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We investigate the (large-scale) bar fraction in a mass-complete sample of M > 10^10.5 Msun disk galaxies at 0.2 10^11 Msun), where the fraction of bars in early-type disks becomes significantly lower, at all redshifts, than that in late-type disks. The bar fractions for galaxies with low and high SSFRs closely follow those of the morphologically-selected early-type and late-type populations, respectively. This indicates a close correspondence between morphology and SSFR in disk galaxies at these earlier epochs. Interestingly, the total bar fraction in 10^10.5 10^11 Msun disks it remains roughly constant. This indicates that, already by z ~ 0.6, spectral and morphological transformations in the most massive disk galaxies have largely converged to the familiar Hubble sequence that we observe in the local Universe, while for intermediate mass disks this convergence is ongoing until at least z ~ 0.2. Moreover, these results highlight the importance of employing mass-limited samples for quantifying the evolution of barred galaxies. Finally, the evolution of the barred galaxy populations investigated does not depend on the large-scale environmental density (at least, on the scales which can be probed with the available photometric redshifts).