Grain harvest time in ancient Greece

[Epictetus]

When was wheat harvested in ancient Greece? I found this in Hesiod:

When the Pleiades, daughters of Atlas, are rising (10), begin your harvest, and your ploughing when they are going to set (11). Forty nights and days they are hidden and appear again as the year moves round, when first you sharpen your sickle. This is the law of the plains, and of those who live near the sea, and who inhabit rich country, the glens and dingles far from the tossing sea…

Translator’s notes:
(10) Early in May.
(11) In November.

Hesiod, Works and Days, 383+

And this:

Set your slaves to winnow Demeter's holy grain, when strong Orion (28) first appears, on a smooth threshing-floor in an airy place.

Translator’s note:

(28) July.

Hesiod, Works and Days, 597+

So according to the translator’s notes, grain was harvested during May, dries for a couple of months, and threshed in July. Does this sound right?

Edit: And what did this mean for the days of the citizen soldier? I had been under the impression that campaigning season was until the harvest, but if that is the case the campaign must have ended in May. This certainly doesn't seem right to me.