Musical Idea 1: Manageably Imaginably Multidimensionality

10.03.2013 § 2 Comments

Let’s take a tour of a multidimensionally musical world!

Before we embark on such a tour of such a world, though, let’s be clear about what a musical dimension actually is. As with the purely mathematical type, musical dimensions can be linear (conventional, with two opposite and infinite directions), rays (with one finite direction), segments (with two finite directions), or even loops; they can also be either continuous or quantized. As for the musical aspects that distinguish this type of dimension by varying along them, they could certainly be basic parameters of sound: tempo, pitch, envelope (ADSR), reverberation time, etc., but they could also be more advanced musical properties like tuning, syncopation, articulation, etc.

This world boasts enough musical dimensions to qualify as ‘multi-‘, but not so many of them that it’s essentially beyond dimensionality: attempt to explore too many dimensions at once, that is, and no intelligence (comparable to that of a man like us, anyway) could manage to imagine the musical tour as anything but noise. Too few dimensions, however, and the artistic potential of touring that world would be nullified, ‘cuz one can’t convey a lot with a little if there’s not a lot (litmus test is: if you can map the tour effectively on a 2D sheet of paper, your world’s probably too basic to consider multidimensional).

Even if the world has just the right amount of dimensions, us tourists might never realize it is dimensional at all if our tour is not guided well. This is the key point of multidimensional music: we already know that maps won’t help us in this place, but we oughn’t be handed n-spherical globes or anything at the gates either; we ought to enter blindly and be made able to stretch our mind across its space using only its sounds as our guide. Tremendous beauty and enjoyment are to be found in this exercise. Geometry is often dazzlingly visualized, but not so often is auralized.

Here’re some examples of how a multidimensionally musical tour could fail: if every time we moved a certain direction in dimension X we also moved the same certain direction in dimension Y, why, we’d never be given a chance to recognize X and Y as separate dimensions. Or, on the other hand, if movements in two dimensions were never once related, they couldn’t engender experiences of multidimensionality, since they’d just feel utterly unrelated. A tutorial tour might simulate a one-speed spaceship gliding forward, changing its direction but always gradually, by keeping the total speed along all dimensions constant and compensating for any decrease along one dimension with corresponding total increase along the others; this would easily allow us to glean the orthogonality of the musical aspects. Dimensions must be both individually illuminated and revealed to be connected for us to ascertain them as such.

Put another way, musical multidimensionality is the idea that one can pattern the changes that otherwise unrelated musical aspects go through in a way that suggests they are in fact related, their continua like dimensions in a mathematical space and the listener riding a graph plotted through it or watching it rotate around her. And the critical thing is that these changes need to be patterned in a particular way as to suggest this spatial relationship: on one hand, you can’t simply twiddle with a bunch of knobs chaotically and expect listeners to hear it as, like, Brownian motion; and on the other (much more subtle) hand, you also can’t simply change two aspects at the same time and expect listeners to conclude that their simultaneity is a result of multidimensionally.

This latter counterexample calls for further clarification. So suppose you moved a couple sliders (controlling unrelated musical aspects) up and down in sine and cosine waves — you can’t expect your listeners to hear the circular relation between these two aspects. Sure, that pattern of operating sliders would draw a circle if you plotted the result on a visual plane, but I can’t stress enough how important it is to mind how blind our listeners are: music has no visual element; we do not have the luxury of such precision of perception. I highly doubt that listeners would be able to distinguish this circle from a mere diagonal square with points on the axises, as if you had simply toggled the sliders at an even rate, making sure still to offset them a quarter of an iteration from each other, but without bothering to (trigonometric style) carefully slow down each time you approached an extreme and speed up in the middle. Listeners could not really discern the smoothness of transitioning from one aspect into another (as opposed to the square’s corners) or how at the midpoints between one aspect’s extreme and another’s that more than half of each aspect is present (to be exact, sin(pi/4) = sqrt(2)/2) (because a circle’s curves bulge outward from the square they inscribe).

And executing this sound as simply as possible, drawing it out as a 45 degree tilted square would probably only serve to confuse or obfuscate the instructions to the performer. If spatiality is ill-suited as instructions for your music, then it’s probably not multidimensional yet. Even though you the composer know that you’ve composed these two aspects in a circle, it is not distinctly perceptible as multidimensional, and thus it fails as such. We have to construct significantly more distinctly multidimensional relationships between the aspects to induce aural imagining (we need a word for this… “sonicining”?) of multidimensionality.

Allow me to give a specific example of a good musically multidimensional experience. Attack envelope, echo amount, and buzziness are normally independent attributes of a timbre, so let’s pick them. We’ll call attack x, echo y, and buzz z. Then let’s give ourselves a metaphor to help grasp the movements we’re going make in this space: we’ll sit on a special ferris wheel, where x is east/west, y is north/south, and z is up/down.

When we’re at the top of the wheel, then, the sound is buzzy, and when we’re at the bottom, it’s not. That’s only the first process that’ll be happening simultaneously; the two halfway-up points sound completely different from each other, because one is the extreme point north and the other is the extreme point south, so the music sounds very different when we’re on our way up than it does when we’re on our way down. The pattern of the sound at this point goes 1) buzzy & slightly echoey 2) echoey & slightly buzzy 3) slightly echoey & not buzzy at all 4) slightly buzzy & not echoey at all.

But we’re still moving only in a single plane of two dimensions — we haven’t yet incorporated our third aspect. So now imagine that the foundation of the ferris wheel is mounted to a rotating disc, such that we’ve got a sort of carousel-ferris hybrid that can smoothly rotate between being oriented north/south to east/west and back. Thus we’re going to continue to see the alternation between buzzy and not, but now the echo is also going to enter into a sort of alternation with the attack. It is only at this point that we have first started getting some distinctively multidimensional implications to the procession of changes in our musical aspects.

You see, if it were the case that the instances of “echoey” in the four part pattern we described earlier were blending into instances of “attacky” merely uniformly, then even an intent listener would be hard-pressed to describe the sequence as the result of motion on this very-merry-go-round. In our example, however, echoey and attacky do not blend merely uniformly: if we consider only the x-y, attack-echo plane, looking straight down on it from above and tracing the path we made on a map, it would look something like a rounded star (the number of points would depend on the ratio between the rotation period of the merry-go-round part and the rotation period of the ferris wheel part). Had the echoey and attacky been fading between each other uniformly, it might have been more like rather than being on a ferris wheel atop this merry-go-round, we were simply in an elevator at the edge of it, going up and down in buzziness, but not in a way that had any effect on the other two aspects (and thus we’re essentially reduced to the circular counter-example I gave earlier). This rather specifically complex relationship between how echoey and how attacky the timbre can only be identified with this spatial course, and thus it has achieved multidimensional musicality.

So there you have it. If y’all know of any manageably imaginably multidimensionally musical worlds like this already out there, ready to explore, please let me know. Or, if any of you fellow demiurges out there want to make some with me, I’m all ears.

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