# Two at once

A polyrhythm plays two rhythms of different lengths over the same span. You do not count both at once. You learn the single rhythm they make together.

> Lesson 11 of 12.
>
> - You learn: To hold two different beats at the same time, three against two and four against three, and to say the single rhythm they make together.
> - Why now: Until now every row shared one beat. Here the rows run at different speeds. It needs an even three (lesson 9) and the habit of reading rows (lesson 4), which is why it is near the end.
> - You need: Lessons 4 and 9.

## 3 over 2

Three even notes in the time of two. The bottom row of the grid, Together, is the combined rhythm: four hits that make a phrase. The words in the gap bar are a way of saying it.

**3 over 2**

    Three    x x x   (3 in the time of 2)
    Two      x x   (2 in the time of 2)

In notation: the two rows are stacked on two lines so you can see them line up. The upper line has a bracket with a 3: three notes in the space of two. Both lines start together on the accented note. After that the three notes and the two notes land in different places and meet again only when the cycle comes round.

## A warm-up: five in a beat

Before 5 over 4, hear five even notes in a single beat. It is the first cut that feels like neither a pair nor a triple, and it is the five in “5 over 4”.

**Quintuplets**

    hits     x x x x x x x x x x

In notation: five sixteenth notes under a 5: five notes in the time of four. Brackets like this are called tuplets; the number says how many notes, and the notes are written as if they were the ordinary notes of the smaller number.

## 4 over 3 and 5 over 4

**4 over 3**

    Four     x x x x   (4 in the time of 3)
    Three    x x x   (3 in the time of 3)

**5 over 4**

    Five     x x x x x   (5 in the time of 4)
    Four     x x x x   (4 in the time of 4)

In notation: the 5:4 bracket is over the top line, with four plain quarter notes beneath it on the other. Every row is stacked on the same time scale, so the one note they share is directly above the other.

## Hemiola

Hemiola is the same idea one after the other: two groups of three become three groups of two in the same time. The bar seems to change gear.

**Hemiola (3+3 into 2+2+2)**

    hits     x . . x . . x . x . x .

In notation: hemiola is two bars of 6/8. The first has two dotted quarter notes (two groups of three), the second has three plain quarter notes (three groups of two). Both bars are the same length but cut differently, and the accents (>) show where you feel the beat.

1. Say the words for the combined rhythm until you can say them evenly.
2. Clap the words with one hand.
3. Give the notes of one lane to each hand (tap one on your knee, clap the other), starting with the two-lane.
4. Only when it is easy, think of both lanes at once.

## Self-check

- Say the 3 over 2 phrase evenly for a minute
- Play 3 against 2 with two hands, one tapping and one clapping
- Hear the hemiola as a change of gear

## Play it on your instrument

- Piano: Three against two between the hands, built up through the independence steps. (Independence)

All instruments: apply.html