You know, the Beethoven ditty. I got conflicting or inadequate answers from Google, more discussion of the “Fur” but not much about the “Elise”.
I’m looking for the pronunciation one might use at an American cocktail party as opposed to the direct German one, unless the German one makes me sound smarter.
Is it “Fur” like on a bear, or more like “Fyur” ?
A-LEES or A-LEESSA or E_LISSA etc etc
With three years of high school German, so I’d pronounce it:
Fyoor e-LEE-sa
The “u” in the first word actually has an umlaut above it (the two dots), which changes the pronunciation of the vowel.
Found with Google search and using the Cached page
Search = Fur Elise Pronunciation
The Cache Page I found
Because the /u/ in “Fur” is umlauted, the German pronunciation
is closer to the English /fir/. “Elise,” in English, is
pronounced with a silent final “e,” but the final
“e” is pronounced in German. If you want to anglicize the
pronunciation, you might pronounce “Fur” as you suggest and
drop the sound of the final “e.”
It’s “Für Elise”.
Fyr E-LI-SE. The “I” is like the “I” in Bill.
I normally hear it as “Fyoor eh-LEASE” in American English, and that’s how I say it unless I’m speaking to someone who knows better, and then perhaps I will umlaut the “u” and add the final schwa on the name.
The first word is Für, F - u umlaut - r, which can also be spelled Feur. That gives a hint to its pronunciation.
In German, the f is harder than in American English. The u umlaut is pronounced like an e or u as in English “uh” or “euh” combined with pursing the lips. Start with a very neutral e as in eh (but without the h), then pull your lips together like you’re gonna whistle.
The best way to learn how to say u umlaut is to hear a German say it!
The r is, like all German r, a “roll”, said more in the throat and with the tongue clamped between the teeth. Very similar to a French r.
Elise is “Eh-l-ee-sss-eh”. No silent letters in German, especially no silent final letters. Some letters combine into one sound; for instance, sch is “sh”, but all three need to be there.
So it’s approximately “f-e-u-uh-r Eh-lee-sss-eh”.
Weird. I was thinking about the piece this morning. Of course, I happened to be listening to Brahms’ piano concertos…
That’s incorrect. It would be spelled “fuer”, not “feur”. Feur would be pronounced similar to the English “foyer”.
When you pronounce a vowel with an umlaut you shape your mouth much differently than our English pronunciation. More like narrowing your mouth and squeezing out the sound.
Closest:
Fir aylEEzuh.
The u umlaut is tough to translate into english, but fir is close
The r is more at the back of the throat, but your better off just omitting it then pronouncing it like an american r.
The first e in elise is pronounced like a long a as in they
the i is pronounced like ee
the s is pronounced like a z
the last e is a schwa.
One has to account for regional variances. I’ve heard it pronounced “that song, you know, that goes deedle deedle deedle deedle dum,” or “hey, Tiffany, there’s a piano store, play that one song you know.” The would-be player’s friends called it “let me try…how does it go? I always forget how many deedle deedles it has. And which black notes do I start at again, there’s so many!”
I always pronounced it “get out of my piano store and never play that stupid song here again.” 
Well, I can tell you it’s not pronounced “For Eloise”. (which I what I say every dang time despite knowing better.)
General rule for umlauted vowels. For an umlaut-u, shape your lips as for an “oo” (as in “moo”), but pronounce an “ee” (as in “bee”). For an umlaut-o, same thing except pronounce more of a short i (as in “bit”).
Plus, a German “r” (in most dialects, at least) is not a rolled “r”. In Europe, Rolled "r"s are generally encountered in the Slavic languages and many Romance languages (French excepted.) They also show up in Scottish variants of English, and are more formally known as “avelolar trills.” The German and French "r"s are voiced uvular fricatives, aka a “uvular r”.
I’ve just been saying “Furry Lisa”
Wouldn’t that make a great name for a female werewolf?
“Für” is pronounced almost like “fear.” THe “ü” sound is pronunced with your lips shaped to say “oo,” but the inside of your mouth arranged as if to say “ee.”
In other words, say “ee” with your lips pursed into an “oo” shape, and you’ll get the right sound.
I’d thought of the same thing, Dr! Note to all lady lurkers thinking of registering: There 's a name waiting for you! 
uglybeech is so far the only one who caught the voiced pronunciation of the invervocalic <s> in German. It sounds like /z/, not /s/. Elise = @-LEEZ-@ (where @=schwa).
:smack: I can’t believe I missed that!
Right. Saved me the trouble. It’s a /y/ in phonetic transcription - a rounded /i/. “Rounded” means the lips are rounded (as if you were saying “ooh!”), but the tongue and mouth are otherwise in position to say “ee”. Same as in the French “tu”.
There are four rounded front vowels in German. Each of the two graphemes <ö> and <ü> stands for two different vowel sounds, tense/long and lax/short. Tense/long ö like in Höhe is comparable in length and narrow tongue position to the long e in Ehe, while lax/short ö as in Hölle is like the e in hell with regard to relaxed tongue position, except with lips rounded. Compare how German schöne corresponds to Yiddish Shayna. Tense/long ü as in fühle has length and narrow tongue position similar to the tense/long vowel i as in viel. Short/lax ü as in fünf is like the short/lax i in Fink. Compare the Yiddish word for five, finf. Yiddish loses all the front vowel rounding and merges the “umlauted” vowels with the four sounds of e and i.
Actually, “umlaut” in the original sense referred to phonotactic vowel shift from back to front within a word, under the influence of a front vowel in a suffix. Ex. Frau (back vowel), Fräulein (vowel fronting via umlaut triggered by the suffix). Umlaut properly does not refer to vowels that were fronted and rounded to begin with, like in the word Öl.
Back to the OP: The vowel in für is a short, lax, high, rounded front vowel. It’s like a rounded version of the vowel /i/ as heard in English fin. In English, this vowel does not occur before r, instead it shifts to a neutral vowel due to r-coloring, so I can’t think of any exact examples. English fear is maybe the nearest approximation, if you substituted a lax short front vowel for the long tense vowel. And then rounded it.
On second thought, maybe Öl isn’t the best example of non-umlaut, since if you delve into its etymology, it was an umlaut process that resulted in that vowel ö. It came from Latin oleus, and although the e in that word disappeared in German, it left behind its influence in the fronted vowel ö. I’m not sure if I can come up with a good example of non-umlaut rounded front vowels in native German words. I’m flipping through a German dictionary, but all the examples I’m finding can be explained by umlaut.