polyrhythms

[DAAHOOD]

all these rhythms are based on the same 1/16th or whatever smallest beat

no because you can isolate one group and turn it as a reference base tempo (like groupof5 becomes 1/4)but difficult to handle
if you try the second experiment i propose (with groups) you'll feel totally lost in the gobalstructure while hearing percussions polyrythm until you trigg the drum pattern that "reunites" and make "clear" the rythmic audible structure

as for you'r example, line one is 4 1/4; line 2 is 3 1/2 tripplet.
divise line 2 and you'll get 6 1/4 triplet (12 1/8 triplet linked 2 by 2 which determine a common beat-base with line 1 as 1/4 (degroup linked triplet and re-group by 3=4 1/4, same beat as line 1)
but it exactly shows that polyrythm has to be managed with a simple clear material in order to get complexity and precision in the performance

[DAAHOOD]

what i mean is (excuse my english) that too much concept and rules lead to restriction in creativity. even the most complex and singular polyrythms composition has to be considered as simple as possible

one note is monophony, 2 notes is polyphony
one rythm is monorythm, 2 rythms is polyrythm even if tempo/metric is the same(considering that two identical rythms are actually the same whatever the instrument combination)

2 metrics at the same time (5/4 and 4/4) for example is more like...poly-metric then !!

[VicDiesel]

all these rhythms are based on the same 1/16th or whatever smallest beat

no because you can isolate one group and turn it as a reference base tempo (like groupof5 becomes 1/4)but difficult to handle

I guess.

if you try the second experiment i propose (with groups) you'll feel totally lost in the gobalstructure while hearing percussions polyrythm until you trigg the drum pattern that "reunites" and make "clear" the rythmic audible structure

But that's precisely what I mean: there is an underlying basic click.

as for you'r example, line one is 4 1/4; line 2 is 3 1/2 tripplet.
divise line 2 and you'll get 6 1/4 triplet (12 1/8 triplet linked 2 by 2 which determine a common beat-base with line 1 as 1/4 (degroup linked triplet and re-group by 3=4 1/4, same beat as line 1)

No. The common beat base is the whole measure. You are trying to divide the quarter note in three and the triplet notes in four, and then say "look there is 12-clicks-to-the-bar basic rhythm. So how about if the two players do

Code: Select all

o         o . . .    o          o         o
1        2  e&a  3          4          1

o             o  -  -   o             o
1            2   &  a   3              1

Are you now claiming that there is a basic rhythm with 144 (9 x 16) clicks to the bar? That's unrealistic.

If two people can play 3 against 4 by dividing the bar, they are really hearing 3/4 time and 4/4 time independently, so dividing that up in any manner is not hard at all.

Victor.

[DAAHOOD]

If two people can play 3 against 4 by dividing the bar, they are really hearing 3/4 time and 4/4 time independently, so dividing that up in any manner is not hard at all.

i see what you mean but they won't hear 3 but merely 9/8(tipically ternary) because of the decomposition you give
(different to the binary 4-3 correspondance)
remove tripplets and at last it's nothing but a 3 1/2 tripplet on basic 4/4 (as before)
obviously there is no "short" correspondance between 4(or 8 ) and 9 and i wonder how you can have 2 musicians playing both rythms simultaneous while they have to "hear" each other's part in order to play straight (where's the music, where is the confort of playing?) ,though computer can easily make the trick
this is rather a sound effect to me (as experience 1) than a clear and "easy-to-handle" polyrythm
i believe that you don't help much people to figure polyrythm out with such a complicated example

[VicDiesel]

remove tripplets and at last it's nothing but a 3 1/2 tripplet on basic 4/4 (as before)

Yes, but I'm not removing them. My point is that you can have polyrythms by dividing some long unit (for instance the whole measure) in completely different ways, at the same time.

i wonder how you can have 2 musicians playing both rythms simultaneous while they have to "hear" each other's part in order to play straight

Easy. You listen for the whole measure.

(where's the music, where is the confort of playing?)

Trust me, I've done it. You can even ritardando simultaneously.

,though computer can easily make the trick
this is rather a sound effect to me (as experience 1) than a clear and "easy-to-handle" polyrythm

You're too much focused on 20th century music. If you go back 4 or 5 centuries then this is the most normal thing. I have the sheet music somewhere of a piec written around 1500 where two players are dividing some really long measure (5 seconds or so) at the same time in 8 and in 9. Personally I couldn't play it, but the guy who showed it to me said that students of his played it in concert.

It's a more sophisticated sense of time, which we seem to have lost.

Victor.

PS listen to this. At 0:50 there is passage of 3/4 against 4/4, both containing sixteenth notes.

[DAAHOOD]

very nice example

to me ,what you call 4/4 (at 0'50) is more like a 6/8 (with every 1/4 dotted marked by these 3 1/16 notes) in combination with the "bass" pattern rythm (3/4) that lays behind
the basic subdivision to this polyrythm is then 1/8 (as i can hear and figure it myself out)

i remember a very strange polyrythm at a "pygmées aka" performance in paris.there were 2 groups and polyrythm went like:
first group: 17/4 then 15/4 and loop
second group 15/4 then 17/4 and loop
though there was clear numeric correspondance (32/4, both)
the result was indeed amazing (fluid and complex at the same time),it was music for party and pygmees are not very known to be great theorist or musicologist (children were singing the polyrythm too)

You're too much focused on 20th century music

no i just try to make clear

It's a more sophisticated sense of time, which we seem to have lost.

right, the rumba clave fits equally to binary and ternary tempo(same clave almost), that's why rumba player handle so easily different metric division (such as your example )that seems sometimes to complicate to the European listeners (though cuban listeners and dancers consider that as the basic of the music)

[VicDiesel]

very nice example

to me ,what you call 4/4 (at 0'50) is more like a 6/8

No, the whole piece is in 3/4. In that particular variation (leading up to 0:50) you can interpret it as 6/8; then 3 of those 1/8 notes get divided into 4 quarters, and later 8 sixteenths. So there is a real 4/4. Ok, maybe it's a 2/4 over a 3/8.

Victor.

PS if you backtrack through that URL you can find the score.

[liqih]

hello,
I didn't read the whole thread and my english is not 100% correct but I'd like to say this:

even though we always try to get it down to the math way, the "polyrhithms" are not always mathematical consistent,

musicans should consider polyrithmic any groove
which feels circular and counterpointed, that is almost always done with two patterns streaming parallely and with odd to even superimposition.

Some people use the adjective polyrithmic
for breakbeats, as the rythms figure changes fast, I don't like that usage but anyway it's just a word

[Sascha Franck]

To me, polyrhythms, as long as we stick to one common BPM value, are just something like what you'll find in "timeline" playing. There's whatever given "basic tempo and basic grid" and you can play everything alongside it.
Obviously enough, of course there can be triplet (and whatever) values overlapping binary rhythmic values (just as in every day music).

However, to me polyrhythms always meant to be rhythms not suiting the general metrum accordingly.
This might be horribly simplified, but it seems to work for me.

I will try to come up with a few examples of my own the next days. Not sure about the posting issue as my 7 weeks tour starts tomorrow.

[VicDiesel]

To me, polyrhythms, as long as we stick to one common BPM value, are just something like what you'll find in "timeline" playing. There's whatever given "basic tempo and basic grid" and you can play everything alongside it.

I'm not exactly sure what you're saying, but a light just went on: the kind of polyrhythm that I know from playing with real instruments is probaby very hard to do with sequencers. If you have 192 subdivisions per beat or measure, there is only one factor or 3 in that, so 9-against-8 is not even possible with a sequencer.

Victor.

[Sascha Franck]

I'm not exactly sure what you're saying, but a light just went on: the kind of polyrhythm that I know from playing with real instruments is probaby very hard to do with sequencers. If you have 192 subdivisions per beat or measure, there is only one factor or 3 in that, so 9-against-8 is not even possible with a sequencer.

Well, usually there's more subdivisions these days (such as 960ppqn or so) in sequencers, but in general I'd have to agree. Yet, the "concept of polyrhythms" should be available in sequencers nonetheless.

[herodotus]

I would give as a definition of a poly-rhythm "x equally long notes in the time of y equally (but differently) long notes, where x is not y".

Clearly that does not fall under your definition. So how do you call that?

Victor.

Actually, that does fall under the previous definition. If you look you will see that this musical example from my last post:



Conforms to your definition in every respect.

The difference is that you are describing a musical phenomenon and I am describing the theoretical concept behind that phenomenon, and behind some other phenomena as well. My thrust here is to call attention to this theoretical concept.

I think the problem here might be that the term: 'metrical value' hasn't been defined.

All polyrhythms, and indeed all rhythms in measured music, are coordinated on some sort of timeline or grid. That grid is sometimes obvious, sometimes not. But it is always there as a frame of reference. It can easily be expressed as a note value. For example, the most common grid in electronic dance music is the sixteenth note grid. Well known to any user of ReBirth.

This 'grid note value' is the unit for measuring 'metrical value' here.

In the last example, the grid is a quarter note grid. The first staff is a line of 4 dotted half notes (each with a metrical value of 3 quarter notes) and the second staff, a line of 3 whole notes (each with a metrical value of 4 quarter notes).

In this example:



We have the exact same polyrhythm on a grid of sixteenth notes.

In this example:



We have the exact same polyrhythm on a grid of thirty-second notes.

In each case, the note relationships remain identical.

All conform to the earlier stated definition:

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.


The 'different kind of polyrhythm' discussed earlier simply uses measures, or rather, metrical 'cells' instead of notes as the 'unit'.

[VicDiesel]

Well, usually there's more subdivisions these days (such as 960ppqn or so)

Which actually still doesn't help: 960 = 3x320 = 3x5x2^6, so you still can't divide it in 9.

Victor.

[VicDiesel]

All polyrhythms, and indeed all rhythms in measured music, are coordinated on some sort of timeline or grid.

I wish you guys would give up this sequencer mindset!

In this example:



We have the exact same polyrhythm on a grid of sixteenth notes.

That's how a sequencer would do it. A real life human would take the whole measure as basic, and then divide it in 3 or 4, and subdivide any of the resulting beats in any other way.

In your example, the one guy is playing groups of 3 sixteenths. Ok, so a basic grid of sixteenth notes would work. But what if he would divide one of those notes in 4? Are you seriously going to claim a basic grid of sixty-fourths, and that he's playing groups of 3 of those?

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.

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.

Victor

[herodotus]

All polyrhythms, and indeed all rhythms in measured music, are coordinated on some sort of timeline or grid.

I wish you guys would give up this sequencer mindset!

In this example:



We have the exact same polyrhythm on a grid of sixteenth notes.

That's how a sequencer would do it. A real life human would take the whole measure as basic, and then divide it in 3 or 4, and subdivide any of the resulting beats in any other way.

In your example, the one guy is playing groups of 3 sixteenths. Ok, so a basic grid of sixteenth notes would work. But what if he would divide one of those notes in 4? Are you seriously going to claim a basic grid of sixty-fourths, and that he's playing groups of 3 of those?

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.

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.

Victor

Sir,

You keep making psychological objections to an attempt at a non-psychological explanation.

I am not saying that a person playing this sort of thing live (and I have been such a person on more than one occasion), is making internal computations based on sixty-fourths notes at quarter note=120. I have never said this, or anything like this.

I haven't even brought up playing these things live. How people wrap their minds around playing music based on these concepts is something that many books could be written about. There are many different techniques, some of which work quite well. I have been in bands where two different people counted the same section of a song completely differently, but when they played it live, it was as tight as anything.

This sort of player psychology is fascinating, an example of 'unity in diversity' as poetic as I can imagine.

But what I am talking about is Music theory: an idealized world, where the same pitch can have different names; where everything is always perfectly in tune; where ancient rules derived from a system of notes related by acoustically pure intervals are applied to a system of notes with no acoustically pure intervals except the octave.

And in this idealized world, there is a direct and demonstrable structural relationship between

This:

this:

and this:
.

Knowing about this kind of relationship and how it works can very definitely be of help if one is working with polyrhythms of whatever sort, or if one is trying to analyze complex polyrhythmic music like Messiaen or Nancarrow or yes, Zappa.

The fact that the one may often be performed counting out the beats, while the other may often be played without such counting, as a musico-psychological unity, has nothing to do with the existence or usefulness of this structural relationship.