units of time in the genitive, need help construing

Suetonius, Augustus, ch. 40

here:

http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.02.0061%3Alife%3Daug.%3Achapter%3D40

Populi recensum uicatim egit, ac ne plebs frumentationum causa frequentius ab negotiis auocaretur, ter in annum quaternum mensium tesseras dare destinauit; sed desideranti consuetudinem ueterem concessit rursus, ut sui cuiusque mensis acciperet.

Context: Suetonius describes the governmental achievements of Augustus.

I think I understand the sentence, but I can’t account for a couple of phrases.

first: “ter in annum quaternum mensium tesseras dare”


ter in annum: three times in each year–seems straightforward
tesseras dare: to give out the grain tickets–no problem here
but
quaternum mensium: this is genitive plural. Does it complement “ter” (three times)?

second: “ut sui cuiusque mensis acciperet”
cuiusque mensis: genitive singular. This has to mean that the man might get his grain tickets each month. But what does it complement? Maybe an implied “tesseram”?

My best guess:

“. . . he decided to distribute food tickets of [i.e., valid for] four months three times a year, but he made a concession to [anyone/someone] desiring the old practice, that [such a person] could obtain [a ticket; tesseram is understood] of his own/for himself [sui; genitive of the reflexive pronoun, not a reflexive adjective] of/for each month.”

Thanks for the careful analysis Qimmik.

FWIW, I have just seen, as if with new eyes, the beginning of A&G on “Genitive Case”, #341.

The genitive is regularly used to express the relation of one noun to another. Hence it is sometimes called the adjective case. . . .

I had read that many times before, but had not properly apprehended it.