4:3 Polyrhythms in top 40 music

[Clef_de_fa]

Clef, I'm jealous. You have already reached your destination. My "polyrhythm" train has been delayed.

This morning, I followed your advice and played a simple pattern where I changed the quarter notes into triplets that included accented and ghost notes.
It was the 3 over 2 or 6 over 4 polyrhythm.

http://cdn1.talkbass.com/data/attachment-files/2015/08/2580740_cc69422b6ce4d84201c07d7d34ef9d6f.mp3

Something like this with a few dynamic variations.
View attachment 679786

Now, I'm trying to figure out how to play the 2 over 3 polyrhythm.
What should I play differently?

what you wrote is more 6:4. 2:3 would be a duplet over a 3/4 time sig. 3:2 could be a triplet of half note over a 2/2 time sig which is pretty much the same thing as 6:4


And no, don't be jealous. I'm no near any destination as this is just me remembering knowledge I learned, I still don't play music anymore. I just like to talk about it.

 

[markjsmithbass]

While on the subject of polyrhythms, a book that really opened my eyes to a lot of stuff was Modern Rhythmic Notation by Gardner Read. A lot of the problems people have with understanding all these numbers and ratios are to do with notation. Any polyrhythm can be written in countless different ways and there is no set 'correct' way. Notation has been stretched through music history to accommodate ever more complicated concepts. Gardner Read takes you through loads of examples of rhythmic problems and shows how various composers have dealt with them. You only have to check out some of the music of Conlon Nancarrow to see how notation has been adapted in pretty much communicating mathematical equations.

 

[Whousedtoplay]

While on the subject of polyrhythms, a book that really opened my eyes to a lot of stuff was Modern Rhythmic Notation by Gardner Read. A lot of the problems people have with understanding all these numbers and ratios are to do with notation. Any polyrhythm can be written in countless different ways and there is no set 'correct' way. Notation has been stretched through music history to accommodate ever more complicated concepts. Gardner Read takes you through loads of examples of rhythmic problems and shows how various composers have dealt with them. You only have to check out some of the music of Conlon Nancarrow to see how notation has been adapted in pretty much communicating mathematical equations.

Mark,

In order to play the 3 over 2 polyrhythm, I substituted one quarter note to three triplet eighths.

No questions, but...

If I wanted to play the 3 over 4 polyrhythm, I would do it the same way by subdividing one quarter not into three triplet eighths.

I'm just trying to reconcile those triplets with the following snapshot:

 

[markjsmithbass]

I don't understand that diagram (4 pattern and 5 pattern). I don't know what the squares are representing.

With polyrhythms like these you have to understand what distance of time is being divided. You mentioned 3:2 and 3:4 and the examples provide the answer of 3 in the space of 2 quarter notes and 4 quarter notes. But you can have any number of quarter, eighth, sixteenth, 32nd (etc.) divided by any other number. It's not as clear cut as 3 quarters in the space of 2 quarters or 3 quarters in the space of 4 quarters.

Incidentally, I once had a conversation with David Ocker (Frank Zappa's copyist) about a septuplet in The Black Page. Frank insisted on using a 16th note septuplet even though it should traditionally be written as an 8th note septuplet. This was because it sounded closer to the 16th note. However, you don't move up to the next rhythmic subdivision until you've reached the maximum of the previous subdivision. So you would have the following divisions of a bar of 4/4:
4:4 (quarter notes)
5:4 (quarter note quintuplet)
6:4 (quarter note sextuplet/triplet)
7:4 (quarter note septuplet) etc.
8:8
9:8
10:8
11:8
12:8
13:8
14:8
15:8
16:16 etc

So without any indication of beats, you would see a division of a bar into 6 or 2 beats into 3 as quarter notes of some kind i.e. Quarter note triplets.

The reason I mention this is because it can be one of the most confusing parts of the polyrhythm notation and plays a part in a lot of the notated examples mentioned.

When you mention 5:4 and 4:5 you have to also realise these are not the same kind of rhythm. 5:4 is 5 notes in the space of 4 beats (whatever type) and 4:5 is 4 notes in the space of 5 beats (whatever type). I say this because the graphic example says 4 over 5. So we're either dealing with bars of 5/4 or 5 beats in a different time signature (which could mean working across the barline).

To create a 4:5 polyrhythm you take 5 beats, divide into 16th notes and play every fourth one.

(1) e & a 2 (e) & a 3 e (&) a 4 e & (a) 5 e & a

Actually, now I've looked back up at the diagram I've spotted the problem. The 5 is grouped 12 123. If you look at it like that it makes more sense. The 4 notes span 4 bars of 5/4 (or 5/8 or 5/16).

 

[Whousedtoplay]

Mark,

Thank you for your response. I've never had any problems with my superficial knowledge of polyrthythms, but I always compared equal notes: 3 over 2, 5 over 4, etc...

Suddenly, I encountered the variations of Polyrhythms like the following 6 over 4:

About that diagram.

That diagram of 4 over 5 is from a video for the drummers.



Dave Atkins says,
---------------------------------------------------------------------
"Each box represents one count. Don't worry about any time signature or any note values.
Start with 4-pattern on the top and put X on every 4-counts.
Now, let's add a second line take a pattern of 5 that repeats every five counts.
I put an X on the first and 3nd count, and every five counts I repeat that pattern..."
----------------------------------------------------------

And that's how I got confused.

 

[T_E]

Uhm... no. The OP's "pop" examples are NOT 4:3 polyrhythms.

The first red flag, is that all these examples are in the meter of 4/4. So, the polyrhythm ratio would need to be X:4.

1:4, 2:4, 8:4, 16:4 are the easy ones, and are generally not thought of as polyrhythms, since they are easy to sense additions or divisions of the quarter-note. Some will have mild difficulty faithfully producing 6:4 (or 3:2). Things get difficult with 5:4, 7:4, 27:4, etc. You get the idea.

The second red flag is that just because four dotted eights take the same time as three quarter-notes, this does NOT make a 4:3 polyrhythm, when the meter is 4/4.

The OP's examples are a simple rhythmic phrasing device utilizing dotted eights. This has been ocurring for centuries, and did not start with Britney Spears.

Probably one of the most "famous" examples of a rhythmic phrasing device utilizing a grouping of three, occurs in "Here Comes the Sun" -- four dotted-quarter-notes (or a grouping of three eighth-notes) followed by two quarter-notes, in the space of eight quarter-notes (2 measures of 4/4). No polyrhthms. Simple rhythmic phrasing.

Had the OP's examples been in a meter of 3/4 (i.e., a waltz), and there were four evenly spaced rhythms occurring within the 3/4 meaure, over three quarter-notes, sure... then it would be a 4:3 polyrhythm. Or perhaps, a meter of 5/8, and there were four evenly spaced rhythms occurring within this 5/8 measure, then it would be a 4:5 polyrhythm.

And, there are infinite examples.

But that is not what's happening in the OP's examples.

I didn't bother reading the ad infinitum responses with pictures, so maybe this was already covered.

I did spy the name "Pete Magadini", yep... he's the authority.

 

[Whousedtoplay]

Uhm... no. The OP's "pop" examples are NOT 4:3 polyrhythms.

The first red flag, is that all these examples are in the meter of 4/4. So, the polyrhythm ratio would need to be X:4.

1:4, 2:4, 8:4, 16:4 are the easy ones, and are generally not thought of as polyrhythms, since they are easy to sense additions or divisions of the quarter-note. Some will have mild difficulty faithfully producing 6:4 (or 3:2). Things get difficult with 5:4, 7:4, 27:4, etc. You get the idea.

The second red flag is that just because four dotted eights take the same time as three quarter-notes, this does NOT make a 4:3 polyrhythm, when the meter is 4/4.

The OP's examples are a simple rhythmic phrasing device utilizing dotted eights. This has been ocurring for centuries, and did not start with Britney Spears.

Probably one of the most "famous" examples of a rhythmic phrasing device utilizing a grouping of three, occurs in "Here Comes the Sun" -- four dotted-quarter-notes (or a grouping of three eighth-notes) followed by two quarter-notes, in the space of eight quarter-notes (2 measures of 4/4). No polyrhthms. Simple rhythmic phrasing.

Had the OP's examples been in a meter of 3/4 (i.e., a waltz), and there were four evenly spaced rhythms occurring within the 3/4 meaure, over three quarter-notes, sure... then it would be a 4:3 polyrhythm. Or perhaps, a meter of 5/8, and there were four evenly spaced rhythms occurring within this 5/8 measure, then it would be a 4:5 polyrhythm.

And, there are infinite examples.

But that is not what's happening in the OP's examples.

I didn't bother reading the ad infinitum responses with pictures, so maybe this was already covered.

I did spy the name "Pete Magadini", yep... he's the authority.

T_E,

The OP is Adam Neely - an excellent and very knowledgeable musician, composer, and a PRO bass player.
"He is a member of the BMI Jazz Composers workshop, and a received a Masters of Music in Jazz Composition from the Manhattan School of Music in 2012; therefore, I doubt that Adam would post anything that could be "questionable." Quite a few bass players all over the world are learning a lot from Adam.

Now.
Do you agree with the following statement?
Polyrhythm - Wikipedia, the free encyclopedia
"Polyrhythm is the simultaneous use of two or more conflicting rhythms, that are not readily perceived as deriving from one another, or as simple manifestations of the same meter.
The rhythmic conflict may be the basis of an entire piece of music (cross-rhythm), or a momentary disruption."

The following snapshot shows two ways of notating the same 5:4 polyrhythm.
Do you agree with that example?

You mentioned Peter Magadini.
Please check the next snapshot from his book.
As you can see, Peter Magadini shows that you can subdivide the notes and still have the same 6 over 4 polyrhythm while playing 10 notes over 4 (Measure 4).

Here is my next question.
This example shows a simple 3 over 4 polyrhythm.

What if we preserve the same triplet notation and "feel", and just accentuate different triplet notes, but still play only three notes, is it going to be 3 over 4?

 

[T_E]

T_E,

The OP is Adam Neely - an excellent and very knowledgeable musician, composer, and a PRO bass player.
"He is a member of the BMI Jazz Composers workshop, and a received a Masters of Music in Jazz Composition from the Manhattan School of Music in 2012; therefore, I doubt that Adam would post anything that could be "questionable." Quite a few bass players all over the world are learning a lot from Adam.

Okay. However, this particular video is "questionable". I know absolutely nothing about the OP, therefor I have no prejudice. I'm ONLY commenting on the disseminated information.

Now.
Do you agree with the following statement?
Polyrhythm - Wikipedia, the free encyclopedia
"Polyrhythm is the simultaneous use of two or more conflicting rhythms, that are not readily perceived as deriving from one another, or as simple manifestations of the same meter.
The rhythmic conflict may be the basis of an entire piece of music (cross-rhythm), or a momentary disruption."

I avoid wikipedia on these matters.

The following snapshot shows two ways of notating the same 5:4 polyrhythm.
Do you agree with that example?

View attachment 681044

Image A) Looking first at the Time Signature (4/4), and seeing that the BOTTOM stave is a steady quarter-note rhythm, yes the TOP stave rhythm against the BOTTOM stave rhythm would yield a 5:4 polyrhythm.

Image B) Looking first at the Time Signature (5/4), and seeing that the TOP stave is a steady quarter-note rhythm, yes the BOTTOM stave rhythm against the TOP stave would yield a 4:5 polyrhythm.

They'll probably sound the same - I'll trust your math concerning the MM. However, the Time Signature dictates the Denominator. This is where the OP gets into trouble - he's ignored the Time Signature.

You mentioned Peter Magadini.
Please check the next snapshot from his book.
As you can see, Peter Magadini shows that you can subdivide the notes and still have the same 6 over 4 polyrhythm while playing 10 notes over 4 (Measure 4).

View attachment 681045

See comments below.

Here is my next question.
This example shows a simple 3 over 4 polyrhythm.
View attachment 681046
What if we preserve the same triplet notation and "feel", and just accentuate different triplet notes, but still play only three notes, is it going to be 3 over 4?
View attachment 681047

Your two examples are actually 12:4. You are simply accenting/sounding certain subdivision of the 12-group.

This is what Magadini is demonstrating in your example. Everything is bassed off a 6:4 polyrhythm. He then further divides.

To very easily understand this, start with a Time Signature of 4/4. The BOTTOM staff will be straight Quarter-Notes, the TOP staff will have additions or subdivision of the Quarter-Note.

A) One Whole over Four Quarter-Notes = 1:4
B) Two Half-Notes over Four Quarter-Notes = 2:4
C) Four Quarter-Notes over Four Quarter-Notes = 4:4
D) Eight Eighth-Notes over Four Quarter-Notes = 8:4
E) Sixteen Sixteenth-Notes over Four Quarter-Notes = 16:4
F) Six Quarter-Note-Triplets over Four Quarter-Notes = 6:4
E) Twelve Eighth-Note-Triplets over Four Quarter-Notes = 12:4

One is NOT required to play/sound each and every subdivision - PLAY the rests!

Master that Magadini excerpt, then in place of various notes change them to rests. Do symetrical grouping, then asymetrical groupings. And understand, that whatever you decide to do, you will ALWAYS be in a 6:4 Polyrhythm.

 

[Whousedtoplay]

Okay. However, this particular video is "questionable". I know absolutely nothing about the OP, therefor I have no prejudice. I'm ONLY commenting on the disseminated information.



I avoid wikipedia on these matters.



Image A) Looking first at the Time Signature (4/4), and seeing that the BOTTOM stave is a steady quarter-note rhythm, yes the TOP stave rhythm against the BOTTOM stave rhythm would yield a 5:4 polyrhythm.

Image B) Looking first at the Time Signature (5/4), and seeing that the TOP stave is a steady quarter-note rhythm, yes the BOTTOM stave rhythm against the TOP stave would yield a 4:5 polyrhythm.

They'll probably sound the same - I'll trust your math concerning the MM. However, the Time Signature dictates the Denominator. This is where the OP gets into trouble - he's ignored the Time Signature.



See comments below.



Your two examples are actually 12:4. You are simply accenting/sounding certain subdivision of the 12-group.

This is what Magadini is demonstrating in your example. Everything is bassed off a 6:4 polyrhythm. He then further divides.

To very easily understand this, start with a Time Signature of 4/4. The BOTTOM staff will be straight Quarter-Notes, the TOP staff will have additions or subdivision of the Quarter-Note.

A) One Whole over Four Quarter-Notes = 1:4
B) Two Half-Notes over Four Quarter-Notes = 2:4
C) Four Quarter-Notes over Four Quarter-Notes = 4:4
D) Eight Eighth-Notes over Four Quarter-Notes = 8:4
E) Sixteen Sixteenth-Notes over Four Quarter-Notes = 16:4
F) Six Quarter-Note-Triplets over Four Quarter-Notes = 6:4
E) Twelve Eighth-Note-Triplets over Four Quarter-Notes = 12:4

One is NOT required to play/sound each and every subdivision - PLAY the rests!

Master that Magadini excerpt, then in place of various notes change them to rests. Do symetrical grouping, then asymetrical groupings. And understand, that whatever you decide to do, you will ALWAYS be in a 6:4 Polyrhythm.

Thanks for your comment.

Please check the following two snapshots:
You said, " E) Twelve Eighth-Note-Triplets over Four Quarter-Notes = 12:4"
3 against 1 = 12 against 4

Next, you said this, "then in place of various notes change them to rests."
I've followed your advice and changed various notes from 12 over 4 to rests and got this.

It's a clear 3 over 4 polyrhythm, but you said even if you replace various notes with the rests, it's still going to be the same polyrhythm, which at the very beginning was 12 over 4.

To sum up.

I think you cannot substitute various notes with the same value rests and still have the same initial polyrhytm.

Magadini also replaced some triplet notes from 12:4 with the same value rests and got
3 against 2 = 6 against 4.

Also, if we subdivide the basic pulse quarter notes into the eighths, are still going to have 12 over 4 or 12 over 8?

 

[T_E]

I don't believe I made myself clear. The "Parent Polyrhythm" is 6:4 - That's what Magadini is demonstrating.

He starts out with a simple, clear 6:4 polyrhythm (m. 2). Call them "SIX Quarter-Note-Triplets" over "FOUR Quarter-Notes". Remember that "Quarter-Note-Triplets" is the same as "3:2".

He then begins to further divide the independent top rhythm values (i.e., the "Quarter-Note-Triplet"), that began as an equidistant grouping of SIX over FOUR - ms. 3 & 4.

In m. 3, he takes the first and fourth Quarter-Note-Triplets and divides them in half.

In m. 4, he takes the first and fourth Quarter-Note-Triplets and divides them in thirds.

This still retains the basic 6:4 "Parent" polyrhythm - refer to m. 2.

Magadini's example is pretty easy to produce, we've all heard this mixing of pulses that can occur in Compound Meters. Jazz waltz' often superimpose a 2:3 feel.

What I was suggesting you try, is to not always strike/sound/play each and every rhythm notated. Rather change some to rests. Play the rests.

You could even tie some of the rhythm-notes to the next. By doing this you STILL retain the initial 6:4 polyrhythm - always refering to m. 2.

One can easily, and I'm sure Magadini did this, further complicate the ratio, such as 5:4, 7:4, 11:4, 100:3, etc.

I do not have a copy of Magadini's book to refer to. I think I lent it to either Britney or Miley.

Thanks for your comment.

Please check the following two snapshots:
You said, " E) Twelve Eighth-Note-Triplets over Four Quarter-Notes = 12:4"
3 against 1 = 12 against 4
View attachment 681389

Next, you said this, "then in place of various notes change them to rests."
I've followed your advice and changed various notes from 12 over 4 to rests and got this.
View attachment 681415
It's a clear 3 over 4 polyrhythm, but you said even if you replace various notes with the rests, it's still going to be the same polyrhythm, which at the very beginning was 12 over 4.

To sum up.

I think you cannot substitute various notes with the same value rests and still have the same initial polyrhytm.

Magadini also replaced some triplet notes from 12:4 with the same value rests and got
3 against 2 = 6 against 4.
View attachment 681436



Also, if we subdivide the basic pulse quarter notes into the eighths, are still going to have 12 over 4 or 12 over 8?
View attachment 681439

 

[T_E]

Also, if we subdivide the basic pulse quarter notes into the eighths, are still going to have 12 over 4 or 12 over 8?

Refer to the Time Signature.

If it's 4/4, then it's "12 over 4".

If it's 8/8, then it's "12 over 8".

You are allowed to subdivide either the top rhythm, as well as the bottom -- but the reference is the Time Signature.

Look at how Magadini does it.

 

[Whousedtoplay]

I don't believe I made myself clear. The "Parent Polyrhythm" is 6:4 - That's what Magadini is demonstrating.

He starts out with a simple, clear 6:4 polyrhythm (m. 2). Call them "SIX Quarter-Note-Triplets" over "FOUR Quarter-Notes". Remember that "Quarter-Note-Triplets" is the same as "3:2".

He then begins to further divide the independent top rhythm values (i.e., the "Quarter-Note-Triplet"), that began as an equidistant grouping of SIX over FOUR - ms. 3 & 4.

In m. 3, he takes the first and fourth Quarter-Note-Triplets and divides them in half.

In m. 4, he takes the first and fourth Quarter-Note-Triplets and divides them in thirds.

This still retains the basic 6:4 "Parent" polyrhythm - refer to m. 2.

Magadini's example is pretty easy to produce, we've all heard this mixing of pulses that can occur in Compound Meters. Jazz waltz' often superimpose a 2:3 feel.

What I was suggesting you try, is to not always strike/sound/play each and every rhythm notated. Rather change some to rests. Play the rests.

You could even tie some of the rhythm-notes to the next. By doing this you STILL retain the initial 6:4 polyrhythm - always refering to m. 2.

One can easily, and I'm sure Magadini did this, further complicate the ratio, such as 5:4, 7:4, 11:4, 100:3, etc.

I do not have a copy of Magadini's book to refer to. I think I lent it to either Britney or Miley.

I have Magadini's book. He is NOT very clear about his statement. He writes, "Eighths added", "combinations", etc...

 

[T_E]

Man, that gives me a headache!

I have Magadini's book. He is NOT very clear about his statement. He writes, "Eighths added", "combinations", etc...
View attachment 681484
View attachment 681485
View attachment 681487

 

[Febs]

I see that Stick Player is back.

 

[Whousedtoplay]

Man, that gives me a headache!

...but my tension headache has subsided.

 

[Bob_Ross]

Link Removed

I apologize for not reading this entire thread in great detail -- looks like there's some good stuff herein -- but I hope someone has already pointed out what was glaringly obvious to me when I spotted this diagram:

It's incorrect.

It doesn't show a polyrhythm at all, at least not in the conventional X:Y relationship. What it shows is one (out of a bazillion possible) particular polymeter, specifically 4/8 against 5/8 (presuming those boxes are eighth note subdivisions)

There is a way to display a 4:5 polyrhythm using a similar grid, however the grid would have to keep alternating between eighth note triplets and straight eighth notes. I haven't bothered to figure out whether that same grid display approach can also do 5:4. (Admittedly years ago I stopped getting hung up on dissecting rhythmic analysis too finely because I found that the easiest way to incorporate complex polyrhythms into my musical vocabulary was to simply learn how to hear them as a unit.)

 

[SteveCS]

I see that Stick Player is back.

Who?

 

[Whousedtoplay]

I apologize for not reading this entire thread in great detail -- looks like there's some good stuff herein -- but I hope someone has already pointed out what was glaringly obvious to me when I spotted this diagram:

It's incorrect.

It doesn't show a polyrhythm at all, at least not in the conventional X:Y relationship. What it shows is one (out of a bazillion possible) particular polymeter, specifically 4/8 against 5/8 (presuming those boxes are eighth note subdivisions)

There is a way to display a 4:5 polyrhythm using a similar grid, however the grid would have to keep alternating between eighth note triplets and straight eighth notes. I haven't bothered to figure out whether that same grid display approach can also do 5:4. (Admittedly years ago I stopped getting hung up on dissecting rhythmic analysis too finely because I found that the easiest way to incorporate complex polyrhythms into my musical vocabulary was to simply learn how to hear them as a unit.)

At a very superficial level, I've never had any issues with the traditional understanding of polyrhythms.
On a regular basis, I play some tapping exercises that includes some kind of polyrhythms, but...
I've started asking more refined questions after reading Peter Magadini's book on polyrhythms.
Peter Magadini's terms like, "Basic Pulse" got me a little bit confused.
In almost all quoted or "snapshot-ed" examples of polyrhythms, the "Basic Pulse" coincides with the count/Beat, as the quarter notes as "Basic Pulse".
If we have "Basic Pulse", what is "Advanced/Complex Pulse"?


P.S. For some strange reason, I think that Adam's first example in his video should be 3 over 4 - the main disco rhythm is in 4/4 and the bass plays 3 notes in the span of 4 beats.

 

[Whousedtoplay]

Who?

 

[SteveCS]

View attachment 681771

Thx.