There was a logical progression from physical frame to physical frame, and time flowed on in the process. But what experimentation has shown (and the mathematical formalism to back it up) is that we cannot possibly know with exactitude all properties of a system simultaneously. There is a degree of uncertainty based on how precise we wish to focus on one part.

Music, too, has this inbuilt uncertainty when a performer (or performers) picks up their instrument and begins to improvise a piece of music. No longer can the audience say "here is where I am, so this is where we must be going," but instead, they must be satisfied with "here I am, but what does that mean for the rest of the piece?" There is just no saying where a piece could go, how the dynamics will change, what the volume might do a few seconds from now. It is this inherent uncertainty that allows everyone to engage in the music at the moment and forget about the orientation in time. The music doesn't have a definite shape at a later time, for it can only progress through the "now." This spontaneity I think is what gives improvisation its alluring properties, and in my opinion, the same can be said about the dynamics of our own universe.

The John Fox Company

Although I particularly enjoyed the music that arose from the various experimentations in my previous group, I decided to try something a little different by teaming up with Nate and Ben to produce some more experimental music via The John Fox Company (a rather peculiar nomenclature). As we demonstrated for the class, our music is reliant on electronic devices to aid us in the texturing of the soundscape. Of paramount importance is the looping system we are continually updating each week, where we shift around the roles of instrumentation and electronics operator, but the goal is the same - to dynamically generate themes out of layered sounds.

The looping capability allows us to begin with an idea, set it "in stone," and then explore new ideas that relate to previous ideas. In a sense, we are going on a random walk but we have a concrete memory of where we've been. Each new idea, each sequence of sounds, is imprinted in the music, and the sound as a whole begins to grow. Again, order from chaos is created. Each random tidbit of sound is superimposed on all previous random sounds to create a super-structure that exhibits order. Each individual thought, when separated from this continuous stream of music into discrete bits, seems to have no apparent meaning when isolated.

Another thing that is worth noting is that we have also been testing the boundaries of improvisation in a subtle way. When we sit down and perform a song outside of class, we typically generate a theme from that particular session. Once we have a theme, we consider it another song that we have, as though we could simply write it down and have it forever. Instead, after randomly creating a song by pure improvisation, a theme surfaces, which we then extract and say "That's a new song. Let's call it ____." However, when we perform that song again, we are merely picking the theme as a starting point, and not playing the song exactly as it was first performed. We still improvise, but we stick to the theme that initially emerged. So far we have produced some interesting and fun pieces, and we continue to shuffle around the equipment that we employ, so I think we are headed in a good direction as a group.

The complex plane is your audience.

After reading the first couple chapters of Sync or Swarm, I'm beginning to view improvisation a little differently. The first couple times we played music in class I was nervous about playing out and expressing myself through the music. I'm beginning to become more comfortable with playing and throwing ideas out there even if they're not what I envisioned at that moment. Either I am becoming comfortable with the styles of the people I'm playing with, or I am coming to accept that music doesn't have to be as rigid as a composed piece, that I can take it where I want and it is still music. Though it is probably a mixture of both, I feel that I am gaining a stronger sense of a group dynamic when playing because though my individual contributions at first seem spontaneous and unplanned, I am becoming more aware that I am constantly listening to what everyone else is doing in the moment and continually creating phrases in my head that seem to match the current dynamic.

This is where I feel the connection to the complex analysis course I am taking is strongest and is why I think it's a truly valid connection because it seems so coincidental. Here are these individuals, these points in the complex plane, creating music with their instruments, applying these functions over and over, taking feedback from the initial function and reentering it to create at first seemingly random behavior on the point level, the level of each individual playing. But when viewed from above at the planar level, the level of the audience, there is a boundary created, within which beautiful patterns can arise, much in the same way a song, and with it emotions elicited from the audience, can spring up from seemingly random contributions from each individual member.

It really makes me wonder what sorts of order will arise from apparent disorder. More to come on that later.