Kewl. I've read the application section through and can't find what the tone problem is. I've added an intext source note but even as the matter stood the section began "according to Gurdjieff" and so far as I can see doesn't deviate from that attitude or tone. Where does it? Can you quote something objectionable? The section simply explicates the concept. If every sentence is meant to begin "none of this is scientifically proven but the idea is" then we can apply the same principle to other sites. I understand the concern about promotion, and have seen plenty of articles on wikipedia which justify it, but I can't see that this is one of them. Also the referencing tag is mispalced. The tag the article needs is the one calling for page numbers, that would be a fair cop. 
This is not to say that the article as it stands has no problems apart from page numbers. The subject of the enneagram is a huge one, the difficulty from the wikipedia point of view may be that a satisfactory article would be too long. The problem will probably have to be covered by more complete references....the "enneagram of essence types" as developed by Collins-lineage Fourth way should be mentioned for example; and the work done on the enneagram by Bennet-lineage people.