*mei̯h₁-

Based on many cognates found especially in Hittite and Luwian, a root mī- with the semantics of ‘soft’ can be posited, generally agreed to go back to a root (noun or verb) *meih₁- (HEG L-M:222, EDHIL:584 all with further literature; contra HED M:173f. who posits a *-h₂, which is phonologically unacceptable). It is noteworthy that the root of all derivatives, even in the zero-grade, is regularly spelled plene, which might be taken as an indication for a root-final laryngeal. Likewise, a root final *h₃ would have been preserved before the u-suffix and the derivative in *-lo- (see below), which leaves only *h₁ as a possibility.

From this root an adjectival u-stem can be reconstructed for Proto-Anatolian, i.e. *mih₁-Éu̯-/-u-´ ‘soft’. Furthermore, there are parallel derivatives derived directly from the root, i.e. with an adjectival suffix *-lo- and a substantivization in *-u-; cf. CLuw. mīlu- ‘fruits (?)’, Hitt. mīlūli- n. ‘soft tissue, soft body part’ and CLuw. mīlušga/i- ‘gentle’, i.e. PAnat. *mih₁-lo- + -u-. Concerning CLuw. mi(ya)ša- n. ‘(a body part)’, Rieken 2019c:222f. argues (contra Oettinger 2003a) that it goes back to a neuter s-stem that was secondarily thematized, i.e. *mei̯h₁-e/os-. One should also compare PAnat. *mói̯h₁-/mih₁-´ ‘to grow’.

[D.S.]

The Anatolian ḫi-verb PAnat. *mói̯h₁‑/*mih₁‑´⁽ⁱ⁾ ‘to grow’ is often connected to the root under investigation due to the common semantic sphere of vegetal growth and ripening; cf., e.g., the adjectives Lat. mītis ‘sweet and juicy’ and OIr. moith, maeth ‘soft’, both of which may be used to describe “ripe fruits” (Lat. mitia poma, OIr. meas maeth). A semantic development ‘to grow, ripen’ → (resultative) ‘grown, ripe’ > ‘soft, sweet’ > ‘soft, gentle, pleasant’ is indeed probable, cf. LIV²:428 n. 1 s.v. 2.*meiH‑.The opposite direction, viz. ‘soft’ → ‘to become soft, ripen’, whence ‘to grow’, would imply a fientive function of a ḫi-verb that is elsewhere unattested.In this case, either each of the up to five reconstructable formationsCf. PAnat. *mih₁‑Éu̯‑/‑u‑´ ‘soft’, PIE *mih₁‑ló- ‘soft’, PIE *mei̯h₁-o/es‑ ‘softness’, and perhaps PIE *mih₁-ti- (Ital., Celt., cf. above) and *m(e)i̯h₁-ro- (BSl., Alb., cf. above). Furthermore, it has to be noted that a u-stem derived from PIE *mih₁‑ló- ‘soft’ may be also attested in Latv. mĩļš ‘nice, sweet’, but this is not necessarily old.would individually have developed the resultative meaning ‘ripened, ripe’ (hence, ‘soft, gentle, pleasant’)This deverbal scenario would lead to problems regarding the s-stem PAnat. *mei̯h₁-o/es‑ because one would rather expect ‘size’ (← ‘grown’) or ‘ripeness’ (← ‘ripe’) as a resultative meaning (on resultative s‑stems, cf. Stüber 2002a:234–236), which, however, can hardly underlie the attested meanings ‘(a soft body part)’ (CLuw.) or ‘pleasure’ (IIr.).or these formations are collectively based on a root that already shows the resultative meaning ‘soft’ (< ‘ripened’). The former proposal is methodologically unlikely, not least because the meaning ‘ripened’ is attested rather weakly. The latter proposal ultimately recommends reconstructing two homophonous roots already for PIE, viz. PIE 1.*mei̯h₁- ‘to grow’, which is attested only in Anatolian, and 2.*mei̯h₁- ‘soft’ (< ‘ripened’).
However, since the majority of formations based on the root under investigation can easily be traced back to an adjectival root denoting a physical property, it meets the semantic requirements of a “Caland-root”, cf., e.g., Rau 2009a:78f. The root may thus be reconstructed as adjectival PIE 2.*mei̯h₁- ‘soft’ (IEW:711f.).

The root in question not only shows a semantic proximity to the Caland system (cf. above), but also comprises various formations that are derived from it and are typically associated with the Caland system (cf. Rau 2009a:67–75): an adjectival abstract PIE *mei̯h₁-(o/e)s‑ ‘softness’ as well as certain adjectives, viz. PIE *m(e)i̯h₁-ro- (BSl., Alb., cf. above), a proterokinetic u-stem adjective PAnat. *mih₁‑Éu̯‑/‑u‑´ ‘soft’, and PIE *mih₁‑ló- ‘soft’. To complete the picture, Hittite also exhibits certain verbal formations like a fientive/stative Hitt. mīēšš‑^(mi) ‘to be(come) mild’ (CHD L–N:243f.) and a factitive Hitt. mīnu‑^(mi) ‘to make mild, heal’ (CHD L–N:291f.). In view of this high amount of specific formations, it is highly advisable to reconstruct the underlying root as PIE 2.*mei̯h₁- adj. ‘soft’.
Phonologically, the anlauting *m- of the root in question is clear, and its seṭ-character is suggested by various facts, including the long vowel and the acute tone in Lith. mýlas ‘dear’ (< PIE *mih₁‑ló- ‘soft’). The root-final position of the laryngeal (not †meh₁i̯‑, as per Schrijver 1991a:244) is proven, e.g, by the short root vowel of Ved. máyas- (not †māyas- < †meh₁i̯-o/es‑), cf. Zair 2012a:119f. Since *h₂ and *h₃ are preserved in Anatolian (for the latter, cf. above and Melchert 2011a), the root can be reconstructed as PIE 2.*mei̯h₁- ‘soft’.If, however, the root is connected with PAnat. *mói̯h₁‑/*mih₁‑´⁽ⁱ⁾ ‘to grow’, it stands beside the conceivably underlying verbal root PIE 1.*mei̯h₁- ‘to grow’ and should thus be reconstructed as the secondary (adjectival) root PIE 2.*mei̯h₁- ‘soft’.

[A.O.]

PIIr. *mái̯(H)as- ‘pleasure’, cf. CLuw. mi(ya)ša- ‘(a body part)’

Lat. mītis ‘sweet and juicy (of fruit), soft (of material), gentle’ (Plaut.+)EDLIL:383 tentatively connects Lat. mītis with the root PIE *meh₁- ‘to measure’ (LIV²:424f., Pal. memiya- ‘to speak (?)’), which does not make any sense. 
WH II:96f., EM:407, EDLIL:383, OLD²:1231Although Lat. mīrus ‘wonderful’ is compared by some (cf., e.g., Demiraj 1997a:269), it rather belongs to the root PIE *smei̯- ‘to laugh, smile’ (LIV²:568f.). This root does not show any laryngeal reflex, which, however, is necessary in the case under investigation, cf. below sub Morphological reconstruction.

OIr. moith, maeth, moeth ‘soft, tender, yielding; (sbst.) cartilage (vel sim.)’, W mwydion m. ‘soft inner part, kernel, pith’, (?)MBret. boedenn f. ‘marrow, pulp, substance’, etc.
EDPC:279, eDIL s.v. maeth, moeth (2019), Zair 2012a:119f., 232

BSl. *m(e)iHró- ‘peace’, cf. OLith. mieras, Latv. miêrs ‘peace’ (EDBIL:316, ALEW 2.0 s.v. mieras [2021-04-27], LEW I:449),The Baltic lexemes may have been borrowed from Slavic, cf. EDBIL:316, ALEW 2.0 s.v. mieras (2021-04-27) with ref.OCS mirŭ, Russ. mir ‘peace, world’, etc. (EDSIL:318, Vasmer II:137)
Trautmann 1923a:175
BSl. *miH-ló- ‘pleasant, dear’, cf. CLuw. mīlu- ‘fruits(?)’

Alb. mírë ‘good’
AED:267, Huld 1984a:92, Demiraj 1997a:268f., Matzinger 2006a:155Otherwise, Alb. mirë may also be a loan from Lat. mīrus ‘wonderful’, cf. Huld 1984a:92 with ref.