  Two new numbers, $\nu$ and $\zeta$, inspired by particle-hole symmetry are
introduced. These numbers have extreme values at a closed shell and vanish
mid-shell. A combination of even powers of these numbers has been used to model
experimentally measured quantities such as $R4/2=E(4^+_1)/E(2^+_1)$ and the
"microscopic" contribution to binding energies. A binding energy fit consisting
of a total of six fit coefficients, including one new shell term, reproduces
the experimental binding energies of 2353 nuclei with an r.m.s. standard
deviation of 1.55 MeV. The difference between the experimental and fit values
of observables, specifically the $R4/2$, provides an indication of where shell
closure features are less pronounced and where sub-shells closures occur.
