Have you been struggling with polyrhythms? Are simple catchphrases like “Hot Cuppa Tea” not giving you the confidence you desire? Or are you looking to master more complex polyrhythms beyond the basics?

No matter your starting point, this article will help you understand and master any polyrhythm. I'll explain the simple math virtuoso performers use to ensure their polyrhythms are meter-perfect. By the end of this article, you’ll understand the simple LCM method that virtuoso performers use to master polyrhythms. I’ll even include an LCM calculator and number line generator so you can practice your polyrhythms right now.

**What is a polyrhythm?**

A polyrhythm is when

- Two rhythms are played simultaneously

**AND**

- Those two rhythms can not be divided into one another (without a remainder).

To understand this more clearly, let’s compare some primary rhythms to several different polyrhythms.

## Examples: 2:4, 3:6,

**Basic Rhythms**

#### 2:4

In this example, we have eighth notes and sixteenth notes. The eighth notes divide the beat into 2, while the sixteenth notes divide it into 4. In other words, there are two eighth notes for every beat and four sixteenth notes for every beat.

Every other eighth note will line up precisely with a sixteenth note when playing this. This is because 4 is divided by 2 (4/2=2, so every other note will line up). In fact, you can see the sixteenth and eighth notes line up perfectly in the written music.

#### 3:6

In this example, in compound time (3 eighth notes per beat), we have 3 eighth and 6 sixteenth notes per beat. Using simple division to see if this is a polyrhythm, we see it is not: 3/6 = 3. Looking at the music, we can see that the notes line up every third beat.

**Polyrhythms**

#### 3:2

In this example, both rhythms are written as eighth notes. However, one has a “3” written under it, indicating that it is a triplet (3 notes per beat). The other set of eighth notes is only 2 notes per beat.

3:2 Polyrhythm

No matter how you divide these (3/2 or 2/3), you do not get a nice, neat, even division. These note groups will only line up at the beginning of the beat. Once they get going, they don’t line up again until the next cycle begins.

#### 4:3

In this example, we have 3 quarter notes fitting into the same amount of time as 4 quarter notes. This gives us a 4:3 (or 3:4) polyrhythm. Obviously, they won't line up (except at the beginning. In fact, you can visually see this in the written notation:

4:3 Polyrhythm

**3 over 4: How to talk about polyrhythms**

When reading about polyrhythms, you often see a colon between two numbers. But how do you actually talk about it?

Polyrhythms are described as being “over” the fundamental rhythm, called the pulse. The polyrhythm 3:4 is called “3 over 4.”

The pulse is the basic rhythm in a piece. Adding a counterpulse is what makes it into a polyrhythm. You can also call this the composite rhythm.

How do you know which is the pulse and which is the counterpulse? Like much of music, it depends on the context.

Here, we have two examples. The first is in 4|4. If you know how to read time signatures, you know that in 4|4, the eighth note divides the beat into 2. Adding a triplet makes this a polyrhythm; this is 3 over 2.

3:2 Rhythm in 4|4 time (common time)

Next, we see the same polyrhythm (a combination of 2 and 3) in 6|8. Since the beats in 6|8 are usually divided into 3, the division of 2 is unusual. Therefore, this rhythm is “2 over 3.”

2:3 in 6|8 time

While these two rhythms have slightly different names, depending on musical context, they are fundamentally the same thing; 2 beats and 3 beats happening in the same amount of time. Therefore, they’re performed (almost) exactly the same way.

*These naming conventions are only helpful when discussing situations where a meter is clearly defined and/or the polyrhythms appear infrequently. In situations where the polyrhythm is more consistent (cross-rhythmic music), one person may feel it as 3 over 2. In contrast, another may feel it as 2 over 3. Both are legitimate interpretations. *

## Learning to play Polyrhythms

## Listen First

As a dedicated Suzuki Guitar Method teacher, I’ve seen how my students progress when they acquire music as a language; by listening before "speaking". The easiest way to develop a new skill is to listen first. The more the better.

This is just as true for polyrhythms (although they’re much less engaging than listening to a new song you want to learn). So, I’ve provided several common polyrhythms here for you to listen to, along with a video showing the beats in action.

**3:2 Polyrhythm**

"Hot cupa tea"

**4:3 Polyrhythm**

"Pass the goddamn butter"

**5:4 Polyrhythm**

"I'm Looking for a Home To Buy"

Listening first can have its downfalls. Make sure that your source material is of high quality! An incorrect recording will lead to incorrect playing.

### Using a Polymetric Metronome

The above examples were created using the Tempo Pro metronome on iOS. This metronome is my go-to metronome due to the simplicity of setting up subdivisions and polyrhythms.

Using a polyrhythmic metronome can be helpful, especially when you already have a basic sense of the rhythm and/or you’re only playing one part of the rhythm (while another musician plays the other part).

However, a polymetric metronome won't be helpful if you don’t understand the rhythm. Instead, you’ll want to use the LCM Method to develop a clear understanding of the polyrhythm.

### One Method To Rule Them All: The LCM Method

While listening to other performances and using a polymetric metronome can help develop your polyrhythmic abilities, the LCM method is the only way to break polyrhythms down and work on them accurately at a slow tempo. Only once you’ve done this can you speed them up and confidently know you’re performing them accurately.

Here's how to do it:

### Step One: Find the LCM

The LCM is the Least Common Multiple. For those who need a basic math review, the Least Common Multiple is the smallest number that two different numbers (in this case, your polyrhythm numbers) can be multiplied into.

For example, the common 2:3 polyrhythm has an LCM of 6. By dividing the beat into 6, we can feel a steady subdivision that allows us to simultaneously count in 2 and 3.

3:2 Polyrhythm

How can you figure out the LCM? There are a few ways. You can watch this Kahn Academy video and brush up on your math. Or you can google “What is the Least Common Multiple of X and Y?”.

Or, better yet, you can use my Polyrhythm Calculator, which will generate the proper LCM number line for you to use for your practice sessions.

### Step Two: Make a number line

Write a number line for the LCM. Our least common multiple is 6, so we'd write:

1 2 3 4 5 6

Easy Peasy Lemon Squeezy. Next…

### Step Three: Figure out Spacing

Now that we have the Least Common Multiple (6) of our 2:3 polyrhythm, we need to figure out spacing. To do this, we divide the pulse and counterpulse into the Least Common Multiple:

- LCM/subdivision = Spacing.
- 6/2 (eighth notes) = 3.
- 6/3 (triplets) = 2.

### Step Four: Annotate The Number Line

The next step is determining what numbers to circle on our number line. Using the spacing numbers from the previous step, we know that:

For the eighth notes, a beat happens on every third number. For the triplet, a beat happens on every second number.

You can see this clearly when it's illustrated using TUBS (Time Unit Box System)(I first learned about TUBS in the fantastic book *A Rhythmic Vocabulary*, a book which went a long way to improving my rhythmic abilities.)

3:2 (or 2:3) illustrated in a TUBS

While the TUBS system is a fantastic way of visualizing rhythms, I prefer a simple number line when practicing. That way, my eyes don't need to move up and down as much to see what I'm doing (a problem I also talk about in my Ultimate Guide to Note Reading article). Here you can see how that works:

TUBS consolidated into a number line

And, of course, it's also much faster to write out a number line and circle and/or underline the appropriate numbers.

**Here are the steps to create an LCM numberline:**

Remember from before: 6/3 (triplets) = 2. So, starting with the first number in the number line, we will circle (or, I'll bold here) every second number to get our triplet division of the LCM.

**1** 2 **3** 4 **5** 6

Note: We're starting on 1, not zero, so the numbers circled are not 2, 4, 6, etc.

Next, I'll underline the eighth note division. 6/2 = 3, so I will underline every 3rd note (by underlining, rather than circling again, I can see which numbers are part of the pulse and which numbers are part of the counterpulse).

** 1** 2

**3**

__4__

**5**6

While counting these number lines out loud will work at slow speeds, some words we use for the numbers present challenges at even moderate speeds.

This is because some numbers (7) have a polysyllabic name (se-ven), making it difficult to feel them as one beat.

To solve this problem, use monosyllabic syllables for polysyllabic numbers. This will allow you to feel these numbers as a single beat when spoken out loud since each syllable corresponds to a beat.

Sometimes, this syllable can be an abbreviated form of the word. With other numbers, you may use a different language (French is a popular choice). Here are some examples:

7: “sev” or “sept”

10: “oh” (for zero), “dix”

11: “lev” (eleven), onze

12: “elv” (twelve), douze

13: treize

14: quart (quarotze)

15: quinze

16: sieze

This can take a bit of mental effort. And after 16, making single-syllable words becomes very difficult. Breaking the count into smaller, repeating segments may be more beneficial. See step 3.1 under “Drill, Baby, Drill!” below.

**Common Polyrhythm Number lines**

**How to count a 3:4 or 4:3 Polyrhythm**

The least common multiple of 3 and 4 is 12. The spacings are:

- 3: 12/3=4
- 4: 12/4=3

The number line is:

** 1** 2 3

**4**

__5__6

**7**8

__9__

**10**11 12

Note: All the common examples on this page have a least common multiple that = x * y. In these instances, the "spacing" division step will always result in the opposite part of the polyrhythm as the spacing answer, so you can skip that step.

However, consider the polyrhythm of 6:4. The LCM here is 12, and you'll need to do the actual division of the LCM step to get the appropriate answer.

While factually correct, this isn't the greatest example. Why spend time practicing a 6:4 rhythm? It's precisely the same as a 3:2 rhythm played twice in a row.

**How to count a 4:5 or 5:4 Polyrhthm**

The least common multiple of 4 and 5 is 20. The spacings are:

- 4: 20/4=5
- 5: 20/5=4

The number line is:

** 1** 2 3 4

**5**

__6__7 8

**9**10

__11__12

**13**14 15

__16__

**17**18 19 20

## Polyrhythm Practice Generator

This Polyrhythm Count Generator uses the familiar and common-sense method of starting the count on 1 since that’s what most people are comfortable with. However, I use Tabuteau Rhythm Counting, which is far superior for many reasons. More on that below.

### Step Four: Drill, Baby, Drill!

Start by counting the numberline out loud. Start by clapping on every circled and bolded/circled number. This will give you the composite rhythm, or the polyrhthm.

As you feel more comfortable, tap (your leg, a table, etc) on the underlined numbers with one hand, and the bolded/circled numbers with the other hand. When you do this, you will be playing the pulse with one hand and the counterpulse with the other. This step is especially important for polyphonic players (piano and classical guitar), drums, and any other instrument where separate parts of your body (hands, or fingers/thumb for classical guitar) are playing either the pulse and counterpulse.

Next, **u****se a metronome to speed it up! **Start with one click for every number. Slowly speed it up, just like you would do with any other problematic musical passage.

**Learn to feel how each part of the composite rhythm divides into the other**. This will allow you to develop even more speed for two reasons. First, you’ll feel a bigger beat, allowing you to move faster. Second, you won’t need to count as high; simplifying the count can help you play faster.

To do this, create a Neely Chart (I’ve named this after Adam Neely because I learned this method from his video on polyrhythms, which is linked below. Naming this will help us differentiate it from the LCM Number Line method, used above).

Need help counting uncommon beat divisions? After reading McGill’s amazing treatise on how to play musically, I switched to counting my rhythms using the method developed by Marcel Tabuteau. This method places the LARGEST number on the downbeat rather than one (**4** 1 2 3 | **4** 1 2 3 rather than the traditional **1** 2 3 4 | **1** 2 3 4). For various reasons, I found it much easier to subdivide the beat into odd divisions and easily switch between them with much less practice than I was used to. In fact, it also increased the musicality of my playing. The reasons for this are covered in-depth in McGill’s Sound in Motion. It’s a book I can’t recommend highly enough (to advanced musicians).

**Neely Number Chart Examples**

*Note: I use the Tabuteau Rhythm Counting Method for the reasons described in the above tip. Let’s use 3:4 as an example. To make a Neely Number Chart, do the following*

**1.** Take the counterpulse of your polyrhythm (4 in our example) and write a number line that long.

4 1 2 3

**2.** Repeat step 1 for the number of pulses in your polyrhthm. (3 in our 3:4 example)

4 | 1 | 2 | 3 |

4 | 1 | 2 | 3 |

4 | 1 | 2 | 3 |

**3.** Underline the first number in each line. This represents the pulse. As you can see, this happens 3 times in this example of a 3:4 polyrhthm.

4 | 1 | 2 | 3 |

4 | 1 | 2 | 3 |

4 | 1 | 2 | 3 |

**4.** Take the pulse in your polyrhythm (3). Starting with the first number in your number line, circle (here, bolded) every third number. As you can see, this happens four times in our pattern; this gives us the counterpulse of the polyrhythm (4 in the 3:4 example).

4 | 1 | 2 | 3 |

4 | 1 | 2 | 3 |

4 | 1 | 2 | 3 |

To practice this, count so that the metronome lines up with the first number of each line. To help you differentiate between the two versions of the polyrhythm (3:4 and 4:3), accent the first number of each line (which lines up with the metronome).

*Need a visual? You can see Adam Neely himself do this here: *

You’ll also want to practice the reverse rhythm to deepen your understanding of this rhythm. For our example of 3:4, this means practicing 4:3. Here is the Neey Chart for 4:3

3 | 1 | 2 |

3 | 1 | 2 |

3 | 1 | 2 |

3 | 1 | 2 |

To aid your understanding, I wrote both Neely Charts (3:4 and 4:3) in a single row so you can compare them to the LCM Number Line. As you can see, all the accented beats line up, no matter how you count them (however, whether a note is underlined or bolded will depend on whether you’re counting in 3:4 or 4:3, even though the two sound exactly the same in isolation).

12 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |

4 | 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 | 1 | 2 | 3 |

3 | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 |

Once you are comfortable counting using Neely Charts, you’re ready to use a polyrhythmic metronome (I prefer Tempo Advance for its ease of use) to help you speed up the rhythm. Set up your polyrhythm and start with a tempo slow enough that you can count along (note that the metronome will NOT play every single number; it will only play the numbers you clap on, that is, the underlined and circled/bolded numbers).

Start ramping up the tempo once you’re comfortable at a slow speed. You’ll likely need to get up to a speed that’s too fast to count every single number; you’ll need to be able to “feel” the polyrhythm. While this sounds daunting, the polyrhythmic metronome can help you do this gradually.

- Mastery: Feeling the Big Beat
- Polyrhythms are (usually) complex subdivisions; to play them accurately, you’ll want to be able to play them with a metronome only happening on the “big beat.” Whether you’re counting using an LCM Numberline or a Neely Chart, the metronome only happens on the first number in the chart or line. Here, I’ve shown this by making that number larger.

12 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |

4 | 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 | 1 | 2 | 3 |

3 | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 |

Before you begin this practice stage, you should have a solid understanding of what the polyrhythmic feels like, even if it is very slow. At this point, mnemonics can help you “lock in” the rhythm at a faster speed. Here are mnemonics for common polyrhythms.

- 3:2, 2:3: Hot Cuppa Tea
- 3:4, 4:3: Give Advice to Mother (or, more typically, Pass the Goddamn butter)
- 4:5, 5:4: I'm Looking for a Home To Buy

You can also use a polyrhythmic metronome (I prefer Tempo Advanced for its ease of use) to help you speed up the rhythm. However, remember that to truly “lock in” the rhythm, you must be able to perform it using a basic metronome. The polyrhythmic metronome is helpful only to help you speed up a polyrhythm you can already count and get it to a speed where you can begin to feel it.

**Conclusion**

This method of learning polyrhythms is near and dear to my heart, as it was a method I “discovered” on my own (in the days before you could find such niche information on the web or YouTube) when my college professor gave me absolutely useless advice when I needed to play a 5:4 rhythm ("Just Play 4 and fit 5 in between" ?!?).

I knew that was absolutely useless, so I finally figured out the LCM method by brute force. I shared my discovery with my professor; however, he was dismissive. Whatever, it worked for me.

Years later, I got extreme validation. I read an article describing the same method in Soundboard Magazine, Volume 34, no. 2 (2008). The article was written by renowned new-music guitarist David Tanenbaum. Of course, today, this solution is easy to find on the web; it’s basically common knowledge! Hopefully, everyone will learn this method when it’s time to play their first polyrhythms.

Please let me know if this was helpful to you and what other rhythm questions you may have in the comments below!

Thank you again, ( I already said a big thank you on another of your posts).

Sure thing, Gloria! (I didn’t see any comments on another post, but I’m glad your finding them useful!)