We present a technique that applies spectral synthesis to medium resolution spectroscopy (MRS, R ~ 6000) in the red (6300 A < lambda < 9100 A) to measure [Fe/H] and [alpha/Fe] of individual red giant stars over a wide metallicity range. We apply our technique to 264 red giant stars in seven Galactic globular clusters and demonstrate that it reproduces the metallicities and alpha enhancements derived from high resolution spectroscopy (HRS). The MRS technique excludes the three Ca II triplet lines and instead relies on a plethora of weaker lines. Unlike empirical metallicity estimators, such as the equivalent width of the Ca II triplet, the synthetic method presented here is applicable over an arbitrarily wide metallicity range and is independent of assumptions about the alpha enhancement. Estimates of cluster mean [Fe/H] from different HRS studies show typical scatter of ~0.1 dex but can be larger than 0.2 dex for metal-rich clusters. The scatter in HRS abundance estimates among individual stars in a given cluster is also comparable to 0.1 dex. By comparison, the scatter among MRS [Fe/H] estimates of individual stars in a given cluster is ~0.1 dex for most clusters but 0.17 dex for the most metal-rich cluster, M71 (<[Fe/H]> = -0.8). A star-by-star comparison of HRS vs. MRS [alpha/Fe] estimates indicates that the precision in [alpha/Fe]_MRS is 0.05 dex. The errors in [Fe/H]_MRS and [alpha/Fe]_MRS increase beyond 0.25 dex only below signal-to-noise ratios of 20 A^(-1), which is typical for existing MRS of the red giant stars in Leo I, one of the most distant Milky Way satellites (250 kpc).
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