Coherent vibronic oscillations in the ground state of carotenoids have been investigated by means of three-pulse four-wave mixing spectroscopy. Here, we especially focused our attention on the influence of the temporal separation between the first and the second pulses, i.e., the coherent period $\ensuremath{\tau}$, on the third-order nonlinear signals. The vibronic oscillations of the fundamental modes are clearly observed when $\ensuremath{\tau}$ is set to zero. They appear via an impulsive resonant Raman process and reflect the spectral feature of a conventional Raman spectrum very well. Interestingly, in addition to the coherent vibronic oscillations of the fundamental modes, we found that high-intensity coherent vibronic oscillations of the overtones and the coupled modes appear when a nonzero value of $\ensuremath{\tau}$ is employed. These coupled modes become dominant at a rather large coherent period of $\ensuremath{\tau}$ $\ensuremath{\sim}$ 60 fs. A simple extension of our previous calculations that assume electronic harmonic potentials and vibronic Brownian oscillators cannot explain the present experimental results. Instead, we propose a model that takes into consideration the mixing between singlet states and the higher-order interaction of molecular vibrations with electronic states, which is in quantitative agreement with the experimental results. Our finding opens the way to controlling even Raman inactive vibronic oscillations using light.