How subtle is the difference between the pronounciations of "a" and "ä"?
My mind is a bit perplexed with this one... my native language is Greek, and our vowels are very "open" and have only one way of being pronounced each (unlike in English). So the Finnish "a", from what I've seen, is similar to our "α" (a). However, probably due to being influenced by learning German for some years, when I see "ä", my mind goes to how Germans pronounce it, which is closer to our "e" than our "a" (also probably because the Finnish "ö" is similar to the German "ö", so I've yet to make that distinction). But still, its pronounciation is not clear in my ear.
Also, due to English not being my native language, the pronounciation tips for "ä" in the "Tips" section don't really help me - and I fully recognize there's nothing the contributors can do about that, just saying why I'm reaching out here about it :)
Now, there's this Finnish song I love, On Suuri Sun Rantas Autius. It's sung here (https://www.youtube.com/watch?v=QoZwHkYu6aM) by a Finnish singer and here (https://www.youtube.com/watch?v=pI16H3UvL5k) by a Dutch ensemble. Now, those two seem to me to have a similar pronounciation, and considering that Johanna Kurkela is native Finnish, I trust her pronounciation the most. However, I am only now learning Finnish so I may not get some of the subtle differences, and I've heard this song sung by non-Finnish choirs where their "ä" was very close to an open "a", and... it sounded weird.
After that probably-too-detailed explanation, I kinda wonder if, from someone who is obviously not native Finnish, would it be better for the "ä" to sound like the Finnish "a" or the German "ä" - until, at least, I get used to the actual difference.
To Finnish ears the difference is indeed not subtle at all, but to those not accustomed it might take some effort (similarly in French people keep saying to me that there's a difference between the various e's which I struggle to hear...).
And when listening to the songs you posted, the Dutch singer is indeed pronouncing ä almost like a, Kurkela does it correctly.
The first two lines of the song are actually pretty good exercise for the two types of vowels, "on suuri sun rantas autius / sitä sentään ikävöin", the first line has a-o-u words, the second ä-ö.
A-o-u are called back vowels and ä-ö-y front vowels because while the shape of the lips is the same for a and ä (and o/ö and u/y), the front vowels are formed more on front and tongue is pushed behind the front teeth, while in back vowels tongue doesn't necessarily touch the front teeth (e and i are front vowels too, even if they can do the vowel harmony with both back vowels and other front vowels).
For exaggerated versions, if one sticks the tongue out, it's pretty difficult to form back vowels but front vowels work just fine :)
The distinction between the two sounds is important to maintain, because Finnish has vowel harmony. You cannot have Y, Ä, Ö in the same words as A, O, U. There are so many minimal pairs in Finnish that will get you into trouble if you forget this. sääri, "leg"; saari, "island". hellä, "tender"; hella, "kitchen stove".
A, /ɑ/, is pronounced at the back of the mouth, very low, where the root of the tongue is. It's similar to the vowel sound in the English "car". Ä, /æ/, is pronounced in the front part of the mouth and it's similar to the vowel sound in the English "cat". Again it's pronounced very low, but right under the lower teeth in the fleshy corner near your jaw. When you form it, your tongue rests against the lower teeth. It's there so that it does not leave your mouth when you push it slightly forward. The tip is quite relaxed, so it's not actually the tip resting on the teeth but the upper part of tongue behind the tip. And then you pretend you are a sheep: bääääää! You can actually try to produce it first with sticking your tongue out and focusing on keeping the sound under the teeth, if doing the whole procedure feels too complicated at first. Both /ɑ/ and /æ/ are open sounds so there's plenty of room for air between the tongue and the ceiling of the mouth.
You must have seen a chart like this before. It's a "picture" of our mouth cavity. The teeth and the lips are on the left. This one shows where the Finnish vowels are produced:
The Greek and the Spanish speakers have it the hardest. The Greek and the Spanish /a/ is pronounced right behind the centre of the floor of the mouth and there are absolutely no vowels pronounced anywhere near the area under the lower teeth. So maybe the reason why the Finnish sounds feel so close to one another is that your /a/ is pronounced halfway from one Finnish sound to another. Return to the first paragraph. Sorry. :(
In German and Italian, the "normal a" is pretty similar to the Greek and Spanish one (just even more central). You could try to drop the /ɛ/ in the German Bär and in the Italian "caffè" under the teeth to produce a Finnish Ä, if the instructions in the first paragraph do not work.
French speakers have an interesting way of getting around this: learn to control your nose. Although Finnish does not have any nasal vowels per se, it usually helps a French speaker to think of /ɑ/ and /æ/ as nasals in the beginning, since they are pronounced in similar positions. The "normal French a", /a/, as in "sa", is pronounced very close to the teeth. BUT. /ɑ̃/ in the French word "sans" is the same sound as the Finnish one, pronounced in exactly the same position. Except that it's nasal and the Finnish one is not. /ɛ̃/, as in the French word "vin", on the other hand, is pronounced just a tad higher than /æ/. Bring the nasal down as low as you get it and control your nose and voilà! Here is a link to Forvo to a page where you can listen to the Finnish words saan ("I get") and sään ("of weather") pronounced. You should be able to hear the similarities now. :)
It's not at all a subtle difference to native Finns, but to a native speaker of a language that doesn't have that sound, especially if that language has a similar but slightly different sound, it can be difficult to get it right. I just checked the list of sounds in modern standard Greek, and it seems that it does not have the same sound. But since you seem to have good English, at least in written form, the good news is that English does have the same sound. More specifically, it is the /æ/ sound, an example of which can be heard in the pronounciation of the vowel sound in the word "cat".
I also had the same problem as a native French speaker and expected it to sound like the Swedish ä. Common examples of English words with both sounds are "car" and "cat", but to me, the difference is mainly due to the short vs. long sound and the intonation, not the "a" sound. That said, after more than 3 years spent in Finland I can better hear the difference so I think it's a matter of getting used to it.
I'm not a native speaker of English, German or Finnish - but I think it is a bad idea to substitute other sounds for ä. It sounds very different to me than the Finnish a or the German ä (which can sound more like e for many speakers). And if mispronounced, maybe you might be misunderstood. Long ä in Swedish would be a good match (short ä is close to the vowel in the German word es), as is the sound in the English word as. I would practice this sound, both to pronounce Finnish and English better. Mais, 'fay ce que vouldras'; es ist mir egal, virklich.
Here is an interactive chart to hear every single possible vowel sound on Earth: https://www.ipachart.com/
The symbol for the Finnish ä is /æ/, so click on it to hear what it sounds like.
The symbol for the Finnish a is /ɑ/.
Can you hear the difference? /æ/ is in the front of your mouth, and /ɑ/ is in the back of your mouth.