Properties of a definition of the SI second based on several optical transitions

The current definition of the SI second based on the Cs ground state hyperfine transition is expected to be replaced by a new definition based on optical frequency standards in the next decade. Several options are currently under consideration for the new definition, including a definition based on the weighted geometric mean of several transitions. In this paper, we review several properties of this option, and most notably introduce a quantitative method to set the weights of transitions, and a graphical representation of the unit that make the distinction between the definition and the realisation of the unit easier to understand.