Tune shifts caused by horizontal closed orbit deviations in sextupoles

One of the uncomfortable features of the Chasman-Green lattice is that the chromaticity-correcting sextupoles are all very strong compared with those in the FODO-type lattice. Because of their strengths, when their arrangement creates certain harmonic components, the dynamic aperture is severely reduced and on is forced to add more sextupoles to eliminate harmful harmonic components.During the course of design studies, S. Kramer has made many computer runs to investigate tune shifts resulting from horizontal orbit deviations in sextupoles. An interesting observation is that the average tune shift is definitely related to the dependence of tunes on the betatron oscillation amplitudes (or, equivalently, the transverse emittances). This note is an ``attempt`` to explain the connection at least qualitatively. It is no more than an attempt since the explanation is not yet quantitative and it may even be somewhat inconsistent.