De institutione musica II.4: De relativae quantitatis differentiis.
Of that discrete quantity which is by itself we have spoken sufficiently in the Arithmetic. Of quantity related to something there are three simple kinds: the multiple, the superparticular, and the superpartient. When the multiple is mingled with the superparticular and the superpartient, two others arise from them, namely the multiple superparticular and the multiple superpartient. The rule for all these is this: if you wish to compare the unit with all the numbers in the natural series, the fixed order of the multiple will be woven. For two to one is double, three to the same triple, four quadruple, and so on in the same manner, as the description below shows.
If you seek the superparticular proportion, compare the natural number with itself with the unit removed: three with two (for it is sesquialter), four with three, which is sesquitertian, five with four, which is sesquiquartan, and so on in the same manner, as the description below shows.
The superpartients you will find in this way. Set out the natural number, beginning with three. If you pass over one, you will observe that the superbipartient is produced; if two, the supertripartient; if three, the superquadripartient; and the same in the rest.
Looking to this order, the careful reader will also examine the proportions compounded of the multiple and the superparticular, or of the multiple and the superpartient. But of all these it has been said more briefly in the Arithmetic.