  Based on previous work of the authors, to any $S$-adic development of a
subshift $X$ a "directive sequence" of commutative diagrams is associated,
which consists at every level $n \geq 0$ of the measure cone and the letter
frequency cone of the level subshift $X_n$ associated canonically to the given
$S$-adic development.
  The issuing rich picture enables one to deduce results about $X$ with
unexpected directness. For instance, we exhibit a large class of minimal
subshifts with entropy zero that all have infinitely many ergodic probability
measures.
  As a side result we also exhibit, for any integer $d \geq 2$, an $S$-adic
development of a minimal, aperiodic, uniquely ergodic subshift $X$, where all
level alphabets ${\cal A}_n$ have cardinality $d\,$, while none of the $d-2$
bottom level morphisms is recognizable in its level subshift $X_n \subset {\cal
A}_n^\mathbb Z$.
