In Sindarin the diphthong [ei] developed into [ai] in final syllables (including monosyllables), a sound change noted by David Salo (GS/§4.199, 2004). Roman Rausch examined this phonetic development in great detail (including its earlier conceptual variations in the 1920s and 1930s) in his article On the Diphthongs ei, ai in Noldorin and Sindarin (DEANS, 2008); my conclusions mostly align with his. This sound change did not apply to primitive diphthong [ei], which had already become [ī] in the Old Sindarin period. It did apply to later diphthongs that arose from the vocalizations of spirants or i-intrusion:

• ✶keglē [> *keʒle > *keil(e)] > S. cail “fence or palisade of spikes or sharp stakes” (UT/282).
• ✶nek-tē [> *neχte] > neith > S. naith “angle” (PE17/55).
• ✶delya > deil > S. dail “lovely, beautiful” (PE17/151).
• ✶lisyā > liχı̯ā > leχı̯ > leich > S. laich “sweet” (PE17/148).
• ✶RAN [> *ranya> *reni(a)] > rein > S. rain “erratic wandering” vs. Q. ranya (VT42/13).

As shown by the last two examples, earlier sound changes like i-fronting and a-affection meant that the diphthong [ei] could also arise in words where the primitive base vowel was not [e], and these too ultimately produced the diphthong [ai]. Here are some polysyllabic examples:

• ✶atatya > S. edaid “double” (VT42/26).
• [*satarī] > sedair plural of S. sadar “trusty follower, loyal companion” (PE17/183).

This change of [ei] to [ai] is the only way the diphthong [ai] could appear in Sindarin, since earlier the diphthong [ai] became [ae], both the primitive diphthong [ai] as well as diphthongs arising from the vocalization of spirants. Where [ei] appeared in a non-final syllable, however, it survived:

• S. einior “elder” (PM/358).
• S. leithian “release from bondage” (S/162).
• S. neithan “one deprived, exile” (PE17/167).

This means that in general, [ai] and [ei] were in complementary positions: [ai] in final syllables and [ei] in non-final syllables. This seems to remain an active phonetic rule in Sindarin, so that newly-formed compounds continue to obey this rule. For example, consider the name S. Ar-Feiniel “White Lady” (S/60) which seems to contain S. fain “white”. There are a handful of examples where [ei] appears in final syllables, however. These can be explained as either (a) archaic forms or (b) remnants of Noldorin ideas (see below). A partial list of exceptions includes:

• S. Feir “Mortal” vs. Q. Firya (WJ/387).
• S. eilph plural of alph “swan” (UT/265).
• S. edhelvein “elven fair” (PE17/56).
• S. †mein “first” vs. Q. minya (VT42/10).

The last of these was explicitly marked as archaic, and was replaced in colloquial Sindarin by minui. There are a number of examples where [ai] appears in non-final syllables, and these examples are more difficult to explain:

• S. Dairuin (S/155), one of the companions of Barahir, this name may not be Sindarin.
• S. Gwaihir “Windlord” (LotR/261), probably an archaic name, which should have become **Gwaehir; see gwae “wind”.
• S. raitha- “to try, strive” (PE17/167), a verb with a number of irregularities, probably representing (transient?) conceptual variations; it was originally written reitha- (deleted), and Tolkien wrote an e above raitha, possibly indicating its restoration.

One side effect of this sound change is that all primitive adjectives of the form [-aCya], [-eCya] or [-iCya] became [-aiC], since i-fronting pushed [a] to [e] and a-affection pulled [i] to [e], and the diphthong [ei] that resulted from i-intrusion became [ai] in all these cases. It is a somewhat open question how adjectives of the form [-oCya] or [-uCya] developed: see the entry on how [œi] became [ui] or [y].

Conceptual Developments: Tolkien vacillated on whether [ei] became [ai] at various periods of his life.

Gnomish Developments (1910s): An early chart of Gnome Vowels shows primitive ai was usually preserved, but primitive ei usually became ê (PE15/13). As discussed by Roman Rausch in his Historical Phonology of Goldogrin (HPG/§1.2), these two sound changes were well represented among words in the Gnomish Lexicon, but where ei arose later from the vocalization of spirants, it became ai (HPG/§2.6). Unlike Sindarin, this seems to occur in all syllables, not just final ones:

• ᴱ✶eχt·taþ· [> *eithos] > G. aithos “thorn bush” (GL/18).
• ᴱ✶kekt(ǝ)lḗ [> *keithl] > G. caithl “source, fount, origin” (GL/25).
• ᴱ✶leχ-sa [> *leis] > G. lais “green sward, glade” (GL/53).

The diphthong [ei] did not appear in non-archaic words in the Gnomish Lexicon, but it did start to appear in some words in the Gnomish Lexicon Slips, probably representing a conceptual shift where ei could be preserved in non-final syllables (see Early Noldorin Developments below):

• G. eiben “cherry” (PE13/113) vs. earlier aibin “cherry tree” (GL/18).
• G. eilin “pool” (PE13/113) vs. earlier ailion “lake” (GL/17).

Some of these examples even seem to show ai > ei, but most of these are probably the result of newly-introduced i-affection ([a] > [e] before [i]), since the diphthong ai continues to appear in the Gnomish Lexicon Slips:

• ᴱ✶faiðn > G. feigien “worse” (PE13/114).
• ᴱ✶alyan- > G. eilian “branch” (PE13/113).
• ᴱ✶tálı̯èndǝ > G. teilin “stunt or jest” (PE13/116).

Early Noldorin Developments (1920s): In a chart of Early Noldorin diphthongal changes from the 1920s, Tolkien indicated that generally [ei] > [ai] (PE15/64). As discussed by Roman Rausch in his Historical Phonologies of Ilkorin, Telerin and Noldorin around 1923 (HPITN/§4.2.4), often primitive [ei] became [ui] instead. However, where [ei] arose later from vocalization of spirants, it almost always became [ai] in final syllables, much like later Sindarin (HPITN/§4.1.3; §4.2.5):

• ᴱ✶ekta > ᴱN. aith “thorn” (PE13/136).
• ᴱ✶g’lamektá or ᴱ✶k’lamektā > ᴱN. glavaith “blaze” (PE13/144, 162).
• ᴱ✶dágniya or dagniı̯- > dein > ᴱN. dain “height, summit” (PE13/141, 161).

But in non-final syllables [ei] remained:

• ᴱN. eithlos “fountain” vs. ᴱN. aithl “spring, fount, source” (PE13/158).
• ᴱN. eithra- “to prick, stab” vs. ᴱN. aith “thorn, †spear” (PE13/158).
• ᴱ√LETH > ᴱN. leithia- “to release” (LB/154).

Early Noldorin plural patterns also indicate that ei > ai where it resulted from i-intrusion, similar to the Sindarin plural pattern:

• ᴱN. bair plural of ᴱN. bar “house” (PE13/122).
• ᴱN. brainn plural of ᴱN. brann “fierce” (PE13/139).
• ᴱN. gwaig plural of ᴱN. gwag “crooked” (PE13/122).
• ᴱN. rhainc plural of ᴱN. rhanc “corpse” (PE13/152).
• ᴱN. eglair plural of ᴱN. aglar “glory” (PE13/136).
• ᴱN. oerthainc or erthainc plural of ᴱN. orthanc “masked; unbroken” (PE13/156, 164).

Unlike the normal plural patterns of Noldorin and Sindarin of the 1930s and later, in the Early Noldorin of the 1920s i-intrusion could penetrate clusters of two consonants, as seen in the examples above. Furthermore, for plurals of words ending in an r-cluster of consonants, it seems ei did not become ai, but rather reduced to e:

• ᴱN. he(i)rdh plural of ᴱN. hardh “wound” (PE13/147).
• ᴱN. cerbh plural of ᴱN. carbh “deed” (PE13/140).
• ᴱN. te(i)rf plural of ᴱN. tarf “dry” (PE13/165).

In his article On the Diphthongs ei, ai in Noldorin and Sindarin (DEANS/§4.5), Roman Rausch suggested that this might once again have become the normal pattern for plurals in Sindarin, with [ei] surviving before liquids [l] and [r] and reducing to [e], based on the three examples S. eilph plural of S. alph “swan” (UT/265), S. nern plural of S. narn “tale” (MR/373), and sern plural of (N. of the 1940s) sarn “stone” (WR/132). I am not convinced, however, since nern and sern can also be explained by consonant clusters resisting i-intrusion, which was the most common pattern from the 1930s and later. There was variant plural sairn (rather than **seirn) beside sern (WR/132), which I think is further evidence that these examples were not a restoration of Early Noldorin plural patterns, although S. eilph remains a strange and hard-to-explain outlier.

In any case, it seems that the normal phonetic development patterns in the Early Noldorin of the 1920s were that when a later diphthong [ei] arose from spirant vocalization or i-intrusion, then it (a) remained in non-final syllables and (b) became [ai] in final syllables, including monosyllables, except (c) where [ei] appeared before an r-cluster, in which case it reduced to [e].

Noldorin Developments (1930s): Tolkien described the development of the diphthong [ei] in some detail in a chart of diphthongal developments from his notes on the Noldorin usage of the Feanorian Alphabet from the 1930s (PE22/39, relevant information only):

Old short epenthetic diphthongs:

• [ĕı̯] e or affected a + epenthetic ı̯. lÖ later became either [e] or becoming long was identified with [e͡i].
• [œ̆ı̯] affected ŏ, ŭ in unstressed syllables + epenthetic ı̯. hÖ| œi later > ei, and so to [e] or [e͡i].

The long diphthongs - ON diphthongs, diphthongization of ON ō, or new diphthongs from short vowel + vowel (in contractions or in contact with vocalized ʒ, χ), or from long vowels + epenthetic ı̯ ...

• [e͡i] e + ʒ, χ or affected a + ʒ, χ; the same + i in contraction. Later length[ening] of ĕi. l`B l~B later G lÖ - usually lÖ (beside l~B).

Here the later diphthong [ei] that arose from either spirantal vocalizations or i-intrusion did not develop into [ai], but rather survived if long (typical of monosyllables) and reduced to e if short (mainly in the final syllables of polysyllables). This is consistent with many of the examples in The Etymologies:

• ᴹ✶bányā > N. bein “beautiful” (Ety/BAN) vs. S. bain (PE17/165).
• ᴹ√SPAN > N. fein “white” (Ety/SPAN) vs. S. fain (PE17/36).
• ON. andatektha > N. andeith “long-mark” (Ety/TEK) vs. S. andaith (PE17/123).
• ᴹ√KIR > N. ceir “ship” (Ety/KIR) vs. S. cair (PE17/147).

See also the examples in the entry on how [ei] sometimes became [e] in unstressed final syllables in Noldorin. Note that in Noldorin, since [ei] did not become [ai], it seems that [ei] from [-aCya], [-eCya] or [-iCya] blended with [œi] from [-oCya] and [-uCya] after [œ] became [e], and every one of these ultimately produced [eiC]:

• ᴹ✶runya [> *ronya] > rhoein [rhœin] > N. rhein “slot, spoor, track, footprint” (Ety/RUN).

As noted by Roman Rausch (DEANS/§3.6), Tolkien seems to have varied from this pattern in a number of places in The Etymologies. There are a fair number of examples where Tolkien vacillated between [ei] and [ai]:

• ᴹ√EK > N. aith “spear-point” (Ety/EK), later revised to eith (EtyAC/EK).
• ᴹ✶galyā [> *geil] > N. gail “bright, light” (Ety/KAL).
• ᴹ√LEK > N. lhein, lhain “free(d)” (Ety/LEK).
• ᴹ✶(a)ranı̯ā > N. rhain “free” (EtyAC/RAN) beside deleted erein, and with e written above indicating a variant form rhein.

Roman Rausch suggested (and I concur) that this was likely an early emergence of the Sindarin pattern (itself a partial restoration of the Early Noldorin pattern) whereby [ei] became [ai] in final syllables (DEANS/§3.6). There are no examples in The Etymologies of ei/ai vacillation in non-final syllables. Furthermore, as Tolkien wrote The Lord of the Rings drafts in the 1940s, ai in final syllables became the normal pattern:

• N. Emyn R(h)ain “Border Hills” (TI/268, 281).
• N. Haradwaith “Sutherland, Men of the South” (TI/304, 434) vs. N. gweith in The Etymologies (Ety/WEG, EtyAC/WEG).
• N. echain “new, built again” (TI/424).
• N. bair “houses” plural of bár (WR/380) vs. its plural beir from the 1930s (PE22/36).

This remained the case in the Sindarin of the 1950s and 60s, with sporadic exceptions as noted above. As suggested by Roman Rausch (DEANS/§3.6), it is possible that even in the 1930s ei > ai might have been a dialectical variation. In a deleted entry of The Etymologies, Tolkien gave N. Maiðros as the form of this name in the “Feanorian dialect”, more properly in other dialects Meiðros, reformed in Gondolin as Maeðros (EtyAC/MAƷ).

Summary of Conceptual Developments: In the Gnomish Lexicon of the 1910s, later diphthongs [ei] became [ai] universally and [ei] did not appear at all, but [ei] began to appear in non-final syllables in the Gnomish Lexicon Slips when i-affection was introduced. In the Early Noldorin of the 1920s, later [ei] survived in non-final syllables but became [ai] in final syllables, except before r-clusters where it reduced to [e]; this phonetic development occurred more often that it did in later conceptual stages, because in Early Noldorin consonant clusters did not resist i-intrusion. In the Noldorin of the 1930s, later diphthong [ei] generally survived in both final and non-final syllables, although it was sometimes reduced to [e] in polysyllables. By the 1940s, the Sindarin pattern began to emerge where [ei] once again became [ai] in final syllables, a partial restoration of the Early Noldorin pattern. At all conceptual stages, the primitive diphthong [ei] had a distinct phonetic development from the later diphthong [ei] that arose from the vocalization of spirants and i-intrusion, though the exact primitive developments also evolved over time.

Neo-Sindarin: It is usual in Neo-Sindarin writing to revise entries from The Etymologies with [ei] in final syllables to [ai] for better consistency with the Sindarin of The Lord of the Rings. Roman Rausch suggested (DEANS/§4.5) that Noldorin [ei] from [œi] should be adapted differently, however: see the entry on how [œi] became [ui] or [y].

GS/§4.199 GS/§4.232 @@@ Feanorian maið