In Part Three of Gioseffo Zarlino's "Le Istitutioni Harmoniche", "The Art of Counterpoint", Zarlino argues that the diatessaron (or perfect fourth) is not a dissonance, as the musicians of his time had relegated it to, but a consonance. He defends this assertion (only in part, although I won't be discussing the other arguments here) by stating:
An interval that has a rational proportion between high and low pitch is consonant, as is shown in the definition of the philosopher [Aristotle] given in Chapter 12 of the second book [Posterior Analytics]. Therefore the fourth, having such a proportion, is consonant. A minor proposition is demonstrated by Philoponus, who, adding to the philospher's definition in the Second Book of the Poteriora, calls the sesquitertia (which is the true ration of the fourth) a rational number.
Zarlino verifies his second premise (that the fourth has a rational proportion) with Philoponus's statement that 4:3 (the ratio of the fourth), or the sesquitertia, is a rational number.
My first question is, is it safe to assume that by an interval with a "rational proportion", Zarlino means an interval that is a rational number, or is this a conflation on his part? If it is the case that he does mean this, what is his definition of a rational proportion/number? It cannot be synonymous with the modern definition (a number that can be made by dividing two integers), as dissonant intervals of every conventional tuning system in Europe at the time (as far as I know) would also be consonant because they are rational (albeit ugly) numbers. Can someone clear this up for me?