[Reveling John]

Oh my.. 4 hours later I'm waking up with some crazy notions...

Does anyone know anything about performing mathematical functions in base-12? I know only that it is possible, but I don't know where to start.

The reason I ask is that I think alot of these numbers we are discussing and more importantly the relationships between the numbers may be better understood in a base-12 numbering system. I'm not even sure what the notation for such a system would look like. Probably could not use the symbols 0,1,2,3...9..... that would be very confusing. For example, in hexadecimal the symbol '10' represents a quantity of 16. So if we're going to go down this rabbit hole lets spare ourselves from '10' means 12. Maybe we can use letters as digits?

Another thing is that what I said before has apparently been rattling around my brain during sleep because I woke up thinking about the way that we traditionally measure waves and determine their value. First, let me clarify that language. When we "measure" a phenomena in order to "determine it's value" we are actually filtering out all but a few pieces of information about the experience and using that little bit of information to construct a general description of the entire experience as well as to predict the quality of future experiences base on that "measurement". In the case of sound waves, we are measuring the rate of change of the most dominant trend in that wave and using that rate to describe the audible experience of the wave as well as making the prediction that if we reproduce the same rate of change in the form of another wave we will have the same experience. So if a wave form that someone calls "C" can be described as consisting of a rate of change of 144 cycles per second, the next wave that I synthesize with a rate of 144hz should reproduce the audible quality of "C".

Here's the interesting thing about that. If I produce a wave of 144hz using a guitar electrically connected to an amp as my oscillating mechanism, my "C" will sound a certain way. If I take this exact same guitar and use all of the exact same circumstance to produce this wave EXCEPT for one change---I'm going to turn my "Distortion" knob all the way up---the result is an experience that, while I might call it "C" and it may have a lot of similarities to that first experience, will also be qualitatively different; possibly completely different, depending on the type of "distortion" I am using (I put distortion in quotes because it's a very loaded term--not too accurate in terms of what it is actually doing to the wave form). Another example is an organ. In a pipe organ, one note is represented by a chorus of pitches, which means that instead of there being this theoretical ratio of 1:1 between note and pitch, there is a ratio of 1:3 or 1:8 or even more. Therefore the note is no longer describing the experience of a single pitch, but is actually describing the experience of the relationships between multiple pitches. On such an organ, the pitches can be configured in such a way that hitting "C" on the keyboard produces a complex wave form that is much closer to "G" in it's qualitative experience than it is to "C" as we experienced it in my original guitar example.

And here's the kicker: All audible waves are a chorus of pitches. The reason the first guitar example sounds different from the second guitar example is that the wave that is produced in the former is composed of a certain combination of pitches which are quantitatively (measurably) different from the pitches that make up the wave that is produced in the latter. So in order to descriptively distinguish the "C" experience of the first setup from the "C" experience of the second I would need substantially more information than the frequency of oscillation of the most dominant trend in each of those waves. In fact the more information I had about each of the many pitches that are cooperating in the production of these waves, the more accurate my mathmatical/scientific description will be. Also, the more accurate my powers of prediction will be, allowing me to synthesize approximations of this wave that are qualitatively closer and closer to the actual experience of the wave.

Now I will sum up my rant:

Waves cannot be described simply by measuring the oscillation of their fundamental tone. Waves are multi-dimensional phenomena and every dimension is active in determining the experience of the wave. Human systems of harmony are based on the assumption that one can isolate elements of a wave, and these systems are constructed from the properties of these isolated elements. However, these elements cannot actually be isolated in the human experience of the wave. In the experience, all elements are integrated at all moments in time.

What does this mean? There are ways of measuring and studying waves that acoustic physicists use which take into account every thing I've discussed so far. Actually any scientist who studies any naturally occurring wave form, be it sound or light or radio or cosmic rays, takes into account this integrative property to waves and is working with a lot of very sophisticated mathematical models. Unfortunately the people who make art, which would be people who use waves (as in light, sound, language, movement) as a means of modeling/redesigning culture and cultural artifacts, by and large do not have very integrative mathematical models to work from, although this is changing rapidly. So instead, through out the centuries and eons they have used the most accurate system of measurement that was available--- the actual experience--- which each individual artist calls on to construct intuitive models of these experiences. These intuitive models serve as both a method of describing the phenomena and also as a method of perfecting the synthesis of subsequent phenomena through the refinement of prediction. I, as an artist have just begun to peek into the world of mathematical modeling through the exploration of electronic music, and I believe that in order to use all of these waves in the most effective ways, I need to understand both an intuitive model that is integrative and a mathematical model that is integrative. Indeed, the more the refined the mathematical model becomes the closer it gets to mirroring the intuitive model. Computer music is a great example of something that began as an instance of computers doing very advanced logical modeling of waves and being redirected by a human user that is working off a set of intuitively produced assumptions, which has gradually become an instance of human beings sharing responsibility for the decision-making process of creative direction with the computers (.i.e. GarageBand will ensure that all of my loops are in the same key and mode if I allow it to, which limits what I can play, but also allows me to play pieces that are more sophisticated than what I would be capable of producing without the assistance of GarageBand).

This is not about music or even sound. This is about all waves and all wave-related phenomena. In order to move further in to the exciting realm of wave surfing, the artist needs to become a scientist, and the scientist needs to become an artist. How each of us do that is certainly not clear to me, but I think forums like this are part of that journey.

Also I believe this is deeply related with the process of Ascension. I don't how to characterize that relationship, but I "intuitively" know that there is something to that.