A few months ago I discovered the Groove Pizza App made by the NYU MusEDLab: a circular rhythm app for creative music making and learning. This app is also great for learning and u...

Hi all,

As always, I strongly recommend that you play everything we talk about on your instrument, and if possible on a keyboard.

That said, there will be a specific post about hearing intervals.

### First step: interval type

#### With natural notes

- For the moment, we won't talk about interval quality, but we will discuss it soon
- We begin with ascending intervals: left to right on the keyboard, bottom to top on the staves

Now, look at the staves, with only the natural notes.

How to calculate the interval between two notes? It's very easy!

We begin with what we call ...

###### seconds

- Take
**C**and**D**. You just go from**C**to**D**, and say "**C, D**". You said two notes: the interval between**C**and**D**is a second - Take
**D**and**E**. You just go from**D**to**E**, and say "**D, E**". You said two notes: the interval between**D**and**E**is a second - Take
**B**and**C**. You just go from**B**to**C**, and say "**B, C**". You said two notes: the interval between**B**and**C**is a second

Now ...

###### thirds

- Take
**C**and**E**. Just say "**C, D, E**": you said three notes: the interval between**C**and**E**is a third - Take
**D**and**F**. Just say "**D, E, F**": you said three notes: the interval between**D**and**F**is a third - Take
**A**and**C**. Just say "**A, B, C**": you said three notes: the interval between**A**and**C**is a third

Then...

###### Fourths

It is the exact same process, as described in this image.

Following the same steps, here are other intervals:

###### Fifths

- Between
**D**and**A**for example (remember, for the moment: always ascending)

###### Sixths

- Between
**E**and**C**for example

###### Sevenths

- Between
**C**and**B**for example

###### Octaves

- Between
**C**and another**C**, 12 semi-tones away for example

###### Bonus : unisson

If you take a note, and the exact same note (the same spot on keyboard), the corresponding interval is what we call an unisson. (not very interesting? in fact, when we will qualify the intervals, we'll see that this is not useless)

#### With any note

What is the interval between **C♯** and **E**.

It's the same process, but before counting, take out the alterations, that is to say sharps (♯) and flats (♭). We are not changing the notes! It is just a formal process. So now you say "**C,D,E**" : you said three notes, so the interval between **C♯** and **E** is a third.

The rule is in fact very simple: alterations do not change the type of the interval. (we'll see that on the other hand, they change its quality)

### Second step: interval quality

As you may have noticed, if you take thirds, for example, there is a difference between the third corresponding to **C** and **E**, and the third corresponding to **E** and **G**.

Let's check the distance (remember the post Distance between notes ?) between those note:

- It takes 4 semi-tones (that is to say two whole tones) to go from
**C**to**E**. We call that a major third - It takes 3 semi-tones (that is to say on whole-tone plus one semi-tone) to get from
**E**to****G. We call that a minor third.

That is what we call qualifying the intervals.

You'll have to remember ( and play !) this table:

interval type | distance in semi-tones | Name | Example |
---|---|---|---|

unison | 0 | perfect unison | A-A |

1 | augmented unison | A-A# | |

second | 1 | minor 2nd | E-F |

2 | major 2nd | B-C# | |

3 | augmented 2nd | Ab-B | |

third | 2 | diminished 3rd | E-Gb |

3 | minor 3rd | F-Ab | |

4 | major 3rd | G-B | |

5 | augmented 3rd | C-E# | |

fourth | 4 | diminished 4th | B-Eb |

5 | perfect 4th | G-C | |

6 | augmented 4th | F-B | |

fifth | 6 | diminished 5th | F-Cb |

7 | perfect 5th | Eb-Bb | |

8 | augmented 5th | D-A# | |

sixth | 7 | diminished 6th | C#-Ab |

8 | minor 6th | G-Eb | |

9 | major 6th | D-B | |

10 | augmented 6th | C-A# | |

seventh | 9 | diminished 7th | C#-Bb |

10 | minor 7th | C-Bb | |

11 | major 7th | D-C# | |

12 | augmented 7th | C-B# |

Sometimes, it can be tricky: there is 3 semi-tones between **E** and **G**, and as well, 3 semi-tones between **Ab** and **B**. But the first one is called a minor third, whereas the second one is called an augmented second. Why so?

Remember the first step of this post:

- Take
**E**and**G**. Just say "**E, F, G**": you said three notes: the interval between**E**and**G**is a third. Now, look at the table above: a third with 3 semi-tones is called a minor third - Take
**Ab**and**B**. Just say "**A, B**" (remember the rule for intervals between any notes?): you said two notes: the interval between**Ab**and**B**is a second. Now look at the table above: a second with 3 semi-tones is called an augmented second.

#### Major and Minor : Why those names?

There is lot to say about interval names...

###### The bad news is:

There is no rule that is consistent with the names AND the corresponding scales AND the physic-acoustics ...

So if the names seem complicated to you ... well ... it's normal ! But you'll get used to it soon.

###### The good news is:

*First*: You won't use a lot intervals like augmented 6th or diminished 3rd!

*Second*: There is a simple rule to remember the most common names. It's all about going up and down.

- Intervals with only natural notes, where the first note is
**C**: all intervals that aren't unison, 5th, 4th or octave are major. (**C**to**D**is a major 2nd,**C**to**E**is a major 3rd,**C**to**A**is a major 6th,**C**to**B**is a major 7th) - Intervals with only natural notes, where the last note is
**C**: all intervals that aren't 5th and 4th are minor. (**B**to**C**is a minor 2nd,**A**to**C**is a minor 3rd,**E**to**C**is a minor 6th,**D**to**C**is a minor 7th) - The other intervals with only notes, beginning or ending with
**C**, that is unison, 4th, 5th or octave, are perfect.

Want to practice ? Take a look at this interactive page, and train your ears here.

Sebastien