The musical ratios can also be thought of as rhythmic patterns such as 2/1, 3/2, 4/3 etc. These rhythmic patterns are polyrhythms where you have two subdivisions of a beat playing over each other at the same time.

In order to determine where the two different rhythms meet there you can multiply the two numbers together and add 1, the sum of the numbers is how many beats the cycle repeats. Let’s take the pattern of 2/1 as an example and look at Time Unit Box System(Tubs) table for the pattern. If the beats were represented in 4/4 time, or 4 quarter notes per measure, on the right hand you have 4 quarter notes, and on the left you have you 2 half notes. Every 3 beats of the pattern the two hands would meet and sound at the same time.

**2/1**

Beat | 1 | 2 | 3 | 4 |
---|---|---|---|---|

Right Hand |
x | x | x | x |

Left Hand |
x | x | x | x |

**3/2**

This pattern will start over after the first 6 beats

Beat | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|

Right |
x | x | x | |||

Left |
x | x |

**4/3**

This pattern will start over after the first 12 beats

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

Right |
x | x | x | x | ||||||||

Left |
x | x |

**5/4**

This pattern will start over after the first 20 beats

Beat | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Right |
x | x | x | x | x | |||||||||||||||

Left |
x | x | x | x |

**5/3**

This pattern will start over after the first 15 beats

Beat | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Right |
x | x | x | x | x | ||||||||||

Left |
x | x | x |

**7/4**

This pattern will start over after the first 28 beats

Beat | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Right |
x | x | x | x | x | x | ||||||||||||||||||||||

Left |
x | x | x | x |

### How Rhythm Becomes Pitch

If you take the above ratios and speed them up to very fast speeds you can hear the rhythms creating the two pitches (or more depending on how many rhythms you have going against each other). Check out http://dantepfer.com/blog/?p=277 for an example of this interesting phenomonem.