Euclidean Rhythms

Coloobar

AQ808 said:

Coloobar said:

AQ808 said:

It seems that you believe, for example that one loop would run at 5/4 time whereas the other runs as 4/4, and then eventually the two will meet. In that case, you'd have two loops playing sounds with the same note lengths.

The way figure works, and I believe patterning does as well, is that the amount of time in a bar/measure is divided by 5 for one sound and 4 for another. It resolves itself to itself every bar, so there is nothing to catch up to, as they don't share the same note length, but they both do begin at the beginning of the loop and end at the end of the loop, so what they share is a single loop.

I was thinking that regardless of the time signature in a loop, all loops will resolve simultaneously at the end of each measure.  So if you want to do, say, a true 5 against 4, you would need to set the measure length to 20 beats like so:

4/4: XoooXoooXoooXoooXooo
5/4: XooooXooooXooooXoooo

Correct me if Patterning doesn't work this way.

Yeah, see in euclidean, you literally have 5 slices of the amount of time in a bar versus 4 slices of that same amount of time.

In standard loop mode, you would simplify what you are doing there to simply one loop of 5 quarter notes and one loop of 4 quarter notes. Then they will play endlessly, so you don't have to constrain them at all, and they will continue and resolve eventually. Same with 7 against 6 or any other combination.

Ok, got it.  What you describe though doesn't really fit the true definition of euclidian rhythm.  https://en.m.wikipedia.org/wiki/Euclidean_rhythm

"Thegreatest common divisor of two numbers is used rhythmically giving the number of beats " as I described above.  

So with 4/4 against 5/4  you're starting the second bar of 4/4 while you're still on the last beat of the first bar of 5/4.  

Btw it's good to know the upper limit is 64... I got the 34 limit from Doug's pre-release video.

AQ808

Coloobar said:

AQ808 said:

Coloobar said:

AQ808 said:

It seems that you believe, for example that one loop would run at 5/4 time whereas the other runs as 4/4, and then eventually the two will meet. In that case, you'd have two loops playing sounds with the same note lengths.

The way figure works, and I believe patterning does as well, is that the amount of time in a bar/measure is divided by 5 for one sound and 4 for another. It resolves itself to itself every bar, so there is nothing to catch up to, as they don't share the same note length, but they both do begin at the beginning of the loop and end at the end of the loop, so what they share is a single loop.

I was thinking that regardless of the time signature in a loop, all loops will resolve simultaneously at the end of each measure.  So if you want to do, say, a true 5 against 4, you would need to set the measure length to 20 beats like so:

4/4: XoooXoooXoooXoooXooo
5/4: XooooXooooXooooXoooo

Correct me if Patterning doesn't work this way.

Yeah, see in euclidean, you literally have 5 slices of the amount of time in a bar versus 4 slices of that same amount of time.

In standard loop mode, you would simplify what you are doing there to simply one loop of 5 quarter notes and one loop of 4 quarter notes. Then they will play endlessly, so you don't have to constrain them at all, and they will continue and resolve eventually. Same with 7 against 6 or any other combination.

Ok, got it.  What you describe though doesn't really fit the true definition of euclidian rhythm.  https://en.m.wikipedia.org/wiki/Euclidean_rhythm

"Thegreatest common divisor of two numbers is used rhythmically giving the number of beats " as I described above.  

So with 4/4 against 5/4  you're starting the second bar of 4/4 while you're still on the last beat of the first bar of 5/4.  

Btw it's good to know the upper limit is 64... I got the 34 limit from Doug's pre-release video.

I think you are confusing "greatest common divisor" with "lowest common denominator".

This article explains the basic math of Euclidean rhythms well:

http://charlesrthompson.com/2015/02/25/using-euclidean-rhythms-to-create-new-beat-patterns/

Now, what is known in the common parlance in apps as "Euclidian rhythm" is definitely not the raw Euclidean thing, but what they do is completely enable Euclidean rhythms if you specifically program them as such. 

However, you not only have the Euclidean rhythmic potential, but use the divisions deriving from the units created however you like. It isn't as rigid, that is.

There is a name for what you're talking about, but I'm forgetting right now. I remember it being the main feature from a King Crimson song long ago on the "Discipline" album. There's a name for it, not Euclidean though. If I get some time later I'll try to track it down.

Coloobar

I see.  Interesting link.  That's not what I was thinking of at all.

AQ808

Coloobar said:

I see.  Interesting link.  That's not what I was thinking of at all.

I'm glad you brought it up since it gave me a chance to delve even deeper than I had before.

I also see I made a mistake earlier when I said, "I think you are confusing "greatest common divisor" with "greatest common denominator"."

I should have wrote "lowest common denominator", and have fixed it.

I do believe that approach you describe is also completely legitimate and useful though.

I found this to be the best short video describing just what Euclidean Rhythms are about.



And what Patterning is doing is basically giving you a Euclidean friendly grid.

If you want to make truly Euclidean Rhythms, you'll have to put beats in the appropriate places in the grid, as I don't believe Patterning allows you to automatically choose from the Euclidean rhythms from the videos I've seen, though I'd be pleased to be wrong about that.

This is the original paper which includes discussion about some historical Euclidean Rhythms, not to mention one he attributes to Frank Zappa! E(4,11).

http://cgm.cs.mcgill.ca/~godfried/publications/banff.pdf

And here is an extended version with even more rhythms:

http://cgm.cs.mcgill.ca/~godfried/publications/banff-extended.pdf

And the author even has a book about it:

https://books.google.com/books?id=ZlKfh83AJEEC&pg=PA132&lpg=PA132&dq=euclidean+rhythm+list&source=bl&ots=oeGf41nFum&sig=WP2gLbFiEUagzo_8_LzRZMg5tWA&hl=en&sa=X&ved=0ahUKEwispe-SsLnJAhWCWT4KHR7nCXEQ6AEIWTAI#v=onepage&q=euclidean rhythm list&f=false

I'm still wanting to find the name of that lowest common denominator approach you described, but am not finding it as easily as I thought I would.

And, if you like this mathematical rhythm subject, I came across this fascinating blog post:

http://www.science20.com/robert_inventor/rhythms_in_maths_most_out_of_time_perfect_drummers_can_be_penrose_tiling_rhythm_cantors_set_rhythm-135919

Wowza!

Coloobar

AQ808 said:

Coloobar said:

I see.  Interesting link.  That's not what I was thinking of at all.

I'm glad you brought it up since it gave me a chance to delve even deeper than I had before.

I also see I made a mistake earlier when I said, "I think you are confusing "greatest common divisor" with "greatest common denominator"."

I should have wrote "lowest common denominator", and have fixed it.

I do believe that approach you describe is also completely legitimate and useful though.

I found this to be the best short video describing just what Euclidean Rhythms are about.



And what Patterning is doing is basically giving you a Euclidean friendly grid.

If you want to make truly Euclidean Rhythms, you'll have to put beats in the appropriate places in the grid, as I don't believe Patterning allows you to automatically choose from the Euclidean rhythms from the videos I've seen, though I'd be pleased to be wrong about that.

This is the original paper which includes discussion about some historical Euclidean Rhythms, not to mention one he attributes to Frank Zappa! E(4,11).

http://cgm.cs.mcgill.ca/~godfried/publications/banff.pdf

And here is an extended version with even more rhythms:

http://cgm.cs.mcgill.ca/~godfried/publications/banff-extended.pdf

And the author even has a book about it:

https://books.google.com/books?id=ZlKfh83AJEEC&pg=PA132&lpg=PA132&dq=euclidean+rhythm+list&source=bl&ots=oeGf41nFum&sig=WP2gLbFiEUagzo_8_LzRZMg5tWA&hl=en&sa=X&ved=0ahUKEwispe-SsLnJAhWCWT4KHR7nCXEQ6AEIWTAI#v=onepage&q=euclidean rhythm list&f=false

I'm still wanting to find the name of that lowest common denominator approach you described, but am not finding it as easily as I thought I would.

And, if you like this mathematical rhythm subject, I came across this fascinating blog post:

http://www.science20.com/robert_inventor/rhythms_in_maths_most_out_of_time_perfect_drummers_can_be_penrose_tiling_rhythm_cantors_set_rhythm-135919

Wowza!

Cool links.  The video describes it well.  The "lowest common denominator approach" I'm after is nowadays called polyrhythm.  Not sure what it was called back in the days of discipline.  It's taken a forefront in the rhythms of modern progressive metal with bands like Tesseract, Periphery, etc.  Here's a little video describing a 3 against 4 polyrhythm: 

AQ808

Coloobar said:

Cool links.  The video describes it well.  The "lowest common denominator approach" I'm after is nowadays called polyrhythm.  Not sure what it was called back in the days of discipline.  It's taken a forefront in the rhythms of modern progressive metal with bands like Tesseract, Periphery, etc.  Here's a little video describing a 3 against 4 polyrhythm: 

I just checked out that video. Great drummer!

However, he is doing what the Euclidean mode in patterning does, in that he is using a measure bar as the loop point for both 4 and 3 to begin and end.

And that is my understanding of what polyrhythm is. The Euclidean rhythm is more about what notes to accent within a polyrhythm.

But that is not what you were discussing earlier where 5/4 is obviously one note longer than 4/4, and it would take a span of 20 quarter notes for them to meet up again. The reason is that all of the beats for both voices would happen at the exact same time.

That is not what is happening in that video, and if you set up Patterning to Euclidean mode and choose 4 parts for one sound and 3 for the other, and tempo matched to his performance, you would be perfectly in line with what he is playing.

In that video, in the amount of time he does 4, he also does 3. The way to tell is that the 3 are constantly slightly off from the 4. The beats don't occur simultaneously.

Know what I mean?

ecamburn

benkamenbenkamen planned - Patterning has become an amazing tool for Euclidean rhythms.  I'd also add werkbench to the list of tools that allow you to vary loop length.  

ecamburn

benkamenbenkamen planned - Patterning has become an amazing tool for Euclidean rhythms.  I'd also add werkbench to the list of tools that allow you to vary loop length.  

Coloobar

Sorry I posted the wrong video link. Try this one starting at about 1:30

That same guy has another video where he claims to be doing a 15/16 against 4/4 polyrhythm. I'm going to have to take his word on that cause what he plays is insane!

ecamburn

cool discussion.  I have no idea how my post from page 1 got posted into these conversations on page 2.  Some weird forum gremlins.  

u0421793

Has anything related to this ever gotten into the top 40?

AQ808

@Coloobar said:

Sorry I posted the wrong video link. Try this one starting at about 1:30 https://m.youtube.com/watch?v=zf90vrVYMtI

That same guy has another video where he claims to be doing a 15/16 against 4/4 polyrhythm. I'm going to have to take his word on that cause what he plays is insane!

Now that posted video, like one of the comments under it says, is not a true polyrhythm.

https://en.wikipedia.org/wiki/Polyrhythm

He is accenting a pattern of notes (every 5) within a single 16 quarter note grid, whereas a polyrhythm could be understood as having 2 or more grids with different divisions (like the Euclidian mode in Patterning offers).

Ah, here's that term I was looking for! 

Polymeter!

https://en.wikipedia.org/wiki/Meter_(music)#Polymeter

(Hmm, the forum is messing up this link, so copy and paste the full link in your browser or you'll end up on a completely different page).

That's what you were describing, and patterning enables that very thing without restriction in their "standard loop mode".

Coloobar

You're a wealth of good information, thanks.  Now that we have all of our definitions straight, here's a nice example of a 4 against 3 euclidean rhythm.  Right after the intro, the drum groove is in 4/4 while maintaining 3/4 time with the china:



There's also some weird euclidian rhythm stuff going on around 3:45 that I haven't been able to decipher. Sounds like 4/4 with the china and god knows what going on with the drum kit.  There's lots of similar examples on this album.

u0421793

Could there ever be such a thing as euclidian rhymes?

AQ808

@u0421793 said:

Could there ever be such a thing as euclidian rhymes?

Well, the video posted said the Euclidean method is applied to string theory and nuclear particle acceleration, so I can't see why not.

Euclidean Geometry, Euclidean Rhythms, Euclidean Rhymes, and let's not forget Euclidean Underwear!

http://www.cafepress.co.uk/+heres_looking_at_euclid_boxer_shorts,1551290055

The sky's the limit!

AQ808

@Coloobar said:

You're a wealth of good information, thanks.  Now that we have all of our definitions straight, here's a nice example of a 4 against 3 euclidean rhythm.  Right after the intro, the drum groove is in 4/4 while maintaining 3/4 time with the china:



There's also some weird euclidian rhythm stuff going on around 3:45 that I haven't been able to decipher. Sounds like 4/4 with the china and god knows what going on with the drum kit.  There's lots of similar examples on this album.

 That was a nice track, there is so much stuff going on there that I'd have to slow it down to completely grasp it. They've got a great hybrid of things going on, thanks for sharing!

AQ808

@u0421793 said:

Has anything related to this ever gotten into the top 40?

 I haven't listened to top 40 radio since 1990, so I really couldn't tell you.

Will

@u0421793 said:
Could there ever be such a thing as euclidian rhymes?

This made me laugh. Then, it made me wonder. Not sure about the rhymes themselves but certainly the rhyme schemes could be. Either a single voice could intertwine rhymes or two voices could do it in real time. @JohnnyGoodyear forced constraint for December?

Coloobar

@u0421793 said:

Could there ever be such a thing as euclidian rhymes?

Reminds me of some of the poems in Godel, Escher, Bach for some reason.

AQ808

Since we've come this far, I might as well throw this concept into the stew as well:

https://en.wikipedia.org/wiki/Polytempo

I remember writing a few requests to Korg about this for Gadget way over a year ago now, but I can't really remember why I was wanting it so bad since I don't use Gadget for anything other than a sound source for midi out of Logic.

I also was annoyed with the lack of user created scales.

Anyways, tempo per track and a master tempo are things I've always looked for in DAWs. I've always liked having significant freedom from a universal grid defining a project.

I get annoyed if I have to do backflips in order to displace something or even alter time signatures within a single track.

Hint to Patterning Devs: Polytempo!

You've already got Polymeter and Polyrhythm covered, go for the trifecta!

audiblevideo

GEB the golden eternal braid. I think that book changed my life.

Wrlds2ndBstGeoshredr

Did a search to clarify why the Patterning programmer calls his mode "Euclidean" when what he describes in his Youtube tutorial is properly called "polyrhythmic", not Euclidean. Does Patterning have some feature I don't know about that implements the Euclidean algorithm, or is he simply mistaken in his terminology?

[Deleted User]

@Wrlds2ndBstGeoshredr said:
Did a search to clarify why the Patterning programmer calls his mode "Euclidean" when what he describes in his Youtube tutorial is properly called "polyrhythmic", not Euclidean. Does Patterning have some feature I don't know about that implements the Euclidean algorithm, or is he simply mistaken in his terminology?

It used to be called Euclidean but not anymore, he corrected that mistake long ago

eross

Concentric is a fun app for polyrhythms

eross

@benkamen said:
I'm just starting work on a drum machine app where each instrument's "loop" can be an independent length up to 64 beats long, and the beat size can be variable as well. i.e. a 64 beat whole note pattern against a 10 beat dotted 16th pattern. So the patterns all phase with each other but keep the same clock source. We'll see how it goes!

A bit different than euclidean though, in that they don't all subdivide the same measure.

oh awesome. can't wait for that one.
How is patterning for iphone coming along? that's the drum machine i've been waiting for.

lukesleepwalker

@eross said:

@benkamen said:
I'm just starting work on a drum machine app where each instrument's "loop" can be an independent length up to 64 beats long, and the beat size can be variable as well. i.e. a 64 beat whole note pattern against a 10 beat dotted 16th pattern. So the patterns all phase with each other but keep the same clock source. We'll see how it goes!

A bit different than euclidean though, in that they don't all subdivide the same measure.

oh awesome. can't wait for that one.
How is patterning for iphone coming along? that's the drum machine i've been waiting for.

you don't have to wait for that one. Ben is referring to Patterning in this post from 2014.

eross

@lukesleepwalker said:

@eross said:

@benkamen said:
I'm just starting work on a drum machine app where each instrument's "loop" can be an independent length up to 64 beats long, and the beat size can be variable as well. i.e. a 64 beat whole note pattern against a 10 beat dotted 16th pattern. So the patterns all phase with each other but keep the same clock source. We'll see how it goes!

A bit different than euclidean though, in that they don't all subdivide the same measure.

oh awesome. can't wait for that one.
How is patterning for iphone coming along? that's the drum machine i've been waiting for.

you don't have to wait for that one. Ben is referring to Patterning in this post from 2014.

lol

eross

@eross said:

@lukesleepwalker said:

@eross said:

@benkamen said:
I'm just starting work on a drum machine app where each instrument's "loop" can be an independent length up to 64 beats long, and the beat size can be variable as well. i.e. a 64 beat whole note pattern against a 10 beat dotted 16th pattern. So the patterns all phase with each other but keep the same clock source. We'll see how it goes!

A bit different than euclidean though, in that they don't all subdivide the same measure.

oh awesome. can't wait for that one.
How is patterning for iphone coming along? that's the drum machine i've been waiting for.

you don't have to wait for that one. Ben is referring to Patterning in this post from 2014.

lol

still waiting for iphone patterning though.

Wrlds2ndBstGeoshredr

@yug said:

It used to be called Euclidean but not anymore, he corrected that mistake long ago

Ah, thanks.

Can anyone tell me what Ruismaker's "Euclidean sequencer" does? Seems like you could make a Euclidean rhythm in any sequencer; what makes this one specifically "Euclidean"?