Polyrhythms part 2, the friendly, helpful thread

[rp314]

No, no, the thread is going fine, as is the new forum.

KVR's forums are not exactly overflowing with transcendental wisdom. To require that this thread be useful to everyone is IMHO more than a bit unfair.

[.jon]

x units with a metrical value of y superimposed over y units with a metrical value of x, where x and y are natural numbers.

That definition is ok, maybe what interests me is why

x units with a metrical value of y superimposed over z units with a metrical value of p, where x,y,z and p are natural numbers.

would not work as well - what is the theory behind "grooving" polyrythms?

And in any case, most theory books are filled with "lists of various possibilities from an endless series"

That might be the case, I must day that I am used to different kind of theory and probably not familiar enough with music "theory" - so far everything I have learned resembles calculus more than actual theory:

In science, a theory is a proposed description, explanation, or model of the manner of interaction of a set of natural phenomena, capable of predicting future occurrences or observations of the same kind, and capable of being tested through experiment or otherwise falsified through empirical observation.

so the fault is possibly in my false exceptations.

Perhaps you could point our way toward a more helpful approach?

Maybe you could try to explain the choices you have made, the instrumentation of the patterns and the reasoning of accents? I've read such things about the samba clave, and they really helped a lot.

Isn't rhythm more than just absolute placements on the grid?

.jon

[Franky]

Thank you for the examples and Midi's!
I appreciate your effort for fellow musicians.
Have a nice year 2007.
Regards, Frank Valet

[Watto]

Wow, even this one's approaching meltdown! Just by way of explaining, I wanted some polyrhythms to practise playing LIVE, in a jazz setting predominantly. Of course it's easy to do this in a sequencer! Much more difficult to play these while others around you are also improvising...

[herodotus]

That definition is ok, maybe what interests me is why

x units with a metrical value of y superimposed over z units with a metrical value of p, where x,y,z and p are natural numbers.

would not work as well -

Well, one could do that and call it a polyrhythm, just as one could call any collection of notes a chord. Personally I think that some of these newer theoretical terms are usually rather loosely conceived and applied. So if 'polyrhythm' ends up meaning something other than what I have described, that is no surprize. And no big deal as far as I am concerned.

what is the theory behind "grooving" polyrythms?

Well, I guess the reason for settling on the previous definition is that it describes a phenomenon common in a great deal of contemporary music, from artists like King Crimson and Ornette Coleman, to Frank Zappa and Led Zeppelin, back in time through Gyorgi Ligeti, Olivier Messiaen, and Harrison Birtwistle, all the way to Stravinsky and Debussy and beyond. The essential idea behind it is that if you play a part in say, 7, three times, and a part in, say, 3, seven times, they form a complete cycle that 'meets up' at predictable intervals, as in this example from the King Crimson song 'Frame by Frame' (The midi file contains the written part repeated 3 times)

Frame by Frame


'Polyrhythms' of the sort that you described would not have this 'meeting up at regular intervals' quality. If we want to call such things polyrhythms, we will have to have more than one type-name like cyclical polyrhythms and non-cyclical polyrhythms.

(It would be great if some egghead had figured this all out and explained it some book, but I have been looking for quite some time, and I have to say that I haven't seen one that comes even close. Of course, I can't read sanskrit, so I can't be sure.....)

I must say that I am used to different kind of theory and probably not familiar enough with music "theory" - so far everything I have learned resembles calculus more than actual theory:

In science, a theory is a proposed description, explanation, or model of the manner of interaction of a set of natural phenomena, capable of predicting future occurrences or observations of the same kind, and capable of being tested through experiment or otherwise falsified through empirical observation.

so the fault is possibly in my false exceptations.

Not really.

The problem is that what we are talking about aren't really natural phenomena in the normal sense of the word. They are creations of the human mind. 'Natural' enough in the broadest sense certainly, but subject to slightly different rules of discourse.

The closest model of what music theory should be is probably the science of Linguistics, which treats language as a natural phenomena, but which doesn't really try to 'predict future occurances', so much as it tries to understand the framework that all such occurances take place in. And while it is rare to test the assertions of linguists through experiment,they can and are very much subject to being 'falsified through empirical observation'.

What music theory is instead, is rather a mess. But that is another subject.

Perhaps you could point our way toward a more helpful approach?

Maybe you could try to explain the choices you have made, the instrumentation of the patterns and the reasoning of accents? I've read such things about the samba clave, and they really helped a lot.

That I can do, sure.

The polyrhythms in the first post of this thread are arranged in 4 different series as follows:
3x2
4x3
5x3
5x4

As you can see, the numbers gradually get larger. To be truly systematic, I should have put 4x2, and 5x2 in there as well, but 4x2 is trivial from a learning standpoint, as most musicians learn it early on, and 5x2......well, that one I just forgot.

In any case, the first example of each is the most basic kind. with the following ones getting 'busier' gradually.

The key thing to note is the 'dual' metrical meaning of each line



What dual meaning??



OK, now in this picture:


5_against_4_basic

the counting pattern is obvious.

But if you put a line of sixteenth notes next to them as a frame of reference, you can see that each of the 5 notes in the '5' line is equivalent to 4 sixteenth notes, while each of the 4 notes in the '4' line is equivalent to 5 sixteenth notes.



This follows from simple, basic facts about measured time.

What this allows is for us to treat each beat of the '5' line as a 'little measure' or 'cell' of 4/16, and each beat of the '4' line as a 'little measure' or 'cell' of 5/16.


5_against_4_elaborated1

Which is also what the first example (from the King Crimson song) is doing (only it articulates the meters with melodic patterns) and what the 'kashmir' example from the other thread is doing


Once you get used to this sort of 'multileveled' rhythmic pattern, you can use it in all sorts of ways.

That was the idea behind those examples.

They are, as you noted previously, but a handful of a vast number of possibilities. But there are enough to get the very basic idea across (I hope).

Isn't rhythm more than just absolute placements on the grid?

Yes.

And there is more to real-life harmony than absolute placements on the grid of twelve tone equal temperment. Nonethless, the grid of twelve tone equal temperment (like on say, almost every Piano or keyboard instrument in common use) can be useful for discussing and working on harmony.

[DAAHOOD]

The closest model of what music theory should be is probably the science of Linguistics

Leonard Bernstein - The Unanswered Question. Cambridge, Mass: Harvard University Press, 1976

awesome publication !

bernstein's explicit theory of music based on chomsky's linguistic concept.

[herodotus]

Thank you for the examples and Midi's!
I appreciate your effort for fellow musicians.
Have a nice year 2007.
Regards, Frank Valet

Hey!

Thanks.

And welcome!

Wow, even this one's approaching meltdown!

Nah!

This sort of bashing about is part of the game.

So far it has been fairly polite.

[[godbox]]

And very helpful, thanks.
So polyrhtyms exist in a kind of metrical least common denominator, then? Is that a fair way to oversimplify it?

[metrosechual]

perhaps we should start a new forum, music theory 2, the helpful and friendly one!

as it is , i am going to study these on my spare time, thank you!

[herodotus]

The closest model of what music theory should be is probably the science of Linguistics

Leonard Bernstein - The Unanswered Question. Cambridge, Mass: Harvard University Press, 1976

awesome publication !

bernstein's explicit theory of music based on chomsky's linguistic concept.

Interesting.

I will have to check that out.

And very helpful, thanks.
So polyrhtyms exist in a kind of metrical least common denominator, then? Is that a fair way to oversimplify it?

Sort of.

This brings up points that I can't address right now.

More later.

[VicDiesel]

So polyrhtyms exist in a kind of metrical least common denominator, then?

Least common multiple.

If you have 9-against-8, then you need a grid with 72 subdivisions.

For 3-against-4 you need 12, and that also works for 6-against-4, so it's indeed the least common multiple.

Victor.

[[godbox]]

So polyrhtyms exist in a kind of metrical least common denominator, then?

Least common multiple.

If you have 9-against-8, then you need a grid with 72 subdivisions.

For 3-against-4 you need 12, and that also works for 6-against-4, so it's indeed the least common multiple.

Victor.

least common multiple

[Sascha Franck]

I think that there's two basic things about polyrhythms which could probably both be looked at like Vic said, by searching for the least common multiple, but from a "feeling" point of view they will still be fundamentally different.

The more "uncommon" one being to superimpose different "basic" rhythmic divisions over each other, such as playing triplets (or quintuplets, whatever you like) over an otherwise even grid (e.g. 8th note triplets over an even 16th pattern).
This seems to be used most in melodic (and improvisational) stuff, I don't think you find that kind of stuff for the basic rhythmic "building" all too often in contemporary pop/rock and whatever styles.

For more or less basic rhythmic stuff It's way more common to "group" notes of whatever even (or odd) "grid" in odd (or even) numbers. Such as in the previously mentioned groups of 3 16th notes over a plain 4/4 16th-based pattern, which have got to be *the* most familiar thing used in funk, jazz and a lot of other styles.
In the end, this kind of polyrhythmic stuff could be described more like "shifting accents", but still, all the things mentioned so far would be valid. Whether you're playing a 4 over 3 or a 3 over 4 pattern, in both cases you need a least common multiple of 12, in case of the mentioned 3 note 16th groups that'd make up for 12 16ths to get them sorted.

[VicDiesel]

I think that there's two basic things about polyrhythms which could probably both be looked at like Vic said, by searching for the least common multiple, but from a "feeling" point of view they will still be fundamentally different.

I've been arguing that with Herodotus for a while. I'll stay out of this thread.

Victor.

[herodotus]

I think that there's two basic things about polyrhythms which could probably both be looked at like Vic said, by searching for the least common multiple, but from a "feeling" point of view they will still be fundamentally different.

I've been arguing that with Herodotus for a while. I'll stay out of this thread.

Victor.

There is still this thread.

There is nothing wrong with argument. I just thought that there should be a thread where people unfamiliar with this stuff could go for some exercises and ideas, without having to wade through the controversy.

Others are very much encouraged to post links to alternative ideas and conceptions.