Musical Idea 23: Gaussianity

03.08.2014 § Leave a comment

The primary threat to the illusion of pitch circularity is detecting when entities are sneaking in from one extreme of pitch or the other. When specifically listening for it, an astute listener doing everything in her power to dispel the illusion she is well aware of, it can be difficult to pull wool. Here is a highly technical idea to obscure the edges a bit, though — in adding a little shimmer, making it more difficult to detect entry and departure.

In short, my idea is for a recursive Shepard-Risset Glissando:

  1. To begin, compare a single sine wave of frequency X to a Shepard-Risset Glissando centered on X, i.e., the SRG whose gaussian curve (mapping a volume to each frequency) has its peak at X. In other words, think of the Shepard-Risset glissando’s characteristic infinite stack of gradually ascending/descending octave-spaced tones peaking in volume at frequency X as “SRG-ing” frequency X.

  2. Next, take an SRG’s gaussian curve and “SRG” it in turn: If that single curve’s peak frequency X was treated like that single sine wave, then to complete the analogy such a curve once “SRG-ed” would consist of a composite of multiple gaussian curves whose peaks were spaced an octave apart and dynamically increased/decreased in frequency while fading in and out according to a higher level gaussian curve peaking at X.

  3. That higher level gaussian curve would in turn be “SRG’ed” into stacked octaves of decreasing/increasing frequencies fading in and out according to a yet higher gaussian curve, and so on and so on.

To imagine what this should sound like, first imagine a traditional Shepard-Risset glissando, let’s say one creating the illusion of infinite pitch descent. Now imagine that its gaussian curve’s peak were to gradually move higher in frequency: seemingly paradoxically, one would hear tones infinitely descending, while overall the pitch rose until it was supersonic. Next, imagine that instead of that overall pitch simply rising until it left hearing range, it faded out in volume well in advance of that while sameltimeously a new volume peak an octave lower faded in while rising in frequency from below.

That’s what one would hear after just one additional layer of SRG-ing. Now with additional layers it becomes increasingly difficult to imagine or describe in words what one would really be hearing, but I can at least say that one would not be hearing anything significantly different from the original SRG: the tones would still infinitely descend while the overall pitch stayed right at X. The main difference would be that there would be a lot more motion in the volumes of the tones as they made their descent, giving a shimmering or wobbly feel to it, which I hope would make it more difficult for listeners to isolate the individual octave iterations.

Initially we might assume that each layer the direction of the SRG’ing (i.e., whether it creates the illusion of infinite ascent or descent) should alternate: ascending, descending, ascending, descending, ascending, etc. because otherwise the new layer would merely increase or decrease the overall volume of the previous layering. That would only be so if the ratio between the rate of cycling through peaks/tones and the frequency interval between those peaks/tones were the same, but changing those parameters across layers might create some incredible effects! Perhaps having every layer descend but at different rates would work well, and perhaps the rates would consistently increase or decrease each time approaching either infinity or zero (a final static single gaussian curve peaking at X). Perhaps the rates wouldn’t even have to be linear. Perhaps intervals greater or lesser than octaves between peaks of the composite gaussian curves would work better (as the interval between peaks in volume rather than the tones themselves is a bit more shadowy, they are somewhat freed from the constraint of pitch class equivalency), or a variety would be best, or maybe they themselves should be dynamic.

(The presence of such Gaussian functions over amplitude in the music can also become a handy resource in certain situations. If the tempo ever increases to the point where the music would be incomprehensible otherwise, the variance on the Gaussian can be simply tightened until it focuses in on a single pitch or chord, saving the situation. Or working from the other direction, a timbre of a single note could be revealed to contain an entire song by exploding out by way of its Gaussian unfurling.)

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