### Goal

Name intervals including those not found on the chart.

## Interval Qualities

Before we leaned on the chart to gain a starting point but it is time to expand! Interval qualities have an order to them. Here is a picture demonstrating the order:

Notice that a perfect interval **cannot be major or minor**. It can become augmented or diminished but never major or minor. Following the chart, say we have a diminished interval. Then it could become Perfect or Minor. Let's say it becomes minor, then it could become major or go back to being diminished. Let's say it becomes major. Then it could become augmented or minor.

There are some odd cases where diminished or augmented are not enough, in those cases you can use double diminished or double augmented and continue to expand in this way, although it is very rare that it is needed.

### Why these names?

The interval quality names fundamentally come from collections of whole steps and half steps. Such a collection is a way to construct a scale. A whole step is 2 half steps. For example, you can construct any major scale using the formula

WHOLE WHOLE HALF WHOLE WHOLE WHOLE HALF

Meaning you can start on a C and go up a half step (2 notes), you land on a D. This is the second note of the scale. Then if you go up another whole step from there we land on an E, the third note of the scale. We can continue in this way to make the entire major scale.

The names Major and Minor, Augmented and Diminished come from the size of the step. Each step has a “bigger” version and a “smaller” version. Bigger is major (literally in Latin) and smaller is minor (literally in Latin). The names augmented and diminished are just extensions of this. The reason perfect intervals go straight to augmented and diminished is a little more complicated.

P1 is perfect because there is no “bigger” or “smaller”, it is itself! Similarly, after 12 notes you reach the next octave. There is no smaller or bigger “step”. So major and minor do not make much sense.

P5 and P4 however kind of break this logic. Smaller and bigger steps do exist, namely the tritone. There also exist historical texts that do mention major and minor 4th and 5ths (Musica Enchiriadis). However these intervals are treated like there is only “one” size for them, so they are a bit odd. One reason is these intervals have very simple ratios giving them a consonant sound (as opposed to a dissonant sound) which is another possible explanation.

## Perfect Intervals

Perfect intervals occur for very simple ratios.

1:1 - The note is itself, unity.

2:1 - The octave, the note is twice the reference

3:2 - The Perfect 5th

4:3 - The Perfect 4th

If these ratios are satisfied then the interval is considered perfect. **Perfect intervals can never be major or minor!!!!**

## Major and Minor Intervals

Anything that is not perfect is either major or minor. So if the number is not a 1, 4, 5, or 8 then you should consider a major or a minor. In some cases augmented and diminished.

## How to know if it is augmented or diminished

The chart gives us all major and minor intervals! **So any deviation from the chart indicates an augmented or diminished interval.** If we don’t have enough semitones then it is diminished. If we have too many then it is augmented.

Consider for example the augmented unison, or augmented first.

Here we see the interval number is a 1. However the number of half steps is 1. On the chart we have too many half steps, the chart expects 0 for an interval number of 1 but we have 1 half step. Therefore we are too high and the interval is an augmented unison, or augmented first.

Now consider the diminished second:

Here we have an interval number of 2 but the number of half steps this time is 0. A minor 2 is the lowest 2 we have for the interval number that expects 1 half step on the chart. We therefore don’t have enough half steps and thus the interval is a diminished second.

If the interval had a double sharp, like this:

Then we would now be at -1 half steps and the interval would be a double diminished second. There is no real reason to use such an interval it is just here for demonstration purposes of how the system works.

Consider the following:

Here we have an interval number of 5, but the number of half steps is 8. This is not on the chart and we see we have too many half steps because the chart expects 7, therefore this is an augmented 5th.

Consider:

Here we have an interval number of 3, but the number of half steps is 2. This is not on the chart as an interval number of 3 expects either 3 or 4 half steps. We have 1 less than 3 so it must be a diminished 3rd.

In this way we can name any interval. These intervals are far less common but you will come across them from time to time, so you should know how to identify them and make them.

## Interval Name |
## Interval Abbreviation |
## Number of Semitones (Half Steps) |
---|---|---|

## Unison / Perfect First |
## P1 |
## 0 |

## Minor Second |
## m2 |
## 1 |

## Major Second |
## M2 |
## 2 |

## Minor Third |
## m3 |
## 3 |

## Major Third |
## M3 |
## 4 |

## Perfect Fourth |
## P4 |
## 5 |

## Augmented Fourth / Tritone / Diminished Fifth |
## Aug4 / Dim 5 / TT |
## 6 |

## Perfect Fifth |
## P5 |
## 7 |

## Minor Sixth |
## m6 |
## 8 |

## Major Sixth |
## M6 |
## 9 |

## Minor Seventh |
## m7 |
## 10 |

## Major Seventh |
## M7 |
## 11 |

## Perfect Octave |
## P8 |
## 12 |

## Interval Construction

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