At low temperature the photoluminescence of single-wall carbon nanotubes show a large variety of spectral profiles ranging from ultranarrow lines in suspended nanotubes to broad and asymmetrical line shapes that puzzle the current interpretation in terms of exciton-phonon coupling. Here, we present a complete set of photoluminescence profiles in matrix embedded nanotubes including unprecedented narrow emission lines. We demonstrate that the diversity of the low-temperature luminescence profiles in nanotubes originates in tiny modifications of their low-energy acoustic phonon modes. When low-energy modes are locally suppressed, a sharp photoluminescence line as narrow as 0.7 meV is restored. Furthermore, multipeak luminescence profiles with specific temperature dependence show the presence of confined phonon modes.