Luminous BA-SGs allow topics ranging from NLTE physics and the evolution of
massive stars to the chemical evolution of galaxies and cosmology to be
addressed. A hybrid NLTE technique for the quantitative spectroscopy of BA-SGs
is discussed. Thorough tests and first applications of the spectrum synthesis
method are presented for four bright Galactic objects. Stellar parameters are
derived from spectroscopic indicators. The internal accuracy of the method
allows the 1sigma-uncertainties to be reduced to <1-2% in Teff and to
0.05-0.10dex in log g. Elemental abundances are determined for over 20 chemical
species, with many of the astrophysically most interesting in NLTE. The NLTE
computations reduce random errors and remove systematic trends in the analysis.
Inappropriate LTE analyses tend to systematically underestimate iron group
abundances and overestimate the light and alpha-process element abundances by
up to factors of 2-3 on the mean. Contrary to common assumptions, significant
NLTE abundance corrections of ~0.3dex can be found even for the weakest lines.
NLTE abundance uncertainties amount to typically 0.05-0.10dex (random) and
\~0.10dex (systematic 1sigma-errors). Near-solar abundances are derived for the
heavier elements, and patterns indicative of mixing with nuclear-processed
matter for the light elements. These imply a blue-loop scenario for Eta Leo,
while the other three objects appear to have evolved directly from the main
sequence. In the most ambitious computations several ten-thousand spectral
lines are accounted for, permitting the accurate reproduction of the entire
observed spectra from the visual to NIR. This prerequisite for the quantitative
interpretation of medium-resolution spectra opens up BA-SGs as versatile tools
for extragalactic stellar astronomy beyond the Local Group. (abridged)Comment: 36 pages, 18 figures, accepted for publication in A&