The debate over whether there were rules in music sounds like a great GD topic. So, heck, I started one:
http://www.straightdope.com/ubb/Forum7/HTML/000176.html
Carpe hoc!
Aw, c’mon, kOmyers, are we supposed to believe that folks in the hills know what a tune/melody/theme/whatever is, but that anyone getting into sophisticated classical music rapidly forgets what such a thing is? You keep going back to classical music. Classical music may, in some cases, just be exercises in embellishment, but I believe most of its well-known works center on one or more melodic themes. However, my original posted question really contemplated dealing only with popular tunes, which continue to be churned out at quite a rate, though maybe slowing some, after a good, solid, rapid-fire century, and very many tunes before having come about before that. Many, many of them bear the same names. That is trivial to verify. But also, quite a number of these tunes seem to me to be very close to being the same tune – if not exactly so. Can’t we simply forget classical music and all its elaborations for the time being, and deal with those things we can easily whistle, as another poster put it?
Now, 88^100 in no way deals with my question. First off a piano is only one of the many instruments that can be used to play a tune, and not all of them have 88 keys. And the number of keys on any real instrument, or some equivalent chosen in synthetic music, is irrelevant – for one reason, because the same note may be used anywhere in the sequence of a tune, including any number of adjacent positions. But, worst, the basic idea in this gross approach gives, as you mention, a tremendous portion of its “tune space” to nothing but totally unmusical, random or over-patterned garbage. Tunes are played on particular scales, within pitch limits much less than the extremes of some instruments, such as pianos, on which they are played. Tunes repeatedly wander off in ‘tension’ and then resolve to pitches of set ratios to those on which they start.
Various types of fences can be put around all but the most exotic music, without imposing more than reasonable constraints on their tunes. I once looked into the pitches “naturally” chosen by 1/f noise (so-called “pink” noise) (obtainable naturally from semiconductors or otherwise mathematically), with which a physics PhD who stayed at my house was experimenting at the time. The note sequences chosen by this noise compare quite closely to those found in classical music. (Hey, how did we get back to that? But part of Chopin’s genius was due to 1/f noise in his head.) However, 1/f noise knows nought at all of the resolution of themes, because it pays no attention to any key. Additionally, rythm and phrase constraints are necessary to shape popular tunes of the non-exotic, harmonic type. You have to set up wide-ranging, but not unlimited, fences on those parameters, in order to corral all reasonable romantic tunes. You can’t just build what is almost a Christo fence ( http://people.a2000.nl/ttijen/MAPENG.html ); you have to make it include only the green grass and water holes.
Anyhow, we gotta find some way to arm the melody police. . .so that we don’t get taken by tunes that have been crunched out at least several times before under different names. 
I think tunes’re like area codes; you can’t just keep dumping them out forever.
Ray (OK, so after a while, you get a little out of tune.)
NanoByte says, “You keep going back to classical music”
Well, the original post only mentioned “Western esthetic music criteria”, so I figured it was fair game to include classical/jazz/etc, since it avoids the problem you pointed out of repetition in popular music, and there is active composition in both. But ok, we can discard those genres for the purpose of the question if you’d like.
NanoByte also writes, “But also, quite a number of these tunes seem to me to be very close to being the same tune”
Certainly. But is this because we’re running out of tunes? It’ll take quite a lot to convince me of that one :-). I think it’s due to other factors; musical influence of earlier generations, knock offs done intentionally, remakes of old songs, new songs that were composed right after the musician had heard some older song on the radio, “borrowing” a phrase from an older song for effect, or whatever else.
NanoByte says, “First off a piano is only one of the many instruments that can be used to play a tune…”
Can’t disagree there :-). But since the question was pondering how long new tunes can be cranked out, no? Certainly it is possible to play tunes on a piano. It stands to reason that to answer this question, one would want to look at a versatile instrument, not a restrictive one. You can probably find an instrument somewhere that can only play one note, but does that mean we ran out of tunes right after we invented it? You don’t run out of tunes until you run out on the least restrictive instrument.
“within pitch limits much less than the extremes of some instruments, such as pianos, on which they are played”
Ok, I’m still trying to get a handle on what you consider a tune. For my definition, I have music for tunes that uses both the very bottom and the very top note on my piano, and all in between, and they sure sound like tunes to me. But ok: let’s say that it’s not a tune if it uses very high or low notes. (I’m not being sarcastic here, just trying to understand your notion of a tune, which seems to get more restrictive all the time 
).
NanoByte writes, “Now, 88^100 in no way deals with my question”
Ok, fair enough - it’s your question! But I think you need to define the question better. For instance, it seemed perfectly reasonable to me to include tunes that could be played on a piano as potential “new melodies”, but that doesn’t seem to fit in with the spirit of your question. I’m honestly not trying to be obtuse here; i’m interested in the topic too, and I’m trying to understand the spirit of your question.
I think that even under a very strict set of rules (say, notes from no more than 3 octaves, no jazz or classical like progressions, a tune can be no longer than 25 notes, rythym doesn’t count, etc), the number of potential musical sounding tunes is still huge. I mean really truely vast. But tell me concretely what the rules are for a “tune”, and maybe between us we can come up with a more concrete WAG.
k0myers