De institutione musica I.29: Ubi consonantiae reperiantur.
In these comparisons of lowness and highness it is necessary that those consonances be found which are commensurate with one another, that is, which can have a common measure, as in multiples the double is measured by that part which is the difference between the two terms, as between two and four the number two measures both; between two and six, which is triple, two measures both; between nine and eight the same unit measures both. Again, in superparticulars, if the proportion is sesquialter, as four to six, it is two that measures both, which is the difference of both. And if the proportion is sesquitertian, as when eight is compared with six, the same number two measures both. But this does not happen in the other kinds of inequality which we mentioned above, as in the superpartient. For if we compare five with three, two, which is their difference, measures neither. For compared with three once it is less, doubled it exceeds. Likewise, compared with five twice it is less, a third time it goes beyond. And therefore this first kind of inequality is separated from the nature of consonance. Further: that in those that form consonances many things are alike, but in the others not at all, is proved in this way: the double is nothing other than twice the simple, the triple nothing other than three times the simple, the quadruple the same as four times the simple, the sesquialter twice a half, the sesquitertian three times a third part, which is not easily found in the other kinds of inequality.