I was terribly shocked yesterday, when my composition teacher told me, that the dominant does in fact means the triad of the 5th step in the welltemperated system. And not the triad of the 2nd overtone, as it is close to.
I have always thought that theory of harmony was only overcoming the problems of the weird tone system by using a primitive language. But it does never say, what the words really means. Take the dominant - itīs explained as both the triad of the 5th step in the welltempered system and as the triad of the 2nd overtone, now that is not the same and there are no ways, that it can be the compared.
Then there are two possible means of a dominant:
1. the dominant is the triad on 5th step of our tonesystem, a triad that comes close to the triad of the 2nd overtone.
2. the triad of the 5th step of our tonesystem is a triad that comes close to the dominant, the triad of the 2nd overtone.
Can it really be true, that example 1 is the correct? I just think it is stupid not to have a name for the fundamental functions, the ones, that the major/minor-tonality theory are trying to be like.