The characteristic scores and scales (CSS), introduced by Glänzel and Schubert (J Inform Sci 14:123–127, <cite>1988</cite>) and further studied in subsequent papers of Glänzel, can be calculated exactly in a Lotkaian framework. We prove that these
CSS are simple exponents of the average number of items per source in general IPPs. The proofs are given using size-frequency
functions as well as using rank-frequency functions. We note that CSS do not necessarily have to be defined as averages but
that medians can be used as well. Also for these CSS we present exact formulae in the Lotkaian framework and both types of
CSS are compared. We also link these formulae with the h-index.