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By making use of the diagonalization of the complete d(3) energy matrix in a trigonally distorted cubic-field and the theory of pressure-induced shifts (PS) of energy spectra, the whole energy spectrum of alpha-Al2O3:Mn4+ and PS of levels have been calculated. All the calculated results are in excellent agreement with the experimental data. The comparison between the results of alpha-Al2O3:Mn4+ and ruby has been made. It is found that on one hand, R-1-line and R-2-line PS of alpha-Al2O3:Mn4+ and ruby are linear in pressure over 0 similar to 100 kbar, and their values of the principal parameter for PS are very close to each other. On the other hand, the sensitivities of R-1-line and R-2-line PS of alpha-Al2O3:Mn4+ axe higher than those of ruby respectively, which comes mainly from the difference between the values of parameters at normal pressure of two crystals; moreover, the expansion of d-electron wavefunctions of alpha-Al2O3:Mn4+ with compression is slightly larger than the one of ruby, and the effective charge experienced by d-electrons of alpha-Al2O3:Mn4+ decreases with compression more rapidly than the one of ruby. In the final analysis, all these can be explained in terms of the facts that the two crystals are doped alpha-Al2O3 with two isoelectronic ions; the strengths of the crystal field and covalency of alpha-Al2O3:Mn4+ are larger than those of ruby respectively, due to the charge of Mn4+ to be larger than that of Cr3+.