The sign relationship in aspect analysis is only valid for 30-degree multiple (12th harmonic) aspects. I think many astrologers who only use major 12th harmonic aspects assume sign relationship is truely what drives the aspects.
I would disagree. I consider aspects as part of a process, a process related to the waveform of the energy relationship. While it is true that 12th harmonic aspects do coincide with the meanings of the zodiacal signs, this demonstrates that the zodiac is properly laid out, not that aspects derive thier power from the zodiac.
A square represents a turning point, a conflict, a change of direction not because the signs are at odds, but because the natural sinusoidal wave of energy actually takes a change in direction 90 degrees into the waveform.
In the case of a square:
We have two waveforms 90 degrees out of phase. When one waveform is at its maximum deviation from zero, the other waveform is at zero. This shows the extreme differences of energy levels being expressed.
In the case of an opposition:
We have two waveforms 180 degrees out of phase. When one waveform is at full deviation, the other is also at full deviation, but of the opposite polarity. Yet, when the waveforms come to zero amplitude, they meet up. Here we see the power of the opposition: complimentary, yet opposite forces at work, with a similar middle meeting point, much like two signs in opposition of in the zodiac.
When one begins to use aspects that are not divisible by 30, and realizes the power of these aspects is nothing to scoff at, one further questions the reality of the signs forming the power of the aspects. The semi-square, an extremely powerful 8th harmonic aspect, could take place between two adjacent signs or between two signs with a third sign in the middle (such as with the sextile). The sesquiquadrate could take place between signs normally trine or quincunx to eachother, etc etc.
in the same respect, when one considers sidereal positions, and realizes that an "out of sign" aspect in the tropical zodac is often an "in-sign" aspect in the sidereal zodiac, one again questions which one may be right.
After much consideration of the technical methodology behind aspects, I have to side with Dane Rudhyar's approach to astrological aspects, which he outlines in his book "Astrological Aspects: A Process Oriented Approach" which is a truely amazing piece of work. I highly recommend anyone interested in the study of astrological aspects pick up a copy, as it will open your mind to a whole new understanding of aspects, as well as provide exceptional explainations of the minor aspects. If only this material was not still protected by copyright, I would take the time to digitize the entire work.
This is not to say that when considering an aspect, that sign relationships should be ruled out completely. in fact, they are the next-most-important consideration when determining how an aspect will play out. If one has a square by waveform relationship that is actually a sextile by sign relationship, one will still be driven to action and forced to reconcile the differences of the two objects, but the process will tend to play out in a more organized, coherent manner due to the balanced, organized nature of the sign energies being in natural sextile relation.
One who has a square by wave process and a sextile by sign process may consider themselves lucky, as the conflict between the objects in question may be easier to resolve, and the tension produced tends to be mitigated by the sign's sextile relationship. On the other hand, when the waveform process square is a quincunx by sign, the excessive uneasyness and thought-provoking power of the quincucx can add to the tension, forcing the native to constantly consider and analyze the differences expressed by the square waveform aspect. Remember that the quincunx is a mental aspect, as the native is driven to tidy up all loose ends before the oppositional process, which forces the reconcilation of opposite, yet equal, forces.
That said, it is important to realize that both the aspect by degrees as well as the aspect by sign interact. I personally consider the aspect by degree more important, but the sign relationship is nothing to scoff at either. One can only gain a true understand of the process at work by considering both factors.
I suppose this whole subject is as debateable as sidereal vs tropical or this-house-system vs that-house-system, but I figured I'd provide my take on the matter