NOTE 3/2016: I've added the whole article here: http://solunars.net/viewtopic.php?f=19&t=4563
As part of the "closer is stronger" view, technically "an orb begins nowhere exactly and builds up to its peak power at the point of exact aspect." It's not a matter of whether an aspect "exists," but of its relative strength. This variability in aspect strength is not likely linear - a linear progression makes no sense when compared to the rest of nature's behavior, and it isn't what shows in astrological research. As Garth Allen wrote,
DIGRESSION: I first anchored this basic understanding when reading Bradley's book on stock market forecasting. He proposed a view of aspects that he abandoned at the end of his life, but which I think is basically correct. The view is that aspect strength tapers according to a sine curve. On the theory that (for the major, classic aspects) the largest orb - the dividing line, for example, between when two planets are in trine and then are in square - has to be half-way between. Therefore, "zero aspectivity" would be 15° either side (the farthest you could go without moving into a different aspect). Setting the sine curve at its lowest value for a 15° orb, it just so happens (even though it's a curve, not linear) that the 50% point is exactly at 7.5°. I interpreted the 50% threshold as "more likely to manifest than not." - I therefore picked that as my outside orb for these aspects. (The sine curve also has some other interesting "threshold" qualities. For example, 99.5% effectiveness - what would found to 100% - falls almost exactly at the 1° orb point, which I find very interesting.) Because the gap between a conjunction and opposition and the nearest classic aspect is double the gap between a trine and square, or sextile and square, I realized this matched the observation that conjunctions and oppositions may have larger orbs. I empirically found that "ultimate drop off" (more likely to manifest than not) to be 10° for those aspects. - More on all of this later.The one certainty that emerges from our present understanding, though, is that the power of an aspect tapers off from its peak in a curvilinear fashion until it becomes so weak at a fair distance from partile, as to be unappreciable."
Garth Allen then gave the method he used for orbs - both for structuring a statistical study and for examining individual birth charts - preceeding it with some interesting results from his earlier statistical studies on aspects.
The average chart contyains 5 or 6 major (i.e., 5 classical) asspectysd within 3°00'. He calls these "first-order aspects, or aspects of the first order, since they are undoubtedly the strongest." (An individual chart can vary widely from this "5 or 6" average.)
Aspects between 3°00' and 6°00' he called :second-order aspects." Those from 6°00' to 9°00' he called "third-order aspects." All of this was for convenience, and he acknowledged that, "There is no special reason for using these terms, these orders." They served him "in making sure that I pay first attention to the closest couplings before bothering about the wider ones." (This one sentence, btw, has been the core of my horoscope analysis practice for 40 years or so.)
The 3° divisions are somewhat arbitrary, but also conform to some things actually observed in the aggregate in the past. Repeatedly, he had found that when an aspect pair was statistically significant in some study, it was significant within roughly a 3° zone, give or take. (Notice that this doesn't prove what an orb shold be, only what orb shows factors strong enough to stand out in examination of a group rather than an individual.)
Among professional athletes, the statistical score peaked at 2°50'.
Among lifelong bachelors, they peaked at 3°35'.
He adds a further consideration in passing, that, in examining an individual chart, one should consider the relative uniqueness of an aspect within one's community. All the aspects out through Mars-Pluto complete their cycle in 2.5 years or less. These, therefore, have the strongest importance of uniqueness. (Note how this makes Jupiter-outward and Saturn-outward aspects for a factor of your wider community.) Since I was studying astrology from the beginning of high school, I have always carried the "threshold test" of, "How much does this factor distinguish you from everyone else in your graduating class, or similar age range?"The drop-off in significance beyond four degres is startlingly steep, and in the statistical studies of particular events there is invariably a glaring absence of cases past the four-degree boundary, justifying the general rule that "ifg it doesn't happen within three degrees, it ain't agonna happen!" In the collecive analysis of suicides, the margin was even narrower.