Some thoughts on Foundation of Rhythm Theory

[pensaku]

I know there are only little known in the sense of Theory about rhythms but I'm gonna try to write it down about what I already know.


We all know there are something called Polyrhythm such as you try to play 3/4 and 4/4 at the same time looks wierd on score and played you don't understand.

Now, try to play 3/4 and 4/4 using only "3 beats" you start to hear something understandable like rock and roll rhythms.

Now, 3/4 and 4/4 but 3rd beat of both is off and try to Implement it with only using 3 beats you get something like very sophiscated.


This is just some thought but if you think from here you might get something..

[IncarnateX]

IMO true polyrhythms has no base at all. Every count should have equal impact within a cyclus. A cyclus in this sense is one where every count is fulfilled within the same period of time. Thus to fulfill a cyclus of 4 against 3 you will need at least 4 x 3 = 12 beats. If you are heading for 2 against 3 against 5, you would need 2 x 3 x 5 = 30 beats and so forth. The right way to score this would simply be on a sheet where there are no barlines. Use the barlines to signify the start and end of a cyclus and write each count within those to avoid reading it in one base or another.

Cheers

[jancivil]

I have in fact scored everything up to something improbable such as 29:4 in 4/4 with that division regimen in order to have that in an ancient program with severe restrictions. As well as to obtain full understanding of it technically, which did serve me mechanically as a performer of these things.

To do 'has no base at all' confuses language about the thing for the actual ideas, though.

For example, Black Page #2, Frank Zappa. It's IN 4/4. The MEANING of the 5 in the time of 4, or the 11 in the time of [edit: 8 32nds], is that it scans like that AGAINST THE PULSE.
What is your actual musical point in 'to avoid reading it in one base or another'? {rhetorical question}

[jancivil]

Also, while cross-rhythm (eg., 5 in the time of 4) is a type of polyrhythm, not all polyrhythm is cross-rhythm.

As per the OP, an emphasis of a 3 vis a vis 2 or 4 and vice versa is often known as hemiola (not necessarily as known in antiquity, NB).
Typically seen in compound time (actually that defines compound time): 6/8 expressed as 2 dotted quarters, for instance, vs. as 3 quarters. So we can describe this as 2/4 and triplets vs straight 8ths. But we should not lose sight of what the idea is, such as in relationship to something primary such as the tune, or the dance rhythm and aspects of that.

But there are things when you cross the bar that are not reducable to a convenient abstraction, because the violation of the barline belongs to what the barline is in a fundamental sense. It resolves to a later count in a later bar, it would be beside the point musically to think to fix it to some other convention.

I don't have anything in notation at hand to show cross the bar that I know of atm. But these bars from Black Page are illustrative as to cross-rhythm and a way of revealing what incarnate brought up but working within the actual time signature; to show the point of calling it in 4/4 and not 'fixing' it as if a problem.



In bar 5 (the first bar you see), and then in bar 8 the 5 16ths [and 6 16ths] in the time of 4 16ths (in the time of a quarter) mean 16ths of a triplet quarter; this is called nested tuplets. So the meaning owes to the 4/4 time in two different ways; ie., the triplet also refers to two beats of the [4/4] bar.

In the next 2 1/2 bars we see 8 in the time of 10 quarters expressed as a 16th tied to a quarter; there would be a couple of reaons for this but of course the basic one is that we_are_in_4, the whole idea of this is we do this against the steady pulse. The original drum solo "Black Page #1" features this, with the hihat staying with the basic pulse.
The other reason, I think, is that while this totally is 4:5, it tends to be difficult to think 4:5 at that rate, and this way is pragmatic/expedient in order to get it done with less trouble. But the tension of that 8 against 10 beats is what it is, a sustained tension per the basic pulse.

[IncarnateX]

What is your actual musical point in 'to avoid reading it in one base or another'? {rhetorical question}

Well, just that instead of scoring 4/4 and 3/4 in each their parameter or just in one of them, you can have them both within the same parameter by e.g. changing it to 12/12 (or 12/4 or 12/8 relative to what is preferred but technically it would mean 12/12) Seems easier to me.

Removing barlines is unconventional but could ease the reading IMO.

And of course youre right, if the meaning is for it to be in 4/4 with 5 as something to counter the basic pulze, then the nautrality I am looking for here doesn't apply. Seems like I take true polyrhythms to be cross-rhythms and that is probably too narrow. Same thing if you want a feeling of shuffle or triplets, then it seems appropiate to write it all in 4/4.

But from this level and beyond, I'll leave it all to you. have no doubt that you can score anything you want the conventional way.

[jancivil]

What is your actual musical point in 'to avoid reading it in one base or another'? {rhetorical question}

Well, just that instead of scoring 4/4 and 3/4 in each their parameter or just in one of them, you can have them both within the same parameter by e.g. changing it to 12/12 (or 12/4 or 12/8 relative to what is preferred but technically it would mean 12/12) Seems easier to me.

It was a rhetorical question; I thought that my understanding of your meaning was fully evident. THIS:

if you want a feeling of shuffle or triplets, then it seems appropiate to write it all in 4/4.

indicates that you have the 'actual musical point'. Since the pulse is, for most music, primary, what we begin with, I don't know why a secondary referent to the pulse as the denominator is easier, it just gets rid of some, to you extraneous description in order to say 'this in the time of that'.

Removing barlines is unconventional but could ease the reading IMO.

There is for instance music by Erik Satie that isn't so complicated in terms of time where he simply doesn't bother with them, perhaps indicating the emphasis is not crucial to his thought or that it would flow suchly. He wasn't above 'weird for the sake of weird' I think. Versus the barline being intrinsically what it is, in the thought.

[IncarnateX]

It was a rhetorical question; I thought that my understanding of your meaning was fully evident. THIS:

It was but we are writing in public and my initial way of explaining it seemed vague and implicit to me, so I ignored the rethorics and used it as an excuse to specify.

indicates that you have the 'actual musical point'. Since the pulse is, for most music, primary, what we begin with,

The way I like to understand "true polyrhythms" is in terms of what you call cross-rhythms and these are ambigious in nature what is exactly that which makes them exciting. Thus, there are no prime pulse besides the one your brain arbitrarily chooses for you. It is the kind of rhythm your brain can reverse several times while hearing by applying accents, counts and periods, which are not really there. And in this sense of neutrality I find the suggested notation meaningful. However in the end it would depend on training and preference, e.g. my sequencer wouldn't give shit about what parameter I wrote a 3 against 4 in and it will sound exactly the same. Humans however, their "computer" can be more tricky.....

it just gets rid of some, to you extraneous description

Exactly! Reducing the info to the smallest amount necessary sounds like a valid reason to me. And I would go even further and not mention the denominator at all and simply call it "12". For practical reasons I would likely write it as 12/8 but understand it as 12/12 or simply 12.

[jancivil]

My point is that rather than extraneous, it might be essential.

Statement of the denomination of the pulse value as arbitrary, as if there is some pure/objective modus operandi? That isn't a musical idea, that's an abstraction.
Your sequencer has no thoughts. I don't think of having thoughts as "tricky", I think thoughts are where it's at.

I do some very unusual things (which happen following my interest and how I trained myself to perform 3:2, 4:2, 5:2 on out to say 20 or 30 reliably) with time.
So I record some things I have to actually go in and measure, I'm working probably more freely with the fabric of time than most people. Some of it will remain mysterious to me, as too complex to suss. I just did the thing, I don't know what it was exactly until I have to. But once I start to work with it, elaborating the idea - making a new part/a new line - there has to be some there, there. Again look at 'nested tuplets'. The Zappa is a fairly simple example, nested once, fives and a six rather than fours 'over' triplet basis. Even here, the triplet means what it means based in the expected quarter note.
So I get some things, 'what the hell is that', that turn out to be something I can quantify (There is a point I can lose interest in it as a practical matter, no need to elaborate, to 'write' past that extent. Point is, the more complex the more need there is to obtain the most solid reference point.) because that's based in a practice.

Let me see if I can explain it.

With 3 and 2 in Hemiola, ie., not a cross-rhythm (which is not my term, that's the usual term), sure there might be an upside-down perspective. But let's do 5 in the time of 2. Yes, we can at some point say 'now, this 5 is the pulse'; and in this case the 2 is 2:5. This is an idea, though, there will be some point to it; abstractly, nothing happened. The point is where is the ground. And the reason for the new pulse is, probably acceleration.

So you get into Elliott Carter and he liked metrical modulation. So this 5:2, say 2 is ticking along one beat per second, let's go with quarter note = 60BPM; the clock of 5 ticks at 150BPM. Now, you want this controlled acceleration you write a 5 over an 8th note and the = sign followed by "150mm", establishing your new rate.

So, when we're actually functioning musically we know what time it is. There is some basis to refer to, in the mind.

Sure, with 3 vis a vis 4 12/8 is perhaps more practical particularly in a sequencer. Just as expressing 4:3 8ths in 12/8 as 4 dotted 16ths is the more concrete definition.
But again, I've done all the work defining the rest of the numbers (same notational method as that, fitting the stated value to a higher nominator, because there was no 'cross rhythm' to the program) out to a certain extent, and say - let's take it to an extent to make it as clear as possible - 11:2, there is not going to be the same practical value as your 12 once you grok it {It's not easier to read}. That 11 is most probably 'up here' and not going to be the ground. And after a point, performing it as itself, eleven in the time of two, is where it's at.

[IncarnateX]

When I say the human mind is tricky, I am stating a fact not an opinion. Gestalt Psychology is one discipline that can tell you how the brain deals with perceptual ambiguity, e.g. how the brain assembles perceptual parts into whole figures that is not part of an stimulation, how it closes gabs in stimulation etc. In terms of reading a sheet the brain has several possible choises of interpretation unless it is trained to interpret it in fixed ways. Thus if playing 3 against 4 written in 4/4 the player may uncounscously emphasize the first of every 4 beats and favor the feeling of 4. Same deal with barlines. A sequencer doesn't do these mistakes, that was my point. The solution in this example is obvious: If you want to help his brain not to favor 3 or 4 for that matter, write it in 12.

As for your 11 against 2 that resembles a cycle of 22 beats and I am not really sure it wouldn't be easier to read to some of us in "22" , e.g. written as 22/8. However you are likely right that it will be hard to achieve any upside down effect in this particular instance. It will be a "11 on top of 2" more than a "11 against 2" in my book.

Cheers

[xoxos]

what i find very interesting is that in the last DC i released a software that procedurally and adaptively (eg. handles realtime tempo changes) generates musical rhythms in arbitrary signatures.

i was quite happy with the musicality of blewm's rhythms, but everybody else just went on thinking about how intelligent they were so oh well.

[jancivil]

We're at cross purposes here. The musical idea reduced to 'perceptual ambiguity'?

A sequencer doesn't do these mistakes, that was my point. The solution in this example is obvious: If you want to help his brain not to favor 3 or 4 for that matter, write it in 12.

That is_not the problem. I have already covered that. Obviously it is obvious. And, I don't make that mistake. I don't have that problem to begin with, I'm competent enough to be objective. That is a problem as a consequent of your solution, essentially. 3 and 4 both exist in 12. There is no cross-rhythm described herein.
As opposed to, 11 does not exist as a division of 4/4 conventionally. We lack a convention to make any 22nd note or whatever it is you hope is going to get over here.

11 in the time of 2.

It will be a "11 on top of 2" more than a "11 against 2" in my book.

I think you don't understand the problem.

let's call the basic durational value a quarter note. Divided by 2s: 4 8th notes; 8 16ths etc. In our problem, we_have_eleven.
I stated 'in the time of two', it is equally 11 in the time of 4 or 8 or 16, because 'tuplets' are named in relationship to the expectation of 2. The 11 is spread as equally over these two beats as anything else. You have to look at it from both perspectives. What do you do with the rest of the duple implications in 22/8? Why "8"? Think it through. Did you conclude that all there would be in this world is 11 and 2?

To obtain 2 in the time of 22/8 we have 11 8ths twice: simplest appears to be a whole note tied to a dotted quarter, and again.
What if we want to go twice as fast and do 4?
We are now reading a half note tied to a dotted 8th four times. To f**king do 4! It's already completely unwieldy.
I've done this up to 29 against 4/4, you can trust me when I state that. I also did a comparison visually with all of the 'in the time of' per 4/4 in a single chart, doing as I just showed. This was useful to me but it absolutely would give headaches, no one sane would agree to read it, and you're arguing to do in avoidance of understanding '11 against 2'. Do it, do these cross rhythms rather than argue 'in my book it's 'on top of' rather than'. Which ones of 11 land on the beat in duple time? Whether 2 or 4, or 8. Please. It's x in the time of _, period. Cross_rhythm. Yes, obviously we can construct a higher nominator and fit to it. 11 doesn't work like your 3 and 4 in 12; 12 is known as compound time, there is a convention ready made for it. This is why I chose the 11, it's abstruse, we don't deal with it in that convention, it's unwieldy too quickly.

Do me the basic courtesy of trying to understand the material, of reading what I wrote, I beg you.

[IncarnateX]

I don't make that mistake. I don't have that problem to begin with, I'm competent enough to be objective.

This is not about you. You are very trained. I would not think you would need any 12 to avoid fallng into a feeling of 3 or 4 in a 3 against 4 rhythm.

And since keeping the ambiguity in polyrhythms IS a muscial idea, there are no reductions of musical ideas here.

For the rest, you have lost me to an extent where I do not find it useful to continue. In the end we are talking about subjective preferences to subjective matters and as far as I am concerned I use my principles when e.g. programming sequencers that do not have the signatures I am seeking, such as making 4 against 7 by having a cyclus of 7 bars of 4, or on a sheet when writing variations over such a rhythm. And if I should explain it to a student, I would use them as well. It works for me. And for the record I did not invent this myself, but learned it from an African percussion teacher twenty years ago.

You do seem to generalize a lot from yor own anectdotes but basically that only tells something about your view. I have stated my case and explained as good as I can. I do not see your problems. Sorry for that. However, if I ever encounter a problem using this strategy, I will return and see if it has anything to do what you are writing here. However, I do not work with extreme signatures such as 11 against 2 or 29 in 4/4 so if these kinds are prerequisites to your problems they may never be relevant to me.

From this point I would really like to hear about others' experience with polyrhythms and what they make of what we have discussed so far.

Cheers

[woggle]

Some music is based around sequences of long and short intervals/beats rather than regularly spaced intervals. You can find an underlying pulse or clock rate of course, the shortest clock rates are of the order of 50ms or 1200bpm found in music like this amadinda music which I have seen described as both additive and divisive.

Differences in rhythm structure are described here https://en.wikipedia.org/wiki/Additive_ ... ive_rhythm

Once you find the underlyiing pulse you can of course write additive musics as though they had a regular divisive rhythm, but that is not how the music is actually perceived by the people who perform and listen to it.

A lot, if not most performed music is, I think, of this form - the rhythmic structure is performed and understood as a cycle of long a short segments. Jazz for example has its usual notated form for swing, yet the same notation can be performed utterly differently in feel according to how the swing is actually felt ie how the swing is understood as a cycle of durations. Jazz played as strict triplets is normally not 'jazz'

[IncarnateX]

Thank you for the link. Here is an example of the ambiguity in polyrhythms I am talking about. This is a westafrican polyrhythm starting with a pulze of 6 over 4, where he first emphasizes 4 as basic pulze, then the 6 as basic pulze and then he triples the 6, which adds a new feeling to the rhythm. It is wonderful.

He explains what is happening starting from 1.10

[jancivil]

I don't make that mistake. I don't have that problem to begin with, I'm competent enough to be objective.

This is not about you. You are very trained. I would not think you would need any 12 to avoid fallng into a feeling of 3 or 4 in a 3 against 4 rhythm.

And since keeping the ambiguity in polyrhythms IS a muscial idea, there are no reductions of musical ideas here.

For the rest, you have lost me to an extent where I do not find it useful to continue. In the end we are talking about subjective preferences to subjective matters

No, why would it be about 'me'? Musicians should not have that problem. You're fabricating a problem as a consequent of your solution. Which serves to avoid understanding. A hemiola type of emphasis of congruent counts is not the problem of cross-rhythm. You don't want to know about this type of cross-rhythm just say that.
If you can't follow it, you'd do better not to fatuously argue about it.