What are 'modal rhythm' and 'mensural rhythm'?

Question

The following is from Harvard Dictionary of Music 2nd Edit.

From the definition of 'Discant' (bold added):

[...] The ideal of contrary motion was mentioned in the 13th-century "Tractatus de Discantu" (in J.-A.-L. de la Fage, Essais, i, 358; CS i, 311) but became an essential characteristic of discant theory only at the end of the 13th century, when modal rhythm was replaced by mensural rhythm.

Full page of context:

I've never heard these two terms: mensural and modal rhythm. Google gave nothing, neither did Britannica.

What do these two terms mean?

Answer 1

Modal rhythm used note linkage to indicate length. Various patterns of notes indicated how to play the following notes.

Mensural rhythm used note forms (minim, breve, semibreve, etc.); using like 2 semi-breves vs a breve to indicate binary rhythm and 3 semi-breves vs a breve to indicate ternary rhythm schemes.

These are well-described in Wikis and various music history books.