  The principles of a previously developed formalism for the covariant
treatment of multi-scalar fields for which (as in a nonlinear sigma model) the
relevant target space is not of affine type -- but curved -- are recapitulated.
Their application is extended from ordinary harmonic models to a more general
category of "harmonious" field models, with emphasis on cases in which the
field is confined to a string or higher brane worldsheet, and for which the
relevant internal symmetry group is non Abelian, so that the conditions for
conservation of the corresponding charge currents become rather delicate,
particularly when the symmetry is gauged. Attention is also given to the
conditions for conservation of currents of a different kind -- representing
surface fluxes of generalised momentum or energy -- associated with symmetries
not of the internal target space but of the underlying spacetime background
structure, including the metric and any relevant gauge field. For the
corresponding current to be conserved the latter need not be manifestly
invariant: preservation modulo a gauge adjustment will suffice. The simplest
case is that of "strong" symmetry, meaning invariance under the action of an
effective Lie derivative (an appropriately gauge adjusted modification of an
ordinary Lie derivative). When the effective symmetry is of the more general
"weak" kind, the kinetic part of the current is not conserved by itself but
only after being supplemented by a suitable contribution from the background.
