The energy spectra of photons following negative muon absorption in $^{12}\mathrm{C}$, $^{16}\mathrm{O}$, $^{27}\mathrm{Al}$, $^{40}\mathrm{Ca}$, $^{\mathrm{nat}}\mathrm{Fe}$, $^{165}\mathrm{Ho}$, and $^{209}\mathrm{Bi}$ have been measured with two NaI spectrometers. The branching ratios for the emission of high energy photons give information on the induced pseudoscalar coupling constant ${g}_{P}$ in nuclear matter. The data for light nuclei are in agreement with the theoretical calculations using the nucleonic value of ${g}_{P}$\ensuremath{\approxeq}7${g}_{A}$ predicted by the partially conserved axial vector current hypothesis, while significantly lower values of ${g}_{P}$ are required to fit the data of the heavier elements with presently existing theoretical predictions. Disregarding the remaining theoretical uncertainties, these results can be interpreted as a further indication of the renormalization of the nucleonic form factors inside the nucleus.