We report the detection of a new interstellar methylpolyyne, CH₃C₆H (methyltriacetylene), with the 100 m Green Bank Telescope. Ten spectral lines of this species were detected toward the Taurus molecular cloud (TMC-1): the K = 0 and K = 1 components of the 12,K-11,K, 13,K-12,K, 14,K-13,K, 15,K-14,K, and 16,K-15,K transitions. Also observed were the K = 0 and K = 1 components of the 6,K-5,K transition of CH₃C₄H (methyldiacetylene). For both methylpolyynes, no higher energy K-components were detected, which is consistent with the 10 K kinetic temperature of the TMC-1 dark cloud. Moreover, radio spectral line data of the cyanopolyyne, methylcyanopolyyne, and methylpolyyne carbon-chain sequences were studied, and strong correlations are found among the values of the three different carbon-chain slopes when total column densities of sequence members are plotted against the number of carbon atoms in the carbon chain. This result suggests that the formation chemistry for all these carbon-chain sequences is common, and the total column density of the next larger, undetected species in each of the three carbon chain sequences is predicted.