So far, I have only outlined **diatonic** intervals. These are not the only intervals that exist, there are also intervals between sharp and flat notes to consider. Here is the full list of both simple and compound intervals:

Intervals from 0 up to 12 semitones are **simple **intervals. Intervals above 13 semiitones are **compound **intervals.

After 12 semitones (the perfect 8^{th}, or octave) we continue naming the intervals in numerical order ie. 9^{th}‘s up to 15^{th}‘s.

So to play a major 9^{th} interval, we would play the root note and the major 2^{nd} note *an octave higher.*

Here are some rules regarding intervals:

- A
**major**interval reduced by one semitone becomes a**minor**interval. - A
**major**interval increased by one semitone becomes an**augmented**interval. - A
**minor**interval reduced by one semitone becomes a**diminished**interval. - A
**minor**interval increased by one semitone becomes a**major**interval. - A
**perfect**interval reduced by one semitone becomes a**diminished**interval. - A
**perfect**interval increased by one semitone becomes an**augmented**interval.

### INVERTING INTERVALS

Intervals can be inverted, so that the higher note becomes the lower note, and vice versa. When we invert an interval, we come up with a new interval, based on the following rules:

To name the inverted interval, subtract the degree of the original interval from 9 (e.g. a 7^{th} becomes a 2^{nd}, a 6^{th} becomes a 3^{rd}, a 4^{th} becomes a 5^{th}, and so on).

A **perfect** interval, when inverted, is still **perfect**.

A **major** interval, when inverted, becomes **minor**, and a **minor** interval becomes **major**.

An **augmented** interval, when inverted, becomes **diminished**, and a **diminished** interval becomes **augmented**.