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I've been playing drumset for over 20 years. What I'm trying to do is play 3/4/5/6 where one limb (arm or leg) will be 3/8 time, one limb will be 4/4 time, one limb will be 5/4 time, and the last limb will be 6/8 time. Now, I've memorized different times like "bread and butter" is two against three and "pass the goddamn butter" is three against four. I've looked up polyrhythm theory on YouTube and it says to find the least common multiple of the different time signatures, which would be 60, but 60/4 time doesn't make sense to me (1 +2 + . . . 60 +). Is there any phrase I can memorize to play 3 against 4 against 5 against 6 or any smaller time signature? Or any clarification on other ways to do this?

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  • It’s not 60/4, you basically count to 60 or imagine/audiate 60 time slots and then figure out which hits are in which of the 60 time slots. The 3 goes on 1, 21, 41. The 4 on 1, 16, 31, 46. And so one. Jan 7, 2023 at 18:00

2 Answers 2

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Before I continue I’m going on the assumption that you want to subdivide say one bar, into 3,4,5 and 6 pulses. If that’s the case then the bottom number of the time signatures is irrelevant. It is actually better to think of it in a single time signature, say 4/4.

You’re right, 60 is your common denominator. Divide 60 by 3,4,5,6 and you get 20,15,12,10. They all play on 1 and 61, which is the next downbeat.

3 will play on 1,21,41,61

4 will play on 1,16,31,46,61

5 will play on 1,13,25,37,49,61

6 will play on 1,11,21,31,41,51,61

Here is a rough color graphic representation of how the hits all line up (or don’t line up). The bottom line is all of them. 3=red,4=blue,5=green,6=yellow,all=black:

enter image description here

The only simultaneous hits are 3+6 on 21 and 41 and 4+6 on 31.

Here’s what it looks like in 4/4 music notation. If you ignore the bottom row and the last column of the graphic you will see that the note spacing is identical to it:

enter image description here

As far as playing it, playing quarters and quarter triplets together is easy and a good starting point. Then adding the half triplets is also pretty easy, just play every other quarter triplet. Good luck with the 5-tuplet! I suggest getting comfortable with 5 against 4 or 5 against 6 alone first.

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Here is a way to do it. Overview:

  • Reliable timing
  • Polyrhythm 3-4-5-6
  • Counting this scheme with kanokol
  • Practical considerations
  • Review
  • Alternative
  • Where to find more
  • Audio simulation

Reliable timing

First of all, forget those phrases. Usually they are not very reliable, and even less with a complex scheme like the one you are after. Rather I suggest to adopt counting as known for a long time in music, dance, singing and listening as the audience from India: kanokol.

Kanokol uses syllables of the same length and in different sounds. What we need here can sound like:

  • 2 beats: Ta-ka
  • 3 beats: Ta-ke-ti
  • 4 beats: Ta-ka-de-mi
  • 5 beats: Ta-ti-ki-da-tum

Let's take as convention, that a capital letter indicates emphasis, like a hit. So Taka Taka has 2 hits, while Taka taka has 1 hit, and both take 4 units in time. (Let's neglect that the Takademi = Taka taka may be the better choice many times.)

So most of the syllables just consume (an equal amount of) time, while the capitalized ones should be audible, emphasized, only.

The different syllables makes it much easier to recall where you are in this sequence. (And compared to music from India your one is short and simple. They can recall and tell very long rhythmic stories with hardly any error this way, after training.)

Polyrhythm 3-4-5-6

With a subdivision by 2 * 2 * 3 * 5 = 60 the (mirrored) distribution of hits for limbs 3, 4, 5 and 6 is:

subdivision

Counting this scheme with kanokol

My strategy for this complex scheme is stating the time-difference, i.e. the number of beats from the 60-pulse, by drawing horizontal rules and just counting.

So from limb-to-limb action, no matter which one, you can code the required number of 60-pulses for 1 measure as either:

  • 10 - 2 - 3 - 5 - 4 - 6
  • and reverse (mirrored)

or:

  • Tatikidatum tatikidatum - Taka - Taketi - Tatikidatum - Takademi - Taketi taketi
  • and reverse (mirrored)

Practical considerations

After assigning your limbs to 3, 4, 5 and 6, practice each one individually first. It may feel nasty with a 60-pulse, but ...

So for limb 6 your counting from hit to hit with said limb is simply:

  • Tatikidatum tatikidatum
  • Taka taketi tatikidatum
  • Takademi taketi taketi
  • and reverse (mirrored)

While for limb 5 it's from hit to hit:

  • Tatikidatum tatikidatum taka
  • Taketi tatikidatum takademi
  • Taketi taketi
  • and reverse (mirrored)

For limb 4 it's:

  • Tatikidatum tatikidatum taka taketi
  • Tatikidatum takademi taketi taketi
  • and reverse (mirrored)

And finally for limb 3 it's:

  • Tatikidatum tatikidatum taka taketi tatikidatum
  • takademi taketi taketi AND directly reverse (mirrored)

(unless I made a minor typo; but you get the idea).

Next try pairs of 2 with this kanokol-story, e.g.:

  • 6 vs 5
  • 4 vs 5
  • 3 vs 6 etc.

Then pairs of 3, finally the whole thing.

Review

Does it have to be that complicated?

Now, the complexity comes from the requirement, which leads to a 60-pulse, i.e. subdividing each measure into 60 equally slices of time.

The story "told" by kanokol IS always the same, resulting in a robust and precise timing. Only each limb has to learn, at which point in the story it's time for noise, i.e. a hit.

If you are better in recalling numbers, just remember the ones under the horizontal rules in the table and make each limb wake up and hit when it's its turn.

Alternative

The alternative is to do without counting, except for counting 4/4 by 1-2-3-4.

Technically polyrhythms are beats produced by oscillators running at different frequencies. So with or without counting in the end your limbs have to run on

  • 3 * f0 (e.g. high tom)
  • 4 * f0 (e.g. kick drum)
  • 5 * f0 (e.g. snare)
  • 6 * f0 (e.g. hihat foot)

Train that and the polyrhythmic beating follows automatically, well, ideally spoken.

Where to find more

"Indian rhythm for the drumset", by Pete Lockett, Hudson Music

The bounce metronome lets you hear 3 (not 4, unfortunately) voices running at different frequencies, online. Suggestion: assign 4 at 60 BPM to the leftmost. Stop and restart to hear the first hit (all together). Unmute, play beeps. Try 4:5:6, 4:3:6 and so on.

Audio simulation

How will it look like, how will it sound on the drum set?

Unfortunately DAWs etc. won't provide subdivisions of 60. I.e. they seem to stick to dividing by 2, 4, ... 32, 3, ..., but not by 5, 6 or even 60. I wasn't sure, if programs like Musescore will play Johns notation correctly.

So as a trick I used LMMS, beat-editor, to generate 4:6:3:5 :

  • kick drum 60 BPM (limb 4)
  • hihat 90 BPM (limb 6)
  • tom 45 BPM (limb 3)
  • snare 75 BPM (limb 5)

Now you can see Johns colored sketch in terms of audio signals after importing into Audacity. The highlighted section is just one measure, and can be played back as a loop. The final screenshot shows 1 measure of this 3:4:5:6 polyrhythm after mix-down into 1 track. It ends at 4:000 seconds, and shows just a little portion from the next measures start. (Note the symmetry of this polyrhythm, when starting in the middle at 2 s and moving left and right simultaneously.)

audio simulation

mixed down

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