Aspects, part 3, Harmonic Families & Nomenclature
[Part 1, Part 2, Part 3, Part 4]
Looking at aspects this way, we begin to see that the meaning of a given aspect depends on the arithmological significance of its harmonic. So, instead of interpreting a conjunction according to the "just because" definition that has been passed down to us for it, we can understand it in terms of the symbolism of 1, of unity; similarly, the opposition is understood in terms of the duality of the 2; etc. This understanding of the aspects as specific fractions of the circle allow us to extend the idea of aspects to essentially any division of the circle, with up to 360 harmonic families, containing a total (if removing reducibles and reflections; i.e., to speak of only distinct angular values) of 19,727 aspects!
Don't faint! No one expects any of us to use or understand, much less remember, that many. Instead, think of these additional possibilities as something similar to the idea of a zoom on a camera, telescope or microscope, and so forth. The higher the harmonic value, the more precisely you're focusing in on a specific theme or issue. Cochrane, for instance, interprets higher harmonic families as functions of their divisors. For instance, H2, the opposition, would be a key or core meaning, while H4, as a multiple of 2 would be a more focused look at the themes suggested by the 2, while H8 would be a tighter focus, H16 even more so, H32 again, H64, H128 and H256 the most refined expression of the pure "two"ness in the 360 families. Thus the harmonic families that are a power of some lower harmonic—{2, 4, 8, 16, 32, 64, 128, 256}, {3, 9, 27, 81, 243}, {4, 16, 64, 256}, {5, 25, 125}, {6, 36, 216}, {7, 49, 343}, etc.—can be interpreted as increasingly focused analyses of the purest form of their lowest or root harmonic. Other higher families can be interpreted as mixtures of their core values. For instance, H324 could be considered a mixture of the issues of H2 and H3 as 324 = 2 x 2 x 3 x 3 x 3 x 3, which could be H2 x H162, H3 x H108, H4 x H81, H6 x H54, H9 x H36, H12 x H27 or as the square of H18, any or all, depending on the issues significant in the chart at hand.
Here we come to the subject of nomenclature, however. As you might guess, as we wade into such a sea of symbols, it would become, if not impossible, at least unrealistic, to individually name all of these nearly twenty thousand aspects. It is my contention that it's not even desirable to try! What I mean is, by this understanding it is the number, especially the harmonic number, that is important to us in understanding these aspects, so it is the number that we ought to keep in mind, not a more abstracted name that disconnects us from the important details. When I first encountered the work cited by Cochrane, I was happy to see that he routinely refers to harmonic aspects not by a name but by their fractional value, thus he talks of 5/28 or 9/64, etc. This is how I propose to treat these aspects as well. Not only will this help us keep the important symbols in mind, it will help us, and others, avoid mistakes like that the "quindecile" seems to have presented to so many.
I encountered discussion of this "quindecile" a few years ago when reading Tyl's remarks on it and, later, his student's work on the same—but I couldn't help but be confused by the fact that he was working with the 165° aspect, which isn't a quindecile, or even part of the quindecile family! When I encountered Blaschke's SAO book later, I noticed he had also observed the error, but his proffered "correction" also missed the mark: in that he renamed Tyl's "quindecile" the "contraquindecile" (on what provenance, I know not), and called the first member of the 165° aspect's harmonic family the "quindecile", though that too is a mistake. Why? Harmonic families are named not for their angular measure but for the divisor that yields that angular measure as the quotient of 360 divided by the harmonic. One-hundred sixty-five is 360 / 24 x 11, meaning that it's part of H24, the quattuorvigintile family, not the quindecile. Quindecile would be H15, which is {1/15, 2/15, 4/15, 7/15} or {24°, 48°, 96°, 168°}, which by traditional naming models would be the quindecile (24°), biquindecile (48°), quadriquindecile (96°) and septiquindecile (168°)—a bit of a mouthful, yes, but then the 165° would have been called the undeciquattuorvigintile! Am I alone in thinking it would be preferable to refer to this aspect as 11/24 than by names like these? Before you answer, consider this: "undeciquattuorvigintile" isn't even close to the most difficult these names would become if we were to adhere to the traditional naming methods. For instance, the family name alone for H360 would be trecentisexagentile—and there are 48 distinct members of that family, each of which after the first would take a prefix on that name, such that 179/360 would be… centiundoctagitrecentisexagentile! So, again, wouldn't you rather say 179/360?
Considering all of these things, it should have become apparent by now that in using these models every object in a chart is in some aspect to every other: in harmonic analysis there are no unaspected planets. This is not in any way meant to undermine the efforts of Tierney and others in the study of that field, just as harmonic study is not meant to replace or undermine traditional approaches; this is simply another tool in the study of charts. But with so many aspects available, we come to question of how do we know which to use, or which are most significant, which itself brings us to the question of orbs.
