The Vietnam war memorial needed to be "harmonious" with its surrounding site. In this context, what does harmonious mean? The construction had to be the same as the other monumentsvisitors would hear peaceful musicthe memorial had to blend pleasingly with its environmentan anthem was to be created to support the memorial

The memorial had to blend pleasingly with its environment.

Explanation:

When we say "harmonious", it generally mean to be at peace with someone, to be together with, or together in feeling or action, in harmony.

So, when the sentence -

The Vietnam war memorial needed to be "harmonious" with its surrounding site

uses the word "harmonious" in it, it means that the memorial had to blend pleasingly with its environment. It means that it has to be in sync or in common theme or standing / element with the others.