In this paper we develop an evolutionary stellar population synthesis model to predict spectral energy distributions (SEDs) for single-age, single-metallicity stellar populations (SSPs) at resolution ~1.8 Å in two reduced but very important spectral regions around 4000 and 5000 Å. The input stellar database is composed of a subsample of ~500 stars selected from the original Jones spectral library This is the first time that such an evolutionary model has employed such an extensive empirical stellar spectral library, at such high resolution, for supporting its SED predictions. A spectral library corresponding to simple old stellar populations with metallicities in the range -0.7<=[Fe/H]<=+0.2 is presented here, as well as an extensive discussion about the most popular system of absorption indices at intermediate resolution, the Lick system, showing the advantages of using the new model predictions. Also, we show for the first time the behavior of the Rose system of indices, at higher resolution, as a function of the age and the metallicity of the stellar population. The newly synthesized model spectra can be used to analyze the observed galaxy spectrum in a very easy and flexible way, allowing us to adapt the theoretical predictions to the characteristics of the data instead of proceeding in the opposite direction as, for example, we must do when transforming the observational data for using model predictions based on a particular instrument-dependent system of indices at a specific resolution. The synthetic SSP spectra, with flux-calibrated spectral response, can be smoothed to the same resolution as the observations or to the measured galaxy internal velocity dispersion, allowing us to analyze the observed spectrum in its own system. Therefore, we are able to utilize all the information contained in the data at their spectral resolution. After performing this step, the entire observational spectrum can be compared at one time, or the analysis can be done by measuring a particular set of features in the synthesized and the observational spectra rather than by trying to correct the latter from broadening or instrumental effects. The SSP model spectra were calibrated at relatively high resolution with two well-studied metal-rich globular clusters in our Galaxy, 47 Tuc and NGC 6624, providing very good fits and being able to detect well-known spectral peculiarities such as the CN anomaly of 47 Tuc. The model was also applied to an early-type galaxy, NGC 3379, revealing its well-known abundance of magnesium relative to iron and showing the appropriateness of the new model predictions as well as the way in which they can be used for studying the elemental ratios of these stellar systems. In fact, different models of different metallicities provide equal approaches to the galaxy spectrum: once Hβ is properly constrained, we are able to fit either the iron features (with a metallicity somewhat in the range -0.4<=[Fe/H]<=0) or the magnesium features (with a metallicity in the range 0<=[Fe/H]<=+0.2), but not both simultaneously.