No, you only tune in once
…, any type of magical melee weapon could be created as a saber, so you could acquire a vicious saber or a vorpal saber.
The previous sentence simply refers to the fact that a saber can be enchanted in the same way as any other magical weapon.
That is, the magical weapons in the Dungeon Masters guide (and other sources) establish the type of weapons that can hold a given type of enchantment.
For example, "Vicious weapon" says "Weapon (anyone)". Which means that you could potentially find any type of weapon that has this kind of magic: a vicious longsword, a vicious warhammer and so on.
So, what this is saying is that you could get a violent knife in the same way that you could get a vicious long sword. But even if the sword of sword always requires tuning, this has no additional effect, since it is only limited by the amount of elements it can tune (not by "enchantments").