Many Word Press templates are using H1 for the blog title, no tag for blog description and one more H1 tag for article (post) title. I'm not sure that this is the best way to assign tags from page SEO standpoint. What you would consider to be the best tag assignment?
H1 should be the post/page header/title, and should be the only H1 on the page. I usually tweak any off the shelf themes so that the blog name is some arbitrary style as having it as a H1 is meaningless.
So, it seems that it is better to use H2 for blog title, H2 or H3 for blog description (it may contain some of your targeted keywords) and H1 tag for article (post) title.