Warning: Incoming wall of text

Okay, so I was busy in class today not doing my work and I came across some strange rhythmic and metric ideas. It started when I was fooling around with grouping triplets in 4's and 5's, by accenting every fourth or fifth triplet eighth note instead of every 3.

A bar of 4/4 can contain 12 triplet eighth notes, 3+3+3+3 when grouped normally.
You could also group them in 4's (4+4+4) giving you 3 sets of 4 and an interesting rhythmic effect. I took it further and tried a 4+4+4+4 grouping, extending the bar beyond 4/4, and leaving me with 16 triplet eighth notes.

In trying to name this time signature, I looked at the 16 triplet eighth notes as 3+3+3+3+3+1 rather than 4+4+4+4 as 3 triplet eighth notes are equal to a quarter note. This worked out to 5/4 with an extra triplet eighth note. Since 3 triplet eighths notes are equal to a quarter note, I gathered one triplet eighth note would be equal to a third of a quarter note, giving me a time signature of 5⅓/4 (five and one third over four).

What's interesting about this time signature is that it divides 4 bars of 4/4 exactly in 3. I can already imagine some very cool polymetric ideas involving these time signatures.

I found similar time signatures by grouping the triplet eighth notes in different ways. I suppose the same idea could be applied to other n-tuplets (quintuplets, septuplets), though I doubt time signatures such as three and one fifth over four would be very practical or useful.

My questions are:
1. Does any of this make sense?
2. Are there examples of usage of these kinds of time signatures?
3. I forgot this one gimme a sec.

THANKS IN ADVANCE.

edit: Added a GP/MIDI file. The kick drum is quarter notes for 8 bars of 4/4 and the guitar can be seen as 6 bars of 5⅓/4
edit2: thanks for the correction arch, I hope I fixed that
Attachments:
polymeter.zip
Quote by TGautier13
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Last edited by ramm_ty at Oct 22, 2008,
I you had typed in "Fractional Meter" in Google you would've found your answer.

Nevertheless, your post inspired some ideas in me.
*reported*... twice in one reply!

OH NOES!!! Theowy is scawY!!!
While time signatures are not fractions, simplify yours as if you were simplifying a compound fraction. That gets you 4/3, which is somewhat crazy, but it's certainly better than a compound fraction (compound fractions aren't simplified!)
Last edited by bangoodcharlote at Oct 22, 2008,
Quote by bangoodcharlote
While time signatures are not fractions, simplify yours as if you were simplifying a compound fraction.
You can't, it always comes out as a fraction.
Quote by TGautier13
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We believe - so we're misled
We assume - so we're played
We confide - so we're deceived
We trust - so we're betrayed
1. Yes, though I would have notated it 16/8 personally.
2. Wikipedia is your friend. A few modern composers have employed them.
3. No.
You just exploded my brain. 4/3? What's a 3?

I understand how you did that, but 4/3 seems much more confusing than 5⅓/4 (to me).
Quote by TGautier13
Because e-cred on a sub-par 4Chan knockoff forum is what everyone strives to achieve.
We believe - so we're misled
We assume - so we're played
We confide - so we're deceived
We trust - so we're betrayed
Quote by ramm_ty
You just exploded my brain. 4/3? What's a 3?

I understand how you did that, but 4/3 seems much more confusing than 5⅓/4 (to me).

Indeed. BGC, you have confused me and not in a good way. I've seen fractional time signatures, but I've yet to see a 4/3 time signature and I'm ok with that...
Quote by Nightfyre
Indeed. BGC, you have confused me and not in a good way. I've seen fractional time signatures, but I've yet to see a 4/3 time signature and I'm ok with that...

It's exactly what it looks like: four beats, which each beat having the length of one third of a bar of 4/4. Obviously, in order to be able to use 4/3 you first have to establish exactly how long a bar of 4/4 is, so time signatures like 4/3 would far better be described as 4/4 unless put in some sort of context.
Someones knowledge of guitar companies spelling determines what amps you can own. Really smart people can own things like Framus because they sound like they might be spelled with a "y" but they aren't.
I think I understand, thanks for comments everyone.
Quote by TGautier13
Because e-cred on a sub-par 4Chan knockoff forum is what everyone strives to achieve.
We believe - so we're misled
We assume - so we're played
We confide - so we're deceived
We trust - so we're betrayed
So you mean that in 4/3 the unit of time is the tripled half note? I don't know if such note value is even allowed to be used as unit of time in time signatures...

In 4/3, you have 4 tripled half notes, each of them allow 4/3 of a quarter note.
So basicly you are dividing the 4 beats in 4/3 equal parts (just like a simple metre divides it in 2 and a compound metre in 3).
How you divide a beat in 4/3 quarter notes I don't know, but suming those parts would get a somewhat super-compound metre...
So you mean that in 4/3 the unit of time is the tripled half note?

No, it describes a bar consisting of four beats, with each beat having the length of 1/3 of a bar of 4/4.

I don't know if such note value is even allowed to be used as unit of time in time signatures

Why wouldn't it be?
Someones knowledge of guitar companies spelling determines what amps you can own. Really smart people can own things like Framus because they sound like they might be spelled with a "y" but they aren't.
1/3 of a bar of 4/4 is a triplet half note, is it not?
Quote by TGautier13
Because e-cred on a sub-par 4Chan knockoff forum is what everyone strives to achieve.
We believe - so we're misled
We assume - so we're played
We confide - so we're deceived
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Quote by ramm_ty
1/3 of a bar of 4/4 is a triplet half note, is it not?

I guess it would be equivalent to that length of time. I'd be hesitant to actually describe it as a "tripled half note", since we're not dealing with triplets.
Someones knowledge of guitar companies spelling determines what amps you can own. Really smart people can own things like Framus because they sound like they might be spelled with a "y" but they aren't.
How do you get 1/3 of anything if we're not dealing with triplets?

Doesn't filling a bar of 4/3 have to involve triplets by definition?
Quote by TGautier13
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We confide - so we're deceived
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Last edited by ramm_ty at Oct 22, 2008,
Quote by ramm_ty
Since 3 triplet eighths notes are equal to a quarter note, I gathered one triplet eighth note would be equal to a third of a quarter note, giving me a time signature of 5⅓/4

to make it a non-fractional, you'd make it 4/3 TS

3rd meaning a half note triplet, in a 3:2 ratio.
Quote by Archeo Avis
No, it describes a bar consisting of four beats, with each beat having the length of 1/3 of a bar of 4/4.

Well, considering a bar of 4/4 equals a whole note, a third of a whole note is a ternary division of it, meaning 3 tripled half notes, or in this case (each beat), one.

Why wouldn't it be?

I don't know, I am talking traditionally.
Various musicians write in complex irrational time signatures like 2/6, 5/24, etc, but I am not too sure if there is another way of notating them...

Also, I wonder how you have to write time signatures which uses note values longer than whole notes as unit of beat...
Also, I wonder how you have to write time signatures which uses note values longer than whole notes as unit of beat

A whole note is not the largest note value. There are notes that span two three, or even four whole notes, and I don't see any reason why you couldn't use them as a beat unit (though I don't see why you would)
Someones knowledge of guitar companies spelling determines what amps you can own. Really smart people can own things like Framus because they sound like they might be spelled with a "y" but they aren't.
Quote by Archeo Avis
A whole note is not the largest note value. There are notes that span two three, or even four whole notes, and I don't see any reason why you couldn't use them as a beat unit (though I don't see why you would)

But how do you write the time signature if 1 is the smallest denominator (which represents a whole note)?

You write 5/4^-1?
But how do you write the time signature if 1 is the smallest denominator (which represents a whole note)?

I think that's more of a limitation of the current convention regarding the way times signatures are written. There are a few advocates of the idea that that the beat unit should be written as a note symbol (quaver, semi quaver, etc), which I think is a much more sensible idea since it, among other benefits, eliminates the need for compound time signatures.
Someones knowledge of guitar companies spelling determines what amps you can own. Really smart people can own things like Framus because they sound like they might be spelled with a "y" but they aren't.
It's definatley a cool idea, but I think its could be just narrowed down to simple Polyrhythm.

Your first example

A bar of 4/4 can contain 12 triplet eighth notes, 3+3+3+3 when grouped normally.
You could also group them in 4's (4+4+4) giving you 3 sets of 4 and an interesting rhythmic effect. I took it further and tried a 4+4+4+4 grouping, extending the bar beyond 4/4, and leaving me with 16 triplet eighth notes.

In the first time your accenting the first beat of every 8th note triplet, resulting in 4 attacks in a 4/4 bar.

Than you were talking about accenting every 4th note, ersulting in 3 attacks in a 4/4 bar.

1 2 3 4 5 6 7 8 9 10 11 12

So, in one version you have 4 attacks, in the other you have 3 attacks.

Just down to the attacks, the 4 attack, would be playing straight crotchets, and the 3 attack, playing Minum Triplets.

Playing them both together would result in a 4:3 or 3:4 Polyrhythm, depending on which rhythm is dominant, which would be established by what the other instruments are doing.

4:3 being 4 beats in the time of 3 beats
3:4 being 3 beats in the time of 4 beats.

Now if your working in 4/4, and having 4 groups of 4 8th note triplet notes, I would say, as Nightfyre did, to write it in 16/8

If your grouping it as 5 groups of 3. This is triplets in 5/4 of a compound version of 5/4, 15/8.

Adding one 8th note is 16/8

Your idea could be done easily with any tuplet grouping (or non-tuplet grouping for that matter)

Take Quintuplets (16th note).

In a bar of 4/4, you have 20 notes.

You could accent this as 4 groups of 5, as already done, or 5 groups of 4.

If you wanted to be a real asshole, you could accent the quintuplets in 3's

Taking 3 bars of 4/4 to get back to original, the possibilities are endless, enjoy.