We report new metallicities for stars of Galactic globular cluster M4 using the largest number of stars ever observed at high spectral resolution in any cluster. We analyzed 7250 spectra for 2771 cluster stars gathered with the VLT FLAMES+GIRAFFE spectrograph at VLT. These medium resolution spectra cover by a small wavelength range, and often have very low signal-to-noise ratios. We attacked this dataset by reconsidering the whole method of abundance analysis of large stellar samples from beginning to end. We developed a new algorithm that automatically determines the atmospheric parameters of a star. Nearly all data preparation steps for spectroscopic analyses are processed on the syntheses, not the observed spectra. For 322 Red Giant Branch stars with $V ≤ 14.7$ we obtain a nearly constant metallicity, $ = -1.07$ ($σ$ = 0.02). No difference in the metallicity at the level of $0.01 ~\textrm{dex}$ is observed between the two RGB sequences identified by \cite{Monelli:2013us}. For 1869 Subgiant and Main Sequence Stars $V > 14.7$ we obtain $ = -1.16$ ($σ$ = 0.09) after fixing the microturbulent velocity. These values are consistent with previous studies that have performed detailed analyses of brighter RGB stars at higher spectroscopic resolution and wavelength coverage. It is not clear if the small mean metallicity difference between brighter and fainter M4 members is real or is the result of the low signal-to-noise characteristics of the fainter stars. The strength of our approach is shown by recovering a metallicity close to a single value for more than two thousand stars, using a dataset that is non-optimal for atmospheric analyses. This technique is particularly suitable for noisy data taken in difficult observing conditions. ; Comment: 17 pages, 20 figures, 3 tables. Accepted for publication in The Astronomical Journal