The Wikipedia article on Beethoven's 7th symphony talks about how "the work as a whole is known for its use of rhythmic devices suggestive of a dance, such as dotted rhythm" and "[the Vivace] is dominated by lively dance-like dotted rhythms". I can hear the dotted rhythms, but what is their connection to dance? Does anyone have any references? Which dances are dotted rhythm based? I couldn't find anything on Google and I don't know much about dance.
Beethoven said nothing about dancing. In fact the first performance of the 7th was at a charity concert to raise money for veterans of the Napoleonic wars, and Beethoven's own introductory speech said
We are moved by nothing but pure patriotism and the joyful sacrifice of our powers for those who have sacrificed so much for us.
However, Wagner described the symphony as "the apotheosis of dance'' and everybody knows Wagner was a genius, so that must be the right interpretation.
I wouldn't read too much into the 'dance-like' comment. There are lots of dance rhythms - a stately Pavane, a flowing Waltz, a spritely Minuet, an energetic Jig, a frantic Tarentella etc. etc. Someone thought the Beethoven reminded him of one of these. A valid opinion, but not Holy Writ.
It is referring to the dotted 6/8 rhythm after the dramatic intro. I have also heard this 2 sections might have the subtitle: invitation to the dance
The fast 6/8 reminds me on a gigue or tarantella (event. also a waltz - as 6/8 can be heard as 2 x 3/4 measures)
As it is said in the quotation below the gigue has 3/4 (triplets) or 12/16th and the tarantella has an up-beat of a half bar.