Parallax is the most beautiful, most fascinating, most amazing way of creating a website that I've personally seen. If you have not seen or maybe you don't know what Parallax is well let me explain.
This is not limited to one h1 per website but rather one h1 tag per open page and this is where parallax themes cross the line. Parallax themes or websites have most of their content basically on one page. Even though it might seem there are many pages, there usually aren't that many. It is possible however to design the site in a way that there are separate pages, but for this theory's sake, we are talking about parallax designed websites having only one page as the main page or one multiple paged page. To really enjoy the beauty of parallax themes all the information generally is one page.
Great, now we have that covered. If all your important information is divided into parts on the one-page parallax themed website you are most probably missing out on using more potential headings. Headings or H1 is the single most important tag or part of a website because this tells search engines like Google exactly what the entire page is about. It uses that tag to determine just how relevant the rest of the content is and it uses that single tag as the top signal for potential ranking. The heading is the name and function. Usually, normal websites contain many pages but each page has its own h1 tag.
Generally, traditional sites are also easier to index and search engines understand traditional sites better because the content is relevant to the h1 tags, this is most of the time at least. A one-page website such as these parallax designed sites generally have many pages on one page, each single added page has their own unique content and often these pages differ from one another entirely in topic and semantics but technically as mentioned earlier they are in fact all the same page. Google also believes that searches leading to websites that are made up of many pages squashed onto one page confuses users because in the search they might be getting or seeing loads of text but when the site loaded it didn't navigate to the wanted and searched for text.
Instead, often users land on the main page of the parallax effect and it would normally not contain the text they were looking for or found the site for. This would also mean if a site had Google analytics code installed and the user did not found what he was searching for that he would then bounce. The bounce rate causes the Google search engine algorithm to realize that the site was not useful at all and the user left because he did not find what he was looking for. Secondly, bounce rates on 1-page websites are anyway almost extremely high because of the most obvious reason.
There are no other pages to browse and to the algorithm, this might be extremely weird. The nice thing about parallax is that large corporations can use it, they probably have the correct backlinks to tell search engines why people find the site important or want to browse it but for the average normal small business or person, this is not the best way to show off whatever it is you want to show. The exception being of course if all pages related very closely to each other and the content compliments itself. If all the semi-pages or single "pages" on the one-page parallax website is basically one big topic and h2 is used as each semi-page's title it could work. The best way is still beautifully designed websites containing multiple single pages and non-parallax themed sites.