You want to know what each time signature *sounds* like? 4/4, 2/2, and 2/4 can sound very much alike - each is chosen pretty much to make it easier to write the sheet music. But a 2/4 is generally thought of as a "two-beat swing", where the bass plays only the downbeats - think bluegrass or polka. 3/4 is, well, a waltz. Pick a waltz, that's what it sounds like - although there are many ways to play waltzes. "Waltz Across Texas", "Take it to the Limit", "All Blue". 6/8 - "House of the Rising Sun" by the Animals, "Bring it on Home to Me" by Sam Cooke, to name just two. Often counted in 2, where each beat is a dotted quarter. 5/4, 7/8, etc. are generally subdivided, e.g., "Take Five" is counted as "1-2-3 1-2". What else do you need to know?
You can always start listening to Dream Theater and other prog type of bands. Metallica "And Justice For All" uses a lot of non- 4/4 time signatures (for example, Blackened has a lot of 6/4 stuff). To start composing in odd times, you can try a regular pattern that you are comfortable with and add/subtract half beats or full beats to it to feel how it changes up things. If you do that, I hope you have an open minded drummer!
Definately check out Dream Theater for time signatures, some amazing examples, also some Niacin stuff play around with some interesting time sigs.
I actually wouldn't check out Dream Theater for help in beginning to understand time signatures - their stuff is typically oddly subdivided and disjointed.
What exactly are you looking to learn bayou brawler? Time sigs are just counting. The feel is in how you subdivide it.
Three songs which title alludes to their time signature: "Eleven" from Primus' "Sailing The Seas Of Cheese" (11/8), "Thirteen" from Frank Zappa's "You Can't Do That On Stage Vol. 6" (13/8) and "five-five-FIVE" from Zappa's "Shut Up'n Play Yer Guitar" which has a pattern of two 5/8 measures followed by a 5/4 measure (hence the caps). IMO, that pattern can also be measured as a single 20/8 measure, but the subdivision is very clear in the song. Los Lobotomys' "Party In Simon's Pants" also has a weird 17/8 time signature, not to mention lots of Rush tunes.
You forgot to mention the band that is named after a time signature: "A Perfect Circle" was the medievel nomenclature for 9/8 (three divisions of three, symbolizing the trinity, ergo "perfect").
if you mention A Perfect Cirlce it is almost required to mention Tool who also do odd time-sig stuff.
I don't recall "A Perfect Circle" doing very much "odd-time sig stuff" just a lot of heavy 3-feel rhythms, hence the name. I was just pointing that out for fun in response to the post about songs with reference to time signatures in the name of the song.
Go listen to a song called "Judging By The Size Of Carnie". It goes from 4/8 to 5/8 to 6/8 to 7/8 to 8/8 then to 9/8. Girls love weird time sigs.............
That's not all that weird since they're all divisible by /8, consistent pulse throughout and you're just counting in groupings. The really weird(i.e. difficult to feel, hard to quantify) signatures are the ones that bounce around what you're dividing your notes by, when the pulse shifts around. I can't say girls like that stuff as much though. I did a piece in 9/8(18/16) against 8.5/8(17/16) for a girl's 18th b-day and got nothing in return! hahaha.