A hundred and thirty five degrees is three eighths of the circle, which places the sesqui-quadrate in the eighth harmonic alongside the semi-square. The name says the same thing in older language: a square and a half, ninety degrees plus forty five. It is also called the sesquiquadrate, the sesquisquare and the trioctile, and the multiplicity of names is a fair indication of how unsettled its place has been.
Its standing follows its partner's exactly. Neither angle can be reached by counting signs, since eight does not divide twelve, so neither exists in sign-based doctrine and both are found only by degree. Both come into circulation through Kepler's harmonic argument and are taken up in earnest only from the nineteenth century. Both are given narrow orbs, usually about two degrees, and both are read as friction rather than crisis. Where writers distinguish them, the semi-square is described as internal or chronic and the sesqui-quadrate as breaking outward into events, but that distinction is a convention of the modern literature rather than a finding, and different authors reverse it.
One structural point is worth keeping. Because a hundred and thirty five degrees is not a multiple of thirty, the two planets involved can stand in signs that are in aversion to one another, meaning that a traditional reading would hold them unable to interact at all while a harmonic reading holds them in a tense relation. That is not a disagreement about strength. It is a disagreement about whether anything is there, and it is the same fault line that runs under every one of the minor aspects.