Thus, if the player can reach 2x melee speed through buffs, the yoyo string will be 75% longer. The exact multiplier for yoyo string length is (1+3*(melee speed))/4, where melee speed is 1.0 without buffs. This can be very helpful in the early game, when yoyos are very short and hard to hit bosses with, and against bosses where you need to keep a distance (such as Empress of Light).
Melee speed bonuses increase the length of a Yoyo's string, but not its attack rate. The Terragrim, Arkhalis, and Starlight's main attacks are considered projectiles, and do not benefit from melee speed boosts. It does, however, affect the speed at which the projectile travels, and it still affects the base weapon (for instance, attacking directly with the Terra Blade will benefit from increased weapon speed). Even if a Terra Blade gets a +100% bonus, it will not shoot projectiles at a faster rate than before. Melee speed only affects the actual swinging animation and not the rate at which a weapon fires projectiles. For most endgame weapons, it does not increase DPS, as most of them fall into one of the following categories. Melee speed bonuses affect different types of melee weapons in different ways.