Ptolemy’s Digression: Astrology’s Aspects and Musical Intervals
Statement of the Problem
This essay addresses a problem in the development and continuity of astrology: how do astrologers, past and present, account for the astrological aspects? Aspects are the means by which a planet or position (Ascendant, Lot of Fortune) has contact from another planet or other planets. Once an astrologer has designated planet or a position to answer a question posed to the astrological chart, aspects to the designated position provide information to answer a question and determine an outcome.
How is it that this connection by aspect occurs? Because aspects are based on the distances of two positions from each other along the zodiac, the solution is not obvious. Of course, one needn’t question aspects at all. The teachings on aspects from ancient India are very straightforward. All aspects are cast forward in the zodiac, and each planet aspects the house (and sign) opposite to it. Additionally, Mars aspects the fourth and eighth houses from itself, Jupiter aspects the fifth and ninth, and Saturn aspects the third and tenth from itself.
These rules are part of the astrological craft passed down from their tradition. Most ancient western astrologers also used aspects without questioning them, and were not different from their Indian cousins in this regard. However, the Hellenistic mind, and that of Ptolemy in Tetrabiblos I, sought to give astrology a coherent theoretical form, and integrate astrology more firmly with other fields of understanding. This attempt is, in large part, the reason why the Tetrabiblos is the most important single work in the history of western astrology.
We will closely examine Tetrabiblos I Chapter 13. Here Ptolemy gives two accounts for aspects. The first one, the subject of this paper, is based on what we might call “fractions” and “super-fractions,” moriai and eprmoraia. The second argument of Chapter 14 depicts sympathetic and unsympathetic aspects through the nature of the zodiacal signs or zoidia brought into aspect.
Ptolemy’s first account in Chapter 13, although of a different style than the surrounding material, gives a provocative and critical account of aspects – one related to harmonics and the diatonic musical scale in particular. Later astrologers, from the Renaissance into the modern era, subordinated musical harmonics to an arithmetic template alone. They have brought more information to astrological analysis but perhaps with a shakier theoretical foundation.
When, as a new astrology student, I first learned about them, the account given was wholly arithmetical and geometrical: because we can divide the whole circle by halves, quarters, thirds, and sixths, we can connect planets to one another by aspect. These relationships also give us the line, square, and what astrologers call the trine and sextile; they are geometrically the side of a triangle and hexagon within a circle. These aspects divide the whole circle into sections divisible by the twelve signs of the zodiac. We might also ask, however, why it is that we do not consider the dodecahedron, a twelve-sided figure, and thus an aspect of 30°? This should fit conveniently with the others, but this was not considered a true aspect in the ancient tradition, nor, indeed, by most modern astrologers.
What is it about number relationships that empower planets to act upon one another, based on their distance from each other?
The modern mind has an easier time comprehending action at a distance, because the physics of the modern era has given this understanding to us. And if we are not of a theoretical bent, we have our various remotes to unlock our cars, open the garage door, turn on and off our televisions and radios, and so on.
Because of our background in popular science and technology, modern astrologers do not raise a skeptical eye to our understanding and use of the astrological aspects. This does not solve the problem, however, since neither gravity nor electromagnetic waves can account for their action.
Most of the Greek words for aspects are those of seeing or looking. Directly or indirectly, aspects are acts of visual perception.
Ancient astrologers indeed thought of aspects in terms of seeing and being seen. A planet “looks ahead” – epothoreõ — to another planet, forward in the zodiac, to which it is in aspect. In return, the aspected planet “casts rays” – aktinoboleõ – back to the aspecting planet. Additionally, an aspecting planet may “testify to” or “witness” – epimarturõ – another planet.
Our English “aspect” is indeed such a word, as is the Indian word for aspects, drishtis, from the word “to gaze.”
Two planets in the same sign or zoidion – the modern “conjunction” — are not in aspect. Seeing words are not used for these relationships: instead, planets in the same zoidion are considered with one another. The planet must be outside its own immediate zodiacal environment than the other in order to see or be seen.
Modern astrologers might note that vision is action at a distance, since we routinely see things distant from us. Our science books tell us that light waves are along a range of bandwidth of a vast vibratory spectrum that surrounds us. These waves allow an outside object to be represented to us, although an otter or a bat might “see” something quite different.
Modern theories of vision hardly apply to astrology’s distinction between aspects that are based on the distance that are, in turn, based upon number. Nor are ancient theories of vision helpful to us. Nor perhaps to Ptolemy, who did not use visual perception to account for aspects, although most aspect words imply this kind of action.
Ancient tradition gives a variety of accounts for visual perception. To our modern sensibilities, they range from relatively straightforward to rather weird. Aristotle’s De Anima takes not vision but touch as the most basic – and paradigmatic –sense faculty, and posits that vision, like the other sense faculties, has a medium (metaxu) by which the object carries itself to the perceiving subject. For vision, this medium is light. The object somehow alters the light by which the view of the object comes to the subject.
“For what is to be colour is, as we say, just this, that it is capable of exciting change in the operantly (actual) transparent medium: and the actuality of the transparent is light.” (418b) 
According to the Stoics, what binds together the object of perception and the subject is the tensing of pneuma. In the case of seeing, “the seeing-pneuma in the eye makes the object visible by ‘tensing’ the air-pneuma into a kind of illuminated cone with the object at base and eye at apex; the tension of this air is experienced as sight.” The Epicurean school posited that images flow from the objects themselves in a constant manner and the eye picks them up.
Another possibility, of uncertain seriousness, is found in Plato’s Timaeus, 45 B-D. After commenting on the fact that the human body is well suited for the faculty of sight, especially to look up toward the heavens, he notes that vision occurs through means of the fire of daylight, another kind of fire in one’s eye faculty, and fire emanating from the object seen. As they connect, we see something. In his astrological analysis, Ptolemy also uses words for seeing and looking (as well as witnessing or testifying) when referring to aspects. He does not use these words in Tetrabiblos Iwhen giving an account of the aspects themselves. If the act of looking or seeing requires a medium to connect object of sight and subject, it is not at all clear what a medium would be that could carry the aspects of astrology. The medium must be the aspect intervals themselves, but how?