In Sindarin the diphthongs [ai] and [oi] developed into [ae] and [oe] respectively, a set of sound changes noted by David Salo (GS/§4.190). The development [ai] > [ae] applied to both original primitive diphthongs as well as any diphthongs that arose later from the vocalizations of spirants:

• ✶maikā > S. maeg “sharp” (WJ/337).
• ✶daira > S. daer “large, great” (VT42/11).
• ✶tagra [> *taʒra > *tair(a)] > S. taer “lofty” (PE17/186).
• ✶maʒtā > maχtā [> *maitha] > S. maetha “handle, wield, manage” (VT47/6).

For [oi] > [oe], however, this sound change was different from the development of the primitive diphthong [oi], which became [ui] instead, as Tolkien stated in notes from the late 1960s (VT48/7). Compare the following early and late developments:

• Early oi: ✶oio > S. ui “ever” (Let/278).
• Later oi: ✶ugrā > ogra [> *oʒra > *oir(a)] > S. oer “nasty” (PE22/160).

In Sindarin it seems the long slack vowel ǭ in combination with i also ultimately became oe, and so perhaps it merged with the later diphthong oi and shared its development, something also suggested by David Salo (GS/§4.190):

• ✶gāyā [> *gǭia] > S. goe “terror, great fear” (PM/363).
• ✶wāyā [> *(g)wǭia] > S. gwoe “wind” (PE17/34).

In the second example, Tolkien indicated that gwoe later became gwae, possibly a remnant of the Noldorin ae/oe vacillations (see below). There are also a couple of Sindarin examples that hint that sometimes even primitive [oi] may have become [oe]:

• √SLOY > lhoew “poison” and lhoer “venom” vs. Q. hloima and Q. hloirë (PE17/185).

These developments are hard to explain, and could represent either conceptual vacillations on Tolkien’s part, or perhaps these nouns originally contained an a-fortified [ǭ] and so developed [ǭi] > [oi] > [oe].

Conceptual Developments: The development of the diphthongs [ai] and [oi] went through a number of conceptual changes over Tolkien’s life.

Gnomish Developments (1910s): As discussed by Roman Rausch in his Historical Phonology of Goldogrin (HPG/§1.2), the diphthong [ai] generally survived in the Gnomish of the 1910s. This survival was mentioned by Tolkien himself in a very early chart of Gnome Vowels, though he did say it sometimes became e or i when unstressed (PE15/13). The diphthong ae does not appear in the Gnomish Lexicon, and in fact the reverse development [ae] > [ai] is attested:

• ᴱ✶ŋuaʒet- > gwa’ed > G. gwaid “kinsmen, relations; companion” (GL/43).

Primitive [oi] became [ui] in Gnomish as it did in later Sindarin, but in Gnomish the later diphthongs [oi] that arose from the vocalization of spirants also became [ui] (not [oe]), a development noted by Roman Rausch (HPG/§2.6):

• ᴱ✶foχo [> *foχs > *fois] > G. fuis “hoard” (GL/36).
• [*sok-t- > *soχth > *soith] > G. suith “drink, draught” vs. G. soctha- “give to drink” (GL/68).

Thus it seems in the 1910s, [oi] did not have distinct early/late developments as it did in Sindarin.

Early Noldorin Developments (1920s): As discussed by Roman Rausch in his Historical Phonologies of Ilkorin, Telerin and Noldorin around 1923 (HPITN/§4.2.4), the primitive diphthong [ai] became [oi] in (Early) Old Noldorin but then changed back to [ai]:

• ᴱ✶aiya- > ᴱON. oidh > ᴱN. aidh “pain, anguish, woe” (PE13/158).
• ᴱ✶aika > ᴱON. oig > ᴱN. aig “high, steep” (PE13/158).
• [*ailind- >] ᴱON. oilin > ᴱN. ailin “lake” vs. ᴱQ. ailind- (PE13/158).

Primitive [oi] generally became [ui] (as was the case in earlier Gnomish and later Sindarin), but it could become [ai] if it appeared before [w]:

• ᴱ✶t:loise > ᴱN. tlui “slender” (PE13/154).
• ᴱ✶koile > ᴱN. cuil “life” (PE13/141).
• ᴱ✶t:loiwe > ᴱN. tlaiw “sling” (PE13/154).
• [*oiwe >] ᴱN. aiw “bird” vs. ᴱQ. oive (PE13/136, 158).

This means the sound change [ai] > [oi] must have been after [oi] > [ui], but [oi] > [ui] may have been inhibited before [w] and so fell in with later [oi] as it shifted back to [ai]. A specialized phonetic development before [w] reappears in a different form in the Noldorin of the 1930s (see below). Where the diphthongs [ai] and [oi] arose from the vocalization of spirants in Early Noldorin, they generally remained unchanged, perhaps indicating these vocalizations occurred after the general diphthongal developments:

• ᴱ✶kapse > ᴱN. cais “leap” (PE13/140).
• [*mapta >] ᴱN. maith “ravishment; seizure” vs. ᴱQ. mapta (PE13/163).
• [*oktā >] ᴱN. oith “feud” vs. ᴱQ. ohta “war” (PE13/151, 164).
• [*pukta > *hoχtha] > ᴱN. hoith “coitus” vs. ᴱQ. pukta or puhta (PE13/147, 163); here a-affection plays a role.
• ᴱ✶okswē > ᴱN. oif “terror, phantom” vs. ᴱQ. oswe (PE13/151, 164).

In one case, though, an oi arising from a spirantal vocalization became ui:

• ᴱ✶loktu > ᴱN. luith “magic, spell”, with alternate form lhuth (PE13/149).

Noldorin Developments (1930s): Late developments of the diphthong [oi] were mostly not a factor in the Noldorin of the 1930s for two reasons. First, primitive diphthongs [oi] became [ui] (as it did in earlier Gnomish and later Sindarin), but also the diphthongal combination [ǭi] became [ui] very early (in Old Noldorin) as well:

• ᴹ✶wāyā > wōia > ON. uia > N. ui “envelope” (Ety/WAY).
• ᴹ✶nāyǝ > noi > ON. nui “lament” (Ety/NAY).
• ᴹ✶istāyā [> *istǭio] > N. istui “learned” (Ety/IS).

Second, in the 1930s the vocalizations of spirants after the vowel [o] produced [ou] > [au] (PE22/39). Thus, the diphthong [oi] did not reappear later from spirantal vocalizations (as it did in Sindarin).

As for the phonetic development of [ai] in the Noldorin of the 1930s, it is well known that Tolkien vacillated between [ae] and [oe] as the ultimate result. Helge Fauskanger discussed the variation in his article: “AE or OE?” (AL). David Salo also noted the variation in his discussion of Noldorin phonology (GS/§4.230). There are several examples where Tolkien had both [ae] and [oe] in specific entries in The Etymologies:

• ᴹ√GÁYAS > ON. gaia > N. goe, gae “dread” (Ety/GÁYAS; EtyAC/GÁYAS).
• ᴹ√KHAYA > N. hae (hoe) “*far” (EtyAC/KHAYA).
• ᴹ√LAIK > ON. laika > N. lhaeg or lhoeg “keen” (Ety/LAIK; EtyAC/LAIK).
• ᴹ√GAY [> ON. *gaira] > N. gaer, goer “red, ruddy”, in an earlier entry just gaer (Ety/GAY; EtyAC/GAIRĀ).

Other examples in The Etymologies showed just ae or oe without variant forms. Since it seems Tolkien could not make up his mind on the exact phonetic developments, it is hard to determine the conditions that produced either [ae] or [oe] by looking at The Etymologies alone. Some additional information on these phonetic developments have been published since the time Fausganker and Salo did their original analyses, however: a chart of diphthongs appeared in Tolkien’s notes on the Noldorin use of the Feanorian Alphabet from the 1930s described these phonetic developments in some detail (PE22/39, relevant parts only):

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 ...

• [oi] [<] ON ai. archaic h~B, later > [oe] q.v. ...
• [a͡i] [<] ON ai after w, or a + i in contraction. archaic ]~B, later > [ae] q.v.
• [a͡e] [<] older ai, as above; or ă + ʒ, χ. ]l, later G ]Þ — usually ]Þ (beside ]l).
• [o͡e] [<] older oi, as above; or o + e in contraction. hl, later G hÝ — usually hÝ (beside hl).

Based on these notes, it seems that the normal development of [ai] was to [oi] (as was the case in Early Noldorin of the 1920s) which then went on to become [oe]. However, [ai] after the semi-vowel [w] remained, and it merged with [ai] produced from the vocalization of spirants and later became [ae]. The special development of ai > ae after w was also mentioned elsewhere in the Feanorian Alphabet document:

ae in chwae, awae etc. was the regular development of ON ai after w (PE22/31).

Examples in The Etymologies are consistent with these rules. All examples resulting from vocalization of spirants or appearing after w consistently show ae rather than oe:

• ᴹ✶sagmā [> *saimh(a)] > N. saew “poison” (Ety/SAG).
• ᴹ✶ragnā > ON. ragna [> *rain(a)] > N. rhaen “crooked” (Ety/RAG).
• ᴹ✶taksē [> *tais(e)] > N. taes “nail” (Ety/TAK).
• ᴹ√WAIWA > N. gwaew “wind” (Ety/WĀ).
• ᴹ✶wǣdē > ON. waide > N. gwaeð “bond” (Ety/WED).

All of the examples appearing before final w also consistently show ae, so perhaps this special development applied in this case as well:

• ᴹ✶aiwē > N. aew “(small) bird” (Ety/AIWĒ).
• ᴹ✶slaiwā > ON. thlaiwa > thlaew > N. flaew “sickly, sick, ill” (Ety/SLIW).
• ᴹ√YAY > ON. yaiwe > N. iaew “mocking, scorn” (Ety/YAY).

The diphthong [oe] was largely produced in cases of a primitive diphthong [ai] that did not appear before or after [w]:

• ᴹ√AI̯R > N. oer “sea” (Ety/AY).
• ᴹ√SPAY [> *spaika] > N. foeg “mean, poor, bad” vs. ᴹQ. faika (Ety/SPAY).
• ᴹ√MIL-IK [> *mailē] > N. moel “lust” vs. ᴹQ. maile (Ety/SPAY).
• ᴹ√RÁYAK [> *raikā] > N. rhoeg “wrong” vs. ᴹQ. raika (Ety/RÁYAK).

Thus, the seeming inconsistencies in The Etymologies represent a more regular set of rules than it appears at first glance. There are, however, definitely some conceptual vacillations for the development of [ai] on Tolkien’s part in the 1930s, including the exceptions noted above and others. In the somewhat earlier Comparitive Tables of phonetic development, Tolkien described a different phonetic development: ᴹ✶ai, ᴹ✶ǣ > ON. ę̄ > ei > N. ae (PE19/25). There a couple of examples of intermediate ę̄ in the 1930s and 40s (assuming long ē represents ę̄):

• ᴹ✶gaisrā > gǣsra > ON. gērrha > N. gaer “dreadful” (Ety/GÁYAS).
• ON. glaibe > glēbe > glaef > N. glaew [“salve”] (TMME/53).

In this entry containing N. gaer, Tolkien also vacillated between gae, goe “dread” (see above). This vacillation between ae and oe persisted until quite late in the writing of The Lord of the Rings: in the draft of the appendices, Tolkien first wrote loer for “summer” before revising it to laer (PM/135, 136). By the time The Lord of the Rings was published, however, it seems Tolkien had made up his mind, and the normal development of [ai] was to [ae], never [oe].

Neo-Sindarin: It is usual in Neo-Sindarin writing to revise entries from The Etymologies with [oe] to [ae] for better consistency with the Sindarin of The Lord of the Rings.

In The Etymologies, the Noldorin development of the primitive diphthong ᴹ✶ai is unclear. In some cases, it became ae: N. gwaew “wind” < ᴹ√WAIWA (Ety/WĀ). In others, it became oe: N. moed “handy, skilled” < ON. maite (Ety/MAƷ). Tolkien seems to have vacillated between the two results, for example gaer (EtyAC/GAIRĀ) >> goer (Ety/GAY) and lhaeb (EtyAC/LÁYAK) >> lhoeb (Ety/LÁYAK).

Possible Phonetic Rules: In the contemporaneous Comparative Tables (PE19/18-28), the phonetic development was primitive ᴹ✶ai > ON. ę̄ > ei > N. ae (PE19/25, column 9). There is one example in The Etymologies that seems to follow a similar development: ᴹ✶gaisrā > gǣsra > ON. gērrha > N. gaer “dreadful” (Ety/GÁYAS). Another example appears in a fragmentary note discussing ai > ae from 1940: ON. glaibe > glēbe > glaef > N. glaew “ointment” (TMME/53). It seems likely that entry in the table represents Tolkien’s basic idea for the Noldorin development of this diphthong.

Examples in The Etymologies seem to indicate that, where it appeared, the diphthong oe was a further development from ae, for example: ᴹ√GAY > N. gaer, goer (Ety/GAY) and ᴹ√KHAYA > N. hae (hoe) (EtyAC/KHAYA). There are several cases in which the diphthong ae is consistently preserved, however:

• Where the diphthong arose from the vocalization of primitive g, such as: ᴹ✶sagrā > N. saer (Ety/SAG) and ON. ragna > N. rhaen (Ety/RAG).
• Where the diphthong arose from the vocalization of primitive p or k, such as: ᴹ✶yakta- > N. iaeth (Ety/YAK) and apsa > N. aes (Ety/AP).
• Where the diphthong was preceded or followed by w, such as: gwaew (Ety/WĀ), glaew (Ety/LIB²) and gwaedh (Ety/WED). In case of preceding w, this development was explicity mentioned by Tolkien: “ae ... was the regular development of ON ai after w” (PE22/31).

It is possible that at this stage, Tolkien considered the normal development to be ai > ae > oe, except that ae was preserved in words with the combination aew or its antecedents: ᴹ✶[ai{wbm}]. Furthermore, the shift of ae > oe occurred before the vocalizations of primitive g, p, k, so that:

• ᴹ✶[ag{lrmn}] > [aɣ{lrmn}] > [ai{lrmn}] > N. [ae{lrmn}]
• ᴹ✶[a{pk}{st}] > [a{ɸx}{xθ}] > [ai{xθ}] > N. [ae{xθ}]

There are quite a few ae-forms in The Etymologies that cannot be explained by this rule, however:

• ᴹ√NAY > N. nae (Ety/NAY)
• ᴹ✶laire > N. lhaer (EtyAC/LIR¹), later revised to ᴹ√GLIR > N. glaer (Ety/GLIR).

It seems that Tolkien’s ideas on the Noldorin development of primitive ᴹ✶ai were in flux as he wrote The Etymologies, making it very difficult to discern his intentions.

Conceptual Development: The Silmarillion drafts from the 1930s generally had ae-forms: N. Belegaer (LR/19) and N. Aelin-uial (LR/262) versus the oe-forms in The Etymologies: N. Belegoer (Ety/AY) and N. Oelinuial (Ety/AY). As noted above, the development in the Comparative Tables from the (?early) 1930s was ᴹ✶ai > ON. ę̄ > N. ae (PE19/25). It seems likely that Tolkien introduced the oe-forms as he was composing The Etymologies.

The variations between ae and oe continued in Lord of the Rings drafts from the 1940s, for example N. Taragaer “Ruddyhorn” (RS/419) versus earlier goer “ruddy” (Ety/GAY) but N. loer “summer” (PM/135) versus later S. laer¹ (LotR/1107). In the published versions of The Lord of the Rings and in Silmarillion revisions from the 1950s-60s, the oe-forms had largely disappeared, making it likely that Tolkien abandoned this particular phonetic rule.

Alternate Theories: I am not sure who first pointed out the ae/oe variation in The Etymologies, but it is well established in the literature. Helge Fauskanger discussed the variation in his article: “AE or OE?” (AL). David Salo also noted the variation in his discussion of Noldorin phonology (GS/68, §4.230). My analysis agrees with the broad outlines of both these treatments, but given the ambiguity of the underlying evidence, the details are open to interpretation.