How does the tô bach (little roof) affect the sound of a letter as in a to â , e to ê, o to ô etc? As in these examples: Na bŵ na bê – without a peep, mynd yn fân ac yn fuan – going ten to the dozen and tô bach itself.
The ‘to bach’ (which ironically doesn’t have a to bach) lengthens the sound of the vowel slightly. You’ll pick up the differences as you listen.
A better explanation will come along, I’m sure, but for now try to think of sticking a silent ‘H’ in after the vowel with a to bach.
e.e.
Man = man
Mân = mahn
ayyb.
It works in my head anyway. 
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Prynhawn da
The “to bach” or acen grom (circumflex accent) lengthens the sound of the vowel, as stated above. It is very commonly used to differentiate between words which are spelt the same way but pronounced differently;
gwen (feminine version of gwyn)= white (pronounced gwen)
gwên- smile (pronounced gw-air-n)
tal- tall (pronounced tal)
tâl- payment (tahl)
Man- place/ spot (man)
Mân- minor (mahn)
Tan- until (tan)
Tân- fire (tahn)
Note however that some words have long vowel sounds and do not possess the to bach, in this case it is generally due to the fact that they do not need to be distinguished from as only one form exists- for example;
Haf (summer) is pronounced with a long vowel sound- there is no such word as “hâf”.
Nos (night) is pronounced with a long vowel sound- there is no such word as “nôs”.
To (roof) is pronounced with the long vowel sound- there is no such word as “tô”
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Just to add to Daniel and Gruntius’s responses, the to bach/acen grom/circumflex is mainly used to show that a vowel is to be pronounced long where the spelling would otherwise suggest a short vowel. I won’t attempt to list all the spelling rules here, but a few examples:
In words of one syllable, vowels (other than i or u) are generally pronounced short before n, l or r (as in the examples tal, man, tan in Daniel’s email above). Where the vowel is long, a to bach is needed (hence tâl, mân, tân above).
Similarly, vowels in one-syllable words are almost invariably short before p, t, c, m, ng, or before ‘clusters’ of consonants (i.e. more than one of them) - exceptions are marked by the to bach, e.g.
cant [pronounced like ‘kant’] (hundred) vs. cânt [like English ‘can’t’] (formal version of they will get/will be allowed to, etc)
You’ll also often see it in the final syllable of words of more than one syllable - here it indicates that (a) the last syllable is stressed and (b) the vowel is long:
caniatâd [kan-ya-TAHD] - permission
I’ve seen it used in words where it’s not actually needed to show the vowel is long but to differentiate it from an identically-pronounced word…but my mind’s gone blank and I can’t think of an example right now…
There may be other uses and there are, of course, exceptions (e.g. dyn ‘man’ is pronounced with a long vowel, even though the spelling would predict a short vowel and there’s no acen grom) but hopefully that covers the basics…
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Diolch yn fawr iawn pawb for these responses - very helpful indeed.
How about ‘hen’?
There is no ‘to bach’ on hen. Hen has only one meaning in Welsh - old, so no room for confusion.
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Yes, I know! I am hen ddraig, after all. I just wanted to point it out as an example! Because some people raised outside Wales auto-pronounce it like a clucking bird about to lay an egg!! 
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But chances are that they would still be perfectly understood, and in time their pronunciation would become naturally refined by listening to others, especially if they have learnt with SSiW. 
The real confusion comes when, as @danielschoen points out…[quote=“danielschoen, post:3, topic:11843”]
words which are spelt the same way but pronounced differently
[/quote]
For example - ‘Dw i’n mynd at y tân’ versus ‘Dw i’n mynd at y tan.’
But luckily, context accounts for a lot. 
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Ton and tôn is another. Interestingly, the plural of ton (wave) is tonnau while the plural of tôn (tone or tune) is tonau.
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I read somewhere (sort of as above) that the to bach will also show you when the vowel sound will be different to what you might expect. I guess only if it is a long/open vowel sound when you are expecting short and not the opposite.
Anyway, I assume that in the case of the village of Pyle (in English) near Bridgend, the Welsh pronunciation Pil with a tor bach will be “peel”. Apparently it is isn’t a real Welsh word but might be derived from the nearby pill (navigation channel). However, I am in a minority of one in hoping that it refers to the church tower, which I would (slightly incorrectly) call a pele tower.
I would say that’s an exception to the spelling rule (whereby the vowels other than i and u are short before n, l or r in monosyllabic words).
There are no shortage of exceptions (see also ‘dyn’ in my earlier post - long vowel where a short one would be expected; ‘prin’ short vowel where a long one would be expected, etc, etc). But the key point is that the primary purpose of the to bach is to indicate a long vowel where a short one would be expected.
Ton has a short vowel, tôn a long vowel (hence the accent is needed). The distinction is preserved in the plural forms (at least in S. dialects). In words of more than one syllable, vowels can be short/open or half-long/close before n, l and r, hence:
- tonnau - short/open vowel (hence double ‘n’)
- tonau - half-long/close vowel (hence only ‘n’)
I gather in N dialects they would both be pronounced with a short vowel, so the doubling would be phonetically redundant (even though it usefully dinstinguishes between the two words in writing).
There are similar rules for the doubling of ‘r’. Unfortunately, ‘l’ can’t be doubled because you’d end up with ‘ll’, which is a different sound…
Have I confused everyone even more?! (It does all make sense, kind of, even if I haven’t explained it very well…)
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This is why the title of Gwyneth Glyn’s sea-themed second album Tonnau is a delightful play on words in Eifionydd, and doesn’t work quite so well in Abercraf.
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Ha, indeed!
Yes, I get how the single n becomes double for plural and visa versa for the other version. Interesting.
Also, does Ton in South Wales still refer to “ley lands” (fallow for a season) or would that only be in place names? To be fair, I can’t imagine myself using the term (leyland) in English either, unless I was talking of a mini car or the town off the M6.
Now WY while they do that?
