For example, if one uses the classical definition of a sequence, the set of computable numbers is not closed under the basic operation of taking the supremum of a bounded sequence (for example, consider a Specker sequence).
The earliest definitely datable example of fauxbourdon is in a motet by Dufay, Supremum est mortalibus, which was written for the treaty reconciling the differences between Pope Eugene IV and Sigismund, after which Sigismund was crowned as Holy Roman Emperor, which happened on May 31, 1433.