It’s well known that in Sindarin/Noldorin, the spirants [x] and [f] (the latter most probably at its earlier stage [ɸ]) became vowels before the spirants [θ] and [s], resulting in diphthongs. Some examples:

√MAG: S. maetha- “to handle” < [maiθa-] < [maxθa-] < [maɣta-]
√NEK: S. naith “angle” < [neiθe] < [nexθe] < [nekte]
ᴹ√TUP: N. taus “thatch” < [tousa] < [toɸsa] < [tupsa] < [tupse]
ᴹ√TEK: N. teith “mark, stroke” < [texθa] < [tekta]

This last example became taith in Sindarin, since [ei] > [ai] in final syllables.

The vowel that developed from [x] and [ɸ] was either [i] or [u], but this is obscured by the fact that the diphthong often underwent further developments: [ou] > [au], [ai] > [ae] and (in Sindarin) [ei] > [ai]. In the case of N. taus, the development is extremely obscured, because primitive final [se] became [sa] (most clearly seen in [kʰyelesē] > [khelesa] > ON. kheleha) resulting in a-affection that shifted the base-vowel [u] to [o].

The question is, under what conditions did the vowels [i] and [u] develop?

Noldorin Development

Based on the evidence, it seems that in Noldorin the development depended on the character of the preceding vowel: [i] developed from both [x] and [ɸ] after the front-vowels [a], [e] and [i], while [u] developed from [x] and [ɸ] after the back-vowels [o] and [u]. In addition to the above, we have the following relevant examples from the Etymologies:

[x] becoming [u] after back-vowels [o] and [u]:

ᴹ√LOKH: N. lhaws “hair” < [lous] < [loxse] < [lokʰse]
ᴹ√LUK: N. lhûth “spell, charm” < [luuθe] < [luxθe] < [lukte]
ᴹ√LUK: N. lhútha- “to enchant” < [luuθa-] < [luxθa-] < [lukta-]
ᴹ√KOT: N. auth “war, battle” < [ouθa] < [oxθa] < [okta]
ᴹ√SUK: N. sûth “draught” < [suuθe] < [suxθe] < [sukte]
ᴹ√SUK: N. sautha- “to drain” < [souθa-] < [soxθa-] < [sukta-]

The last example sautha- is rather peculiar. It seems that somehow the [u] underwent a-affection to [o] (perhaps based on the uninflected form of the verb), but it’s not clear why this happened for sautha- but not lhútha-.

[ɸ] becoming [i] after front-vowel [a]:

ᴹ√AP: N. aes “cooked food, meat” < [aisa] < [aɸsa] < [apsa]
ᴹ√LAP: N. lhaes “babe” < [laise] < [laɸse] [lapse]

In Noldorin, there are two aberrant examples:

[x] becoming [i] after back-vowel [u]:

ᴹ√YUK: N. iuith “use” < [juiθe] < [juxθe] < [jukte]
ᴹ√YUK: N. iuitha- “to employ” < [juiθa-] < [juxθa-] < [jukta-]

Perhaps in this case the initial [j] (y sound) influenced the process resulting in the vowel [i] instead of the expected [u]. Or this example could be a precursor to the Sindarin developments (see below).

Sindarin Development

In Sindarin, we have fewer examples to work with. Based on the small sample size, however, it seems the development depended entirely on the character of the consonant [x] or [ɸ] and the preceding vowel didn’t matter at all.

[ɸ] becoming [u] after front-vowel [e]:

√LEP: S. leutha- “to pick (up/out)” < [leuθa-] < [leɸθa-] < [lepta-]

[x] becoming [i] after back-vowel [u]:

√NUK: S. nuitha- “to stunt” < [nuiθa-] < [nuxθa-] < [nukta-]
√RUK: S. gruitha- “to terrify” < [gruiθa-] < [gruxθa-] < [grukta-]

If we accept this as the general rule in Sindarin, then the Noldorin words given in the previous section would no longer be valid in Sindarin.

Possible Neologism and David Salo’s Theories

If vocalized [x] always became [i] and vocalized [ɸ] always became [u] in Sindarin, we would be forced to coin neologisms for these Noldorin words:

From [x] becoming [i]:

N. auth “war, battle” >> ᴺS. oeth
N. lhaws “hair” >> ᴺS. laes
N. lhûth “spell, charm” >> ᴺS. luith
N. lhútha- “to enchant” ᴺS. luitha-
N. sautha- “to drain” >> ᴺS. suitha-
N. sûth “draught” >> ᴺS. suith

From [ɸ] becoming [u]:

N. aes “cooked food, meat” >> ᴺS. aus
N. lhaes “babe” >> ᴺS. laus

The neologisms ᴺS. oeth “war” and ᴺS. aus “meat” are especially painful, since the words N. auth and N. aes are both widely used in (Neo) Sindarin.

David Salo examined the same evidence and drew somewhat different conclusions. He mostly followed the Noldorin development in Gateway to Sindarin, but further assumes that [ɸ] became [x] before [s] (GS/§4.82). He then proposed that resulting [x] became [u] after [o] (GS/§4.90) and [i] after [a], [e] and [i] (GS/§4.91) which is identical to the Noldorin development of [x]. However, he uses the Sindarin development in one case: with [x] becoming [i] after [u] (GS/§4.91). He treats N. taus and sautha- as aberrations (GS/§4.89).

Using these rules, David Salo included the neologisms ᴺS. luith, ᴺS. luitha- and ᴺS. suith in Gateway to Sindarin (GS/270, 286) so these three neologisms are probably less controversial. The form ᴺS. suith “draught” also appears in Didier Willis’s Sindarin dictionary, but he has ᴺS. lûth “spell, charm” and ᴺS. lútha- “to enchant”. I think Salo’s neologisms are preferable in this case.

Furthermore, if we accept Salo’s theory that [ɸ] became [x] before [s] (GS/§4.82), then the last two Noldorin examples above can be salvaged, since we would have [apsa] > [aɸsa] > [axsa] > [aisa] > aes “meat” and similarly [lapse] > [laxse] > laes “babe”. The word S. leutha- “to pick up” would remain unchanged because the [ɸ] preceded [θ] instead of [s] (Salo did not address this word because it was published after Gateway to Sindarin). This theory would, however, mess up the development of N. taus “thatch” (but see below).

Salo’s last relevant theory is that [oxθ] and [oxs] > [ouθ] and [ous] as an abnormal development, following the Noldorin pattern rather than Sindarin (GS/§4.90). There are no Sindarin examples of [oxθ] and [oxs], so nothing contradicts this theory. This would allow us to salvage N. l(h)aus “hair” and (more importantly) N. auth “war”. It’s hard to justify this peculiar development phonetically, but it is probably a better option than coining a neologism for auth “war”. Incidentally, it also salvages N. taus “thatch” but with a slightly different development:

[tupse] > [tupsa] > [toɸsa] > [toxsa] > [tousa] > [taus]

Conclusions

I think the bulk of the evidence is that [ɸ] became [u] before [θ] and [x] became [i] before [θ] in Sindarin, so I am going to assume this is the general rule. This is a particularly important phonetic development, since it often applies to (Neo) Sindarin verbs derived from the primitive causative verbal suffix tā, a very common case.

However, I am also going to accept Salo’s theory that [ɸ] became [x] before [s] (GS/§4.82) since nothing contradicts it and this allows us to salvage N. aes “meat” and l(h)aes “babe”. I am also going to accept his more dubious theory that [oxθ] and [oxs] became [ouθ] and [ous], because again nothing contradicts it and this let’s us salvage auth “war”. If we go down this path, the only neologisms we need are the ones that appear in Gateway to Sindarin:

N. lhûth “spell, charm” >> ᴺS. luith
N. lhútha- “to enchant” ᴺS. luitha-
N. sûth “draught” >> ᴺS. suith

This is going to be my working theory on the (Neo) Sindarin vocalizations of [ɸ] and [x] before spirants until further evidence arises.