In both Sindarin and Noldorin, where n and r came into contact in compounds after the loss of vowels at morpheme boundaries, the n became dh. Tolkien actually mentioned this phonetic rule in The Lord of the Rings appendices:

DH represents the voiced (soft) th of English these clothes. It is usually related to d, as in S. galadh “tree” compared with Q. alda; but is sometimes derived from n+r, as in Caradhras “Redhorn” from caran-rass (LotR/1113).

Tolkien mentioned this change in several other places, including:

Elen, pl. Elin, with class-plural Eledhrim, Elf, Elves. dhr is < n-r in secondary contact (Quendi and Eldar, circa 1960, WJ/363).

Note ndr > nr not đr (as nr, nnr, see Consonants): So Belerian(d)ren “Beleriandic” but Gondoliðren “Gondolic” (Feanorian Alphabet, 1930s, PE22/36).

This last quote indicates this change did not occur where there was another consonant between the n and r (later lost). There are a number of Sindarin and Noldorin words with nr, which could be examples of this “preserved by clusters” development:

• N. anrand “cycle, age, (lit.) long cycle” from an(d)rand (Ety/RAD, PE22/41).
• S. Finrod from fin(d)rod (VT41/9).
• S. Aranrúth “King’s Ire” (S/201) = aran + rûth (SA/ar(a), rûth).

The nr in Aranrúth is unlikely to have this origin, but here the n might be preserved by dissimilation away from the final spirant th (hat tip to Vyacheslav Stepanov for this suggestion); something similar happened with úthaes < úthaeth.

Elsewhere, nr > ðr is the norm:

• S. Caradhras “Red Horn” = caran + rass (LotR/1113, PE17/36).
• N. iðrin “year, *(lit.) year-circle” = în + rhinn (Ety/RIN, YEN).
• N. odhron and odhril “parent (male and female)” from primitive on- + masculine and feminine suffixes (Ety/ONO).

Conceptual Developments: There are a couple examples of this sound change in the Gnomish of the 1910s and Early Noldorin of the 1920s:

• G. gledhrin “slender” = glen(n) + -rin beside alternate form glen(d)rin (GL/39).
• ᴱN. agladhren “radiant” = aglann + -ren (PE13/136, 158), replacing deleted aglathren (PE13/136).

It seems Tolkien adopted this sound change very early and retained it thereafter.

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