Justice is a part of Moderation

"Moderation doesn't work that way, but actually stretches throughout the whole, from top to bottom of the entire scale, making the weaker, the stronger and those in the middle-whether you wish to view them as such in terms of prudence, or, if you wish, in terms of strength, or multitude, money or anything else whatsoever of that this unanimity is moderation, an accord of worse and better, according to nature, as to which must rule in the city and in each one." (432a)

"He doesn't let each part in him mind other people's business or the three classes in the soul meddle with each other, but really sets his own house in good order and rules himself, he arranges himself, becomes his own friend, and harmonizes the three parts, exactly like three notes in a harmonic scale, lowest, highest and middle. And if there are some other parts in between, he binds them together and becomes entirely one from many, moderate and harmonized. Then and only then, he acts, if he does act in some way-either concerning the acquisition of money, or the care of the body, or something political, or concerning private contracts." (343d-e)

When harmonizing in music you are creating a chord. Each chord is created with a different scale and depending on what scale you are in, the chord will change. Each chord is made up of parts of the scale and without the parts of the scale the chord cannot be completed. Justice is a part of moderation because justice works in harmony with moderation. Moderation is the whole and just is only a partial piece. As the first quote says, "moderation in the entire scale." This is because moderation is the building blocks of everything else. You cannot have justice without moderation since justice is only a part of the scale. Justice is the harmonizing of many things and when you put the three parts together it is good, but if you have all parts of moderation all at once, then it will be all parts and not a specific.