A quotation that may hint at the older origin:
The Caldron of Poesy
Anecdota from Irish manuscripts
Volume 5, pg. 25, line 7
http://www.ucc.ie/academic/smg/CDI/PDFs_textarchive/AnecdotaV.pdf "lūaithe echaighe nemmedōon mīs míthime."
".i. comlūath é 7 int ech inns.aighther isin āenach a mī medhōnach int samraid"
middle of June = month of the middle of the summer
There is the old name for May, Céitein, which means first (month) of summer:
Céitein
May, Old Irish cétam (g. cétaman), cetsoman (cetshaman) in Cor.Gl., where it is explained as cét-sam-sín, the first weather-motion of sam or summer. The word means the "first of summer" - cét+sam-, the sam of samhradh, q.v. The termination is possibly influenced by other time words. See Samhuinn.
http://www.ceantar.org/Dicts/MB2/mb08.html samhradh
summer, Irish samhradh, sámhradh, Early Irish samrad, sam, Welsh, Cornish haf, Middle Breton haff, Breton hanv: *samo-; Sanskrit sámâ, year, Zend hama, summer, Armenian am, year; further English summer, Greek @Gc@`méra, day. The termination rad = rado-n (n.
http://www.ceantar.org/Dicts/MB2/mb32.html foghar
harvest, Irish fóghmhar, Middle Irish fogamur, autumn, Early Irish fogamur, fogomur, last month of autumn: *fo-gamur, the gamur being from the root of geamhradh, winter, q.v. The idea is "sub hiemem". Cf. Welsh cynauaf, harvest, Old Welsh kynnhaeaf, from cyn, before, and gauaf, winter.
http://www.ceantar.org/Dicts/MB2/mb18.html There also seems to be a pattern:
May - Beginning of Summer
June - Middle of Summer
July - End of Summer
August - Beginning of Fall
September - Middle of Fall
October - End of Fall
This is also apparent because of the principal feasts being on May 1, August 1, and November 1 to mark the completion of a season and the start of a new one. And you have the quarter days which mark the mid point of the seasons. It just seems to make sense.
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