The difference between ‘byth’ and ‘erioed’ (Y gwahaniaeth rhwng ‘byth’ ac ‘erioed’)
Both mean ever/never, 'ever' in a question, never in negatives, replacing ‘ddim’ where it would occur in such a sentence. But they differ in which tense each can be used.
erioed/byth -> ever/never (adverb)
byth bythoedd/yn oes oesoedd -> for ever and ever (just an idiomatic phrase)
“Dwi ddim yn meddwl amdano fe.” I don't think about it.
Alternatively, you could use ddim, and then tack on byth/erioed at the end of the sentence.
Tenses and usage (Amserau a defnydd)
Erioed is used in “completed tenses in the past”, the present perfect, simple past and pluperfect (past perfect) tenses, replacing ddim in the negative.
“Dwi erioed wedi meddwl amdano fe.” I have never thought about it.
“Dwi ddim wedi meddwl amdano fe erioed.” [Present perfect]
“Wnes i erioed feddwl amdano fe.” I never thought about it.
“Wnes i ddim meddwl amdano fe erioed.” [Simple past]
*Note: Eriod, unlike ddim, does not prevent the soft mutation from occurring. “Wnes i ddim meddwl”, ond “wnes i erioed feddwl”.
“Do'n i erioed wedi meddwl amdano fe.” I had never thought about it. [Past perfect]
Byth is used with all other tenses: present, future, imperfect (past continuous), conditional.
“Dwi byth yn meddwl amdano fe.” I never think about it. [Simple present]
“Fydda i byth yn meddwl amdano fe!” I will never think about it! [Future]
“Do'n i byth yn meddwl amdano fe.” I was never thinking/never used to think about it. [Imperfect]
“Faswn i/fyddwn i byth yn meddwl amdano fe.” I would never think about it. [Conditional]
Erioed is an interesting word in its etymology, Wiktionary (fy ffrind gorau yn y byd, yn wir) says it comes from er (like ers, meaning since) + ei (3rd person singular basically) + oed (time, age). Literally ‘never’ = ‘since their time’.
If you've never had ice-cream, ti erioed wedi cael hufen-iâ, you've never had ice cream since your time (on earth, presumably), though why you wouldn't have ice cream ever is beyond me. Dwi'n mynd i fwyta hufen iâ nawr, in fact. Fel trît :)
(On the other hand, byth shares a root with the word ‘byd’, meaning ‘world’ but also used in the negative sense with dim to mean nothing: dim byd. Maybe it's the way French uses the word 'monde' meaning world, where ‘tout le monde’, literally the whole world, just means ‘everyone’ (dramatic much!), but I am just thinking out here.
I think about it because it makes it easier to remember the Welsh structure when I've seen these structures before elsewhere, helps me get comfortable with them far quicker than if I were starting from scratch, but also because these sort of structures where you use two words to form a negative, and the word that actually carries the negative notion gets dropped in favour of the word that sticks out to us the most, which may even carry the positive notion, has been around for a while in a few languages!
English had a similar thing way back when (the reason this is under a Keep Reading is because it's 2 AM and so I might be getting stuff wrong here, but I think the 'way back when' in question was Middle English. Don't want to feed anyone lies though! I'll double check that with a history of English/linguistics textbook later), when the structure for an English negative was "[subject] ne [conjugated verb] not". ‘I ne saye not’ was how you'd say that you don't say. The ‘ne’ dropped off in time, and over time ‘do’ joined the ‘not’ and moved to the front giving us ‘I do not say, and ‘not’ is sufficient to convey negation.
French currently has the Middle English structure: ‘Je ne dis pas.’ In colloquial French, you do see the 'ne' dropping off too, 'je dis pas' is understood to mean the same and pas in itself is sufficient to convey negation.
In Welsh, ‘dim byd’ means nothing, but ‘dim’ initially just meant ‘a thing’ in Old Welsh, and ‘dim byd’ was closer to ‘anything’ than ‘nothing’ (Wiktionary implies it might've come from something along the lines of “a thing of the world”, whereas it now seen as “nothing (of) the world”) , and there was an old word at the beginning of the sentence to convey the negation when it was used in this way to mean nothing.
(A word which, because it is 2 AM I cannot for the life of me be sure of getting right. But similar to how other negative verbs like 'dwyt/dydy/dyw', 'does' etc. came to acquire their 'd's from the negative word 'nid' that would go before them, while 'wyt/ydy/yw/oes' retained their usual non-negative notions, dim had something too, but I can't remember.
“Nid oes dim byd yma” literally just meant “there isn't (nid -> not) anything here”, and that just became “Does dim byd yma”.)
Some digging around tells me that this is called ‘semantic bleaching’.
Anyway, what was all this about? Byth, it comes from the Old Irish word meaning world. And that's that! (...along with potential mistakes)