  QCD lattice simulations with 2+1 flavours typically start at rather large
up-down and strange quark masses and extrapolate first the strange quark mass
to its physical value and then the up-down quark mass. An alternative method of
tuning the quark masses is discussed here in which the singlet quark mass is
kept fixed, which ensures that the kaon always has mass less than the physical
kaon mass. Using group theory the possible quark mass polynomials for a Taylor
expansion about the flavour symmetric line are found, which enables highly
constrained fits to be used in the extrapolation of hadrons to the physical
pion mass. Numerical results confirm the usefulness of this expansion and an
extrapolation to the physical pion mass gives hadron mass values to within a
few percent of their experimental values.
