So, considering a statement like "Dath oráiste atá ar a gúna," I know that we're talking about a girl because of (the absence of) lenition, right? That is, "a" is possessive, but because it's gúna and not ghúna, I know that its feminine and not masculine ( Cailín agus a tuismitheoirí = a girl and her parents Buachaill agus a thuismitheoirí = A boy and his parents)?

EDIT:

For example...

Dath fionn atá ar ár gcuid gruaige. Color blonde is on our hair.

Dath fionn atá ar a chuid gruaige. Color blonde is on his hair.

Dath fionn atá ar mo chuid gruaige. Color blonde is on my hair.

Dath fionn atá ar a gcuid gruaige. Color blonde is on their hair.

Yah?

Yeah.

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne

Yay!

Arg.

As I understand it, a preposition plus the definite article will trigger an eclipses of the noun that follows it.

E.g. "Dath bándearg atá ar an gcrios."

But I am told that the following does not trigger eclipses: "Dath donn atá ar an teach."

Why is that? Is there gender at play here or something? I thought it would be "Dath donn atá ar an dteach."

It's because most dialects don't eclipse t and d after article + preposition. Although in Munster Irish t and d are eclipsed as well.

ar an dtigh = on the house (tigh is the Munster words for house).

It would take a little bit more detail to explain why most dialects don't eclipse t and d in this case, if you're interested in knowing just ask.

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The dialect I use is Cork Irish.
Ar sgáth a chéile a mhairid na daoine, lag agus láidir, uasal is íseal

I am interested, thanks.

Something to do with the historic beginnings of the urú (voicing/nasalisation at work boundaries).

P and f would become b and v, i.e. 'fear', 'ar an bhfear' (the n of an changing the f, as it were).

In the same vein, so to speak:

c --> g, corn (ag an gcorn)

p --> b, post (ar an bpost).

b, and g were 'nasalised' (made into m and g)
b --> m, bobailín (as an mbobailín)

m was already nasalised and v/w arose from another process

Irish had no z (having fell in with slender r in prehistory)

l, n, and r were no amenable to change

Th and dh had disappeared by the late Middle Irish period (I think; classical period anyways)

That left d, t, s. They, along with l/n/r, th/dhand z, are all coronal consonants as the tongue tip (or 'crown') is needed to produce them. Since the n of 'an' was/is 'tip of the tongue' and both came into contact, and due to fast speech, the voicing/nasalisation was resisted (ar an doras not ar an ndoras. (This form has arisen in Kerry Irish by analogy as anyways the n doesn't need to be pronounced today))

I think in the genitive plural, the article was 'am', so it would have been 'ar (n)am ndoras (in the old days no strong plurals, or very few anyways)

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__̴ı̴̴̡̡̡ ̡͌l̡̡̡ ̡͌l̡*̡̡ ̴̡ı̴̴̡ ̡̡͡|̲̲̲͡͡͡ ̲▫̲͡ ̲̲̲͡͡π̲̲͡͡ ̲̲͡▫̲̲͡͡ ̲|̡̡̡ ̡ ̴̡ı̴̡̡ ̡͌l̡̡̡̡.___

Basically:

ar/ag/as etc AN [Noun] = ar/ag/as an mbord etc

(except for l/n/r/ng, v/w, z/th/dh (as they were already voiced/nasalised and/or did not exist))

and since the article was 'an' and n is tip of the tongue and t/d/s are tip of the tongue too, they kind of got 'stuck together' and the change didn't happen

ag an sagart
ag an doras
ag an tarbh

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__̴ı̴̴̡̡̡ ̡͌l̡̡̡ ̡͌l̡*̡̡ ̴̡ı̴̴̡ ̡̡͡|̲̲̲͡͡͡ ̲▫̲͡ ̲̲̲͡͡π̲̲͡͡ ̲̲͡▫̲̲͡͡ ̲|̡̡̡ ̡ ̴̡ı̴̡̡ ̡͌l̡̡̡̡.___

As an aside, one way of thinking of urú and seimhiú is to imagine being in a huge warehouse and measuring just how far the sounds of one's mouth travel. For some sounds (like the 'a' in father) they will travel far and for other (like the 'th' in cloth) they will not, so if you made up a language full of vowels, the listener (or echo) would /respond/rebound from further ahead (maybe this is why whistle languages develop in valleys)

In a list format, this is called 'levels of sonorancy' and is roughly like so:

á, ú, ó etc
r, l, n, ng
w, y
z, zh, dh,
d, g
t, th, f

Urú in a sense, raises the sound and the process of lenition softens it down the scale, till eventually it disappears between vowels and the circle is complete and it gets all mystical and become one with the universe and stuff

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__̴ı̴̴̡̡̡ ̡͌l̡̡̡ ̡͌l̡*̡̡ ̴̡ı̴̴̡ ̡̡͡|̲̲̲͡͡͡ ̲▫̲͡ ̲̲̲͡͡π̲̲͡͡ ̲̲͡▫̲̲͡͡ ̲|̡̡̡ ̡ ̴̡ı̴̡̡ ̡͌l̡̡̡̡.___