Irrational Meter

Can someone explain it?

An irrational meter is a time signature where the bottom number is not divisible by 2. Some composers use irrational meters for specific rhtyhms and stresses. Some composers feel that irrational meters are a better way to express polyrythms/syncopations as well. Its been some time since I've studied and looked into irrational meters. I personally am not to big on irrational meters.

Just to show you how far some people take irrational meters...

When I was a college student I was taking a modern ear training and theory course. On the subject of irrational meters the professor asked us to find the time signature of Pi (All you math lovers will have this answer in no time).

22/7!

And they have the cheek to complain about John Cage? Stockhausen?

22/7!

Yes, 22/7 is correct. Do you know what the time signature would be if you decided to rationalize Pi?

And they have the cheek to complain about John Cage? Stockhausen?

Yes, some of the thinking behind irrational time signatures can get a little out of hand if not silly. But, its still possible to have more conservative music with irrational time signatures. That's probably why people may "have the cheeck" to complain about John Cage and Stockhausen.

Time signature: e/pi

Have fun counting. :)

e/pi = 1.5

Dunno where you learnt maths.....

Anyway.. 22/7 is not pi.. it's just an approximation. It's not a "rationalization".

Its an approximation, yes. But expressed/represented as the time signature 22/7 is the answer. That's why the question was presented to the students on the subject or irrational meters.

You can't count in an irrational meter though. It's impossible, except for approximations. The concept is entirely useless.

Musically, its not useless. Its not that you would be calling 22/7 and exact representation of Pi as an irrational time signature. Instead you are using the approximation 22/7 to give indication as to the rhythmic division. Having 22/7 as a time signature could suggest a polyrhythm of 22:7 (22 against 7).

Ok, so I was trying to figure this out a bit more because you guys still haven't really told me anything I didn't learn from the wiki article. In the attached midi, I kinda jerry rigged an example of irrational meter (my sequencer doesnt officially support it after all) so I guess just tell me if I'm right? What I'm TRYING to do is go from 4/4 to 4/3 then back to 4/4. Then 4/4 to 4/5 then back to 4/4.

irrational meter example.mid

I'm sorry about not answering your question more completely. I haven't looked at you example as I'm kind of on the run, but since you brought up

4/3 I'll use it as an example to help explain a little. Hope it helps.

4/3 - In one sense this can mean 4 beats per measure and the dotted half noted gets one beat.

4/3 - In another sense this can mean that throughout the piece the rhythm of the music will always be expressed as 4:3 (4 against 3)

4/3 - In this more experimental sense it could mean that there are 4 beats to a measure but the 1/3 note gets one beat.

As you already know by now your irrational time signatures have odd number as denominators and can be used in varies ways depending on what your are trying to accomplish.

e/pi = 1.5

Dunno where you learnt maths.....

Not sure if you're being serious. Because e < pi ......

e=2.7 (around that)

pi=3.14 (around that again). And for me who am Greek it's π hahaha!

Now e/pi is certainly not 1.5, and have little relationships as far as I know, the one being with limits and all that and pi having to do with circles...

Anyways...

Back to your discussions... :) (I just don't care about irrational meter to discuss it... ony of those silly things that happened and then don't seem to matter that greatly...)

Yea, I was joking about it being 1.5

The entire concept of an irrational meter is entirely useless.

When you approximate an irrational number, it is no longer irrational! So therefore, why isn't it just called "weird number time sigs" instead of irrational, because like I said, you can't count it if it's irrational.

Can anybody show me something with an example of this?

Now e/pi is certainly not 1.5, and have little relationships as far as I know, the one being with limits and all that and pi having to do with circles...

Euler's Identity ties e and pi.

While I'm not too fond of the concept either, I wouldn't say that it's useless because you can only approximate it, as that always applies when playing music. Unless you are a computer, you can always only approximate written music. The more trained you are, the closer you can get, but you won't ever reach it (which also isn't really necessary). It's your task as a musician to interprete the piece by deciding how closely you "need" to get to what's written. In the case of irrational meters, that means deciding which rational approximation to pi is close enough for your purposes.

Yea, I was joking about it being 1.5

Oh, I see. Care to show us where in your post you expressed that feeling of making a joke? Because there are no smileys, no "jjk"'s or anything else, so naturally everyone else mistook this for a serious statement (as I did myself). And also, accusing people of not knowing something while you yourself show that you absolutely don't know what you're talking about (as someone would have thought if you hadn't clarified this was a joke) makes you look really dumb (I am not saying you are, I am merely saying what it looks like), so make sure you do say it's a joke on the same post to avoid further misunderstandings :)

When you approximate an irrational number, it is no longer irrational! So therefore, why isn't it just called "weird number time sigs" instead of irrational, because like I said, you can't count it if it's irrational.

I think you are confusing the mathematical term "irrational" (as in "irrational numbers" - real numbers which can't be expressed as the quotient of two integers) and "irrational rhythms", which is defined by wikipedia as rhythms of the type n/m where " n evenly-spaced beats are played in the time of m beats of the underlying tempo [...] if neither of n and m is divisible by the other. " The example with π was an extreme one, which was used to exhibit the "craziness" of irrational rhythms (quoting Majesty: "Just to show you how far some people take irrational meters..."). So all this fuzz is mostly about nothing :P (check this link as well: Irrational rhythm - Indopedia, the Indological knowledgebase - the first paragraph says some things about that conflict between the musical and mathematical term of "irrational")

The entire concept of an irrational meter is entirely useless.

Well, is it useless if it has helped even one composer compose a piece? Unless you meant "pointless" (taking in consideration the next few phrases of your post), in which case you should have written "pointless" :P

Anyway, I have to go so you guys enjoy the discussion and take care :P

Way to dig up a year old post.

Why should the Daniel of 2006 put smiley faces when he's being sarcastic?

I don't see any reason. ;)

Well, is it useless if it has helped even one composer compose a piece?

Just to make a facetious riposte:

All art is quite useless.

So, yes.

Oh, lol, I didn't notice that this was such an old thread... :P I just saw it in the "last post in X thread" in the forums and thought it was recent. Anyway, Oscar Wilde has said many things, including stuff like "Everybody who is incapable of learning has taken to teaching." ;P

OMG!

This is ONE OLD THREAD! I mean, the guy named "nikolas" in this thread is me, but not the same account! Imagine how old this goes back! :D

You know as far as I'm concerned irrational meters don't exist. I mean, they really DON'T, because there is no such thing as a third note or whatever, and anything you feel like you "need" an irrational meter for can be expressed with tuplets, tempo changes, or a switching between meters that DO exist, such as 4/4 to 6/8.

No such thing as a third note? I triplet divides a note into exactly three parts, and just because the common practice period system of notating divisions that aren't a power of two as tuplets is a bit cumbersome, doesn't mean it's irrelevant. And in music before about 1600 divisions of notes in three were just as common as divisions in two.

It is true that you can "imitate" such meters with tuplets, accents, etc. However you might say as well that you could restrict music to 4/4 only and imitate every other meter within that. Personally I've never seen the need to use a meter such as 4/3, partly because the music I write doesn't tend to have a strong metre, but I could imagine situations where it would be the most appropriate solution.