polyrhythms

[DWb]

Out of interest, would people consider playing independent rhythms in the same meter to be a form of polyrhythm? Or at least an extension of the concept? It seems to have a lot of the same effect, ie something where you can concentrate on any one of several rhythms but not (easily) on all of them simultaneously.

Obviously it's pretty hard to define what's 'independent rhythms' and what's just multiple instruments contributing to the same rhythm...

[herodotus]

Obviously it's pretty hard to define what's 'independent rhythms' and what's just multiple instruments contributing to the same rhythm...

Too true.

Out of interest, would people consider playing independent rhythms in the same meter to be a form of polyrhythm? Or at least an extension of the concept? It seems to have a lot of the same effect, ie something where you can concentrate on any one of several rhythms but not (easily) on all of them simultaneously.

Well, that's just it. These terms have all been used so loosely, and for so long, that it is hard to be precise without missing important nuances.

I have seen the word 'polyrhythm' used by perfectly literate and intelligent people to mean something close to 'really complex-sounding drum music', whether or not there were any of what we have been calling polyrhythms here present. It is possible that this usage shall win the day. Only time will tell.

But I have seen more people use the word 'polyrhythm' to mean something like

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

than any other single usage. And as there is certainly a lot of music conforming to this usage, I thought I would get the ball rolling in that direction.

[VicDiesel]

Knowing about this kind of relationship and how it works can very definitely be of help if one is working with polyrhythms

How? Take my example of playing 3-against-4, and the guy who is doing the 3'ing plays a triplet on one of his notes, while the 4-guy plays 4 sixteenths on one his beats. Quite easy to play.

Now how is it of any help to know that these two parts can be considered as different groupings of an underlying 144-clicks-to-the-bar smallest duration?

My analysis is that the two players considering hte whole measure as basic duration, and each make their own subdivision of it. Mine is right and helpful.

Your analysis is that they play multiples of some microscopic subdivision. Your analysis is also right, but I fail to see how it helps.

Btw, your analysis is not even possible in general. Please make me a picture, not of a quadruplet in 3/4 time, but a triplet in 4/4 time, and show how the triplet notes are a multiple of some underlying duration.

Go ahead.

Victor.

[herodotus]

Knowing about this kind of relationship and how it works can very definitely be of help if one is working with polyrhythms

How? Take my example of playing 3-against-4, and the guy who is doing the 3'ing plays a triplet on one of his notes, while the 4-guy plays 4 sixteenths on one his beats. Quite easy to play.

Cool. I'm with you.

Now how is it of any help to know that these two parts can be considered as different groupings of an underlying 144-clicks-to-the-bar smallest duration?

Composers like Nancarrow and Messiaen and Boulez use the principles I was discussing, i.e. analogous metrical structures at greatly varying tempi, all of the time.

My analysis is that the two players considering hte whole measure as basic duration, and each make their own subdivision of it. Mine is right and helpful.

OK......good for you?

Your analysis is that they play multiples of some microscopic subdivision. Your analysis is also right, but I fail to see how it helps.

See above, Messiaen, Nancarrow, Ligeti....

Btw, your analysis is not even possible in general. Please make me a picture, not of a quadruplet in 3/4 time, but a triplet in 4/4 time, and show how the triplet notes are a multiple of some underlying duration.

Go ahead.

OK, but can I use the grid concept? I mean, you seem to have a problem with that, too.


Give me until tommorrow. Life intervenes.

[VicDiesel]

OK, but can I use the grid concept? I mean, you seem to have a problem with that, too.

Be my guest. My problem is only that it's not helpful.

So, two questions for you: show that it's helpful, and show that's possible to begin with, in the case I just sketched.

Victor.

[herodotus]

OK, but can I use the grid concept? I mean, you seem to have a problem with that, too.

Be my guest. My problem is only that it's not helpful.

So, two questions for you: show that it's helpful, and show that's possible to begin with, in the case I just sketched.

Victor.

OK.

Lets review, shall we?

Your objections started with telling rachmiel and myself that the song 'Kashmir', which we both independently understood to contain the same polyrhythm, didn't contain a 'true' polyrhythm.

Personally I would have thought that if 2 people from opposite sides of the planet independently came to the same conclusion about the structure of a song, and could provide diagrams of this structure, that this would be enough, but no, this isn't a 'true' polyrhythm.

Later, you acknowledged that there were two 'kinds' of polyrhythm. But then you objected to my global definition of them, providing your own definition of this 'other kind' of polyrhythm:

"x equally long notes in the time of y equally (but diffrently) long notes, where x is not y".

I attempted to show that this did in fact mesh with my previous definition; that in order for x and y to meet up at the right place, they, too, had to conform to the rule:

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.

At this point your objection was:

I wish you guys would give up this sequencer mindset!

I must admit that at about this time I started to feel sort of confused.

The vast majority of the people who will read these words use sequencers all of the time. Many people here use them for everything they do. But now I am being told that in order to discuss polyrhythms here I should 'give up this sequencer mindset'?

In fact, many pioneers in electronic music, from Milton Babbit to Karlheinz Stockhausen, were drawn to the electronic medium because of this precise control of rhythm that it afforded.

But lets let this slide and return to your objection:

You're trying to find a common smallest measure, which I think is futile if you play 8 over 9 or so. 8x9=72. No one can hear that subdivision. Or take a Zappa score with 24 over 23 or something like that. You'd have to divide your quarter note in 600-or-so parts. That's obviously silly.

Now I never claimed that anyone could 'hear that subdivision', nor did I put these subdivisions forward as a learning aid. Nor at any point did I say that your way of performing and hearing polyrhythms was wrong.

My point was that, however you play this 'other kind' of polyrhythm, it still has the same underlying metrical structure. This isn't a matter of taste or of preference or of schools of thought. It concerns the nature of measured time. I suppose you could object that this point was too 'remote' or 'academic' to be helpful, but I can't see how it is any more academic than a great deal of mainstream music theory. And it is a good deal less academic than the article I was just reading in 'Perspectives in Musicology'.

In any case, is it not likely that someone here, facing the daunting task of playing a song that featured passages of 9 notes in the space of 8 notes at a live gig, would use a sequencer as a rehearsal aid?

No, the only common grid to two poly-rhythmic (or polymetric, whatever) parts is not a divided note length, but a unified one: in your case a whole 3/4 measure.

Now this is where you are mistaken. Whether or not the 'common grid' analysis of a polyrhythm is useful to a particular person or not, (and I will happily acknowledge that in many cases it is not) it still holds as a principle. It follows ineluctably from standard definitions of musical and chronometric time.

In the case of your (I assume eighth note) triplets in 4/4 time, the grid is one of thirty-second note triplets. Each eighth note triplet has a note value equal to four of the thirty-second note triplet note values while the sixteenth notes are equal to three thirty second note triplet values.

It looks like this:



and sounds like this (at quarter note=40).

Would a person playing triplets against sixteenth notes at 120 bpm compute their part based on these thirty second note triplets? No, of course not.

But there are all sorts of ways that they could use this knowledge creatively. For example: the same grid can be interpreted in more than one way. One can line up one repeating polyrhythm of 8 against 5 with an eighth note grid and treat the same grid as, say, a series of sixteenth notes to line up another repeating polyrhythm of 6 against 4.

Messiaen, in his Turangalîla-Symphonie and even more in his Chronochromie does this sort of thing all of the time, using the grid-concept to coordinate groups of very different polyrhythms. The players are not and need not be aware of this grid, but without it the composer couldn't know basic things like where the fast 8 against 5 polyrhythm would be in its cycle after the slow 6 against 4 polyrhythm had repeated, say, 3 times, or 5 times or whenever. In fact, it is hard to imagine how these parts could be notated or indeed conceived without the grid-concept.

One should also note that Elliot Carters concept of metrical modulation assumes a common grid as a frame of reference.

So there you have it.

[liqih]

Turangalîla-Symphonie is great, do you know From Canyons to Stars?

[liqih]

In any case, is it not likely that someone here, facing the daunting task of playing a song that featured passages of 9 notes in the space of 8 notes at a live gig, would use a sequencer as a rehearsal aid?

this is an interpreatation of 9 on 8 as
3x3 over 2x4

http://www.dashsignature.com/mp3/98.mp3

[liqih]

here is again 9 0n 8 but with differnt figures,
intersting to note how it seems simpler shifting the accents
http://www.dashsignature.com/mp3/98++.mp3

and on the other hand an example of having the kick on the 9 figure
http://www.dashsignature.com/mp3/89.mp3

IMHO to call something "Music Theory", that should include
all the human aspects of the performing, hence the time stretching and the accents shifting which players do to make a musical sense of what they are playing,

or just make a math semplification and call it Theoretical Music, not Music Theory,

of course to reach the Music Theory you may first build a Theoretical Music, that is if you choose the deterministic approach

[VicDiesel]

Your objections started with telling rachmiel and myself that the song 'Kashmir', which we both independently understood to contain the same polyrhythm, didn't contain a 'true' polyrhythm.

Look up poly-rhythm in one source and the first dozen examples they give are of my kind; secondarily they give the Kashmir kind.

Fine.

But then you objected to my global definition of them, providing your own definition of this 'other kind' of polyrhythm:

"x equally long notes in the time of y equally (but diffrently) long notes, where x is not y".

I attempted to show that this did in fact mesh with my previous definition; that in order for x and y to meet up at the right place, they, too, had to conform to the rule:

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.

One problem is your use of "natural number". Take 2-against-3. What are x and y? To me that's two units of value 1/2 against 3 of value 1/3. Those are fractions, not natural numbers. In order to get natural numbers you need to argue (as you indeed do) that the 2 are really 2 groups of some underlying 1/6th of a measure.

Btw, 1/6 is also not a natural number. Would you state what x and y are in this example? I guess you'll come up with an anser, since you start out with the undefined term "unit with a metrical value of <something>" which does not appear in any music theory book I know.

But now I am being told that in order to discuss polyrhythms here I should 'give up this sequencer mindset'?

Yes. You're used to looking at that so-many-ppqn grid. I'm sure when you're playing poly-rhythms that's not useful.

I suppose you could object that this point was too 'remote' or 'academic' to be helpful, but I can't see how it is any more academic

That's not example a defense of your statement that is was actually helpful or insightful.

In any case, is it not likely that someone here, facing the daunting task of playing a song that featured passages of 9 notes in the space of 8 notes at a live gig, would use a sequencer as a rehearsal aid?

Sure. But the grid with a subdivision in 72 is not anywhere present in that.

In the case of your (I assume eighth note) triplets in 4/4 time, the grid is one of thirty-second note triplets.

.

Yeah, that's what I figured later. My intended statement was that there is no grouping of 16th, 32nd, 64th et cetera that would cover that. You need to introduce triplets, quintuplets et cetera in your grid.

One should also note that Elliot Carters concept of metrical modulation assumes a common grid as a frame of reference.

I'll look up your Messiaen references. For now I'll just say in parting that Elliot Carter sounds more "composed on a computer" than any music that's actually composed on a computer. He is one contemporary composer that I completely fail to get. Probably along with Boulez.

Victor.

[DWb]

"x equally long notes in the time of y equally (but diffrently) long notes, where x is not y".

I attempted to show that this did in fact mesh with my previous definition; that in order for x and y to meet up at the right place, they, too, had to conform to the rule:

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.

I think this is technically correct but looking at 3 on 2 or 5 on 4 rhythms, it seems ass-backward to a live instrumentalist's way of thinking about things - and since we're splitting semantic hairs here, how people think about things is what we're after.

Actually (I'm thinking out loud here) it's tempting to say that the listener not being able to hear the music in terms of an underlying rhythm (in 72nd notes or whatever) is the definitive part of something being a polyrhythm - just as polyphony requires the voices to sound like independently moving voices that happen to harmonize rather than a just series of chords.

[VicDiesel]

I think this is technically correct but looking at 3 on 2 or 5 on 4 rhythms, it seems ass-backward to a live instrumentalist's way of thinking about things - and since we're splitting semantic hairs here, how people think about things is what we're after.

My brother!



Victor.

[Toxikator]

You guys are really missing the whole point.

Polymeters includes both meters based on unequal subdivisions of the same bar AND unequal bar lengths.

Polyrhythms/polymeters are simply musical parts where multiple metric ideas are expressed simultaneously. It can range from certain syncopation to incredibly complex computer-calculated organization.

What you're doing is like saying "I say an interval is two simultaneous notes!" "Well, I say an interval is the distance between consecutive notes!"

Both ideas are right because they are both encompassed in the term, and you're fighting over nothing and neither will win (unless one of you is just taking the "both are right" stance, in which case you will, but I don't have the patience for 5 pages of this).

Getting technical over meters is stupid anyway. Meter is about PERCEPTION, not technicality. You might as well argue that 6/8 and 3/4 are the same, or that 2/4 and 4/4 are the same, because at X tempo and Y calculation you can get the same results.

The point is how it's percieved. you can subdivide meters into their lowest common denominator if you want but it's beside the point because meter is about the rhythmic feel, not the math behind it.

[herodotus]

I think this is technically correct but looking at 3 on 2 or 5 on 4 rhythms, it seems ass-backward to a live instrumentalist's way of thinking about things - and since we're splitting semantic hairs here, how people think about things is what we're after.

I am not splitting semantic hairs. I am trying to show a general principle.

I am trying to describe a general law that explains disparate phenomena. So far no one has disproved this law.

I have tried to show how polyrhythms that use rhythmic cells as units are related to polyrhythms that use single notes as units. I have given plentiful diagrams to make these relationships plain.

So far, no one has disproved this relationship.

The 'You am going at it backwards' criticism is relevant only if I were solely trying to describe to a single player how to play one particular kind of polyrhythm. I am not doing that. I am trying to show how this kind of polyrhythm:



Is structurally related to this kind of polyrhythm:



To me this is an interesting parallel, worthy of discussion. especially given the rather conspicuous lack of scholarly books on this subject.

Consequently, I stated a (provisional) general law to describe this relationship.

Again no one has proven this wrong (which would be fine by me, by the way. That is when progress is made) They have just said that I am 'going at it backwards' or said 'you are technically correct but not helpful' or something similar.

But general laws are very rarely helpful in their basic form. They address not the needs of learners, but the nature of the subject under discussion.

And if it weren't for the constant objections (all of the met, btw) of mostly one person, this law wouldn't be all over these pages. It would have been stated once, perhaps twice, back about 3-4 pages ago.

sigh.

Finally, about the objections concerning 'how a real human player understands these things, as opposed to a machine'.

http://www.realmusicmedia.net/5x3x4.mp3

This piece, constructed out of various kinds of 3 part polyrhythms (including the two different kinds mentioned here, only with 3 parts instead of 2) was played live.

On a drumset.

By me.

Alone.

So I do know a little bit about how real humans play these things.

[Toxikator]

I guess the point is that meter is not about the metric subdivisions but the perceived quality. While you have technically connected the two it's not in a necessarily meaningful way.

For lack of a better way of explaining it, it'd be like arguing that a can of cola is the same as a Swiss soccer player because both are built out of atoms and molecules.

Obviously correct, but also obviously beside the point. Yes, at a highly subdivided level there's a relationship between compound-form polymeter and asymmetrical-form or syncopation-form polymeter, but it's an impractical comparison to draw.