Daily entries from the 17th century London diary
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The courante, corrente, coranto and corant are just some of the names given to a family of triple metre dances from the late Renaissance and the Baroque era. Modern usage will sometimes use the different spellings to distinguish types of courante (Italian spelling for the Italian dance, etc.), but in the original sources spellings were inconsistent. Courante literally means running.
In the later Renaissance the dance was done with fast running and jumping steps, as described by Thoinot Arbeau. These steps are sometimes thought to be broken up by hops between the steps, but this is perhaps not supported by Arbeau's confusing and contradictory instructions, which described each "saut" as resulting in the completion of a new foot placement.
During its most common usage, in the Baroque period, the courante came in two varieties: French and Italian. The French type had many cross-accents and was a moderately fast dance, in contrast to the allemande that preceded it. The Italian courante was faster, more free-flowing and running, however, it is not clear whether this is significantly different from the French Renaissance courante described by Arbeau. In a Baroque dance suite, an Italian or French courante typically comes between the allemande and the sarabande, making it the second or third movement.
See Courante
http://www.pepysdiary.com/p/5788.php
“By 1700 the Courant was no longer danced except as a basis of dance used by the dancing masters and became known as “Doctor Dance” through the use of its teaching techniques applied to other dances.
[…] Musically, the Courante was the second movement (Suites de Danses) of the classical baroque suite, typically following the allemande with the accompaniment in triple time (3/4).
[…see] Court Ayres, Pavins, Corantos, &c., Playford, John 1655 “
http://www.streetswing.com/histmain/z3cornt1.htm
Coranto
Coranto singles and doubles aren’t understood very well, but they were definitely very athletic.
Andrew Draskoy suggests this as a low-impact version:
Single left: Leap forward onto left foot, then hop bringing your right foot together with your left.
Double left: Leap forward onto left, forward onto right, forward onto left, in place bringing your right foot together with your left.
If you’re feeling athletic, you move twice as much: Add in a hop in place before each leap or hop above.
http://www.themiddleages.net/life/dances.html