Musical Idea 16: Quantization Gravity

01.25.2014 § Leave a comment

In this series I speak a lot about exploring the possibilities that exist between two musical entities. Today’s entry, quantization gravity, is about exploring the possibilities between a freeform entity and a quantized version of it.

You may be previously familiar with this particular idea of quantization: when you force an aspect of your music to confirm to a limited set of possibilities within its range. To be able to be quantized, an entity must host a continuum or continuous space of possibilities. You can’t quantize a single pitch — at least, quantizing a single pitch to another single pitch is indistinct from the much simpler explanation of changing pitch. Quantizing is only meaningful over a range of values. A good example would be transforming a fretless guitar into a fretted one — the infinite set of pitches along one string will be narrowed down to twenty-four steps in pitch. But quantization is meaningful even over the smallest ranges and sets of values: such as the +/- ms of a drummer attempting to match a metronome, quantized to succeed at it; or the micro-fluctuations in pitch of a later Scelsi piece, quantized all to the same exact frequency. As long as it’s a range reducing to a set within that range, it’s quantization.

An example application would be to rhythm:

  • I just came up with a melody in my head and want to digitize it into my computer, so I sit down at my electronic keyboard and play it out;
  • since it’s not my intent to capture any organic/imperfect/human quality to the performance —
    • that is, I just want to input the ideal form of this music to use in an electronic track which calls for a precise aesthetic
      • (or perhaps just to print ideal sheet music from which other organic/imperfect/human performances might be pressed later),
    • and this should be a much faster method of achieving that than manually clicking and dragging and typing it out with my computer keyboard and mouse —
  • but I’m not a perfect robot and can’t get the timings of notes exactly correct,
  • if I tell the computer to quantize what I played to, say, sixteenth notes,
    • then supposing that my riff doesn’t involve rhythmic intervals more precise than this sixteenth note,
    • and supposing that I’m at least good enough to not regularly play notes off by more a thirty-secondth
      • (half of a sixteenth, which would cause the quantization to believe that I intended the note just before or just after the one which I actually intended),
  • then quantization will be able to save me some time in achieving this.

This example is merely a demonstration of how quantization can be used as a practicality, but quantization is often used to achieve unique sounds that couldn’t be made otherwise.

Consider, for example, an application to pitch: auto-tune. Auto-tune is is a quantization of frequencies from the entire fluid range to a small set of the exact tones of your choosing. Without auto-tune, performers are imperfect at hitting their intended notes, and the human voice naturally fluctuates; with auto-tune, performers can inhumanly match and sustain these frequencies. The most special effect of auto-tune, however, is what it does to the human voice when it’s rapidly changing in pitch (usually when sliding into place on, off from, and between notes): the points along what before would have visually looked like a smooth curve up and down in pitch are snapped onto their respectively closest horizontal lines of the chosen set of pitches, transforming the original curve into right-angled steps which are responsible for those distinctively android-like clipping artifacts.

Neither of these examples involve music yet where the quantized version and the original version co-exist or move between each other. I imagine music, though, where an “underlying ideal” — the unbound, freeform version, what the music is when no quantization restrains it — is influenced by a “quantization lattice” exerting varying amounts of “gravity” on the underlying ideal’s notes to come into more or less alignment with its chosen points. I may write a piece in free pitch or rhythm, then as I dial up or down the gravity of my quantization lattice, which represents my tuning system or beat of choice, I will alternately pull and release on the notes into and out of perfect alignment with that tuning or meter.

You could even have many quantization lattices operating at once. You could have an equal temperament vie for control versus an eikosany, for example. Perhaps these lattices are in near or exact agreement on certain of their pitches or timings, so their gravities only reinforce each other there, while in other stretches their opposite effects either cancel each other peacefully or stir up violent storms of contention, yanking notes back and forth between each other. Whoever wins depends partially on how strong their gravity is at a given time, and what type of gravity they exert — more on this in next week’s entry.

For now, let’s note that the strength of these quantization lattices’ gravities is not their only potential variable. You can apply many dynamic effects to a lattice that you would to music itself, like tonal movement and stretching, pitch circularity, yaw, spatiality, etc. As your music drifts in and out of conformity with this limited set, that is, the limited set itself can be animating.

It’s a piece of cake to come up with superficial examples of that sort, but here’s a rhythmic example that really gets at the roots of quantization gravity (and without even involving gravitational strength). So while we normally think of the underlying ideal as wild and loose and the quantization lattice as the system which reels it in to stability, suppose here we use an underlying ideal which is a simple unwavering steady pulse, while it is the quantization lattice which unpredictably speeds up at times, but always gradually, and temporarily, eventually returning, again gradually, back to the same speed as the underlying ideal.

  1. The first observation to be made is that what we mean by the lattice speeding up is that the pulsing of temporal moments which the underlying ideal is being pulled toward alignment with are getting denser; as it approaches infinite speed, and thus the quantizable-to moments become infinitely dense, the quantization essentially becomes moot, since if every point is permitted, then quantization will have no effect.
  2. The second observation to be made is that when the lattice matches speeds with the underlying ideal, it also has no effect on it; while if in the course of its temporary speedings-up it has managed to become disaligned from the underlying ideal, this is irrelevant because it will merely result in the underlying ideal getting offset uniformly.
  3. The third and final observation to be made, then, and the one which explains the effect, is that when the quantization lattice is in-between these two states, it will be creating a particular breed of limpy mayhem for the underlying ideal. Let’s take this step by step, as the lattice starts speeding up out of matchedness with the underlying ideal:
    • So at first, the ideal will keep up with the lattice; the lattice point comes earlier and earlier relative to where the underlying note would ideally go, but it comes along.
    • It comes along, that is, until the lattice point has gotten so far ahead of the ideal that it has passed the halfway mark, meaning that the previous ideal will be closer to it than it is to the lattice point it would have shifted toward had it shifted like all the others so far; in other words, eventually we’ll reach a point where an ideal will be pulled backward instead of forward.
    • After this hiccup, the process will basically return to normalcy. The lattice point will continue coming earlier and earlier relative to the ideal, eventually aligning with it for a moment, passing it, and continue getting further ahead of it until another hiccup happens.
    • This would be true even if the lattice was not getting increasingly faster; if the lattice ever rests in any stable rate faster than the ideal, it will result in this effect where the ideal tries to be as fast as it, but has to hiccup with these occasional long intervals in order to overall always fit the same average number of hits in any given stretch of time.
    • But the lattice is getting increasingly faster. Eventually these hiccups will come more and more often. We can understand these hiccups to be moments when an ideal spans more than lattice point. At first ideals are spanning generally one lattice point, with hiccups of spanning two of them. Eventually the lattice points will be so dense that the ideals will start spanning three of them at a time (alternating with spanning two at a time — the time of spanning only one will be over). Then the ideals will be alternating between spanning three and four lattice points.
    • The process is over at the point that the ideals are alternating between spanning some arbitrarily large n lattice points and n+1 lattice points. At the point where the +1 is imperceptibly small relative to the n, you cannot tell the difference between the hiccups and the catch-ups.
    • What’s beautiful about this is that throughout the process, we can sense the presence of the quantization lattice and its acceleration, even though the underlying ideal overall keeps overall steady; plus we sense it along a journey through every superparticular rhythmic duration ratio in existence: 2:1, 3:2, 4:3, 5:4, etc.

Note that while I left gravitational strength out of the discussion because it is not necessary to involve it in order to achieve this or necessarily any interesting effect, you can experiment with setting it to different levels or making it simultaneously dynamic to get even more interesting results.

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