The Sindarin word rhîw means winter. Its Quenya equvalent is hrívë. (R.480). An older manuscript version of the name of the month January is Cathriw, which forms a pair with December (Ephriw). (HoMe, xii, 136) Salo glosses Cathriw as “the second or later month of winter,” from cad- (< *kata-) + rhîw ^L> riw.  Compare: July = Cadlaer (the second or later month of summer), and June (Eblaer from eb- (< *epe-) + laer (summer).[1]

Tolkien’s pairs of month names recall the Anglo-Saxon and Hobbitish month names Ærra Jéola (Before Yule) | Æftera Jéola (After Yule); Ærra Líða (Before Midsummer) | Æftera Líða (After Midsummer), and Foreyule | Afteryule; Forelithe | Afterlithe.

Tolkien’s prefix ep-/eb- in the month names Ephriw and Ebloer would seem to be cognate with the Greek prefix έπί- (epi- [ep- before vowels or ‘H’]) which carries the meaning: on, above, toward, by, to, among, and near. Compare epilogue, epithet, epidemic, epitaph, epidermis, epitomize, and ephemeral. The sense in Tolkien’s month names would be that of above, i.e. before the calendar event.

Tolkien’s prefix cad-/cath- would appear to be cognate with the Greek prefix κατά- (kata-) that signifies down, through, from, or completion.  Before vowels it is spelled: cat- and cath-. Compare: catastrophe, catacomb, catalogue, cataclysm. The sense in Tolkien’s month names would be that of below, i.e. after the calendar event.

The Old High German name for January was Hertimânôt, MHG: Hertemânôt; Modern German Hartmonat (Month of Hard Frost). The Grimm German Dictionary suggests that the name may have come from Schneeharst (an ice crust on snow). In Polish, it is Luty (Severe Month). In Dutch, January was Lauw-maand (Frost Month). In the Icelandic calendar, the month that corresponds to our mid-January to mid-February was called Þorri (Frozen Snow Month). The word in Bree for January was Frery, which is cognate with the Old English frēorig (freezing).[2] Compare the German frieren (to freeze), and the archaic English adjective frore (frosty, frozen) which is found in poetry as late as Keats.

Tolkien’s names winter, December and January, therefore, appear to be cognate with the Welsh rhew (ice, frost), the Old Irish réud, the Breton reu, the Manx rio. In Welsh, rhewi means to freeze, rhewiedig signifies iced, frozen, and rhewlyd is freezing, frosty. Though not all scholars agree, Koch posits this Celtic root as the basis for the month name Riuros on the Coligny Calendar.[3]

Given that Tolkien never met a pun he didn’t like, in a Celtic context, the first element of the alternate names for January (Cathriw) and July (Cadloer) suggests the Irish cath (battle), the Welsh cad, the Old Welsh cat, and the Brittonic *kattā. Compare Taliesin’s Cad Goddeu (The Battle of the Trees), Cath Maige Tuired (The Battle of the Plain of the Towers) from the Irish mythology, and the Welsh name Cadwallawer (Battle Ruler) < cad- (battle) + gwaladr (ruler) ^L> waladr.

On the analogy of these Celtic names, Cathriw could be glossed as Battle of the Frost, which has a certain resonance with Ragnarok, the battle between the Norse Gods and the Frost Giants (hrímþursar) at the end of the world.

Since the rhîw in Cathriw has a demonstrably Welsh cognate, the laer in Cadlaer should have one as well. The earlier form for lear in Tolkien’s notes was loer. (HoMe, xii, 136) This appears to be cognate with the Welsh lloer (moon, month, lunation), which fits well into Tolkien’s calendar that is based on “‘months’, governed more or less by the Moon” (R.479; HoMe, xii, 125), like the Anglo-Saxon calendar, the months of which were “governed by the revolution of the moon.”[4]

Linguistically, the word for month is derived from the word for moon by the addition of the suffix –th, which is found in words like depth, width, and breadth. This is a common feature in the Germanic languages. Compare: Old English mónaþ, Old Norse mánaðr, Gothic menoþs, Old High German mánód, Modern German Monat, Modern Danish and Norwegian måned, and Modern Dutch maand. The Modern Russian word for month месяц (mesyats) was also the word for moon, until it was supplanted in the meaning of moon by the word луна (luna).

By reading loer as the Welsh word for month, the compounds Eblaer and Cadlaer would yield the gloss *Before the Moon and *After the Moon. This reading finds a resonance with the Athenian New Year, which —like Easter—was a movable holiday. Easter is celebrated on the first full moon after the vernal equinox. The Athenian New Year began with the first full moon after the summer solstice, which “was the day appointed for the Qlympick [sic] games, a day probably fixed upon to give the best season of the year, and the brightest nights for the celebration of those games.”[5]

The Shire New Year, however, was in January, and Mid-year’s Day was between Eblaer and Cadlaer. (R.482) This corresponds with our current calendar. The Celtic New Year, however, was celebrated on November first,[6] which roughly corresponds to the Old Hobbit calendar, “when their new year began after the harvest” in October. (R.483; HoMe, xii, 121, 123, 127)

Notes:   

[1] David Salo, A Gateway to Sindarin: A Grammar of an Elvish Language from J. R. R. Tolkien's Lord of the Rings, University of Utah Press, 2004, p. 401.

[2] Jim Allan, “The Giving of Names,” An Introduction to Elvish, Frome, Somerset: Bran’s Head, 1978, p. 228.

[3] John Koch, Celtic Culture: A Historical Encyclopedia, volume i, ABC-CLIO, 2006, p. 464.

[4] Sharon Turner, The History of the Anglo-Saxons: From the Earliest Period to the Norman Conquest, volume 1, Paris: Baudry, 1840, p. 137.

[5] William Vincent, The Voyage of Nearchus from the Indus to the Euphrates, London: T. Cadell Jr. and W. Davies, 1797, p. 34.

[6] John Rhys, Celtic Folklore: Welsh and Manx, volume 1, pp. 315-321; See also: James George Frazer, The Golden Bough: A Study in Magic and Religion, volume 1 of 2, London: Macmillan and Company, 1913, p. 225.