So far, I
have outlined only **diatonic** intervals here. 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.

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

**Note:** a perfect 4^{th} interval is also sometimes considered dissonant when not supported by a lower 3^{rd} or 5^{th}