The basic Sindarin word for “house, dwelling” derived from the root √MBAR “settle, dwell” (PE17/109; PE17/164). This Sindarin word (unlike its Quenya counterpart már) can also be used to refer to the “house” of a clan or family, as in Bar Bëora “House of Bëor” (WJ/230) and Narn e·mbar Hador “✱Tale of the House of Hador” (MR/373). It could also mean “-home (for a people)” in compound names for regions as in Eglamar “Home of the Eglain” and Brithombar (WJ/379; S/120), but it seems this use was archaic and in more recent names the trend was to use dôr “land” (PE17/164).
This word appears as both bâr with long â and bar with short a. As a general rule, it has a long â when used as an independent word, following the general Sindarin principle whereby short vowels (usually) lengthened in monosyllables. It has a short vowel when appearing in compounds or as a “pseudo-prefix” in names like Bar-en-Danwedh “House of Ransom” (S/203).
Conceptual Development: This word dates all the way back to the Gnomish Lexicon of the 1910s, where (adverbial?) G. bar appeared as a variant of G. barthi or barai “at home, home” (GL/21). In the Gnomish Lexicon its noun form seems to be G. bara “home” (GL/21), but in the contemporaneous Gnomish Grammar it was bar “home” (GG/8). These Gnomish words were all derived from the early root ᴱ√MBARA “dwell, live” (QL/63).
In Gnomish Lexicon slips, Tolkien modified the word to G. bawr “house” derived from primitive ᴱ✶mbāră (PE13/116). In the Name-list to the Fall of Gondolin Tolkien had G. bar “dwelling” (PE15/21). In the Early Noldorin Grammar of the 1920s it was ᴱN. bâr “house”, though a change in its mutated form {i·bhar >>} i·mâr indicates some vacillation on its primitive form (PE13/120 and note #2). In Early Noldorin word-lists of this period it was bar “house” (PE13/138).
In The Etymologies of the 1930s it was N. bár “home” written in the margin next to the root ᴹ√MBAR “dwell, inhabit” (EtyAC/MBAR), but it also meant “Earth” in the name N. Barthan “Earth-smith” (Ety/TAN). In later notes (date unknown) this name was S. Barthan “World-artificer” (LT1A/Talka Marda). In notes on The Feanorian Alphabet from the 1930s it was †băr “home”, which became bār after vowels lengthened in monosyllables (PE22/36).
In notes from the 1960s, Tolkien described this word in some detail, first saying:
> In Sindarin bar [< ✱mbăr-] (pl. bair) was used for a single house or dwelling, especially of the larger and more permanent sort; barð [< ✱mbardā̆] was much as English “home”, the (proper) place for one (or a community) to dwell in (PE17/164).
Here it seems bar = “house, dwelling” but bardh = “home”. However, in a later iteration of these notes Tolkien said:
> There were thus tendencies both (a) for Noldorin terms for things peculiar to their culture to be translated into Sindarin forms or imitated ... Examples ... were (a) the use of Sindarin bâr (< ✱mbăr(a)) for “house” a settled built dwelling of a family, larger or smaller: in true Sindarin use it only denoted a small area in which some group had at last settled more or less permanently (PE17/164).
This was revised slightly to read:
> There was thus a tendency: (a) for Noldorin words and terms for things peculiar to their culture to be translated into Sindarin, or imitated ... Examples of these processes are: (a) the use of Sindarin bâr (< ✱mbăr(a)) for “house”: the permanent building serving as the home of a family, larger or smaller, though in genuine older Sindarin use this word referred to a (small) area, in which some group had at last settled, more or less permanently (PE17/164).
Both these later paragraph imply that the original sense of Sindarin bâr was something like “✱settlement (of a group or community)” but came to mean “house, dwelling” under the influence of Quenya már.
Of its uses in compounds Tolkien said:
> This was also in old compounds used (like Q -mar) for a region, but not in ordinary language ... Only in old names was -bar used like Q -mar for a region inhabited by a people. For this Sindarin used usually -dor (< ndor) “land” (PE17/165).
This root was connected to the sense “dwell” for all of Tolkien’s life. In the Qenya Lexicon of the 1910s it appeared as ᴱ√MBARA “dwell, live”, though in Qenya it was blended with ᴱ√ŊWAÐA “tarry, linger” since [[eq|initial [ŋʷ] became [m]]] (QL/60). In Gnomish the two roots remained distinct: G. bar “home” (GL/21) vs. G. gwadh- “dwell” (GL/46). However, other Gnomish derivatives hint at an unstrengthened variant ᴱ√MARA: G. mar “Earth, ground, soil” and G. Môr “The Earth”, of which Tolkien said “mar and môr probably conceal two roots and a confusion; mbara” (GL/56). The source of this confusion might be ᴱ√MARA “ripe” (QL/59, 63).
In The Etymologies of the 1930s the root appeared as ᴹ√MBAR “dwell, inhabit” (Ety/MBAR); an earlier version of this entry had the extra gloss “build” (EtyAC/MBAR). In The Etymologies, it seems this root was a strengthened form of ᴹ√BAR “raise” (Ety/BAR), but the root ᴹ√MBARAT “fate” seems to be unrelated at this point (Ety/MBARAT). The root mbar- was mentioned in the Outline of Phonetic Development (OP1) from the 1940s (PE19/36) and again as √MBAR “{house >>} dwell” in the second version of Tengwesta Qenderinwa (TQ2) from around 1950 (PE18/92).
The root √MBAR still had the basic sense “dwell” in Notes on Galadriel’s Song (NGS) from the late 1950s or early 1960s (PE17/64); in those notes it seems it was distinct from both √BAR “raise” and √MAR(AT) or √MBART “doom, fate” (PE17/66). But in notes on Fate from 1968 (NM/226-231; PE17/104-109), Tolkien shifted the meaning of the root:
> English “settle” in its various branches of meaning closely resembles the development of the meanings of √MBAR: thus settlement can mean the act of colonizing or taking up an abode, or the area or place so occupied (by a family or community); or (the terms of) an agreement fixed after debate. The development was not, however, the same: the senses of settle proceed from a sense “place in or take up” a firm position, especially in a place that seems suitable; from which the sense of settling affairs that were in confusion or doubt arose. √MBAR meant basically to make a decision, and the meanings relating to dwelling or occupying land proceeded from that (PE17/105).
This new definition for √MBAR was to support a more direct connection between this root and words like Q. umbar “fate”, hence establishing an etymological relationship to extended √MBARAT for the first time, for example with √MBAR > ✶mbartā- “to define, decree, destine” (PE17/104).
Neo-Eldarin: For purposes of Neo-Eldarin, I think this late 1960s meaning “settle, decide, establish; (by extension) dwell” is probably the best.