Sesquiquadrates. WTF?
A sesquiquadrate, at 135º, falls between the major aspects of the trine (120º) and opposition (180º), and it’s not quite an inconjunct (150º).
In Horoscope Symbols , Robert Hand writes (concerning sesquiquadrates and semisquares):
These are not weak aspects. An exact semisquare or sesquiquadrate is more important than a square that is several degrees out, and many traditional astrologers who have ignored these so-called minor aspects have missed out on important information.
In Aspects in Astrology: A Guide to Understanding Planetary Relationships in the Horoscope
I suggest that the reason why semi-squares and sesquiquadrates manifest so readily in terms of outward events is simply because of the greater unconsciousness of these aspects.
Both Hand and Tompkins describe sesquiquadrates as being an energy similar in expression to the square, but less intense.