We report on the local and (sub-) chain dynamics in a new class of tapered multiblock copolymers synthesized by the repeated statistical living anionic copolymerization of a mixture of isoprene and styrene P(I-co-S)(n), as well as a mixture of isoprene with 4-methyl styrene P(I-co-4MS)(n), with up to 10 blocks (1 <= n <= 5). Unlike ordinary diblock copolymers, these multiblock copolymers have a broad interface but at the same time exhibit superior mechanical properties because of the multiblock structure. We employ dielectric spectroscopy aiming at the local and chain dynamics of polyisoprene (PI). To this end, we compare and contrast tapered multiblock copolymers to homopolymers and sequential diblock copolymers, exploiting the distinctive dynamic behavior of PI. Dielectric spectroscopy probes mainly the Rouse dynamics of the PI subchain with the free end and provides an "effective" PI chain length, participating in the dynamics. The estimated PI chain lengths in the tapered di- and multiblock architectures are in qualitative agreement with the lengths obtained by oxidative degradation experiments and by independent Monte Carlo simulations. A quantitative comparison revealed considerably longer chain lengths by dielectric spectroscopy (by nearly a factor of 6). The consistently smaller molecular weight in the simulation could result from an overestimation (underestimation) of the reactivity ratios of S (I) units.