Thanks for getting my name right on the second try, AHunter3. (I have been using the name Jomo Mojo for over 20 years, and that cartoon monkey is just a very recent upstart.) I’m at work now and somehow the Netscape here doesn’t have the right plugin to allow me to hear it. I’ll catch it when I get home late tonight.
3/4 and 6/8 aren’t considered odd time signatures at all. Ever heard of the blues? The waltz?
Well, this is really IMHO material now, but…
9/8: “Apocalypse in 9/8” from “Supper’s Ready” by Genesis
this one is pretty wacky and polyrhythmic (and one of my favorites), with Tony Banks playing a keyboard solo in 4/4 time (I believe) over the 9/8 guitar riff for most of the movement–then they both sync up in 9/8 for a very intense bridge.
7/8: “Them Bones” (“Dem Bones”?) by Alice in Chains. This was a real surprise to hear coming from them, esp. since they hadn’t really become known for their wack vocal harmonies when this song became popular. They were still just that grumpy metal band that opened for Van Halen.
i knew it was only a matter of time before somebody busted out Apocalypse in 9/8… that one sure is a mind-bender.
two more REALLY well-known examples would be the Beatles’ “All You Need Is Love” (7 beats in the verse) and “Good Morning” (10 beats in the verse).
there’s also the synth-solo in the Bee Gee’s “Jive Talkin’,” a break in 7 with an effect very similar to the previously mentioned Blondie song “Heart of Glass.”
and, as long as we’re back in the eighties, how about Andy Summers’ hyper-Freudian “Mother” from the Police’s “Synchronicity” (not so Freudian) album? Seven wonderful beats.
The 13 and 9 are meaningless as there is no 13th or 9th note in music notation. You can certainly have as many beats per measure as you like but the the denominator in the notation is which note represents a single beat.
I think the theme from “Mr. Holland’s Opus” is in 9/8 or something funky like that. Sorry if I’m wrong–long time since high school orchestra.
The OP asks:
and the best answer so far is
So it has to be a power of two because we don’t have a way to write third or fifth or seventh notes? This isn’t a very satisfying reason. How about we replace the circle with a triangle, pentagon, heptagon, nonagon, etc. to represent each of them respectively. Can we now have 5/5 or 5/9 time?
OK, Padeye came in and posted while I was writing. So is 5/4 the same as 5/8, except that in the written form, you’re using quarter notes in place of eighth notes, eighth notes in place of sixteenth notes, etc? Would they play identically?
Now, if you alternated between 4/4 and 3/3 time, the use of third notes wouldn’t just be a curiosity of the writing, would it? (Assuming each measure had the same total time length.) Or would you just denote this as a different tempo somehow?
The opening riff from Mike Oldfield’s Tubular Bells, as used in the film The Exorcist, uses a patern consisting of three bars of 7/8 then one of 9/8 (repeat forever). The rest of TB features many different time signatures, some of them rather unusual. Of course, this was all back in the dim and distant 70s when he had good ideas.
ZenBeam: There’s no such thing as a “third note.” Western music is built on powers of two, as Ethilrist originally pointed out.
The names of the notes – half, quarter, sixteenth – are built on an assumption of a standard four-beat measure. A half note (or half rest) takes two beats, i.e. half of the four-beat bar. A quarter note (or rest), by similar reasoning, takes one beat. (British musicians, I believe, call this a “quaver.”) An eighth note (“semi-quaver”) takes a half beat, or an eighth of a four-beat measure. And so on down the line: sixteenth-note (“semi-demi-quaver”) = 1/4 beat, or 1/16 measure, thirty-second-note (“semi-demi-hemi-quaver”? yeesh) = 1/8 beat, or 1/32 measure, etc. The one oddity is a whole note (or rest), which technically is supposed to take four beats, but I’ve seen it used as “all of this measure,” usually for time signatures less than 4/4.
In order to get three beats per measure, you can use the time signature 3/4, i.e. three notes of quarter length (waltz time), or you can use 4/4 and group three half notes into a triplet. Western music, again, doesn’t have a “third note,” and simply isn’t built to accommodate it. But you can built extraordinarily complicated metrical structures, and divide the measure into any fraction you like, using this system, by putting some oddball number on top of the 2, 4, 8, 16, or whatever. The many mentioned examples demonstrate this.
It would theoretically be possible to construct such a musical system, and I suppose a more expert musicologist might weigh in and say the little-known Upper Intestinal Tract’s tribe of Zandorian Newt-Milkers in the High Himalayas have a musical tradition built on the square root of five, but that’s a separate discussion.
Odd time signatures is something that really tickles my musically perked brain. I’m just starting to really understand stuff, but I still have a lot of learning to do to really get all this. But anyways, I have some examples to share. I’m glad people have said Superunknown, good good. Also, The Ocean off of Houses of the Holy by Led Zeppelin, the main riff goes from 4/4 to 7/4 (if I’m not mistaken. I still don’t understand the difference when you change to second number). And no one has mentioned Tool, especially their album Anemia (spelling horrible, I’m sure, sounds like on-ih-muh). If you like polyrhythms, odd time signatures, and good quailty progressive rock (not to be confused with mere bad hardcore) Tool rocks ass.
If you have musically knowledgable and talented friends, it’s also fun to play time signatures against one another. Some of them sync up really well, like 4/4 and 7/4.
Several other poster have said that the denominator of a time signature has to be a power of two. While I could be wrong, I’m almost positive that I’ve seen drum parts written in 8/12. Wouldn’t a dotted eigth note be a “12th” note? I think the idea was that you regualar eight notes (without the dot) were used in the score instead of dotted eights to make the notation cleaner. This was in a highly syncopated jazz piece.
Perhaps this is a pecularity of percusion scores since most drummers don’t read sheet music any way. Or maybe I’m just misremembering this altogether.
On denominators:
Yes, the denominator may either be 2^n or 3*(2^n):
4/4: four quarter notes.
3/3: three dotted-quarter notes.
6/8: six eighth notes
8/6: eight dotted-eighth notes.
And so on. In that 8/12 mentioned, the 12 would be a dotted-sixteenth note.
(reference: The computer program Finale, which will allow you to set a piece in 15/48 if you wish).
Note, however, that you still can’t have 9/5 or 13/13.
LL
Several punk songs were written in 6/8, mostly at about 90-100 beats per minute or so. Unfortunately, the only song that springs to mind right now is “Bored with Apathy”, by Houston band Really Red; I doubt most people here have heard of them.
If the New Wave was close enough to punk, Chrissie Hynde of the Pretenders wrote a lot of songs in 7/4 and the like, though the effect was more like the dropping of a beat or two from each phrase (think of “Tattooed Love Boys”, or “Up the Neck”.)
So, what meter is “Black Dog” by Led Zepplin in? 
Speaking of bizarre punk meters, I believe L7’s “This Ain’t Pleasure” off of Bricks are Heavy is 9/8.
You are forgetting ‘Outshined’, which was 7/4. I like playing it because it’s pretty easy (I’ve been playing guitar for 12 years and still suck) but that verse part is a bit tricky to get right, and my old drummer had problems with it too. Yeah, Soundgarden used weird time signatures most of the time, as well as weird guitar tunings (I think there is one song on Badmotorfinger that is in E-A-D-G-B-E tuning).
I meant to mention old Metallica as well…a lot of their older songs had odd time signatures in places, and one of their songs had 4/4 and 2/4 alternating throughout the entire song (‘Dyer’s Eve’).
I think Led Zeppelin was one of the first rock bands to use unorthodox time signatures. This was probably because Page was into Indian music, which uses weird signatures like 15/16.
That can be so much fun! I attended several days of an African drumming seminar where we got to do that. Various traditions (mainly from the Ivory Coast area) commonly feature two or more meters played against each other. The real kick is playing syncopated patterns in more than one meter yourself, say playing a drum with one hand in 4 and a bell with the other in 5. I was just happy to keep it going for 15 seconds before screwing up (I’m not that coordinated!). They had a wonderful dancer there too. He could dance one meter with his upper body and another with his lower.
Incidentally, some late fourteenth-century music the in so-called “mannered” style is highly complex rhythmically. A piece from the English Old Hall manuscript (setting the text Patrem omnipotentem) has four voices realized in 2/4, 3/4, 9/8 and 6/8, respectively, all going at the same time. However, to some degree this is more of a notational artifact (of the composers deliberately trying to set musical puzzles for the performers to figure out) and it’s not certain to what degree these metrical complexities were meant to be percieved by the listener. But it’s still a headache to figure out and put together – unless you get off on that sort of thing. 
Anyway… western European music has had periods of great rhythmic ingenuity (as vital in its own way as African and other non-western musics) even though you’d never know it from common practice music and much twentieth-century popular music.
I’ve sung a number of 20th-century art songs (by Barber and others) that have a different meter notated every few bars or so, sometimes every measure. This, however, does not create so much of a sense of rapidly changing meter as an ‘unmetered’ feel, a bit like chant.
I think I’ve rambled enough off topic.
rivulus
Avant-garde art can be a tricky test of subjectivity. Is it good BECAUSE it’s different (or “wierd”). Think…
Personally, I’ll take a hardwood floor and some good ol’ three-quarter time.
My band has a song that I think has an interesting intro in odd time. It alternates between 11/8 and 10/8 then resolves into 12/8 and repeats - it has a tribal feel.
We count the basic groove like this:
1-2-3 1-2-3 1-2-3 1-2
1-2-3 1-2-3 1-2 1-2
1-2-3 1-2-3 1-2-3 1-2
1-2-3 1-2-3 1-2 1-2
1-2-3 1-2-3 1-2-3 1-2-3
repeat
It took a while to become comfortable and be able to further subdivide this pattern (especially for the drummer!), but it works well now and people really seem to like it.
If you truly want to fry your brain, here is Steve Vai on polyrhythms and odd times:
http://www.vai.com/LittleBlackDots/tempomental.html
Messhuggah (sp?) also has some trippy rhythmic stuff going on, as does Dream Theater.