Three against two means fitting three evenly spaced notes and two evenly spaced notes into the same span of time. Both parts begin together, then meet again at the start of the next cycle. The challenge is keeping each part even while the attacks between them fall at unequal distances.
A six-position grid makes that relationship clear. Put the three-note part on positions 1, 3 and 5, and the two-note part on 1 and 4. Count all six positions evenly before returning to 1.
Featured photograph: Stephen Niemeier / Pexels.
Give the two parts one shared cycle
For this example, let one cycle last two quarter-note beats. In 2/4 at quarter note = 60, that is a two-second bar. The two-note part sounds once on each quarter-note beat. The three-note part divides the whole bar into three equal spans.
The same relationship could occupy a shorter or longer span elsewhere in a score. Choose the boundaries first. A “3:2” label tells you a proportion; it does not, by itself, say how many seconds or written beats the cycle contains.
Six is useful because both two and three divide into it. Each interval in the three-note part lasts two grid positions; each interval in the two-note part lasts three. The grid is a way to locate the rhythm, not a requirement to feel six equally strong beats in the finished music.
Three right-hand attacks against two left-hand attacks
Count six equal positions:
Right hand, three notes
Left hand, two notes
At the two-second cycle used here, the three-note part has an attack every two thirds of a second, equivalent to 90 attacks per minute. The two-note part has one every second, equivalent to 60. Those numbers describe the two layers of this example, rather than competing instructions to set the same metronome.
Hear each part before putting them together
Count “one, two, three, four, five, six” slowly and evenly. Tap your right hand on 1, 3 and 5 while the left rests. Listen for three evenly spaced taps, including the gap from 5 to the next 1. Then let the right hand rest and tap the left on 1 and 4.
Combine the two without changing the count. Both hands play on 1. The right plays on 3, the left on 4, and the right on 5. Position 6 still takes time before the next shared attack. If you restart immediately after 5, you shorten the cycle and disturb both parts.
The combined order is together, right, left, right, but those four events are not evenly spaced. Their gaps are 2, 1, 1, 2 grid units, including the gap back to the next “together.” A spoken phrase can help you remember the order, but it cannot replace those proportions.
The polyrhythm chapter in The Rhythm and Meter Compendium similarly separates the two layers and their combined attack pattern. As the pattern becomes familiar, listen through the combined rhythm for one continuous, even part at a time. You should be able to follow the three without letting the two become uneven, then change your listening focus.
If maintaining either simple layer is already difficult, return to pulse and placement separately before adding the second. The two-hand task should reveal how the layers fit, rather than conceal uncertainty about either layer alone.
Hear the parts separately in Takt
Takt is our metronome and rhythm trainer for iPhone and iPad. Its polyrhythm tool is free and lets you choose the first part, the second part, or both together. These instructions describe iOS version 1.0, which requires iOS or iPadOS 16 or later.
To match the two-second example, start with 60 BPM and 2/4 in the standard metronome. In Meter, that means two beats per bar and a 1/4 beat unit. Leave tempo training off. Open Rhythm, then Polyrhythm, and set First part to 3 and Second part to 2.
Select First part and start playback to hear the three evenly spaced events. Select Second part for the two. Finally select Together. Both streams complete their counts over the selected bar, so this 2/4 setup gives the same cycle we counted above.
The shared visual guide shows where the two streams meet and where their events fall apart. Use it to locate an entry, then listen without following the moving line continuously. You can also mute one part in the app and supply that missing part yourself.
Start with each part alone, then use Together to check the relationship. No Pro subscription is needed for the polyrhythm controls in Takt for iPhone and iPad.
Screenshots and controls shown here are from Takt for iPhone and iPad.
Recognise the same relationship in notation
In the 2/4 example, the upper part can be written as three quarter-note triplets spanning the bar. The lower part has two ordinary quarter notes. The triplet number applies to the whole three-note group; it makes those notes fit the duration of two ordinary quarters.
One 2/4 bar, three notes above two
Three quarter-note triplets
Two quarter notes
You can also encounter three ordinary quarter notes against two dotted-quarter notes across a 6/8 bar. The timing relationship is still 3:2, but the notation and likely felt pulse differ. Read the actual grouping in the music before deciding which layer to count as the main beat.
“Two against three” names the relationship from the other side. Swapping the parts preserves the coincidence pattern, but it can change which pulse you hear as the reference. Try exchanging the hands once the first arrangement is clear; the hand playing two should not be permanently tied to being the left hand.
Keep the proportions when you stop counting six
The six-position count is most helpful while you are finding the entries. Eventually, it can become cumbersome. Let the two-note part establish a steady pulse and hear the three-note part across it. Then let the three-note part feel steady and hear where the two land.
The midpoint of the cycle is a useful check. The second note of the two-part layer falls halfway through the cycle, between the second and third notes of the three-part layer. It should not coincide with either of them. If both hands repeatedly meet in the middle, the parts have slipped toward the same division.
Another common distortion is four evenly spaced combined attacks. Return briefly to the six positions and notice the wider gap after the shared attack, and the wider gap leading back to the next cycle. Preserve those gaps while allowing each individual part to sound even.
Choose a slow pace at which you can hear that relationship, then try it a little faster without changing its shape. The important transfer is the same one involved in moving beyond slow practice: a correct slow pattern needs to remain recognisable when the timing demands change.
Subdivision, polyrhythm and polymeter
Subdivision describes how a span is divided. A triplet by itself is a three-part division; if you then play straight eighth notes afterwards, you have changed divisions in sequence. The University of Iowa rhythm text describes polyrhythm as different divisions occurring simultaneously. For this exercise, both the three-note and two-note layers continue together.
If those basic note relationships are unfamiliar, the subdivisions reference explains the equal parts before they overlap. It is easier to hear a conflict between two clear layers than to construct both layers from uncertain note values.
Polymeter concerns different meters occurring at once. For example, one part might group a common quarter-note pulse into bars of three while another groups it into bars of four. Those bar beginnings meet again after 12 quarter notes. Our 3:2 example instead fits both note groups into one shared two-beat span; it does not require different written meters.
Put the relationship back into a phrase
On the piano, begin with one comfortable pitch in each hand so the rhythmic task stays audible, then restore the written pitches. On another instrument, you can tap one layer while singing or playing the other. Keep the same cycle boundary when you change the sound source.
Include the music just before and after the polyrhythm. An isolated cycle can feel secure while its entrance still hesitates, or its final note shortens to escape into the next bar. Hear the destination as part of the phrase, keeping the last gap intact.
Finally, use less metronome support and check whether both layers remain clear. You have learned more than an order of hand movements when you can follow either part by ear while the other continues.
